**Meet the editor**

Professor Elmer P. Dadios finished his doctoral degree at Loughborough University, United Kingdom in 1996. He was a recipient of the Philippines Department of Science and Technology (DOST) 50 Men and Women of Science and Technology; DOST Scholar Achievers); The National Research Council of the Philippines Basic Research Achievement Award; The National Academy of

Science and Technology (NAST) Outstanding Scientific Paper Award; The De La Salle University Miguel Febres Cordero Research Award. Currently, Dr. Dadios is a University Fellow of the De La Salle University and holds the University's highest faculty rank of Full Professor 10. He is the president of the NEURONEMECH Inc. He has been a consultant for Robotics and Automation in the Philippine government and private corporations. He is the founder of the IEEE Computational Intelligence Society - Philippines Chapter. He is the Founder and President of the Mechatronics and Robotics Society of the Philippines.

Contents

**Preface IX** 

**Part 1 Robotics and Electrical Machines 1** 

Chapter 3 **Modular Fuzzy Logic Controller for** 

Bin Zi

Chapter 5 **Control and Estimation of** 

Chapter 6 **Application of Fuzzy Logic in** 

**Part 2 Control Systems 129** 

Chapter 4 **Fuzzy Control System Design and Analysis** 

**Control of Electrical Machines 107**  Abdel Ghani Aissaoui and Ahmed Tahour

**Adaptive PN Acquisition Scheme in** 

Chapter 7 **Fuzzy Logic Control for Multiresolutive** 

Chapter 1 **Humanoid Robot: Design and Fuzzy Logic** 

Elmer P. Dadios, Jazper Jan C. Biliran,

**Control Technique for Its Intelligent Behaviors 3** 

Chapter 2 **Application of Fuzzy Logic in Mobile Robot Navigation 21**  Tang Sai Hong, Danial Nakhaeinia and Babak Karasfi

> **Motion Control of Two-Wheeled Wheelchair 37**  Salmiah Ahmad, N. H. Siddique and M. O. Tokhi

**Asynchronous Machines Using Fuzzy Logic 81**  José Antonio Cortajarena, Julián De Marcos, Fco. Javier Vicandi, Pedro Alvarez and Patxi Alkorta

**Time-Varying Multipath Ionospheric Channel 131**  Rosa Maria Alsina-Pages, Claudia Mateo Segura, Joan Claudi Socoró Carrié and Pau Bergada

Ron-Ron G. Garcia, D. Johnson, and Adranne Rachel B. Valencia

**for Completely Restrained Cable-Driven Manipulators 59** 

## Contents

#### **Preface** XI

	- **Part 2 Control Systems 129**

X Contents


## Preface

The search for the development of intelligent systems and emerging technologies has attracted so much attention over the centuries and created relentless research activities. The development of robotics and intelligent machines that have similar behavior to humans performing day to day activities is one of the greatest challenge scientist and researchers have to undertake. The quest and discoveries of new concepts and theories for intelligent non-conventional control systems denote significant technology developments that capture new territory for the betterment of humanity. To date, creating new technologies and innovative algorithms is the focused of research and development. Fuzzy logic system is one of the innovative algorithms that showed promising results in developing emerging technologies.

Fuzzy logic was first proposed in 1965 by Lotfi A. Zadeh of the University of California at Berkeley. Fuzzy logic is based on the idea that humans do not think in terms of crisp numbers, but rather in terms of concepts. The degree of membership of an object in a concept may be partial, with an object being partially related to many concepts. By characterizing the idea of partial membership in concepts, fuzzy logic is better able to convert natural language control strategies in a form usable by machines. The application of fuzzy logic in control problem was first introduced by Mamdani in 1974.

This book exhaustively discusses fuzzy logic controls, concepts, theories, and applications. It is categorized into three sections, namely:


In section one, there are four chapters that focus on fuzzy logic applications to robotics, particularly:

	- 4. Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators

The next two chapters are focus on fuzzy logic applications to electrical machines, namely:


In section two, there are seven chapters that focus on control systems, particularly:


Finally, section three consists of six chapters dedicated to concepts and theories, particularly:


The contributions to this book clearly reveal the concepts and theories of fuzzy logic as well as its importance and effectiveness to the development of robotics, electrical machineries, electronics and intelligent control systems. The readers will find this book a unique and significant source of knowledge and reference for the years to come.

> **Elmer P. Dadios**  University Fellow and Full Professor, Department of Manufacturing Engineering and Management, De La Salle University Philippine

**Part 1** 

**Robotics and Electrical Machines**

**1** 

**Humanoid Robot:** 

*De La Salle University, Manila,* 

*Philippines* 

**Design and Fuzzy Logic Control** 

Elmer P. Dadios, Jazper Jan C. Biliran,

**Technique for Its Intelligent Behaviors** 

Ron-Ron G. Garcia, D. Johnson, and Adranne Rachel B. Valencia

A humanoid robot is a robot with its overall appearance based on that of the human body [1]. In general humanoid robots have a torso with a head, two arms and two legs, although some forms of humanoid robots may model only part of the body, for example, the upper torso. Some humanoid robots may also have a face with eyes and mouth equip with facial interfaces [2, 3, 4, 5]. A humanoid robot is autonomous because it can adapt to changes in its environment or itself and continue to reach its goal [6]. This is the main difference between humanoids and other kinds of robots, like industrial robots, which are used to performing

Humanoid robots are created to imitate some of the same physical and mental tasks that humans undergo daily [7]. Scientists and specialists from many different fields including engineering, cognitive science, and linguistics combine their efforts to create a robot as human-like as possible [8, 9]. Their creators' goal for the robot is that for it to both understand human intelligence, reason and act like humans [7]. If humanoids are able to do

There are many issues involves in developing a humanoid robot [1, 10, 11]. But the most difficult is balancing the robot while it does its motion. Babies take several months before they learn to walk; one reason is the gravity affecting our body weight. Like humans, robots also have gravitational force affecting on it. This is the reason why conducting research in

The next section of this chapter is organized as follows: section 2 discusses the physical design of the robot. This involves the design and development of mechanical structure of the robot. Section 3 presents the sensors that are use for gathering environment information. The inputs from these sensors are used for robot perception and intelligence. Section 4 discusses the power needed to fully operate the humanoid robot. Section 5 discusses the microcontroller used that does the control execution and operation of the robot. Section 6 discusses the fuzzy logic algorithm developed for the total intelligence and control of the

**1. Introduction** 

tasks in highly structured environments.

so, they could eventually work alongside with humans.

this field is still very challenging and exciting [14.15].

## **Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors**

Elmer P. Dadios, Jazper Jan C. Biliran, Ron-Ron G. Garcia, D. Johnson, and Adranne Rachel B. Valencia *De La Salle University, Manila, Philippines* 

## **1. Introduction**

A humanoid robot is a robot with its overall appearance based on that of the human body [1]. In general humanoid robots have a torso with a head, two arms and two legs, although some forms of humanoid robots may model only part of the body, for example, the upper torso. Some humanoid robots may also have a face with eyes and mouth equip with facial interfaces [2, 3, 4, 5]. A humanoid robot is autonomous because it can adapt to changes in its environment or itself and continue to reach its goal [6]. This is the main difference between humanoids and other kinds of robots, like industrial robots, which are used to performing tasks in highly structured environments.

Humanoid robots are created to imitate some of the same physical and mental tasks that humans undergo daily [7]. Scientists and specialists from many different fields including engineering, cognitive science, and linguistics combine their efforts to create a robot as human-like as possible [8, 9]. Their creators' goal for the robot is that for it to both understand human intelligence, reason and act like humans [7]. If humanoids are able to do so, they could eventually work alongside with humans.

There are many issues involves in developing a humanoid robot [1, 10, 11]. But the most difficult is balancing the robot while it does its motion. Babies take several months before they learn to walk; one reason is the gravity affecting our body weight. Like humans, robots also have gravitational force affecting on it. This is the reason why conducting research in this field is still very challenging and exciting [14.15].

The next section of this chapter is organized as follows: section 2 discusses the physical design of the robot. This involves the design and development of mechanical structure of the robot. Section 3 presents the sensors that are use for gathering environment information. The inputs from these sensors are used for robot perception and intelligence. Section 4 discusses the power needed to fully operate the humanoid robot. Section 5 discusses the microcontroller used that does the control execution and operation of the robot. Section 6 discusses the fuzzy logic algorithm developed for the total intelligence and control of the

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 5

The arrangement or position of the motors is crucial for the movement of the robot. The motors are connected to each other using aluminum brackets. Design for the aluminum brackets for the arm and legs follow the movements set for the motor. Each bracket is capable of tilting to the left and right for the rotational span allowed by the servo motor. Each aluminum bracket has multiple holes for connecting plates and brackets to one another. The brackets also act as the shield that protects the servo motor and robust enough to avoid damage when it falls. Despite of its rigidity, the bracket material should be lighter and can carry the servo motors as well as the total load of the robot including its circuitry.

The body of the robot is made of a durable acrylic plastic case and is used to protect the control board and circuitry from damage. Several factors were considered in the design of the body casing. The dimensions of the casing were designed to accommodate the IC power battery and the microcontroller. It is also important for the body case to be proportional to

The sensors are needed by the robot to gather information about the conditions of the environment to allow the robot to make necessary decisions about its position or certain actions that the situation requires. In this research, four types of sensors are utilized: infrared and ultrasonic sensors for obstacle detection, tilt sensor for robot balancing, and color sensor

the dimensions of the legs and the arms of the robot.

Fig. 2. The Humanoid Robot with sensors locations.

**3. The sensors used for the humanoid robot intelligence** 

for ball recognition. Details of the position of these sensors are shown in figure 2.

robot. Section 7 present the experiment results conducted in this research. Discussions and analysis of these results are also presented in this section. Finally, section 8 presents the conclusion and recommendations for future work.

## **2. The humanoid robot mechanical design**

The physical structure of the robot developed in this research is shown in figure 1. It has 17 degrees of freedom. Hence, it utilizes 17 servomotors as its actuators to perform its dynamic motions. There are 10 motors employed for the legs, 6 motors for the arms, and 1 motor for the head. The servo motor used in this research requires 3-5 Volts peak-to-peak square wave pulse. Pulse duration is from 0.9ms to 2.1ms with 1.5 ms as center. The pulse refreshes at 50 Hz (20ms). It is operated with a 4.8-6.0 Volts.

Fig. 1. Skeletal design of the humanoid robot with 17 degrees of freedom.

robot. Section 7 present the experiment results conducted in this research. Discussions and analysis of these results are also presented in this section. Finally, section 8 presents the

The physical structure of the robot developed in this research is shown in figure 1. It has 17 degrees of freedom. Hence, it utilizes 17 servomotors as its actuators to perform its dynamic motions. There are 10 motors employed for the legs, 6 motors for the arms, and 1 motor for the head. The servo motor used in this research requires 3-5 Volts peak-to-peak square wave pulse. Pulse duration is from 0.9ms to 2.1ms with 1.5 ms as center. The pulse refreshes at 50

Fig. 1. Skeletal design of the humanoid robot with 17 degrees of freedom.

conclusion and recommendations for future work.

**2. The humanoid robot mechanical design** 

Hz (20ms). It is operated with a 4.8-6.0 Volts.

The arrangement or position of the motors is crucial for the movement of the robot. The motors are connected to each other using aluminum brackets. Design for the aluminum brackets for the arm and legs follow the movements set for the motor. Each bracket is capable of tilting to the left and right for the rotational span allowed by the servo motor. Each aluminum bracket has multiple holes for connecting plates and brackets to one another. The brackets also act as the shield that protects the servo motor and robust enough to avoid damage when it falls. Despite of its rigidity, the bracket material should be lighter and can carry the servo motors as well as the total load of the robot including its circuitry.

The body of the robot is made of a durable acrylic plastic case and is used to protect the control board and circuitry from damage. Several factors were considered in the design of the body casing. The dimensions of the casing were designed to accommodate the IC power battery and the microcontroller. It is also important for the body case to be proportional to the dimensions of the legs and the arms of the robot.

## **3. The sensors used for the humanoid robot intelligence**

The sensors are needed by the robot to gather information about the conditions of the environment to allow the robot to make necessary decisions about its position or certain actions that the situation requires. In this research, four types of sensors are utilized: infrared and ultrasonic sensors for obstacle detection, tilt sensor for robot balancing, and color sensor for ball recognition. Details of the position of these sensors are shown in figure 2.

Fig. 2. The Humanoid Robot with sensors locations.

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 7

The Photo Sensor circuit component is a photoresistor or an LDR (Light Dependent Resistor) in series with a fixed resistor. The LDR must be a part of a voltage divider circuit in order to give an output voltage which varies with illumination. The super bright light emitting diode will provide the light to the LDR. When an object is placed in front of the LDR and LED at about 10-20mm away, some of the light will reflect back to the LDR, depending on the material. A material with a bright color will reflect more light to the LDR. A black material will absorb all the light and nothing will be reflected. In this project, the robot needs to detect a yellow ball for it to kick. The disadvantage with the circuit presented is that it will also detect a material brighter than yellow. However, the scope of this project is only to

Power management is an essential part of the humanoid robot. This part functions to ensure that the proper voltage is supplied to the servos as well as the sensors and the microcontroller. There are circumstances where in the power supplied to the motors exceeds the power required. In cases like this, probable damage could occur. That is why it is

For voltage regulation, the LM338k transistor was used as the primary part of the regulator circuit. The primary choice would have been the LM7805, which is the most widely used transistor. It supplies 5 volts and is capable of generating 1 to 1.5 A of current. However, with the number of motors used in this project, the current rating of the LM7805 would be insufficient. Hence, the LM338k was opted due to its higher current rating at about 1 to 5

There are six outputs in the circuit for the servo motors. Four voltage regulators were used to accommodate 24 motors. Only 17 motors were used but additional outputs were added to accommodate the sensors and other additions. The output voltage can be solved using the

An output of 5.9 volts is desired so R2 is set at 450 ohms, and R1, which is constant, is 120

This research utilizes packed 7.2 volt Lithium Ion Batteries as the power source of the robot. It would then be regulated to approximately 5.9 volts. Lithium Ion batteries are light weight which is a big factor for this project considering the size and the movements needed to be performed by the robot. NiMH batteries (Nickel Metal Hydrite) were also an option but to be able to supply the required voltage needed by the robot, the battery has to be customized, which made the batteries bulky and heavy. Litihium Ion Batteries were also readily

Vo = Vref + (1 + R2/R1) + IadjR2 (1)

Vo = 1.25(1+450/120) + 50uA(340) (2)

Vo = 5.95 V (3)

Amperes, ensuring that ample amount of current is supplied to the motors.

detect the yellow ball, and not to differentiate it from other colors.

**4. Power management and power source** 

essential to have the voltage regulated.

ohms. Vref = 1.25 and Iadj = 50uA.

the value of Vo is obtained.

formula

Substituting,

available.

Figure3 shows the reflective infrared sensor used to detect objects in proximity. The basic circuit involves an IR LED and an IR photodiode. The IR LED will emit light and the photodiode will measure the amount of light reflected back. When an object is in proximity, more light will be reflected to the IR photodiode. The Ultrasonic Sensor SRF04 is used also in this research to avoid obstacles. This is an Ultrasonic Range Finder Designed and manufactured by Devantech and is capable of non-contact distance measurements from 3 cm to 3 m. The SRF04 is also easy to connect to the microcontroller as it only needs two I/O pins. It requires a 10uS minimum TTL level pulse input trigger. The echo pulse is a positive TTL level signal (100 uS – 18 mS), with its width proportional to the range. If no object is detected, the width of the echo is approximately 36 mS.

Fig. 3. Basic Reflective IR Proximity Sensor.

The tilt sensor ADXL202 is used in this research to determine the inclination of the robot which is then used by the controller developed to stabilize and balance the robot. It measures the tilting in two axes of a reference plane. Full motion uses at least three axes and additional sensors. One way to measure tilt angle with reference to the earth's ground is to use the accelerometer. The ADXL202 is a low-cost, low power 2-axis accelerometer which can measure both dynamic acceleration and static acceleration. This accelerometer is small, requires small amount of voltage, and outputs an analog voltage that could readily be used by the main controller. A Photo Sensor is used to identify the yellow ball which the robot has to kick. The circuit of this sensor is basically a voltage divider a simple linear circuit that generates an output voltage that is a fraction of its input voltage. Voltage division refers to the partitioning of a voltage among the components of the divider.

The Photo Sensor circuit component is a photoresistor or an LDR (Light Dependent Resistor) in series with a fixed resistor. The LDR must be a part of a voltage divider circuit in order to give an output voltage which varies with illumination. The super bright light emitting diode will provide the light to the LDR. When an object is placed in front of the LDR and LED at about 10-20mm away, some of the light will reflect back to the LDR, depending on the material. A material with a bright color will reflect more light to the LDR. A black material will absorb all the light and nothing will be reflected. In this project, the robot needs to detect a yellow ball for it to kick. The disadvantage with the circuit presented is that it will also detect a material brighter than yellow. However, the scope of this project is only to detect the yellow ball, and not to differentiate it from other colors.

#### **4. Power management and power source**

Power management is an essential part of the humanoid robot. This part functions to ensure that the proper voltage is supplied to the servos as well as the sensors and the microcontroller. There are circumstances where in the power supplied to the motors exceeds the power required. In cases like this, probable damage could occur. That is why it is essential to have the voltage regulated.

For voltage regulation, the LM338k transistor was used as the primary part of the regulator circuit. The primary choice would have been the LM7805, which is the most widely used transistor. It supplies 5 volts and is capable of generating 1 to 1.5 A of current. However, with the number of motors used in this project, the current rating of the LM7805 would be insufficient. Hence, the LM338k was opted due to its higher current rating at about 1 to 5 Amperes, ensuring that ample amount of current is supplied to the motors.

There are six outputs in the circuit for the servo motors. Four voltage regulators were used to accommodate 24 motors. Only 17 motors were used but additional outputs were added to accommodate the sensors and other additions. The output voltage can be solved using the formula

$$\text{V}\_{\text{O}} = \text{V}\_{\text{ref}} + (1 + \text{R2}/\text{R1}) + \text{I}\_{\text{adj}}\text{R2} \tag{1}$$

An output of 5.9 volts is desired so R2 is set at 450 ohms, and R1, which is constant, is 120 ohms. Vref = 1.25 and Iadj = 50uA.

Substituting,

6 Fuzzy Logic – Controls, Concepts, Theories and Applications

Figure3 shows the reflective infrared sensor used to detect objects in proximity. The basic circuit involves an IR LED and an IR photodiode. The IR LED will emit light and the photodiode will measure the amount of light reflected back. When an object is in proximity, more light will be reflected to the IR photodiode. The Ultrasonic Sensor SRF04 is used also in this research to avoid obstacles. This is an Ultrasonic Range Finder Designed and manufactured by Devantech and is capable of non-contact distance measurements from 3 cm to 3 m. The SRF04 is also easy to connect to the microcontroller as it only needs two I/O pins. It requires a 10uS minimum TTL level pulse input trigger. The echo pulse is a positive TTL level signal (100 uS – 18 mS), with its width proportional to the range. If no object is

The tilt sensor ADXL202 is used in this research to determine the inclination of the robot which is then used by the controller developed to stabilize and balance the robot. It measures the tilting in two axes of a reference plane. Full motion uses at least three axes and additional sensors. One way to measure tilt angle with reference to the earth's ground is to use the accelerometer. The ADXL202 is a low-cost, low power 2-axis accelerometer which can measure both dynamic acceleration and static acceleration. This accelerometer is small, requires small amount of voltage, and outputs an analog voltage that could readily be used by the main controller. A Photo Sensor is used to identify the yellow ball which the robot has to kick. The circuit of this sensor is basically a voltage divider a simple linear circuit that generates an output voltage that is a fraction of its input voltage. Voltage division refers to

detected, the width of the echo is approximately 36 mS.

Fig. 3. Basic Reflective IR Proximity Sensor.

the partitioning of a voltage among the components of the divider.

$$\text{Vo} = 1.25(1 + 450/120) + 50 \text{uA} (340) \tag{2}$$

the value of Vo is obtained.

$$\text{Vo} = \text{5.95 V} \tag{3}$$

This research utilizes packed 7.2 volt Lithium Ion Batteries as the power source of the robot. It would then be regulated to approximately 5.9 volts. Lithium Ion batteries are light weight which is a big factor for this project considering the size and the movements needed to be performed by the robot. NiMH batteries (Nickel Metal Hydrite) were also an option but to be able to supply the required voltage needed by the robot, the battery has to be customized, which made the batteries bulky and heavy. Litihium Ion Batteries were also readily available.

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 9

Fuzzy logic is a problem-solving control system methodology that mimics how humans derive a conclusion based on vague, ambiguous, imprecise, noisy or missing input information [12, 13]. The general idea about fuzzy logic is that it takes the inputs from the sensors which is a crisp value and transforms it into membership values ranging from 0 to 1. It then undergoes fuzzy reasoning process using the obtained membership values with the set of rules created. From the previous process, the system obtains a fuzzy set that will be transformed back to crisp values which controls the servo motors [12, 13]. Fuzzy logic systems are capable of processing inexact data and produce acceptable outputs. In addition, there is no need for very complex mathematical computations to control the robot. Also, the physical design of the robot does not need to be very exact and complicated as the fuzzy logic system can compensate for these flaws. Since the fuzzy logic is implemented using software, adjustments in the system is easier, cheaper and additional space is not needed

Two fuzzy logic system (FLS) controllers are developed in this research for the robot's balancing and stability. One FLS controls the left and right tilt and the other FLS controls the forward and backward tilt. Tilt angle in the first fuzzy logic system, which is for the left and right tilt, is taken and processed. Then the second fuzzy logic system will do the same with the forward and backward tilt angle. The idea is to operate the two fuzzy logic systems independently. This approach is more advantageous in terms of software implementation

The Mamdani's method was used for implementing the fuzzy logic systems because of its simple yet great composition of 'min-max' operations [16]. Sample membership functions are shown in figures 4 to 9. Tables 1 and 2 shows the fuzzy associative memory matrix of the 2 fuzzy logic systems with the corresponding rules. Tables 3 and 4 show the final output on deciding what motors to activate. The idea is all the affected motors are going to increase or decrease their current angle until the system becomes stable. The amount of the angle shift will depend on the position of the motor in the robot. Observably, change in the angle of the motors located near the ground will have greater effect to the whole body than motors

which will only mean additional weight to the robot.

and complexity of the entire fuzzy logic system.

Fig. 4. Backward-Forward Membership Function

located less near the ground.

## **5. The microcontroller: Robot brain**

The Atmega128 microcontroller used in this research serves as the main controller of the entire system. It is in-charge for processing all the input data and output data needed by the robot. Input data refers to the information taken from all the sensors and control switches. Output data are the signals needed by the servo motors in order to provide proper results in different situations for robot actions. Being the only microcontroller in the system, information from all modules is all carried in and out from this single controller. These modules are: the power management unit, the sensor information unit, the servo motor control unit, the artificial intelligence unit, and the central control unit.

The power management unit is the one responsible for distributing and monitoring the power to the entire system supplied by the batteries. If one of these batteries reaches critical level, the power management unit updates the microcontroller about the situation so that the microcontroller will be able to decide if the robot should continue its task or should stop.

The sensor information unit is responsible for all the system inputs of the robot. All of these inputs are fed into the microcontroller and then processed to provide the robot appropriate action for every situation.

The servo motor control unit is responsible for providing signals for each servo motor of the robot. Timing is considered an important factor in this module unlike all other modules where timing is not as important. One problem encountered in this research was that it would be difficult to control all motors from the output port pins of the microcontroller. Because of this problem, several approaches were considered. Using a separate microcontroller was first considered for controlling all the 17 servo motors. But using another microcontroller just for controlling the servo motors will defeat the purpose of using just one microcontroller for the whole system and will only pose new problems for the whole system like the communication and synchronization of the two microcontrollers. The solution was to make use of the Atmega128's timer/counter and connect the 17 servo motors to two 4017 decade counters.

The central control unit is responsible for the main controls of the robot. This module is a switch panel consists of a power supply switch, a reset switch, and 8 action switches. All batteries are connected to the power supply switch which turns the robot on and off. The reset switch is a normally open tact switch that is connected to the active low reset pin of the microcontroller and ground. The action switches determine what action the robot will be performing. These switches are connected to the 8 external interrupt pins of the microcontroller which are configured as level triggered, meaning the interrupt will trigger once the switch is held low. Also, these external interrupts INT0-INT7 have priority levels. INT0 being the most prioritized and INT7 as least prioritized interrupt.

## **6. The robot intelligence: Fuzzy logic system**

The Fuzzy Logic System module is used for the artificial intelligence control algorithm of the robot. This module is responsible for the stability and balancing of the robot while it is performing actions such as walking and kicking. Implementation of fuzzy logic is inside the microcontroller software which is modifiable and adjustable. Since the implementation is in software, this procedure is processed inside the microcontroller in which the input values are taken from the tilt sensor and the output values provide the servo motors correct positions.

The Atmega128 microcontroller used in this research serves as the main controller of the entire system. It is in-charge for processing all the input data and output data needed by the robot. Input data refers to the information taken from all the sensors and control switches. Output data are the signals needed by the servo motors in order to provide proper results in different situations for robot actions. Being the only microcontroller in the system, information from all modules is all carried in and out from this single controller. These modules are: the power management unit, the sensor information unit, the servo motor

The power management unit is the one responsible for distributing and monitoring the power to the entire system supplied by the batteries. If one of these batteries reaches critical level, the power management unit updates the microcontroller about the situation so that the microcontroller will be able to decide if the robot should continue its task or should stop. The sensor information unit is responsible for all the system inputs of the robot. All of these inputs are fed into the microcontroller and then processed to provide the robot appropriate

The servo motor control unit is responsible for providing signals for each servo motor of the robot. Timing is considered an important factor in this module unlike all other modules where timing is not as important. One problem encountered in this research was that it would be difficult to control all motors from the output port pins of the microcontroller. Because of this problem, several approaches were considered. Using a separate microcontroller was first considered for controlling all the 17 servo motors. But using another microcontroller just for controlling the servo motors will defeat the purpose of using just one microcontroller for the whole system and will only pose new problems for the whole system like the communication and synchronization of the two microcontrollers. The solution was to make use of the Atmega128's timer/counter and connect the 17 servo

The central control unit is responsible for the main controls of the robot. This module is a switch panel consists of a power supply switch, a reset switch, and 8 action switches. All batteries are connected to the power supply switch which turns the robot on and off. The reset switch is a normally open tact switch that is connected to the active low reset pin of the microcontroller and ground. The action switches determine what action the robot will be performing. These switches are connected to the 8 external interrupt pins of the microcontroller which are configured as level triggered, meaning the interrupt will trigger once the switch is held low. Also, these external interrupts INT0-INT7 have priority levels.

The Fuzzy Logic System module is used for the artificial intelligence control algorithm of the robot. This module is responsible for the stability and balancing of the robot while it is performing actions such as walking and kicking. Implementation of fuzzy logic is inside the microcontroller software which is modifiable and adjustable. Since the implementation is in software, this procedure is processed inside the microcontroller in which the input values are taken from the tilt sensor and the output values provide the servo motors correct positions.

INT0 being the most prioritized and INT7 as least prioritized interrupt.

**6. The robot intelligence: Fuzzy logic system** 

control unit, the artificial intelligence unit, and the central control unit.

**5. The microcontroller: Robot brain** 

action for every situation.

motors to two 4017 decade counters.

Fuzzy logic is a problem-solving control system methodology that mimics how humans derive a conclusion based on vague, ambiguous, imprecise, noisy or missing input information [12, 13]. The general idea about fuzzy logic is that it takes the inputs from the sensors which is a crisp value and transforms it into membership values ranging from 0 to 1. It then undergoes fuzzy reasoning process using the obtained membership values with the set of rules created. From the previous process, the system obtains a fuzzy set that will be transformed back to crisp values which controls the servo motors [12, 13]. Fuzzy logic systems are capable of processing inexact data and produce acceptable outputs. In addition, there is no need for very complex mathematical computations to control the robot. Also, the physical design of the robot does not need to be very exact and complicated as the fuzzy logic system can compensate for these flaws. Since the fuzzy logic is implemented using software, adjustments in the system is easier, cheaper and additional space is not needed which will only mean additional weight to the robot.

Two fuzzy logic system (FLS) controllers are developed in this research for the robot's balancing and stability. One FLS controls the left and right tilt and the other FLS controls the forward and backward tilt. Tilt angle in the first fuzzy logic system, which is for the left and right tilt, is taken and processed. Then the second fuzzy logic system will do the same with the forward and backward tilt angle. The idea is to operate the two fuzzy logic systems independently. This approach is more advantageous in terms of software implementation and complexity of the entire fuzzy logic system.

The Mamdani's method was used for implementing the fuzzy logic systems because of its simple yet great composition of 'min-max' operations [16]. Sample membership functions are shown in figures 4 to 9. Tables 1 and 2 shows the fuzzy associative memory matrix of the 2 fuzzy logic systems with the corresponding rules. Tables 3 and 4 show the final output on deciding what motors to activate. The idea is all the affected motors are going to increase or decrease their current angle until the system becomes stable. The amount of the angle shift will depend on the position of the motor in the robot. Observably, change in the angle of the motors located near the ground will have greater effect to the whole body than motors located less near the ground.

Fig. 4. Backward-Forward Membership Function

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 11

Fig. 8. R-L Displacement

Fig. 9. Membership Function for R-L Tilt Servo Output

B-F Tilt

B – backward F – forward

Table 1. Fuzzy Logic Controller (FLC) 1 FAM

FLC 1 Displacement

SF B SB SB F B B B

NL NS 0 PS PL

B F F F SB SF SF F C C C C C C

Fig. 5. B-F Displacement

Fig. 6. Membership Function for B-F Tilt Servo Output

Fig. 7. Right-Left Membership Function

Fig. 8. R-L Displacement

Fig. 5. B-F Displacement

Fig. 6. Membership Function for B-F Tilt Servo Output

Fig. 7. Right-Left Membership Function

Fig. 9. Membership Function for R-L Tilt Servo Output


Table 1. Fuzzy Logic Controller (FLC) 1 FAM

#### B – backward

F – forward

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 13

Having established these two fuzzy logic systems, the balancing task will entirely depend on these. Failure to one of these systems would mean failure to the entire balancing task of

In this experiment, a steel plate platform was used to measure the balancing capability of the robot. One end of the platform was gradually elevated so that the robot is standing on an inclined plane and the maximum angle the robot can stay on standing position is

Output Affected Motor L 1,2,3,4,5,6,7,8 SL 1,2,3,4,5,6,7,8

SR 1,2,3,4,5,6,7,8 R 1,2,3,4,5,6,7,8

Output Affected Motor

C None

F 3,4,7,8 SF 3,4,7,8 C None SB 3,4,7,8 B 3,4,7,8

Table 3. Fuzzy Logic System R-L Output

Table 4. Fuzzy Logic System B-F Output

**7.1 Inclined steel plate balancing experiments** 

**7. Experiment results** 

RULES for (FLC) 2

the robot.

1. if tilt is R and delta x is 0 (zero) then output is L. 2. if tilt is R and delta x is PS then output is L. 3. if tilt is R and delta x is PL then output is L. 4. if tilt is SR and delta x is 0 (zero) then output is SL. 5. if tilt is SR and delta x is PS then output is SL. 6. if tilt is SR and delta x is PL then output is L. 7. if tilt is C and delta x is NL then output is C. 8. if tilt is C and delta x is NS then output is C. 9. if tilt is C and delta x is 0 (zero) then output is C. 10. if tilt is C and delta x is PS then output is C. 11. if tilt is C and delta x is PL then output is C. 12. if tilt is SL and delta x is NL then output is R. 13. if tilt is SL and delta x is NS then output is SR. 14. if tilt is SL and delta x is 0 (zero) then output is SR. 15. if tilt is L and delta x is NL then output is R. 16. if tilt is L and delta x is NS then output is R. 17. if tilt is L and delta x is 0 (zero) then output is R.


RULES for (FLC) 1



Table 2. Fuzzy Logic Controller (FLC) 2 FAM

#### RULES for (FLC) 2

12 Fuzzy Logic – Controls, Concepts, Theories and Applications

R - right L - left C - center

SB - slightly backward SF - slightly forward SR - slightly right SL - slightly left

NL - negative large NS - negative small 0 (zero) - negligible PS - positive small PL - positive large RULES for (FLC) 1

1. if tilt is B and delta x is 0 (zero) then output is F. 2. if tilt is B and delta x is PS then output is F. 3. if tilt is B and delta x is PL then output is F. 4. if tilt is SB and delta x is 0 (zero) then output is SF. 5. if tilt is SB and delta x is PS then output is SF. 6. if tilt is SB and delta x is PL then output is F. 7. if tilt is C and delta x is NL then output is C. 8. if tilt is C and delta x is NS then output is C. 9. if tilt is C and delta x is 0 (zero) then output is C. 10. if tilt is C and delta x is PS then output is C. 11. if tilt is C and delta x is PL then output is C. 12. if tilt is SF and delta x is NL then output is B. 13. if tilt is SF and delta x is NS then output is SB. 14. if tilt is SF and delta x is 0 (zero) then output is SB. 15. if tilt is F and delta x is NL then output is B. 16. if tilt is F and delta x is NS then output is B. 17. if tilt is F and delta x is 0 (zero) then output is B.

R-L Tilt

Table 2. Fuzzy Logic Controller (FLC) 2 FAM

FLC 2 Displacement

SL R SR SR L R R R

NL NS 0 PS PL

R L L L SR SL SL L C C C C C C


Having established these two fuzzy logic systems, the balancing task will entirely depend on these. Failure to one of these systems would mean failure to the entire balancing task of the robot.


Table 3. Fuzzy Logic System R-L Output


Table 4. Fuzzy Logic System B-F Output

## **7. Experiment results**

#### **7.1 Inclined steel plate balancing experiments**

In this experiment, a steel plate platform was used to measure the balancing capability of the robot. One end of the platform was gradually elevated so that the robot is standing on an inclined plane and the maximum angle the robot can stay on standing position is

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 15

Fig. 12. Robot Inclined Steel Plate Balancing Experiment. Back position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it

Fig. 13. Robot Inclined Steel Plate Balancing Experiment. Front position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it

Fig. 14a. Humanoid robot steel plate balancing performance with fuzzy logic controller

falls.

falls.

recorded. Figures 10-13 shows the sample results of the real and physical experiments conducted. It can be seen in this figure that the robot uses its left foot to maintain its balance that compensate the angle taken on the inclined plane.

There were 4 tests of experiments conducted based on actual position of the robot relative to the inclined plane. The first test was the robot facing right of elevated steel plate as shown in figure 7. The second test was the robot facing left of the inclined steel plate as shown in figure 8. The third was the robot facing front of the inclined steel plate as shown in figure 9. And the fourth was the robot facing back of the inclined steel plate as shown in figure 10. It can be seen from these pictures that the robot uses its foot and body to maintain its stability. Figures 14a and 14b shows the results of these experiments with a comparison of the performance of the fuzzy logic controller against the conventional controller. Clearly from these results we can see the superiority of the fuzzy logic controller developed.

Fig. 10. Robot Inclined Steel Plate Balancing Experiment. Right position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it falls.

Fig. 11. Robot Inclined Steel Plate Balancing Experiment. Left position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it falls.

recorded. Figures 10-13 shows the sample results of the real and physical experiments conducted. It can be seen in this figure that the robot uses its left foot to maintain its balance

There were 4 tests of experiments conducted based on actual position of the robot relative to the inclined plane. The first test was the robot facing right of elevated steel plate as shown in figure 7. The second test was the robot facing left of the inclined steel plate as shown in figure 8. The third was the robot facing front of the inclined steel plate as shown in figure 9. And the fourth was the robot facing back of the inclined steel plate as shown in figure 10. It can be seen from these pictures that the robot uses its foot and body to maintain its stability. Figures 14a and 14b shows the results of these experiments with a comparison of the performance of the fuzzy logic controller against the conventional controller. Clearly from

Fig. 10. Robot Inclined Steel Plate Balancing Experiment. Right position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it

Fig. 11. Robot Inclined Steel Plate Balancing Experiment. Left position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it

these results we can see the superiority of the fuzzy logic controller developed.

that compensate the angle taken on the inclined plane.

falls.

falls.

Fig. 12. Robot Inclined Steel Plate Balancing Experiment. Back position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it falls.

Fig. 13. Robot Inclined Steel Plate Balancing Experiment. Front position. Note that the hand of the person is not touching the robot. This is just in preparation to catch the robot when it falls.

Fig. 14a. Humanoid robot steel plate balancing performance with fuzzy logic controller

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 17

The robot uses its arm to balance itself in addition to its body alignment. Figure 16 shows the statistics of the robot performance in kicking the ball. The average distance the ball travel after kicking is 14.6 inches. Clearly from this figures the robot is very stable and

The robot uses ultrasonic and infra red sensors to detect the obstacles on its path. The positions of these sensors are evenly distributed on the robot's body. It is at the right, left, and center positions. When only the right sensor detects the obstacle the robot will do left side step motions until no obstacle is found. When only the left sensor detects the obstacle the robot will do right side steps motions until no obstacle is found. When all three ultrasonic sensors detect obstacle the robot will stop. If there are no more obstacles found the robot will walk forward right away. Figure 17 shows the animated motions of the robot in performing this task. The obstacle is on the right side of the robot hence the robot did left side step motion until the obstacle is not found. Figure 18 shows the distance accuracy of the robot in detecting obstacles. In all obstacle avoidance experiments conducted the robot

reliable in performing this motions.

Fig. 16. Humanoid robot ball kicking controller performance.

**7.3 Obstacle avoidance experiments** 

shows very accurate, reliable, and robust behavior.

#### **7.2 Ball kicking experiments**

The humanoid robot developed in this research can identify and kick a yellow tennis ball. A photo sensor is installed on the foot of the robot. Once the sensor found the ball the robot position itself to do the kicking. Complete animation of this task is shown in figure 15.

Fig. 15. Ball kicking experiment results

The robot uses its arm to balance itself in addition to its body alignment. Figure 16 shows the statistics of the robot performance in kicking the ball. The average distance the ball travel after kicking is 14.6 inches. Clearly from this figures the robot is very stable and reliable in performing this motions.

Fig. 16. Humanoid robot ball kicking controller performance.

## **7.3 Obstacle avoidance experiments**

16 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 14b. Humanoid robot steel plate balancing performance without fuzzy logic controller

The humanoid robot developed in this research can identify and kick a yellow tennis ball. A photo sensor is installed on the foot of the robot. Once the sensor found the ball the robot position itself to do the kicking. Complete animation of this task is shown in figure 15.

**7.2 Ball kicking experiments** 

Fig. 15. Ball kicking experiment results

The robot uses ultrasonic and infra red sensors to detect the obstacles on its path. The positions of these sensors are evenly distributed on the robot's body. It is at the right, left, and center positions. When only the right sensor detects the obstacle the robot will do left side step motions until no obstacle is found. When only the left sensor detects the obstacle the robot will do right side steps motions until no obstacle is found. When all three ultrasonic sensors detect obstacle the robot will stop. If there are no more obstacles found the robot will walk forward right away. Figure 17 shows the animated motions of the robot in performing this task. The obstacle is on the right side of the robot hence the robot did left side step motion until the obstacle is not found. Figure 18 shows the distance accuracy of the robot in detecting obstacles. In all obstacle avoidance experiments conducted the robot shows very accurate, reliable, and robust behavior.

Humanoid Robot: Design and Fuzzy Logic Control Technique for Its Intelligent Behaviors 19

The paper showed a working prototype of a humanoid robot with artificial intelligence that has the ability to walk on two legs, kick a tennis ball, balance in an inclined steel plate, avoid obstacles, and dance with the beat of the music. Harmony between the parts of the robot namely mechanical, electrical and software is a must. The mechanical design deals with the overall physical architecture of the robot. It considers everything about the robot's whole skeletal system. The degrees of freedom for the robot are determined in this part. Proportion between the parts of the robot is very important as it would help in its stability thus making

The software design tackles all the decision making of the robot. This acts as the main brain of the robot. Fuzzy logic is implemented in order for the robot to maintain its balance and stability. The controller developed using fuzzy logic in this research exhibits very accurate, reliable, and robust behavior as shown in the defferent experiments conducted in section

Electrical design deals with connecting the mechanical and software parts of the robot to translate into actual robot movement. Tilt sensor, infrared and ultrasonic is provided with ample voltage supply to work efficiently. An analog to digital converter is not needed anymore as Atmega128 has its built in capability. Power sources were designed to output sufficient amounts of energy that would run the motors and sensors efficiently. A double sided PCB is used to implement the circuit main board. The result of using a big and dual sided PCB was a harder time troubleshooting when problems occurred as well as aligning

All of these parts are needed to be done meticulously with the aim of making it very reliable. A design plan should always be followed as well as coordination between all of its parts. A conflict was experienced on whether to use rubber padding or not for the feet. Balancing in an inclined plane would require rubber padding. Without rubber padding, the robot slips down the plane. However, with the rubber padding on, the robot's walking is compromised even with slightly slippery rubber padding. The authors decided not to use the rubber padding as the robot's walking has a higher priority. For future works, it will be good to put an internal vision system on this robot in order for it to recognize and know the

Fig. 19. Humanoid robot dancing results

it easier to control.

the two sides correctly.

environment better.

seven.

**8. Conclusions and recommendation** 

Fig. 17. Humanoid robot obstacle Avoidance - side step and forward motion.

Fig. 18. Robot accuracy in detecting obstacles

#### **7.4 Robot dancing experiments**

The humanoid robot developed in this research has the capability to entertain people by dancing. In this experiment, the beat of the music is synchronized to the robot body, arm, head, and leg motions. Figure 19 shows the sample robot dancing motions with the music beats.

Fig. 19. Humanoid robot dancing results

18 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 17. Humanoid robot obstacle Avoidance - side step and forward motion.

The humanoid robot developed in this research has the capability to entertain people by dancing. In this experiment, the beat of the music is synchronized to the robot body, arm, head, and leg motions. Figure 19 shows the sample robot dancing motions with the music

Fig. 18. Robot accuracy in detecting obstacles

**7.4 Robot dancing experiments** 

beats.

## **8. Conclusions and recommendation**

The paper showed a working prototype of a humanoid robot with artificial intelligence that has the ability to walk on two legs, kick a tennis ball, balance in an inclined steel plate, avoid obstacles, and dance with the beat of the music. Harmony between the parts of the robot namely mechanical, electrical and software is a must. The mechanical design deals with the overall physical architecture of the robot. It considers everything about the robot's whole skeletal system. The degrees of freedom for the robot are determined in this part. Proportion between the parts of the robot is very important as it would help in its stability thus making it easier to control.

The software design tackles all the decision making of the robot. This acts as the main brain of the robot. Fuzzy logic is implemented in order for the robot to maintain its balance and stability. The controller developed using fuzzy logic in this research exhibits very accurate, reliable, and robust behavior as shown in the defferent experiments conducted in section seven.

Electrical design deals with connecting the mechanical and software parts of the robot to translate into actual robot movement. Tilt sensor, infrared and ultrasonic is provided with ample voltage supply to work efficiently. An analog to digital converter is not needed anymore as Atmega128 has its built in capability. Power sources were designed to output sufficient amounts of energy that would run the motors and sensors efficiently. A double sided PCB is used to implement the circuit main board. The result of using a big and dual sided PCB was a harder time troubleshooting when problems occurred as well as aligning the two sides correctly.

All of these parts are needed to be done meticulously with the aim of making it very reliable. A design plan should always be followed as well as coordination between all of its parts. A conflict was experienced on whether to use rubber padding or not for the feet. Balancing in an inclined plane would require rubber padding. Without rubber padding, the robot slips down the plane. However, with the rubber padding on, the robot's walking is compromised even with slightly slippery rubber padding. The authors decided not to use the rubber padding as the robot's walking has a higher priority. For future works, it will be good to put an internal vision system on this robot in order for it to recognize and know the environment better.

**2** 

**Application of Fuzzy Logic** 

**in Mobile Robot Navigation** 

*Universiti Putra Malaysia* 

*Malaysia* 

Tang Sai Hong, Danial Nakhaeinia and Babak Karasfi

An autonomous robot is a programmable and multi-functional machine, able to extract information from its surrounding using different kinds of sensors to plan and execute collision free motions within its environment without human intervention. Navigation is a crucial issue for robots that claim to be mobile. A navigation system can be divided into two layers: High level global planning and Low-level reactive control. In high-level planning, a prior knowledge of environment is available and the robot workspace is completely or partially known. Using the world model, the global planner can determine the robot motion direction and generates minimum-cost paths towards the target in the presence of complex obstacles. However, since it is not capable of changing the motion direction in presence of unforeseen or moving obstacles, it fails to reach target. In contrast, in low-level reactive control, the robot work space is unknown and dynamic. It generates control commands based on perception-action configuration, which the robot uses current sensory information to take appropriate actions without planning process. Thus, it has a quick response in reacting to unforeseen obstacles and uncertainties with changing the motion direction.

Several Artificial intelligence techniques such as reinforcement learning, neural networks, fuzzy logic and genetic algorithms, can be applied for the reactive navigation of mobile robots to improve their performance. Amongst the techniques ability of fuzzy logic to represent linguistic terms and reliable decision making in spite of uncertainty and imprecise

Fuzzy control systems are rule-based or knowledge-based systems containing a collection of fuzzy IF-THEN rules based on the domain knowledge or human experts. The simplicity of fuzzy rule-based systems, capability to perform a wide variety tasks without explicit computations and measurements make it extensively popular among the scientists and researcher. This book chapter presents the significance and effectiveness of fuzzy logic in

After the introduction of fuzzy logic importance in mobile robot navigation, **Section 2** reviews methodology of previous works on navigation of mobile robots using fuzzy logic design. **Section 3,** first gives a brief description about the design of a Fuzzy Controller, then a case study shows how the fuzzy control system is used in mobile robots navigation.

information makes it a useful tool in control systems.

solving the navigation problem. The chapter is organized as follows:

**1. Introduction** 

#### **9. References**


## **Application of Fuzzy Logic in Mobile Robot Navigation**

Tang Sai Hong, Danial Nakhaeinia and Babak Karasfi *Universiti Putra Malaysia Malaysia* 

## **1. Introduction**

20 Fuzzy Logic – Controls, Concepts, Theories and Applications

[1] Kazuo Hirai, "*Current and future perspective of honda humanoid robot",* In Proc. IEEE/RSJ

[2] B. Robins, K. Dautenhahn, R. Te Boekhorst, A. Billard*,"Robotic assistants in therapy and* 

[3] Sproull, L., Subramani, M., Kiesler, S., Walker, J.H. and et al. "*When the interface is a face.* 

[4] Takeuchi, A. and Nagao, K., *"Communicative Facial Displays as A New Conversational* 

[5] Takeuchi, A. and Naito, T., *"Situated Facial displays: Towards Social interaction",* In

[6] S. Kagami, F. Kanehiro, Y. Tamiya, M. Inaba, and H. Inoue, "*AutoBalancer: An Online* 

[7] A. Bruce, I. Nourbakhsh, and R. Simmons, *"The Role of Expressiveness and Attention in Human-Robot Interaction*", In Proceedings, AAAI Fall Symposium. (2001). [8] C. Breazeal, J. Velasquez, "*Toward Teaching a Robot Infant" using Emotive Communication* 

[9] C. Breazeal, J. Velasquez, "*Robot in Society: Friend or Appliance?",* In Proceedings of

[10] K. Nagasaka, M. Inaba, and H. Inoue, " *Walking pattern generation for a humanoid robot based on optimal gradient method"*, In Proc. IEEE Int. Conf. Sys. Man. & Cyber., 1999. [11] J. Yamaguchi, S. Inoue, D. Nishino, and A. Takanishi, " *Development of a bipedal* 

[12] E.P. Dadios, et. al, "Hybrid Fuzzy Logic Strategy for Soccer Robot Game", *Journal of* 

[13] E.P. Dadios, et. al, "Fuzzy Logic Controller for Micro Robot Soccer Game", *Proceedings* 

[14] G. Oriolo, L. Sciavicco, B. Siciliano, and L. Villani, *"Robotics: modelling, planning and* 

[15] B. Siciliano, and O. Khatib, Springer Handbook of Robotics. (ISBN 978-3-540-30301-5),

[16] E.H. Mamdani, "Application Of Fuzzy Algorithm for the Control of a dynamic plant",

Situated Intelligence 98, (Zurich, Switzerland, 1998), 25-40.

Int. Conf. Intell. Robot. & Sys. (IROS), pages 96{101, 1998.

*education of children with autism: can a small humanoid robot help encourage social interaction skills?"* ,pages 105-120 Published online: 8 July 2005, Springer-Verlag

*Modality",.* In Proceedings of INTERCHI 93, (Amsterdam, the Netherlands, 1993),

Proceedings of Human Factors in Computing Systems 95, (1995), ACM Press: New

*Dynamic Balance Compensation Scheme for Humanoid Robots",* In Proc. Int. Workshop

*Acts*", In Proceedings of Simulation of Adaptive Behavior, workshop on Socially

Agents 99 Workshop on emotion-based agent architectures, (Seattle, WA, 1999), 18-

*humanoid robot having antagonistic driven joints and three dof trunk",* In Proc. IEEE/RSJ

*Advanced Computational Intelligence and Intelligent Informatics,* Vol 8 No. 1, pp 65-71,

*of the 27th Annual Conference of the IEEE Industrial Electronics Society (IECON'01)*, Hyatt Regency Tech Center, Denver, Colorado, USA, pp. 2154-2159, Nov. 29 – Dec.

Int. Conf. Intell. Robot. & Sys. (IROS), pages 500-508, 1997.

*Human-Computer Interaction",* 11 (2). 97-124.

ACM Press: New York, 187-193.

Alg. Found. Robot.(WAFR), 2000.

FUJI Technology Press, January 2004.

*control.",* Springer Verlag, London 2010.

Springer Verlag, Berlin Heidelberg, 2008.

IEEE Proc., Vol. 121, pages 1585-1588, 1974.

**9. References** 

2005

26.

2, 2001.

York, 450-455.

An autonomous robot is a programmable and multi-functional machine, able to extract information from its surrounding using different kinds of sensors to plan and execute collision free motions within its environment without human intervention. Navigation is a crucial issue for robots that claim to be mobile. A navigation system can be divided into two layers: High level global planning and Low-level reactive control. In high-level planning, a prior knowledge of environment is available and the robot workspace is completely or partially known. Using the world model, the global planner can determine the robot motion direction and generates minimum-cost paths towards the target in the presence of complex obstacles. However, since it is not capable of changing the motion direction in presence of unforeseen or moving obstacles, it fails to reach target. In contrast, in low-level reactive control, the robot work space is unknown and dynamic. It generates control commands based on perception-action configuration, which the robot uses current sensory information to take appropriate actions without planning process. Thus, it has a quick response in reacting to unforeseen obstacles and uncertainties with changing the motion direction.

Several Artificial intelligence techniques such as reinforcement learning, neural networks, fuzzy logic and genetic algorithms, can be applied for the reactive navigation of mobile robots to improve their performance. Amongst the techniques ability of fuzzy logic to represent linguistic terms and reliable decision making in spite of uncertainty and imprecise information makes it a useful tool in control systems.

Fuzzy control systems are rule-based or knowledge-based systems containing a collection of fuzzy IF-THEN rules based on the domain knowledge or human experts. The simplicity of fuzzy rule-based systems, capability to perform a wide variety tasks without explicit computations and measurements make it extensively popular among the scientists and researcher. This book chapter presents the significance and effectiveness of fuzzy logic in solving the navigation problem. The chapter is organized as follows:

After the introduction of fuzzy logic importance in mobile robot navigation, **Section 2** reviews methodology of previous works on navigation of mobile robots using fuzzy logic design. **Section 3,** first gives a brief description about the design of a Fuzzy Controller, then a case study shows how the fuzzy control system is used in mobile robots navigation.

Application of Fuzzy Logic in Mobile Robot Navigation 23

to each ultrasonic sensor. All these vectors adding together then combine into a single vector of general perception. A fuzzy controller then uses the perception information to guide the robot along arbitrary walls and obstacles. Sanchez et al. (1999) proposed a fuzzy control system for path tracking of an autonomous vehicle in outdoor environment. The fuzzy controller is used to generate steering and velocity required to track the path using the data collected from experiments of driving the vehicle by a human. Bento et al. (2002) implemented a path-tracking method by means of fuzzy logic for a Wheeled Mobile Robot. Input variables of the fuzzy controller are position and orientation of the robot with respect to the path. Output variables are linear velocity and angular velocity. Hajjaji and Bentalba (2003) have designed a fuzzy controller for path tracking control of vehicles using its nonlinear dynamics model. A Takagi–Sugeno (T–S) fuzzy model presents the nonlinear model of the vehicle. Then a model-based fuzzy controller is developed based on the T–S fuzzy model. A wall-following robot presented by Peri & Simon (2005) which the robot's motion is controlled by a fuzzy controller to drive it along a predefined path. Antonelli et al. (2007) address a path tracking approach based on a fuzzy-logic set of rules which emulates the human driving behavior. The fuzzy system input is represented by approximate information concerning the knowledge of the curvature of the desired path ahead the vehicle and the distance between the next bend and the vehicle. The output is the maximum value of the linear velocity needed to attain by the vehicle in order to safely drive on the path. Yu et al. (2009) used Taguchi method to design an optimal fuzzy logic controller for trajectory tracking of a wheeled mobile robot. Recently, Xiong and Qu (2010) developed a method for intelligent vehicles' path tracking with two fuzzy controller combinations which controls vehicle direction and a preview fuzzy control method presented by Liao et al. (2010) for path tracking of intelligent vehicle. The vehicle speed and direction are adjusted by fuzzy control according to future path information and present path

information respectively.

Fig. 1. Typical control input variables for path tracking [9]

Ability of a robot to avoid collision with unforeseen or dynamic obstacles while it is moving towards a target or tracking a path is a vital task in autonomous navigation. Navigation strategies can be classified to global path planning and local path planning. In global path planning, information about the obstacles and a global model of environment is available which mostly Configuration space, Road map, Voronoi diagram and Potential field techniques

**2.2 Obstacle avoidance using fuzzy logic** 

Results from real systems address the fuzzy control influence and effectiveness to solve some of the navigation difficulties and to reduce their navigation costs. Closing this book chapter, **Section 4** concludes the chapter with few comments and summarizes the advantages and limitations of using fuzzy logic in mobile robot navigation. The chapter can be interesting for students, researchers and different scientific communities in the areas of robotics, artificial intelligence, intelligent transportation systems, and fuzzy control.

## **2. Review of fuzzy logic applications for mobile robot navigation**

Robust and reliable navigation in dynamic or unknown environment relies on ability of the robots in moving among unknown obstacles without collision and fast reaction to uncertainties. It is highly desirable to develop these tasks using a technique which utilize human reasoning and decision making. Fuzzy logic provides a means to capture the human mind's expertise. It utilizes this heuristic knowledge for representing and accomplishment of a methodology to develop perception-action based strategies for mobile robots navigation. Furthermore, the methodology of the FLC is very helpful dealing with uncertainties in real world and accurate model of the environment is not absolutely required for navigation. Therefore, based on a simple design, easy implementation and robustness properties of FLC, many approaches were developed to solve mobile robot navigation problem in target tracking, path tracking, obstacle avoidance, behaviour coordination, environment modelling, and layer integration (Saffiotti, 1997). This section reviews the proposed fuzzy control methods which used fuzzy sets for velocity control, rotation control and command fusion with focusing on the three most popular categories of: Path tracking, Obstacle avoidance and Behavior coordination.

## **2.1 Fuzzy logic for path tracking**

Path tracking is a crucial function for autonomous mobile robots to navigate along a desired path. This task includes tracking of previously computed paths using a path planner, a defined path by human operator, tracking of walls, road edges, and other natural features in the robot workspace (Chee et al., 1996). It involves real-time perception of the environment to determine the position and orientation of the robot with respect to the desired path. For example in Figure 1, if the robot is misplaced, the controller task is to steer it back on course and minimize the orientation error (Δφ) and the position error (Δx) (Moustris & Tzafestas, 2005). Path tracking difficulties in dealing with imprecise or incomplete perception of environment, representation of inaccuracy in measurements, sensor fusion and compliance with the kinematic limits of the vehicle motivated many researchers to use fuzzy control techniques for path tracking.

Ollero et al. (1994) developed a new fuzzy path-tracking method by combining fuzzy logic with the geometric pure-pursuit and the generalized predictive control techniques. Fuzzy logic is applied to supervise path trackers. Input of the fuzzy is the current state of the robot to the path to generate the appropriate steering angle. A new approach proposed by Braunstingl et al. (1995) to solve the wall following of mobile robots based on the concept of general perception. To construct a general perception of the surroundings from the measuring data provided by all the sensors and representing, a perception vector is assigned

Results from real systems address the fuzzy control influence and effectiveness to solve some of the navigation difficulties and to reduce their navigation costs. Closing this book chapter, **Section 4** concludes the chapter with few comments and summarizes the advantages and limitations of using fuzzy logic in mobile robot navigation. The chapter can be interesting for students, researchers and different scientific communities in the areas of

Robust and reliable navigation in dynamic or unknown environment relies on ability of the robots in moving among unknown obstacles without collision and fast reaction to uncertainties. It is highly desirable to develop these tasks using a technique which utilize human reasoning and decision making. Fuzzy logic provides a means to capture the human mind's expertise. It utilizes this heuristic knowledge for representing and accomplishment of a methodology to develop perception-action based strategies for mobile robots navigation. Furthermore, the methodology of the FLC is very helpful dealing with uncertainties in real world and accurate model of the environment is not absolutely required for navigation. Therefore, based on a simple design, easy implementation and robustness properties of FLC, many approaches were developed to solve mobile robot navigation problem in target tracking, path tracking, obstacle avoidance, behaviour coordination, environment modelling, and layer integration (Saffiotti, 1997). This section reviews the proposed fuzzy control methods which used fuzzy sets for velocity control, rotation control and command fusion with focusing on the three most popular categories of: Path tracking,

Path tracking is a crucial function for autonomous mobile robots to navigate along a desired path. This task includes tracking of previously computed paths using a path planner, a defined path by human operator, tracking of walls, road edges, and other natural features in the robot workspace (Chee et al., 1996). It involves real-time perception of the environment to determine the position and orientation of the robot with respect to the desired path. For example in Figure 1, if the robot is misplaced, the controller task is to steer it back on course and minimize the orientation error (Δφ) and the position error (Δx) (Moustris & Tzafestas, 2005). Path tracking difficulties in dealing with imprecise or incomplete perception of environment, representation of inaccuracy in measurements, sensor fusion and compliance with the kinematic limits of the vehicle motivated many researchers to use fuzzy control

Ollero et al. (1994) developed a new fuzzy path-tracking method by combining fuzzy logic with the geometric pure-pursuit and the generalized predictive control techniques. Fuzzy logic is applied to supervise path trackers. Input of the fuzzy is the current state of the robot to the path to generate the appropriate steering angle. A new approach proposed by Braunstingl et al. (1995) to solve the wall following of mobile robots based on the concept of general perception. To construct a general perception of the surroundings from the measuring data provided by all the sensors and representing, a perception vector is assigned

robotics, artificial intelligence, intelligent transportation systems, and fuzzy control.

**2. Review of fuzzy logic applications for mobile robot navigation** 

Obstacle avoidance and Behavior coordination.

**2.1 Fuzzy logic for path tracking** 

techniques for path tracking.

to each ultrasonic sensor. All these vectors adding together then combine into a single vector of general perception. A fuzzy controller then uses the perception information to guide the robot along arbitrary walls and obstacles. Sanchez et al. (1999) proposed a fuzzy control system for path tracking of an autonomous vehicle in outdoor environment. The fuzzy controller is used to generate steering and velocity required to track the path using the data collected from experiments of driving the vehicle by a human. Bento et al. (2002) implemented a path-tracking method by means of fuzzy logic for a Wheeled Mobile Robot. Input variables of the fuzzy controller are position and orientation of the robot with respect to the path. Output variables are linear velocity and angular velocity. Hajjaji and Bentalba (2003) have designed a fuzzy controller for path tracking control of vehicles using its nonlinear dynamics model. A Takagi–Sugeno (T–S) fuzzy model presents the nonlinear model of the vehicle. Then a model-based fuzzy controller is developed based on the T–S fuzzy model. A wall-following robot presented by Peri & Simon (2005) which the robot's motion is controlled by a fuzzy controller to drive it along a predefined path. Antonelli et al. (2007) address a path tracking approach based on a fuzzy-logic set of rules which emulates the human driving behavior. The fuzzy system input is represented by approximate information concerning the knowledge of the curvature of the desired path ahead the vehicle and the distance between the next bend and the vehicle. The output is the maximum value of the linear velocity needed to attain by the vehicle in order to safely drive on the path. Yu et al. (2009) used Taguchi method to design an optimal fuzzy logic controller for trajectory tracking of a wheeled mobile robot. Recently, Xiong and Qu (2010) developed a method for intelligent vehicles' path tracking with two fuzzy controller combinations which controls vehicle direction and a preview fuzzy control method presented by Liao et al. (2010) for path tracking of intelligent vehicle. The vehicle speed and direction are adjusted by fuzzy control according to future path information and present path information respectively.

Fig. 1. Typical control input variables for path tracking [9]

#### **2.2 Obstacle avoidance using fuzzy logic**

Ability of a robot to avoid collision with unforeseen or dynamic obstacles while it is moving towards a target or tracking a path is a vital task in autonomous navigation. Navigation strategies can be classified to global path planning and local path planning. In global path planning, information about the obstacles and a global model of environment is available which mostly Configuration space, Road map, Voronoi diagram and Potential field techniques

Application of Fuzzy Logic in Mobile Robot Navigation 25

information and transforms them into the predefined response. The behaviors include path tracking, obstacle avoidance, target tracking, goal reaching and etc. Finally, based on

The problems associated with the behavior-based navigation systems is the *behavior coordination* or *action selection*. The multiple behaviors may produce several command outputs simultaneously which may cause the robot move in unintended directions or system fail entirely. Reliable and robust operation of the system relies on the decision about how to integrate high level planning and low level execution behaviors, which behavior should be activated (arbitration) and how output commands should be combined into one command to drive the robot (command fusion). Early solutions were developed based on

The subsumption architecture is composed of several layers of task-achieving behaviors. Coordination of behaviors is based on Priority arbitration (Competitive architecture). In Priority-based arbitration only a behavior with the highest priority is selected to be active when multiple conflicting behaviors are trigged and the other are ignored (Dupre, 2007; Fatmi et al., 2006). The subsumption approach is based on a static arbitration policy which means that the robot actions are predefined and fixed in dealing with certain situations. Since the behavior coordination is competitive and based on a fixed arbitration, it may leads to erratic operation under certain situations (Fatmi et al., 2006). For example in

When an obstacle is detected in front of the robot and the goal is at right, the priority is with

The motor schemas architecture proposed by Arkin (1989) relies on cooperative coordination (command fusion) of behaviors which the multiple behaviors can produce an

command output(s) of an active behaviour(s) the robot executes an action (Fig.2) [16].

Fig. 2. Behavior- based navigation systems overall architecture

subsumption architecture (Brooks, 1986) and motor schemas (Arkin, 1989).

coordination of goal reaching and obstacle avoidance behaviors with rules like:

*IF Obstacle is left THEN turn right IF goal is right THEN turn right IF Obstacle is front THEN turn left IF goal is left THEN turn left* 

Obstacle avoidance behavior and the robot turns left while the goal is at right.

**Obstacle avoidance rules: Goal reaching rules:** 

*..... ....* 

are used to plan obstacle-free path towards a target. However, in real world a reliable map of obstacle, accurate model of environment and precise sensory data is unavailable due to uncertainties of the environment. While the computed path may remain valid but to response the unforeseen or dynamic obstacles, it is necessary for the robot to alter its path online. In such situations, Fuzzy logic can provide robust and reliable methodologies dealing with the imprecise input with low computational complexity (Yanik et al., 2010). Different obstacle avoidance approaches were developed during past decades which proposed effective solution to the navigation problems in unknown and dynamic environments.

Chee et al. (1996) presented a two-layer fuzzy inference system in which the first layer fuses the sensor readings. The left and right clearances of the robot were found as outputs of the first-layered fuzzy system. The outputs of the first layer together with the goal direction are used as the inputs of the second-layer. Eventually, the final outputs of the controller are the linear velocity and the turning rate of the robot. The second-stage fuzzy inference system employs the collision avoiding, obstacle following and goal tracking behaviours to achieve robust navigation in unknown environments. Dadios and Maravillas (2002) proposed and implemented a fuzzy control approach for cooperative soccer micro robots. A planner generates a path to the destination and fuzzy logic control the robot's heading direction to avoid obstacles and other robots while the dynamic position of obstacles, ball and robots are considered. Zavlangas et al. (2000) developed a reactive navigation method for omnidirectional mobile robots using fuzzy logic. The fuzzy rule-base generates actuating command to get collision free motions in dynamic environment. The fuzzy logic also provides an adjustable transparent system by a set of learning rules or manually. Seraji and Howard (2002) developed a behavior-based navigation method on challenging terrain using fuzzy logic. The navigation strategy is comprised of three behaviors. Local obstacle avoidance behaviour is consists of a set of fuzzy logic rule statements which generates the robot's speed based on obstacle distance. Parhi (2005) described a control system comprises a fuzzy logic controller and a Petri Net for multi robot navigation. The Fuzzy rules steer the robot according to obstacles distribution or targets position. Since the obstacle's position is not known precisely, to avoid obstacles in a cluttered environment fuzzy logic is a proper technique for this task. Combination of the fuzzy logic controller and a set of collision prevention rules implemented as a Petri Net model embedded in the controller of a mobile robot enable it to avoid obstacles that include other mobile robots. A fuzzy controller designed by Lilly (2007) for obstacle avoidance of an autonomous vehicle using negative fuzzy rules. The negative fuzzy rules define a set of actions to be avoided to direct the vehicle to a target in presence of obstacles. Chao et al. (2009) developed a fuzzy control system for target tracking and obstacle avoidance of a mobile robot. Decision making is handled by the fuzzy control strategy based on the sensed environment using a stereo vision information. A vision- based fuzzy obstacle avoidance proposed for a humanoid robot in (Wong et al., 2011). The nearest obstacle to the robot captured by vision system and the difference angle between goal direction and the robot's heading measured by electronic compass are inputs of the fuzzy system to make a decision for appropriate motion of the robot in unknown environment.

#### **2.3 Fuzzy logic for behaviour coordination**

To improve the total performance of a navigation system, complex navigation tasks are broken down into a number of simpler and smaller subsystems (behaviors) which is called behaviorbased system. In a behavior-based system, each behavior receives particular sensory

are used to plan obstacle-free path towards a target. However, in real world a reliable map of obstacle, accurate model of environment and precise sensory data is unavailable due to uncertainties of the environment. While the computed path may remain valid but to response the unforeseen or dynamic obstacles, it is necessary for the robot to alter its path online. In such situations, Fuzzy logic can provide robust and reliable methodologies dealing with the imprecise input with low computational complexity (Yanik et al., 2010). Different obstacle avoidance approaches were developed during past decades which proposed effective solution

Chee et al. (1996) presented a two-layer fuzzy inference system in which the first layer fuses the sensor readings. The left and right clearances of the robot were found as outputs of the first-layered fuzzy system. The outputs of the first layer together with the goal direction are used as the inputs of the second-layer. Eventually, the final outputs of the controller are the linear velocity and the turning rate of the robot. The second-stage fuzzy inference system employs the collision avoiding, obstacle following and goal tracking behaviours to achieve robust navigation in unknown environments. Dadios and Maravillas (2002) proposed and implemented a fuzzy control approach for cooperative soccer micro robots. A planner generates a path to the destination and fuzzy logic control the robot's heading direction to avoid obstacles and other robots while the dynamic position of obstacles, ball and robots are considered. Zavlangas et al. (2000) developed a reactive navigation method for omnidirectional mobile robots using fuzzy logic. The fuzzy rule-base generates actuating command to get collision free motions in dynamic environment. The fuzzy logic also provides an adjustable transparent system by a set of learning rules or manually. Seraji and Howard (2002) developed a behavior-based navigation method on challenging terrain using fuzzy logic. The navigation strategy is comprised of three behaviors. Local obstacle avoidance behaviour is consists of a set of fuzzy logic rule statements which generates the robot's speed based on obstacle distance. Parhi (2005) described a control system comprises a fuzzy logic controller and a Petri Net for multi robot navigation. The Fuzzy rules steer the robot according to obstacles distribution or targets position. Since the obstacle's position is not known precisely, to avoid obstacles in a cluttered environment fuzzy logic is a proper technique for this task. Combination of the fuzzy logic controller and a set of collision prevention rules implemented as a Petri Net model embedded in the controller of a mobile robot enable it to avoid obstacles that include other mobile robots. A fuzzy controller designed by Lilly (2007) for obstacle avoidance of an autonomous vehicle using negative fuzzy rules. The negative fuzzy rules define a set of actions to be avoided to direct the vehicle to a target in presence of obstacles. Chao et al. (2009) developed a fuzzy control system for target tracking and obstacle avoidance of a mobile robot. Decision making is handled by the fuzzy control strategy based on the sensed environment using a stereo vision information. A vision- based fuzzy obstacle avoidance proposed for a humanoid robot in (Wong et al., 2011). The nearest obstacle to the robot captured by vision system and the difference angle between goal direction and the robot's heading measured by electronic compass are inputs of the fuzzy system to make a

to the navigation problems in unknown and dynamic environments.

decision for appropriate motion of the robot in unknown environment.

To improve the total performance of a navigation system, complex navigation tasks are broken down into a number of simpler and smaller subsystems (behaviors) which is called behaviorbased system. In a behavior-based system, each behavior receives particular sensory

**2.3 Fuzzy logic for behaviour coordination** 

information and transforms them into the predefined response. The behaviors include path tracking, obstacle avoidance, target tracking, goal reaching and etc. Finally, based on command output(s) of an active behaviour(s) the robot executes an action (Fig.2) [16].

Fig. 2. Behavior- based navigation systems overall architecture

The problems associated with the behavior-based navigation systems is the *behavior coordination* or *action selection*. The multiple behaviors may produce several command outputs simultaneously which may cause the robot move in unintended directions or system fail entirely. Reliable and robust operation of the system relies on the decision about how to integrate high level planning and low level execution behaviors, which behavior should be activated (arbitration) and how output commands should be combined into one command to drive the robot (command fusion). Early solutions were developed based on subsumption architecture (Brooks, 1986) and motor schemas (Arkin, 1989).

The subsumption architecture is composed of several layers of task-achieving behaviors. Coordination of behaviors is based on Priority arbitration (Competitive architecture). In Priority-based arbitration only a behavior with the highest priority is selected to be active when multiple conflicting behaviors are trigged and the other are ignored (Dupre, 2007; Fatmi et al., 2006). The subsumption approach is based on a static arbitration policy which means that the robot actions are predefined and fixed in dealing with certain situations. Since the behavior coordination is competitive and based on a fixed arbitration, it may leads to erratic operation under certain situations (Fatmi et al., 2006). For example in coordination of goal reaching and obstacle avoidance behaviors with rules like:

#### **Obstacle avoidance rules: Goal reaching rules:**

*IF Obstacle is left THEN turn right IF goal is right THEN turn right IF Obstacle is front THEN turn left IF goal is left THEN turn left* 

*..... ....* 

When an obstacle is detected in front of the robot and the goal is at right, the priority is with Obstacle avoidance behavior and the robot turns left while the goal is at right.

The motor schemas architecture proposed by Arkin (1989) relies on cooperative coordination (command fusion) of behaviors which the multiple behaviors can produce an

Application of Fuzzy Logic in Mobile Robot Navigation 27

First step is *identifying the linguistic input and output variables and* definition of fuzzy sets *(*Initialization). *Fuzzification* or *fuzzy classification* is the process of converting a set of crisp data into a set of fuzzy variables using the membership functions (fuzzy sets). For example in Figure 4, the degree of membership for a given crisp is 0.6. Shape of the membership functions depends on the input data can be triangular, piecewise linear, Gaussian,

A rule base is obtained by a set of IF-THEN rules and *inference* evaluates the rules and combines the results of the rules. The final step is *Defuzzification* which is the process of converting fuzzy rules into a crisp output. An example of a simple fuzzy control system is

The first study shows that how fuzzy logic algorithm can be used for navigation of mobile robots. The selected methodology is a behavior-based approach which fuzzy logic algorithm

Fig. 3. The fuzzy controller structure

Fig. 4. Membership degree of a crisp input *x* in the fuzzy set

trapezoidal or singleton.

shown in figure 5.

**3.2 A case sudy** 

Fig. 5. Example of a fuzzy control system

output concurrently. In this approach output of each behavior is captured based on their particular influence on overall output. The outputs are blended to vote for or against an action. For example in potential fields the outputs are in the vector form. These outputs are combined and the overall response of the system is achieved by the vector summation (Nakhaeinia et al., 2011a). This approach also may lead to conflicting actions or poor performance in certain circumstances. However, fuzzy logic provides a useful mechanism for command fusion coordination and also arbitration fusion coordination. The main fuzzy logic advantages are: i) it can be used for dynamic arbitration which behavior selection is according to the robot's current perceptual state, ii) it allows for easy combination and concurrent execution of various behaviors. A variety of approaches have been developed inspired by the success of fuzzy logic to deal with the behavior coordination limitations.

Leyden (1999) designed a fuzzy logic based navigation system to overcome the subsumption control problem. The proposed system is consists of two behaviors. Output of each behavior is a fuzzy set which are combined using a command fusion process to produce a single fuzzy set. Then, the fuzzy set is defuzzified to make a crisp output. Fatmi et al. (2006) proposed a two layered behavior coordination approach for behavior design and action coordination using fuzzy logic. The first layer is consists of primitive basic behaviors and the second layer is responsible for decision making based on the context about which behavior(s) should be activated and the selected behaviors are blended. In another work presented by (Selekwa, 2005), fuzzy behavior systems proposed for Autonomous navigation of Ground Vehicles in cluttered environment with unknown obstacles. Multivalue reactive fuzzy behaviors are used for arbitrating or fusing of the behaviors which action selection is relied on the available sensor information. In another work by Ramos et al. (2006), a hierarchical fuzzy decision-making algorithm introduced for behaviour coordination of a robot based on arbitration mechanisms. In this method behaviors are not combined and just one behavior with maximum resulting value is selected and executed each time. A Fuzzy action selection approach was developed by Jaafar and McKenzie (2008) for navigation of a virtual agent. The fuzzy controller is comprised of three behaviors. The objective of this work is to solve the behaviour's conflict. The method uses fuzzy α-levels to compute the behavior's weight and the Huwicz criterion is used to select the final action. Wang and Liu (2008) introduced a new behavior-based navigation method called "minimum risk method". This behavior-based method applies the multi-behavior coordination strategy includes the global Goal seeking (GS) and the local Obstacle Avoidance (OA) (or boundary-following) behaviors. The fuzzy logic is applied to design and coordinate the proposed behaviors.

## **3. Fuzzy control system in mobile robot navigation**

In this section, first we show how to design a Fuzzy Controller and then we present a case study to analyze the performance and operation of the fuzzy logic algorithms in the implementation of different behaviors for mobile robot navigation. Most of the proposed methods have applied fuzzy logic algorithm for velocity control, steering control and command fusion in the design of their behaviors. This study evaluates the influence of the design parameters in mobile robots navigation.

#### **3.1 Design of a fuzzy controller**

The schematic diagram of the fuzzy controller is shown in Figure 3. The fuzzy controller design steps include: 1) Initialization, 2) Fuzzification, 3) Inference and 4) Difuzzification.

Fig. 3. The fuzzy controller structure

output concurrently. In this approach output of each behavior is captured based on their particular influence on overall output. The outputs are blended to vote for or against an action. For example in potential fields the outputs are in the vector form. These outputs are combined and the overall response of the system is achieved by the vector summation (Nakhaeinia et al., 2011a). This approach also may lead to conflicting actions or poor performance in certain circumstances. However, fuzzy logic provides a useful mechanism for command fusion coordination and also arbitration fusion coordination. The main fuzzy logic advantages are: i) it can be used for dynamic arbitration which behavior selection is according to the robot's current perceptual state, ii) it allows for easy combination and concurrent execution of various behaviors. A variety of approaches have been developed inspired by the success of fuzzy logic to deal with the behavior coordination limitations.

Leyden (1999) designed a fuzzy logic based navigation system to overcome the subsumption control problem. The proposed system is consists of two behaviors. Output of each behavior is a fuzzy set which are combined using a command fusion process to produce a single fuzzy set. Then, the fuzzy set is defuzzified to make a crisp output. Fatmi et al. (2006) proposed a two layered behavior coordination approach for behavior design and action coordination using fuzzy logic. The first layer is consists of primitive basic behaviors and the second layer is responsible for decision making based on the context about which behavior(s) should be activated and the selected behaviors are blended. In another work presented by (Selekwa, 2005), fuzzy behavior systems proposed for Autonomous navigation of Ground Vehicles in cluttered environment with unknown obstacles. Multivalue reactive fuzzy behaviors are used for arbitrating or fusing of the behaviors which action selection is relied on the available sensor information. In another work by Ramos et al. (2006), a hierarchical fuzzy decision-making algorithm introduced for behaviour coordination of a robot based on arbitration mechanisms. In this method behaviors are not combined and just one behavior with maximum resulting value is selected and executed each time. A Fuzzy action selection approach was developed by Jaafar and McKenzie (2008) for navigation of a virtual agent. The fuzzy controller is comprised of three behaviors. The objective of this work is to solve the behaviour's conflict. The method uses fuzzy α-levels to compute the behavior's weight and the Huwicz criterion is used to select the final action. Wang and Liu (2008) introduced a new behavior-based navigation method called "minimum risk method". This behavior-based method applies the multi-behavior coordination strategy includes the global Goal seeking (GS) and the local Obstacle Avoidance (OA) (or boundary-following) behaviors. The fuzzy logic is applied to design and coordinate the proposed behaviors.

In this section, first we show how to design a Fuzzy Controller and then we present a case study to analyze the performance and operation of the fuzzy logic algorithms in the implementation of different behaviors for mobile robot navigation. Most of the proposed methods have applied fuzzy logic algorithm for velocity control, steering control and command fusion in the design of their behaviors. This study evaluates the influence of the

The schematic diagram of the fuzzy controller is shown in Figure 3. The fuzzy controller design steps include: 1) Initialization, 2) Fuzzification, 3) Inference and 4) Difuzzification.

**3. Fuzzy control system in mobile robot navigation** 

design parameters in mobile robots navigation.

**3.1 Design of a fuzzy controller** 

First step is *identifying the linguistic input and output variables and* definition of fuzzy sets *(*Initialization). *Fuzzification* or *fuzzy classification* is the process of converting a set of crisp data into a set of fuzzy variables using the membership functions (fuzzy sets). For example in Figure 4, the degree of membership for a given crisp is 0.6. Shape of the membership functions depends on the input data can be triangular, piecewise linear, Gaussian, trapezoidal or singleton.

Fig. 4. Membership degree of a crisp input *x* in the fuzzy set

A rule base is obtained by a set of IF-THEN rules and *inference* evaluates the rules and combines the results of the rules. The final step is *Defuzzification* which is the process of converting fuzzy rules into a crisp output. An example of a simple fuzzy control system is shown in figure 5.

Fig. 5. Example of a fuzzy control system

#### **3.2 A case sudy**

The first study shows that how fuzzy logic algorithm can be used for navigation of mobile robots. The selected methodology is a behavior-based approach which fuzzy logic algorithm

Application of Fuzzy Logic in Mobile Robot Navigation 29

Finally, output of the layer is a crisp control commands in terms of a velocity and an angular velocity according to the selected behavior. Figure 9 shows performance and effectiveness of fuzzy logic in navigation of a mobile robot in crowded and unpredictably changing environment. The obtained result reveals robustness and reliability of the fuzzy logic in

In our previous work (Nankhaeinia et al., 2011b) a behaviour-based motion-planning approach was proposed for autonomous navigation of a mobile robot. This approach lies in the integration of three techniques: fuzzy logic (FL), virtual force field (VFF), and boundary

(a) (b)

association with the design and coordination of the behaviours.

Fig. 7. Fuzzy set definition for output variables: (a) Velocity and (b) Steering.

For example: *IF RU is F and FR is F and FL is F and LU is F THEN Gaol Reaching.*

Table 1. Fuzzy rules

following (BF).

is used for the design and action coordination of the behaviors (Fatmi et al., 2006). The navigation approach is consists of two layers. The first layer is comprised of primitive basic behaviors include: Goal reaching, Emergency situation, Obstacle avoidance, and Wall following. The second layer is Supervision layer which is responsible for action (behavior) selection based on the context and blending output of the selected ones. All the behaviors are designed using a fuzzy if-then rule base. Fuzzy controller inputs in the first layer are provided by sensory information. The inputs are distance to the goal (D*rg*) and difference between the goal direction and the robot's current heading (θ*error*). Fuzzy sets for θ*error* are*:*  Negative (*N*), Small Negative (*SN*), Zero (*Z*), Small Positive (*SP*), and Positive (P). Fuzzy sets for *Drg* are: Near (*N*), Small (*S*), and Big (*B*). Membership functions of the inputs are shown in figure 6.

Fig. 6. Fuzzy set definition for input variables: (a) θ*error* and (b) *Drg*

Each behavior is represented using a set of fuzzy if- then rule base to achieve a set of objectives. The fuzzy rule bases are shown in Table1.

The inputs are defuzzified using the fuzzy interference to convert the fuzzy inputs to an output. Defuzzified outputs for Steering are: Right (*R*), Right Forward (*RF*), Forward (*F*), Left Forward (*LF*), and Left (*L*). The fuzzy sets for output variable of Velocity are Zero (*Z*), Small Positive (*SP*), and Positive (*P*). Figure 7 shows the outputs membership functions.

For example the Goal Reaching behaviour is defined using the following rules from the table:

*If θerror is P And Drg is Big THEN Velocity is SP If θerror is P And Drg is Big THEN Steering is L* 

Next step is to decide which behavior should be activated. The Supervision Layer makes the decision based on the *context blending strategy* which first selects appropriate behavior(s), and then outputs of the selected behaviour(s) are blended to produce one command. The robot is equipped with 15 infrared sensors which are clustered to Right up (*RU*), Front right (*FR*), Front Left (*FL*) and Left up (*LU*) as shown in Fig. 8. Inputs of the Supervision layer are distances to obstacles which are measured by the IR sensors readings. The behavior selection is based on the following fuzzy rule base:

*IF context THEN behavior* 


For example: *IF RU is F and FR is F and FL is F and LU is F THEN Gaol Reaching.*

Table 1. Fuzzy rules

28 Fuzzy Logic – Controls, Concepts, Theories and Applications

is used for the design and action coordination of the behaviors (Fatmi et al., 2006). The navigation approach is consists of two layers. The first layer is comprised of primitive basic behaviors include: Goal reaching, Emergency situation, Obstacle avoidance, and Wall following. The second layer is Supervision layer which is responsible for action (behavior) selection based on the context and blending output of the selected ones. All the behaviors are designed using a fuzzy if-then rule base. Fuzzy controller inputs in the first layer are provided by sensory information. The inputs are distance to the goal (D*rg*) and difference between the goal direction and the robot's current heading (θ*error*). Fuzzy sets for θ*error* are*:*  Negative (*N*), Small Negative (*SN*), Zero (*Z*), Small Positive (*SP*), and Positive (P). Fuzzy sets for *Drg* are: Near (*N*), Small (*S*), and Big (*B*). Membership functions of the inputs are shown

Each behavior is represented using a set of fuzzy if- then rule base to achieve a set of

The inputs are defuzzified using the fuzzy interference to convert the fuzzy inputs to an output. Defuzzified outputs for Steering are: Right (*R*), Right Forward (*RF*), Forward (*F*), Left Forward (*LF*), and Left (*L*). The fuzzy sets for output variable of Velocity are Zero (*Z*), Small Positive (*SP*), and Positive (*P*). Figure 7 shows the outputs membership functions.

For example the Goal Reaching behaviour is defined using the following rules from the

Next step is to decide which behavior should be activated. The Supervision Layer makes the decision based on the *context blending strategy* which first selects appropriate behavior(s), and then outputs of the selected behaviour(s) are blended to produce one command. The robot is equipped with 15 infrared sensors which are clustered to Right up (*RU*), Front right (*FR*), Front Left (*FL*) and Left up (*LU*) as shown in Fig. 8. Inputs of the Supervision layer are distances to obstacles which are measured by the IR sensors readings. The behavior

 (a) (b) Fig. 6. Fuzzy set definition for input variables: (a) θ*error* and (b) *Drg*

objectives. The fuzzy rule bases are shown in Table1.

*If θerror is P And Drg is Big THEN Velocity is SP If θerror is P And Drg is Big THEN Steering is L* 

selection is based on the following fuzzy rule base:

*IF context THEN behavior* 

in figure 6.

table:

Fig. 7. Fuzzy set definition for output variables: (a) Velocity and (b) Steering.

Finally, output of the layer is a crisp control commands in terms of a velocity and an angular velocity according to the selected behavior. Figure 9 shows performance and effectiveness of fuzzy logic in navigation of a mobile robot in crowded and unpredictably changing environment. The obtained result reveals robustness and reliability of the fuzzy logic in association with the design and coordination of the behaviours.

In our previous work (Nankhaeinia et al., 2011b) a behaviour-based motion-planning approach was proposed for autonomous navigation of a mobile robot. This approach lies in the integration of three techniques: fuzzy logic (FL), virtual force field (VFF), and boundary following (BF).

Application of Fuzzy Logic in Mobile Robot Navigation 31

(a) (b)

Fig. 10. Fuzzy set definition: a) input variable of OP; b) input variable of TD

Table 2. The fuzzy rule base

Fig. 11. Fuzzy set definition for output variable of Velocity

Fig. 8. Infrared sensors arrangement

Fig. 9. Navigation of the robot in a sample environment

The robot's translational velocity is controlled by the fuzzy controller to get more safety in dealing with obstacles and to optimize the navigation time. The fuzzy controller inputs are obtained from sensorial data. The inputs are obstacle position and target direction (Fig.10).

For the six-set partitioning of obstacle position (OP) and three-set partitioning of target direction (TD) the fuzzy rule base comprises 18 rules. Table 2 represents the fuzzy rule base. As shown in figure 11, the fuzzy controller has one output. The fuzzy sets for the output variable of Velocity are L (low), C (normal speed), and H (high).

As shown in figure 12, the obtained result shows that the fuzzy controller has a great performance in reducing the navigation time in a sample environment (Fig. 13). However, in this work the fuzzy controller has two inputs and one output which the output is translational velocity. To evaluate influence of the fuzzy logic in the design of a navigation

Fig. 8. Infrared sensors arrangement

Fig. 9. Navigation of the robot in a sample environment

variable of Velocity are L (low), C (normal speed), and H (high).

The robot's translational velocity is controlled by the fuzzy controller to get more safety in dealing with obstacles and to optimize the navigation time. The fuzzy controller inputs are obtained from sensorial data. The inputs are obstacle position and target direction (Fig.10). For the six-set partitioning of obstacle position (OP) and three-set partitioning of target direction (TD) the fuzzy rule base comprises 18 rules. Table 2 represents the fuzzy rule base. As shown in figure 11, the fuzzy controller has one output. The fuzzy sets for the output

As shown in figure 12, the obtained result shows that the fuzzy controller has a great performance in reducing the navigation time in a sample environment (Fig. 13). However, in this work the fuzzy controller has two inputs and one output which the output is translational velocity. To evaluate influence of the fuzzy logic in the design of a navigation

Fig. 10. Fuzzy set definition: a) input variable of OP; b) input variable of TD


Table 2. The fuzzy rule base

Fig. 11. Fuzzy set definition for output variable of Velocity

Application of Fuzzy Logic in Mobile Robot Navigation 33

There are 15 fuzzy rule bases (table 3) for the 3-set partitioning of the obstacle position (OP)

Outputs of the controller are Rotational Velocity (**RV**) and Translational Velocity (**TV**). Membership functions and constants of the **RV** and **TV** outputs are shown in figure 15.

The obtained result from navigation of the mobile robot in a sample environment shows influence and effectiveness of the fuzzy controller in reducing the navigation time and increasing safety (Fig. 16). The robot's velocity changes according to the obstacle distance and obstacle position to achieve more safety in dealing with unknown and unforeseen obstacles (Fig. 16(b)). When there is not any obstacle in the robot's path toward the target, it moves with its maximum speed to optimize the navigation time. However, the robot translational speed reduce in the presence of the obstacles and it rotates fast to prevent collision with them. As shown in figure 17 (a), the navigation time was about 90 (ms) which due to using the fuzzy controller it reduces to 48 (ms) (Fig. 17 (b)). In addition, using the fuzzy controller to control

the Rotational Velocity resulted in smooth motion of the robot (Fig. 17(b)).

(a) (b)

Fig. 15. Fuzzy set definition: a) output variable TV; b) output variable of RV

and 5-set partitioning of the obstacle distance (**OD)**.

Table 3. The fuzzy rule base

Fig. 12. a) Trajectory executed in a recursive U-shape environment and b) Fuzzy speed control.

Fig. 13. a) Steering control without (plot 1) and b) with FLC (plot 2)

system more clearly, we designed a fuzzy controller with two inputs and two outputs. Inputs of the proposed controller are obstacle position and obstacle distance. There are three fuzzy sets for obstacle position (Dangerous (D), Uncertain (U) and Safe (S)) and five fuzzy set for obstacle distance (very near (*VN*), near (*N*), medium (*M*), far (*F*), very far (*VF*)). The inputs membership functions are shown in figure 14.

Fig. 14. Fuzzy set definition: a) input variable of OP; b) input variable of OD

(a) (b)

system more clearly, we designed a fuzzy controller with two inputs and two outputs. Inputs of the proposed controller are obstacle position and obstacle distance. There are three fuzzy sets for obstacle position (Dangerous (D), Uncertain (U) and Safe (S)) and five fuzzy set for obstacle distance (very near (*VN*), near (*N*), medium (*M*), far (*F*), very far (*VF*)). The

(a) (b)

Fig. 14. Fuzzy set definition: a) input variable of OP; b) input variable of OD

Fig. 12. a) Trajectory executed in a recursive U-shape environment and b) Fuzzy speed

Fig. 13. a) Steering control without (plot 1) and b) with FLC (plot 2)

inputs membership functions are shown in figure 14.

control.


There are 15 fuzzy rule bases (table 3) for the 3-set partitioning of the obstacle position (OP) and 5-set partitioning of the obstacle distance (**OD)**.

Table 3. The fuzzy rule base

Outputs of the controller are Rotational Velocity (**RV**) and Translational Velocity (**TV**). Membership functions and constants of the **RV** and **TV** outputs are shown in figure 15.

The obtained result from navigation of the mobile robot in a sample environment shows influence and effectiveness of the fuzzy controller in reducing the navigation time and increasing safety (Fig. 16). The robot's velocity changes according to the obstacle distance and obstacle position to achieve more safety in dealing with unknown and unforeseen obstacles (Fig. 16(b)). When there is not any obstacle in the robot's path toward the target, it moves with its maximum speed to optimize the navigation time. However, the robot translational speed reduce in the presence of the obstacles and it rotates fast to prevent collision with them. As shown in figure 17 (a), the navigation time was about 90 (ms) which due to using the fuzzy controller it reduces to 48 (ms) (Fig. 17 (b)). In addition, using the fuzzy controller to control the Rotational Velocity resulted in smooth motion of the robot (Fig. 17(b)).

Fig. 15. Fuzzy set definition: a) output variable TV; b) output variable of RV

Application of Fuzzy Logic in Mobile Robot Navigation 35

have lakes of self tuning and self-organization and difficulty of rule discovery from expert knowledge. According to the considerable performance of the fuzzy logic control, in future works we will design and evaluate the real time performance of different *types of* 

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**5. References** 

Fig. 16. Robot performance in a sample environment: a) Trajectory; b) Velocity profiles

Fig. 17. Example 1: (a) Steering control without FLC; (b) Steering control using FLC

### **4. Conclusion**

Review of different works showed that Fuzzy Logic control is one of the most successful techniques in the design and coordination of behaviors for mobile robots navigation. In this chapter first we performed a study to describe how the fuzzy logic can be applied to design individual behaviors simply and solve complex tasks by the combination of the elementary behaviors. The Fuzzy control addressed a useful mechanism to design various behaviors by the use of linguistic rules. It also provided a robust methodology for combination and arbitration of behaviors. Then, two fuzzy controllers designed to demonstrate influence and robustness of the fuzzy control in a navigation system. The obtained results proved the successful operation and effectiveness of the fuzzy control in generating smooth motion, reducing navigation time and increasing the robot safety. Overall, advantages of fuzzy control in the design of a navigation system are: i) Capability of handling uncertain and imprecise information, ii) Real time operation, iii) Easy combination and coordination of various behaviors, iv) Ability of developing perception-action based strategies, and v) Easy implementation. However, fuzzy navigation methods fail in local minimum situations; they have lakes of self tuning and self-organization and difficulty of rule discovery from expert knowledge. According to the considerable performance of the fuzzy logic control, in future works we will design and evaluate the real time performance of different *types of fuzzy* reasoning and defuzzification methods on the other aspects of robots control.

#### **5. References**

34 Fuzzy Logic – Controls, Concepts, Theories and Applications

(a) (b)

Fig. 16. Robot performance in a sample environment: a) Trajectory; b) Velocity profiles

(a) (b)

Review of different works showed that Fuzzy Logic control is one of the most successful techniques in the design and coordination of behaviors for mobile robots navigation. In this chapter first we performed a study to describe how the fuzzy logic can be applied to design individual behaviors simply and solve complex tasks by the combination of the elementary behaviors. The Fuzzy control addressed a useful mechanism to design various behaviors by the use of linguistic rules. It also provided a robust methodology for combination and arbitration of behaviors. Then, two fuzzy controllers designed to demonstrate influence and robustness of the fuzzy control in a navigation system. The obtained results proved the successful operation and effectiveness of the fuzzy control in generating smooth motion, reducing navigation time and increasing the robot safety. Overall, advantages of fuzzy control in the design of a navigation system are: i) Capability of handling uncertain and imprecise information, ii) Real time operation, iii) Easy combination and coordination of various behaviors, iv) Ability of developing perception-action based strategies, and v) Easy implementation. However, fuzzy navigation methods fail in local minimum situations; they

Fig. 17. Example 1: (a) Steering control without FLC; (b) Steering control using FLC

**4. Conclusion** 


**3** 

**Modular Fuzzy Logic Controller for Motion** 

Most of the wheelchair users are paraplegics, who are not able to move on their own due to permanent injury in their lower extremities. These wheelchairs are four-wheeled and have certain limitations due to design and control mechanism. For example, the wheelchairs cannot move to a higher level, lift the front wheel and stay in an upright position. As a result, wheelchair users cannot reach certain heights to pick and place things on the shelves, and cupboards, etc. without any assistant and also cannot have eye-to-eye conversation with normal people effectively. On the other hand, a two-wheeled wheelchair has a unique characteristic that may help disabled and elderly people who use the wheelchair as the main means of transport and can also use the wheelchair for these added advantages. Now the idea is to transform the standard four-wheeled wheelchair into a two-wheeled upright wheelchair to facilitate such manuoverability. The front wheels (casters) can be lifted up and stabilized as an inverted pendulum, thus increasing the level of height achievable while in the upright position. Similarly, when this upright position is no longer needed it may be transformed back into its normal four-wheeled position. The schematic diagram of the twowheeled wheelchair is shown in Figure 1. The transformation will result in a highly nonlinear and complex system. Since a human has quite significant mass sitting on the wheelchair, the two-wheeled wheelchair can be modeled with double links that mimic

Most of the classical control design methodologies such as Nyquist, Bode, state-space, optimal control, root locus, *H* , and -analysis are based on assumptions that the process is linear and stationary and hence is represented by a finite dimensional constant coefficient linear model. These methods do not suit complex systems well because few of those represent uncertainty and incompleteness in system knowledge or complexity in design. But the fact is the real world is too complex. As the complexity of a system increases, quantitative analysis and precision become difficult. The increasing complexity of dynamical systems such as this coupled with stringent performance criteria, which are sometimes subject to human satisfaction, necessitates the use of more sophiticated control approaches. However, many processes that are nonlinear, uncertain, incomplete or non-stationary have subtle and

double inverted pendulum scenario that need a clever control strategy.

**1. Introduction** 

**Control of Two-Wheeled Wheelchair** 

Salmiah Ahmad1, N. H. Siddique2 and M. O. Tokhi3

*1International Islamic University Malaysia,* 

*2Ulster University,* 

*2,3United Kingdom* 

*1Malaysia* 

*3The University of Sheffield* 


## **Modular Fuzzy Logic Controller for Motion Control of Two-Wheeled Wheelchair**

Salmiah Ahmad1, N. H. Siddique2 and M. O. Tokhi3

*1International Islamic University Malaysia, 2Ulster University, 3The University of Sheffield 1Malaysia 2,3United Kingdom* 

### **1. Introduction**

36 Fuzzy Logic – Controls, Concepts, Theories and Applications

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Most of the wheelchair users are paraplegics, who are not able to move on their own due to permanent injury in their lower extremities. These wheelchairs are four-wheeled and have certain limitations due to design and control mechanism. For example, the wheelchairs cannot move to a higher level, lift the front wheel and stay in an upright position. As a result, wheelchair users cannot reach certain heights to pick and place things on the shelves, and cupboards, etc. without any assistant and also cannot have eye-to-eye conversation with normal people effectively. On the other hand, a two-wheeled wheelchair has a unique characteristic that may help disabled and elderly people who use the wheelchair as the main means of transport and can also use the wheelchair for these added advantages. Now the idea is to transform the standard four-wheeled wheelchair into a two-wheeled upright wheelchair to facilitate such manuoverability. The front wheels (casters) can be lifted up and stabilized as an inverted pendulum, thus increasing the level of height achievable while in the upright position. Similarly, when this upright position is no longer needed it may be transformed back into its normal four-wheeled position. The schematic diagram of the twowheeled wheelchair is shown in Figure 1. The transformation will result in a highly nonlinear and complex system. Since a human has quite significant mass sitting on the wheelchair, the two-wheeled wheelchair can be modeled with double links that mimic double inverted pendulum scenario that need a clever control strategy.

Most of the classical control design methodologies such as Nyquist, Bode, state-space, optimal control, root locus, *H* , and -analysis are based on assumptions that the process is linear and stationary and hence is represented by a finite dimensional constant coefficient linear model. These methods do not suit complex systems well because few of those represent uncertainty and incompleteness in system knowledge or complexity in design. But the fact is the real world is too complex. As the complexity of a system increases, quantitative analysis and precision become difficult. The increasing complexity of dynamical systems such as this coupled with stringent performance criteria, which are sometimes subject to human satisfaction, necessitates the use of more sophiticated control approaches. However, many processes that are nonlinear, uncertain, incomplete or non-stationary have subtle and

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 39

described by expert knowledge, normally possessed by human. A fuzzy logic controller

Input Output

Defuzzification

Mechanism

Fuzzification is a process of transforming an observed input space to fuzzy sets within a universe of discourse. This process consists of associating to each fuzzy set a membership function (MF). These functions can be thought of as maps from the real numbers to the interval *I* 0,1 . If there are *n* fuzzy sets associated with a given quantity *x R* , such *n* maps : , 1, , *FR I i n <sup>i</sup>* are defined. They determine to what extent the linguistic label associated with fuzzy set *i* characterizes the current value of *x*. There are different kinds of MFs used in designing fuzzy controllers. The most common choices are triangular, trapezoidal, Gaussian and bell shaped MFs. There is no exact method for choosing an MF,

Inference is used to describe the process of formulating a nonlinear mapping from a given input space to an output space. The mapping then provides a basis from which decisions can be taken. The process of fuzzy inference involves the MFs, fuzzy logic operators and rule-base. Generally there are three types of commonly used fuzzy inference. They differ mainly in the consequent part of their fuzzy rules, aggregations and defuzzification procedures. Thus selecting a different fuzzy inference will result in different computational time. The three common fuzzy inferences are: Mamdani fuzzy inference, Sugeno fuzzy inference and Tsukamoto fuzzy inference. The choice of a particular inference mechanism is eventually problem dependent and availability of information

Mamdani type fuzzy modeling was proposed as the first attempt to control a steam engine and boiler by a set of linguistic control rules by (Mamdani 1974). In this type of inference, Max-min is the most common rule of composition used. In this composition rule, the inferred output of each rule is a fuzzy set chosen from the minimum firing strength. On the

Rule-base

(FLC) has the basic configuration illustrated in Figure 2.

Fig. 2. Fuzzy logic control

ii. Inference mechanism

about the system in question.

i. Fuzzification

iii. Rule-base iv. Defuzzification

Fuzzification Inference

Generally, a fuzzy logic controller consists of the following components:

and the designer mainly relies upon an expert knowledge or use heuristic rule.

interactive exchanges with the operating environment and are controlled by skilled human operators successfully. Rather than mathematically model the process, the human operator models the process in a heuristic or experiential manner. It is evident that human knowledge is becoming more and more important in control systems design. This experiential perspective in controller design requires the acquisition of heuristic and qualitative, rather than quantitative, knowledge or expertise from the human operator. During the past several decades, fuzzy control has emerged as one of the most active and powerful areas for research in the application of such complex and real world systems using fuzzy set theory (Zadeh, 1965).

Fig. 1. Schematic diagram of wheelchair with three under actuated joints

Due to many significant advantages of wheelchair usage, this research presents findings of the research carried out on the implementation of new architecture of modular intelligent control strategies on the two-wheeled wheelchair model. The multi-objective control involves lifting and stabilizing of Link1 and Link2 of double-inverted pendulum like twowheeled wheelchair, wheelchair backward and forward motion control as well as position. It is hoped that the proposed model, mechanisms and control could be of benefit to a wheelchair user, thus enhancing wheelchair technology for paraplegics and elderly.

#### **2. Intelligent control approach**

Intelligent control systems have evolved from existing controllers in a natural way competing demanding challenges of the time and are not defined in terms of specific algorithms. They employ techniques that can sense and reason without much *a priori* knowledge about the environment and produce control actions in a flexible, adaptive and robust manner (Harris, 1994). In general, by intelligent control approaches, it is mainly meant the methodologies of fuzzy logic, neural networks, and genetic algorithms. These methodologies have shown to be effective in controlling complex nonlinear systems. The control of complex nonlinear systems has been approached over the last few decades using fuzzy logic techniques due to the fact that fuzziness itself is easy to implement and can be described by expert knowledge, normally possessed by human. A fuzzy logic controller (FLC) has the basic configuration illustrated in Figure 2.

Fig. 2. Fuzzy logic control

Generally, a fuzzy logic controller consists of the following components:


38 Fuzzy Logic – Controls, Concepts, Theories and Applications

interactive exchanges with the operating environment and are controlled by skilled human operators successfully. Rather than mathematically model the process, the human operator models the process in a heuristic or experiential manner. It is evident that human knowledge is becoming more and more important in control systems design. This experiential perspective in controller design requires the acquisition of heuristic and qualitative, rather than quantitative, knowledge or expertise from the human operator. During the past several decades, fuzzy control has emerged as one of the most active and powerful areas for research in the application of such complex and real world systems using fuzzy set theory (Zadeh, 1965).

Link2

Link1

δ1

2 

Fig. 1. Schematic diagram of wheelchair with three under actuated joints

Due to many significant advantages of wheelchair usage, this research presents findings of the research carried out on the implementation of new architecture of modular intelligent control strategies on the two-wheeled wheelchair model. The multi-objective control involves lifting and stabilizing of Link1 and Link2 of double-inverted pendulum like twowheeled wheelchair, wheelchair backward and forward motion control as well as position. It is hoped that the proposed model, mechanisms and control could be of benefit to a

Intelligent control systems have evolved from existing controllers in a natural way competing demanding challenges of the time and are not defined in terms of specific algorithms. They employ techniques that can sense and reason without much *a priori* knowledge about the environment and produce control actions in a flexible, adaptive and robust manner (Harris, 1994). In general, by intelligent control approaches, it is mainly meant the methodologies of fuzzy logic, neural networks, and genetic algorithms. These methodologies have shown to be effective in controlling complex nonlinear systems. The control of complex nonlinear systems has been approached over the last few decades using fuzzy logic techniques due to the fact that fuzziness itself is easy to implement and can be

wheelchair user, thus enhancing wheelchair technology for paraplegics and elderly.

δ2

*R* 

**2. Intelligent control approach** 

 and *<sup>L</sup>* 

on each wheel

iv. Defuzzification

Fuzzification is a process of transforming an observed input space to fuzzy sets within a universe of discourse. This process consists of associating to each fuzzy set a membership function (MF). These functions can be thought of as maps from the real numbers to the interval *I* 0,1 . If there are *n* fuzzy sets associated with a given quantity *x R* , such *n* maps : , 1, , *FR I i n <sup>i</sup>* are defined. They determine to what extent the linguistic label associated with fuzzy set *i* characterizes the current value of *x*. There are different kinds of MFs used in designing fuzzy controllers. The most common choices are triangular, trapezoidal, Gaussian and bell shaped MFs. There is no exact method for choosing an MF, and the designer mainly relies upon an expert knowledge or use heuristic rule.

Inference is used to describe the process of formulating a nonlinear mapping from a given input space to an output space. The mapping then provides a basis from which decisions can be taken. The process of fuzzy inference involves the MFs, fuzzy logic operators and rule-base. Generally there are three types of commonly used fuzzy inference. They differ mainly in the consequent part of their fuzzy rules, aggregations and defuzzification procedures. Thus selecting a different fuzzy inference will result in different computational time. The three common fuzzy inferences are: Mamdani fuzzy inference, Sugeno fuzzy inference and Tsukamoto fuzzy inference. The choice of a particular inference mechanism is eventually problem dependent and availability of information about the system in question.

Mamdani type fuzzy modeling was proposed as the first attempt to control a steam engine and boiler by a set of linguistic control rules by (Mamdani 1974). In this type of inference, Max-min is the most common rule of composition used. In this composition rule, the inferred output of each rule is a fuzzy set chosen from the minimum firing strength. On the

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 41

geometric progression in the number of required rules for general purpose tracking and control situations. Moreover, it should be achieved without compromising the robustness

A generic problem with an FLC is that the number of rules grow exponentially with the number of input-output variables and linguistic terms for each variable. For a complete rulebase with input variables *Xi n <sup>i</sup>*| 1, , with linguistic terms *A j ij*| 1, , *mi* and output variables *Yk l <sup>k</sup>*| 1, , with linguistic terms *Bkj*| 1, , *j p <sup>k</sup>* , the number of rules will be

> 1 *n i i R m*

If (X1 is A11) and ... and (Xn is Anm) Then (Y1 is B11) and ... and (Yl is Blp) This large number of rules complicates the design of an FLC, because for each of the *R* different premises the expert must provide a combination of term sets for the output variables, which is nearly impossible for a human expert to guess. It is possible to omit a set of rules if it could be guranteed that a certain combination of input-output variables will never occur during control of the dynamic system. A modular structure of FLCs with

For large scale and complex systems, the reduction in computation and design complexity remains a challenge of intelligent control systems. Hierarchical and modular methodology have gained wide popularity because of its simplicity in design and robustness. There are several approaches in decomposing a system into modules such as decentralized approach, time-scale decomposition, hierarchical system, and workspace decomposition (Siljak, 1991). For control problems with multiple objectives of different priority, sub-controller with a subset of input-output variables can be designed for each objective. Furthermore, each antecedent can be decomposed into single input modules. Each fuzzy module is designed to

minimum number of input-output variables can reduce the number of rules *R*.

(1)

and capability of the complete system.

The rules have the form

**3. Modular fuzzy control**

Fig. 3. MIMO FLC for lifting and stabilizing the wheelchair

other hand, in max-product rule of composition the inferred output of each rule is a fuzzy set scaled down by its firing strength via algebraic product.

A fuzzy system is characterized by a set of linguistic statements based on expert knowledge. The expert knowledge is usually in the form of if-then rules, which are easily implemented by fuzzy conditional statements in fuzzy logic. The collection of fuzzy rules that are expressed as fuzzy conditional statements forms the rule base or the rule set of an FLC. A rule consists of two parts, antecedent and consequent. For example, typical rule in Mamdani-type fuzzy model with four-inputs and three-outputs FLC can be expressed by the following linguistic conditional statement.

If (*X1* is *Ai*) and (*X2* is B*j*) and (*X3* is C*k*) and (*X4* is D*l*)

then (Y1 *is* U*p*) and (Y*2* is V*q*) and (Y*3* is W*r*)

where {X1, X2, X3, X4} are the inputs with linguistic terms { *Ai,* Bj, C*k*, Dl} and {Y1, Y2, Y3} are the outputs with linguistic terms {*Up,* Vq, W*r*}.

Defuzzification is basically a mapping from a space of fuzzy control actions defined over an output universe of discourse into a space of nonfuzzy (crisp) control actions. In a sense this is the inverse of the fuzzification even though mathematically the maps need not be inverses of one another. In general, defuzzification can be viewed as a function : *<sup>n</sup> DF I R* , mapping a fuzzy vector *<sup>F</sup> x* with *n* fuzzy sets to a real number. There are different methods of defuzzification. However, simple methods are available to use depending on the application, among them Centre of Gravity Method (COG), and Weighted Average Method are widely used in Mamdani-type FLC and Sugeno-type FLC. Each method is problem dependent, but the experts should know that these methods are available and should try to see which works best for the application.

The two-wheeled wheelchair model involves lifting and stabilizing the two links (Link1 and Link2) similar to a double-inverted pendulum and hence is a multi-objective control problem. Considering the complexity and non-linearity of the wheelchair, the controller has to be designed in such a way to produce the required torques, namely *<sup>R</sup>* , *<sup>L</sup>* and <sup>2</sup> , for acting at three different locations on the wheelchair for lifting the casters/chair and stabilizing the system. The torque *R* and *<sup>L</sup>* represent the input torque to the right and left wheels respectively. 2 represents the torque between Link1 and Link2 to cater for the whole weight of the human body. Angular positions of Link1 and Link2, 1 and 2 respectively, are measured using sensors attached to the wheelchair. This characterizes the system as a highly nonlinear multi-input multi-output (MIMO) system. Fuzzy logic control is therefore very appropriate to use in this case. To achieve upright position for the two links, they need to be lifted and stabilized to zero degree (relative to vertical axis) upright position. This may be realised with a single controller. However, this will lead to a huge fuzzy rule-base. A conventional fuzzy controller with 4 inputs *e ee e* 1 12 2 , ,, and 3 outputs *R L* , , <sup>2</sup> (inputs-outputs are shown in Figure 3) has significant drawback in terms of computational complexity, which increases with the dimension of the system variables; the number of rules increases exponentially as the number of system variables increases. A strategy is sought to simplify the development process and reduce the

other hand, in max-product rule of composition the inferred output of each rule is a fuzzy

A fuzzy system is characterized by a set of linguistic statements based on expert knowledge. The expert knowledge is usually in the form of if-then rules, which are easily implemented by fuzzy conditional statements in fuzzy logic. The collection of fuzzy rules that are expressed as fuzzy conditional statements forms the rule base or the rule set of an FLC. A rule consists of two parts, antecedent and consequent. For example, typical rule in Mamdani-type fuzzy model with four-inputs and three-outputs FLC can be expressed by

If (*X1* is *Ai*) and (*X2* is B*j*) and (*X3* is C*k*) and (*X4* is D*l*)

then (Y1 *is* U*p*) and (Y*2* is V*q*) and (Y*3* is W*r*) where {X1, X2, X3, X4} are the inputs with linguistic terms { *Ai,* Bj, C*k*, Dl} and {Y1, Y2, Y3} are

Defuzzification is basically a mapping from a space of fuzzy control actions defined over an output universe of discourse into a space of nonfuzzy (crisp) control actions. In a sense this is the inverse of the fuzzification even though mathematically the maps need not be inverses of one another. In general, defuzzification can be viewed as a function : *<sup>n</sup> DF I R* , mapping a fuzzy vector *<sup>F</sup> x* with *n* fuzzy sets to a real number. There are different methods of defuzzification. However, simple methods are available to use depending on the application, among them Centre of Gravity Method (COG), and Weighted Average Method are widely used in Mamdani-type FLC and Sugeno-type FLC. Each method is problem dependent, but the experts should know that these methods are available and should try to

The two-wheeled wheelchair model involves lifting and stabilizing the two links (Link1 and Link2) similar to a double-inverted pendulum and hence is a multi-objective control problem. Considering the complexity and non-linearity of the wheelchair, the controller has

acting at three different locations on the wheelchair for lifting the casters/chair and

respectively, are measured using sensors attached to the wheelchair. This characterizes the system as a highly nonlinear multi-input multi-output (MIMO) system. Fuzzy logic control is therefore very appropriate to use in this case. To achieve upright position for the two links, they need to be lifted and stabilized to zero degree (relative to vertical axis) upright position. This may be realised with a single controller. However, this will lead to a huge

terms of computational complexity, which increases with the dimension of the system variables; the number of rules increases exponentially as the number of system variables increases. A strategy is sought to simplify the development process and reduce the

 , *<sup>L</sup>* 

represent the input torque to the right and left

 

represents the torque between Link1 and Link2 to cater for the

<sup>2</sup> (inputs-outputs are shown in Figure 3) has significant drawback in

 and <sup>2</sup> , for

> and 2

 1 12 2 , ,, and 3

to be designed in such a way to produce the required torques, namely *<sup>R</sup>*

 and *<sup>L</sup>* 

whole weight of the human body. Angular positions of Link1 and Link2, 1

fuzzy rule-base. A conventional fuzzy controller with 4 inputs *e ee e*

set scaled down by its firing strength via algebraic product.

the following linguistic conditional statement.

the outputs with linguistic terms {*Up,* Vq, W*r*}.

see which works best for the application.

stabilizing the system. The torque *R*

wheels respectively. 2

outputs

 *R L* , ,  geometric progression in the number of required rules for general purpose tracking and control situations. Moreover, it should be achieved without compromising the robustness and capability of the complete system.

Fig. 3. MIMO FLC for lifting and stabilizing the wheelchair

A generic problem with an FLC is that the number of rules grow exponentially with the number of input-output variables and linguistic terms for each variable. For a complete rulebase with input variables *Xi n <sup>i</sup>*| 1, , with linguistic terms *A j ij*| 1, , *mi* and output variables *Yk l <sup>k</sup>*| 1, , with linguistic terms *Bkj*| 1, , *j p <sup>k</sup>* , the number of rules will be

$$R = \prod\_{i=1}^{n} m\_i \tag{1}$$

The rules have the form

$$\text{If } (\mathsf{X}\_1 \text{ is } \mathsf{A}\_{11}) \text{ and } \dots \text{ and } (\mathsf{X}\_{\mathsf{n}} \text{ is } \mathsf{A}\_{\mathsf{nm}}) \text{ Then } (\mathsf{Y}\_1 \text{ is } \mathsf{B}\_{11}) \text{ and } \dots \text{ and } (\mathsf{Y}\_{\mathsf{l}} \text{ is } \mathsf{B}\_{\mathsf{p}}).$$

This large number of rules complicates the design of an FLC, because for each of the *R* different premises the expert must provide a combination of term sets for the output variables, which is nearly impossible for a human expert to guess. It is possible to omit a set of rules if it could be guranteed that a certain combination of input-output variables will never occur during control of the dynamic system. A modular structure of FLCs with minimum number of input-output variables can reduce the number of rules *R*.

#### **3. Modular fuzzy control**

For large scale and complex systems, the reduction in computation and design complexity remains a challenge of intelligent control systems. Hierarchical and modular methodology have gained wide popularity because of its simplicity in design and robustness. There are several approaches in decomposing a system into modules such as decentralized approach, time-scale decomposition, hierarchical system, and workspace decomposition (Siljak, 1991). For control problems with multiple objectives of different priority, sub-controller with a subset of input-output variables can be designed for each objective. Furthermore, each antecedent can be decomposed into single input modules. Each fuzzy module is designed to

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 43

of switches that gathers information from the subsystems and sends supervisory (threshold condition) instructions back to the subsystems. The supervisor in this case is the condition, (if the angular position error of Link1 and Link2, -5° < e < 5°, then Link1-stabilizing and Link2-stabilizing are activated). In this case, the switches coordinate the condition fulfilment of all the criteria for the activation of actuator to work accordingly. The reference position for lifting and stabilizing of both links is 0 degree at the upright position. The parameters 'a' and 'b' in the figure show the fuzzy input scaling factors (input gain) such that if the stabilizing subsystem of Link1 or Link2 is activated, the sensitivity of the fuzzy inputs is increased by giving higher gain (about 10 times) of a and b. The outputs from the system that are fed back to the controller are the angular position of Link1 (δ1) and the angular position of Link2 (δ2). The control approach using this modular strategy is believed to work well with the independently allocated tasks. In the figure, eδ1 shows the angular position error of Link1, ∆eδ1 represents the change of angular position error of Link1. The effect of Link2 onto Link1 is taken into account by using the angular position error of Link2, eδ2 as the fuzzy input for FLC1 and FLC2. In these two controllers, eδ2 represents the angular position error of Link2, while ∆eδ2 represents the change of angular position error of Link2. Similarly the effect of Link1 onto Link2 is taken into account by using the angular position

2

0 δ2

Coordinator

Switch

Switch

The MFC is also known as hierarchical fuzzy control (HFC), and the two terms are used interchangeably. It is discussed in detail for two-wheeled application in (Ahmad et al. 2011).

R, <sup>L</sup> δ1

error of Link1, eδ1 as the input for FLC3 and FLC4.

Stabilizing

FLC 2

FLC 1

Lifting

Lifting

FLC 3

Stabilizing

FLC 4

Subsystems

Fig. 5. Modular FLC for Two-wheeled wheelchair.

**4. MFC for two-wheeled wheelchair** 


a

b

0

Supervisor


+

handle one specific input affiliated with one of the decoupled antecedents *Xi n <sup>i</sup>*| 1, , and produces a crisp action *Yk l <sup>k</sup>*| 1, , where *k l* 1, , . Such a generic modular architecture is shown in Figure 4.

Fig. 4. Modular FLC

A typical fuzzy rule issues an appropriate output action by evaluating the related inputs from the measurement data. In the conventional IF-THEN fuzzy inference formulation, all of the system's input parameters are suggested as antecedents in the fuzzy rule. The total possible number of fuzzy rules that can be generated for the rule base is *Lk* where *k* is the number of inputs and *L* is the number of fuzzy linguistic terms or MFs. As compared to the modular FLC design, each input represents one fuzzy control module. The total number of rules for each module is determined by the number of MFs *L*. Thus, the total number of fuzzy rules for all *k* modules is *kL*. This clearly shows a significant reduction in the number of fuzzy rules from *L<sup>k</sup>* to *k* as well as savings in computation.

The mathematical model of the two-wheeled wheelchair incorporates three independent actuators; derived from Figure 1, corresponding to control output to be fed into the system. The angular position of Link1 and Link2, denoted as δ1 and δ2 respectively, are the controlled variables that will determine the system performance. The control challenge relates to the fact that there is more than one mechanism acted upon with the same actuator. For example, to transform the wheelchair into an upright two-wheeled wheelchair, the torques determined by fuzzy control are located at both right and left wheels. At the same time, if linear motion is considered, the same actuator needs to provide enough torque such that the wheelchair will still move forward or backward while in the upright position. Lifting and stabilizing consist of two system output parameters to be considered, namely angular position of Link1, δ1 and angular position of Link2, δ2. Therefore a modular fuzzy logic control (MFC) is adopted to realize this multi-function two-wheeled wheelchair.

The MIMO system with an objective of achieving zero degree upright position is decomposed into small and simpler subsystems: Link1-lifting, Link1-stabilizing, Link2 lifting, and Link2-stabilizing. The structure of the modular FLC for the wheelchair is illustrated in the block diagram in Figure 5. Accordingly, this type of FLC can deal with, for example, N subsystems located at different levels, where each subsystem manages its own control strategy and communicates with the coordinator. The coordinator comprises a pair

handle one specific input affiliated with one of the decoupled antecedents *Xi n <sup>i</sup>*| 1, , and produces a crisp action *Yk l <sup>k</sup>*| 1, , where *k l* 1, , . Such a generic modular

A typical fuzzy rule issues an appropriate output action by evaluating the related inputs from the measurement data. In the conventional IF-THEN fuzzy inference formulation, all of the system's input parameters are suggested as antecedents in the fuzzy rule. The total possible number of fuzzy rules that can be generated for the rule base is *Lk* where *k* is the number of inputs and *L* is the number of fuzzy linguistic terms or MFs. As compared to the modular FLC design, each input represents one fuzzy control module. The total number of rules for each module is determined by the number of MFs *L*. Thus, the total number of fuzzy rules for all *k* modules is *kL*. This clearly shows a significant reduction in the number

The mathematical model of the two-wheeled wheelchair incorporates three independent actuators; derived from Figure 1, corresponding to control output to be fed into the system. The angular position of Link1 and Link2, denoted as δ1 and δ2 respectively, are the controlled variables that will determine the system performance. The control challenge relates to the fact that there is more than one mechanism acted upon with the same actuator. For example, to transform the wheelchair into an upright two-wheeled wheelchair, the torques determined by fuzzy control are located at both right and left wheels. At the same time, if linear motion is considered, the same actuator needs to provide enough torque such that the wheelchair will still move forward or backward while in the upright position. Lifting and stabilizing consist of two system output parameters to be considered, namely angular position of Link1, δ1 and angular position of Link2, δ2. Therefore a modular fuzzy logic control (MFC) is adopted to realize this multi-function two-wheeled wheelchair.

The MIMO system with an objective of achieving zero degree upright position is decomposed into small and simpler subsystems: Link1-lifting, Link1-stabilizing, Link2 lifting, and Link2-stabilizing. The structure of the modular FLC for the wheelchair is illustrated in the block diagram in Figure 5. Accordingly, this type of FLC can deal with, for example, N subsystems located at different levels, where each subsystem manages its own control strategy and communicates with the coordinator. The coordinator comprises a pair

of fuzzy rules from *L<sup>k</sup>* to *k* as well as savings in computation.

architecture is shown in Figure 4.

Fig. 4. Modular FLC

of switches that gathers information from the subsystems and sends supervisory (threshold condition) instructions back to the subsystems. The supervisor in this case is the condition, (if the angular position error of Link1 and Link2, -5° < e < 5°, then Link1-stabilizing and Link2-stabilizing are activated). In this case, the switches coordinate the condition fulfilment of all the criteria for the activation of actuator to work accordingly. The reference position for lifting and stabilizing of both links is 0 degree at the upright position. The parameters 'a' and 'b' in the figure show the fuzzy input scaling factors (input gain) such that if the stabilizing subsystem of Link1 or Link2 is activated, the sensitivity of the fuzzy inputs is increased by giving higher gain (about 10 times) of a and b. The outputs from the system that are fed back to the controller are the angular position of Link1 (δ1) and the angular position of Link2 (δ2). The control approach using this modular strategy is believed to work well with the independently allocated tasks. In the figure, eδ1 shows the angular position error of Link1, ∆eδ1 represents the change of angular position error of Link1. The effect of Link2 onto Link1 is taken into account by using the angular position error of Link2, eδ2 as the fuzzy input for FLC1 and FLC2. In these two controllers, eδ2 represents the angular position error of Link2, while ∆eδ2 represents the change of angular position error of Link2. Similarly the effect of Link1 onto Link2 is taken into account by using the angular position error of Link1, eδ1 as the input for FLC3 and FLC4.

Subsystems

#### **4. MFC for two-wheeled wheelchair**

The MFC is also known as hierarchical fuzzy control (HFC), and the two terms are used interchangeably. It is discussed in detail for two-wheeled application in (Ahmad et al. 2011).

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 45

The system was tested with both configurations and the performances, with and without coupling were comparably similar, see Figure 6. Therefore, as seen the second configuration performed well with fewer fuzzy rules fired, and this configuration is used in implementing




0

100



Angular position

Torque between

Fig. 6. System performance comparison between coupled fuzzy inputs and decoupled fuzzy

The MFC is thus adopted for the two-wheeled wheelchair mechanisms, and the

The MFC can be divided into two significant categories, primary and secondary (Bessacini and Pinkos 1995). The controller is categorized according to different objectives. The control structure for achieving an upright two-wheeled maneuverable wheelchair is depicted in Figure 7. The general function of MFC is to minimize the errors in system responses considered. The primary goal unit caters for the upright control, which consists of lifting and stabilizing to the upright position and the transformation back to normal four-wheeled position of Link1 and Link2. These controllers are active most of the time even during maneuver. The secondary unit is activated by the coordinator (switch), with certain condition pre-set for output activation. It consists of different unique objectives involving linear motion control, steering control, additional chair height extension control. Each

objective in the secondary goal unit is discussed in detail in the following sections.

Link1 and Link2 (Nm)

of Link2 (degree)

0

10

0 10 20 30

coupled decoupled

0 10 20 30

coupled decoupled

Time (s)

Time (s)

the motion control for two-wheeled wheelchair.



inputs in terms of δ1, δ2, R, L and 2.

corresponding research objectives are:

Linear motion control (forward or backward)

Lifting and stabilizing control

Steering motion control

0

100

Wheel Torques (Nm)

200

0

50

Angular position

of Link1 (degree)

100

0 10 20 30

Right torque coupled Left torque coupled Right torque decoupled Left torque decoupled

coupled decoupled

0 10 20 30

Time (s)

Time (s)

The goal of the controller is to produce the required torques, namely *<sup>R</sup>* , *<sup>L</sup>* and <sup>2</sup> , for acting at three different locations on the wheelchair for lifting and stabilizing. The torques *<sup>R</sup>* and *<sup>L</sup>* represent the input torque to the right and left wheels respectively. On the other hand, 2 represents the torque between Link1 and Link2 to be used to cater for the whole weight of the human body. Angular positions of Link1 and Link2, 1 and 2 respectively, are measured using sensors attached to the wheelchair in Visual Nastran (VN). To achieve upright position of the two links, they need to be lifted and stabilized at zero degree upright position. The goal may be treated as a single objective control that is having Link1 and Link2 at the 0 degree upright position with one controller. This will increase significantly the computational complexity, which increases with the number of system variables; the number of rules increases exponentially as the number of system variables increases.

## **4.1 Rules reduction strategy for general purpose tracking and control situations**

The strategy is sought without compromising the robustness and capability of the system. Such a strategy relies mainly on three concepts, (Ahmad et al. 2011).


To assess the effect of coupling in the fuzzy control, the system is tested with two different configurations, which mainly differ at the input side of the controller, as shown in Table 1.


Table 1. Different input configurations of modular fuzzy logic controller

acting at three different locations on the wheelchair for lifting and stabilizing. The

 respectively, are measured using sensors attached to the wheelchair in Visual Nastran (VN). To achieve upright position of the two links, they need to be lifted and stabilized at zero degree upright position. The goal may be treated as a single objective control that is having Link1 and Link2 at the 0 degree upright position with one controller. This will increase significantly the computational complexity, which increases with the number of system variables; the number of rules increases exponentially as the number of system

whole weight of the human body. Angular positions of Link1 and Link2, 1

**4.1 Rules reduction strategy for general purpose tracking and control situations** 

Such a strategy relies mainly on three concepts, (Ahmad et al. 2011).





error of Link1, ∆eδ1 - Angular position error of

error of Link2, ∆eδ2 - Angular position error of

Link1, eδ<sup>1</sup>

Link2, eδ<sup>2</sup>

Link2, eδ<sup>2</sup>

Link1, eδ<sup>1</sup>

The strategy is sought without compromising the robustness and capability of the system.

To assess the effect of coupling in the fuzzy control, the system is tested with two different configurations, which mainly differ at the input side of the controller, as shown in Table 1.

**With coupling effect Without coupling effect** 

5 x 5 x 3 = 75 rules 5 x 5 = 25 rules

Table 1. Different input configurations of modular fuzzy logic controller

Link1, ∆eδ1

Link2, ∆eδ2

represent the input torque to the right and left wheels respectively. On

represents the torque between Link1 and Link2 to be used to cater for the

 , *<sup>L</sup>* 



 and <sup>2</sup> , for

> and

The goal of the controller is to produce the required torques, namely *<sup>R</sup>*

torques *<sup>R</sup>*

2 

the other hand, 2

variables increases.

Independence

**Link1 (Lifting & Stabilizing)** 

**Link2 (Lifting & Stabilizing)** 

**Rules of each lifting** 

**and stabilizing** 

 Functional Relationship Command Manipulation

 and *<sup>L</sup>* 

The system was tested with both configurations and the performances, with and without coupling were comparably similar, see Figure 6. Therefore, as seen the second configuration performed well with fewer fuzzy rules fired, and this configuration is used in implementing the motion control for two-wheeled wheelchair.

Fig. 6. System performance comparison between coupled fuzzy inputs and decoupled fuzzy inputs in terms of δ1, δ2, R, L and 2.

The MFC is thus adopted for the two-wheeled wheelchair mechanisms, and the corresponding research objectives are:


The MFC can be divided into two significant categories, primary and secondary (Bessacini and Pinkos 1995). The controller is categorized according to different objectives. The control structure for achieving an upright two-wheeled maneuverable wheelchair is depicted in Figure 7. The general function of MFC is to minimize the errors in system responses considered. The primary goal unit caters for the upright control, which consists of lifting and stabilizing to the upright position and the transformation back to normal four-wheeled position of Link1 and Link2. These controllers are active most of the time even during maneuver. The secondary unit is activated by the coordinator (switch), with certain condition pre-set for output activation. It consists of different unique objectives involving linear motion control, steering control, additional chair height extension control. Each objective in the secondary goal unit is discussed in detail in the following sections.

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 47

Fig. 8. Block diagram of two-wheeled wheelchair system motion

Fig. 9. Block diagram for linear motion control

shown in Figure 9.

This confined space is normally found in the domestic environment (home, office and library). Within such environment, linear motion is executed alone before steering is done and vice versa. The block diagram for linear motion control of two-wheeled wheelchair is

The FLC for linear motion (FLC3) consists of two inputs and two outputs. The controller inputs are the position error, *e* and the change of position error, ∆*e*, while the controller

Fig. 7. Adapted modular intercepts fuzzy logic system (Bessacini and Pinkos 1995)

#### **4.2 Simulation based performance analysis**

The overall motion control for two-wheeled wheelchair is represented in Figure 8.

#### **a. FLC for linear motion**

The linear motion control generally consists of forward and backward (reverse) motion control. They are both characterized as secondary systems (Bessacini and Pinkos 1995) since the system needs to fulfill the primary target to achieve the upright position for both links. Therefore MFC as discussed in Section 4 is very appropriate to implement.

Similar structure of FLC used for lifting and stabilizing is adopted for linear motion control. The controls differ in terms of input and output scaling factors due to different reference points executed. The control strategy designed in Matlab/Simulink was integrated with wheelchair model, which was developed in VN software environment as a plant. The motion (forward, backward or steering) takes place after lifting and stabilizing has been achieved. Results show that the MFC strategy designed works very well and gives good system performance.

In the current studies of wheelchair mobility, much research has been conducted on wheelchair mobility in large spaces (outdoor mobility) (Vries et al. 1999; Wong et al. 2007). In those researches, the distance and angle are considered at the same time to give output torque of the wheels. On the other hand, note that the two-wheeled wheelchair is designed for use in confined spaces, such that the linear motion and the steering motion are independent.

Fig. 7. Adapted modular intercepts fuzzy logic system (Bessacini and Pinkos 1995)

The overall motion control for two-wheeled wheelchair is represented in Figure 8.

Therefore MFC as discussed in Section 4 is very appropriate to implement.

The linear motion control generally consists of forward and backward (reverse) motion control. They are both characterized as secondary systems (Bessacini and Pinkos 1995) since the system needs to fulfill the primary target to achieve the upright position for both links.

Similar structure of FLC used for lifting and stabilizing is adopted for linear motion control. The controls differ in terms of input and output scaling factors due to different reference points executed. The control strategy designed in Matlab/Simulink was integrated with wheelchair model, which was developed in VN software environment as a plant. The motion (forward, backward or steering) takes place after lifting and stabilizing has been achieved. Results show that the MFC strategy designed works very well and gives good

In the current studies of wheelchair mobility, much research has been conducted on wheelchair mobility in large spaces (outdoor mobility) (Vries et al. 1999; Wong et al. 2007). In those researches, the distance and angle are considered at the same time to give output torque of the wheels. On the other hand, note that the two-wheeled wheelchair is designed for use in confined spaces, such that the linear motion and the steering motion are independent.

**4.2 Simulation based performance analysis** 

**a. FLC for linear motion** 

system performance.

Fig. 8. Block diagram of two-wheeled wheelchair system motion

This confined space is normally found in the domestic environment (home, office and library). Within such environment, linear motion is executed alone before steering is done and vice versa. The block diagram for linear motion control of two-wheeled wheelchair is shown in Figure 9.

Fig. 9. Block diagram for linear motion control

The FLC for linear motion (FLC3) consists of two inputs and two outputs. The controller inputs are the position error, *e* and the change of position error, ∆*e*, while the controller

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 49

(Z), Positive Small (PS) and Positive Big (PB). The membership function for inputs and outputs of FLC3 is shown in Figure 10. Table 2 shows the implemented fuzzy rules for FLC3 controller. The two consecutive rows in the output part represent two fuzzy outputs, τR (first row) and τL (second row). The rules developed are predetermined using expert knowledge available such that all the errors should be brought back to the reference point immediately.

The system was commanded to move forward after 4s, where at this time the two links had been stabilized at the upright position. Figure 11 shows the final position of forward mechanism execution while Figure 12 to Figure 18 show the results over 15s of simulation time for forward movement of the two-wheeled wheelchair. The wheelchair was set to move 1.5m forward from its initial position. The results show that the FLC approach worked very well with the wheelchair system on two wheels. Figure 11 shows the final wheelchair position when it was set to move forward to 1.5m from the origin. It is noted from Figures 12 and 13 that both links settled after 4s from starting time of linear motion, which can be considered quite good performance for the initial attempts of parameters setting. Link1 tilted with a positive angle from the 0° upright position. This configuration was automatically adjusted to initiate the forward motion. The corresponding wheelchair position is shown in Figure 14. It is noted that as much as 0.1m of the steady state error appeared when it settled. Figure 15 shows the wheel torques (τR and τL) from the lifting and stabilizing controller of Link1 (FLC1), and the wheel torques from the linear motion control is shown in Figure 16. The torques vary from +40Nm to -40Nm during the forward motion with positive slope during initial phase of travel. The resultant wheel torques contributed by the lifting and stabilizing control as well as the linear motion control are shown in Figure 17.

The torque between Link1 and Link2 (τ2) given by (FLC2) is shown in Figure 18.

Fig. 11. Final position of 1.5m forward motion

*Forward Motion* 

outputs are the torques, τR and τL. The fuzzy inputs are normalized so that they can be generalized and then processed using the fuzzy rules. Moreover, the input normalization is done due to the complexity of predetermining the range of change of position error, ∆*e*. Gaussian (bell shaped) type membership functions with default parameters given by Matlab/Simulink are used for all inputs and outputs. The membership levels for each input and outputs are five in total. These comprise Negative Big (NB), Negative Small (NS), Zero

Fig. 10. Membership functions for inputs and outputs for FLC3 of linear motion control


Table 2. Fuzzy rules for linear motion

(Z), Positive Small (PS) and Positive Big (PB). The membership function for inputs and outputs of FLC3 is shown in Figure 10. Table 2 shows the implemented fuzzy rules for FLC3 controller. The two consecutive rows in the output part represent two fuzzy outputs, τR (first row) and τL (second row). The rules developed are predetermined using expert knowledge available such that all the errors should be brought back to the reference point immediately.

#### *Forward Motion*

48 Fuzzy Logic – Controls, Concepts, Theories and Applications

outputs are the torques, τR and τL. The fuzzy inputs are normalized so that they can be generalized and then processed using the fuzzy rules. Moreover, the input normalization is done due to the complexity of predetermining the range of change of position error, ∆*e*. Gaussian (bell shaped) type membership functions with default parameters given by Matlab/Simulink are used for all inputs and outputs. The membership levels for each input and outputs are five in total. These comprise Negative Big (NB), Negative Small (NS), Zero

0

1

0

**NB NS Z PS PB** 

PB PB PB PS Z PB PB PB PS Z

PB PB PS Z NS PB PB PS Z NS

PB PS Z NS NB PB PS Z NS NB

PS Z NS NB NB PS Z NS NB NB

Z NS NB NB NB Z NS NB NB NB

0.5

Degree of membership

Fig. 10. Membership functions for inputs and outputs for FLC3 of linear motion control

0.5

Degree of membership

1


NB NS Z PS PB

ChangeOfError

NB NS Z PS PB


Left torque


NB NS Z PS PB

Error

NB NS Z PS PB


Right torque

**∆e**

**NB** 

**NS** 

**Z** 

**PS** 

**PB** 

Table 2. Fuzzy rules for linear motion

0

1

0

**e** 

0.5

Degree of membership

0.5

Degree of membership

1

The system was commanded to move forward after 4s, where at this time the two links had been stabilized at the upright position. Figure 11 shows the final position of forward mechanism execution while Figure 12 to Figure 18 show the results over 15s of simulation time for forward movement of the two-wheeled wheelchair. The wheelchair was set to move 1.5m forward from its initial position. The results show that the FLC approach worked very well with the wheelchair system on two wheels. Figure 11 shows the final wheelchair position when it was set to move forward to 1.5m from the origin. It is noted from Figures 12 and 13 that both links settled after 4s from starting time of linear motion, which can be considered quite good performance for the initial attempts of parameters setting. Link1 tilted with a positive angle from the 0° upright position. This configuration was automatically adjusted to initiate the forward motion. The corresponding wheelchair position is shown in Figure 14. It is noted that as much as 0.1m of the steady state error appeared when it settled. Figure 15 shows the wheel torques (τR and τL) from the lifting and stabilizing controller of Link1 (FLC1), and the wheel torques from the linear motion control is shown in Figure 16. The torques vary from +40Nm to -40Nm during the forward motion with positive slope during initial phase of travel. The resultant wheel torques contributed by the lifting and stabilizing control as well as the linear motion control are shown in Figure 17. The torque between Link1 and Link2 (τ2) given by (FLC2) is shown in Figure 18.

Fig. 11. Final position of 1.5m forward motion

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 51

0 5 10 15

0 5 10 15

Time (s)

0 5 10 15

Time (s)

Right torque Left torque

Right torque Left torque

Right torque Left torque

Time (s)

Fig. 15. Wheel torques, τR and τL due to lifting and stabilizing control, FLC1 (Nm)

Fig. 16. Wheel torques, τR and τL due to linear motion control, FLC3 (Nm)




Fig. 17. Resultant wheel torques due to FLC1 and FLC3 (Nm)


0

50

Resultant torques (Nm)

100

150


Wheel torques from

linear motion control (Nm)

0

50

100


0

50

Wheel torques from lifting

and stabilizing control (Nm)

100

150

Fig. 12. Angular position of Link1, δ1 (degree)

Fig. 13. Angular position of Link2, δ2 (degree)

Fig. 14. Wheelchair position, x (m)

0 5 10 15

Time (s)

0 5 10 15

Time (s)

0 5 10 15

Time (s)



0

Fig. 14. Wheelchair position, x (m)

0.5

1

Wheelchair position (m)

1.5

2

Fig. 13. Angular position of Link2, δ2 (degree)



Angular position of Link2 (degree)

0

10

Fig. 12. Angular position of Link1, δ1 (degree)

0

20

40

Angular position of Link1 (degree)

60

80

100

Fig. 15. Wheel torques, τR and τL due to lifting and stabilizing control, FLC1 (Nm)

Fig. 16. Wheel torques, τR and τL due to linear motion control, FLC3 (Nm)

Fig. 17. Resultant wheel torques due to FLC1 and FLC3 (Nm)

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 53

This new capacity increased the number of DOF of the two-wheeled wheelchair. Thus, it is noticeable challenge to control the two-wheeled wheelchair where limited actuators are available for different functions. Therefore, suitable controllers are needed, and FLC is adopted. Results show that the FLC strategy works well and gives good system

Two inputs and two outputs FLC is developed to control the steering motion. The membership functions used are shown in Figure 20. The membership levels for each input

0

1

0

0.5

Degree of membership

0.5

Degree of membership

1


NB NS Z PS PB

ChangeofError

NB NS Z PS PB


Left torque

performance.

Fig. 19. Block diagram for steering motion control


NB NS Z PS PB

WCrotError

NB NS Z PS PB


Right torque

Fig. 20. Membership levels for inputs and outputs of steering control

0

1

0

0.5

Degree of membership

0.5

Degree of membership

1

Fig. 18. Torque between Link1 and Link2, τ2, FLC2 (Nm)

#### **b. FLC for steering motion**

A steering motion is needed when the two-wheeled wheelchair needs to change its direction. The two-wheeled wheelchair can rotate to the right or to the left depending on which direction it is commanded. There are two different approaches where steering could be realized (Tanimoto et al., 2009). Similar direction of wheel rotation with different magnitudes could lead to steering motion (moving both wheels forward with different magnitudes). The first approach causes bigger turning radius as compared to the second approach. The second approach to realize steering motion is by giving different direction of wheel rotation (moving right wheel forward and left backward). The output torques in this work given by the FLC used for steering motion covers both approaches according to the steering error and the change of the steering error. In contrast to normal steering for mobile robots, steering motion for the two-wheeled wheelchair is executed after the upright position has been achieved; Link1 and Link2 at the 0° upright position. Therefore the complexity in this configuration is higher than the steering motion using four wheels, since other motion controls are active at the same time.

A block diagram for steering motion control of two-wheeled wheelchair is shown in Figure 19. As discussed earlier, for reasons of simplicity, the torques applied to the two wheels are the same in magnitudes (one output torque from the controller) so as to move the wheelchair only forward or backward. Then each right and left wheel torque is made independent to realize the steering motion. The weight here represents the human body weight, for which an average 70kg human is used. Sensors are attached at the respective reference bodies for control and measurement. The control signals applied to the wheelchair model comprise the right torque, τR (Nm), left torque, τL (Nm) and torque between Link1 and Link2, τ2 (Nm). The measured outputs from the wheelchair system that consist of the angular position of Link1, δ1, (degree), angular position of Link2, δ2, (degree) and wheelchair rotation angle about the vertical axis, ψ (degree) are compared with the target references.

The wheelchair system modeled in VN software environment was used as a plant and controlled with the developed FLC in the Matlab/Simulink environment. The steering motion introduced takes place after the lifting and stabilizing mechanism has been achieved.

0 5 10 15

Time (s)

A steering motion is needed when the two-wheeled wheelchair needs to change its direction. The two-wheeled wheelchair can rotate to the right or to the left depending on which direction it is commanded. There are two different approaches where steering could be realized (Tanimoto et al., 2009). Similar direction of wheel rotation with different magnitudes could lead to steering motion (moving both wheels forward with different magnitudes). The first approach causes bigger turning radius as compared to the second approach. The second approach to realize steering motion is by giving different direction of wheel rotation (moving right wheel forward and left backward). The output torques in this work given by the FLC used for steering motion covers both approaches according to the steering error and the change of the steering error. In contrast to normal steering for mobile robots, steering motion for the two-wheeled wheelchair is executed after the upright position has been achieved; Link1 and Link2 at the 0° upright position. Therefore the complexity in this configuration is higher than the steering motion using four wheels, since

A block diagram for steering motion control of two-wheeled wheelchair is shown in Figure 19. As discussed earlier, for reasons of simplicity, the torques applied to the two wheels are the same in magnitudes (one output torque from the controller) so as to move the wheelchair only forward or backward. Then each right and left wheel torque is made independent to realize the steering motion. The weight here represents the human body weight, for which an average 70kg human is used. Sensors are attached at the respective reference bodies for control and measurement. The control signals applied to the wheelchair model comprise the right torque, τR (Nm), left torque, τL (Nm) and torque between Link1 and Link2, τ2 (Nm). The measured outputs from the wheelchair system that consist of the angular position of Link1, δ1, (degree), angular position of Link2, δ2, (degree) and wheelchair rotation angle about the vertical axis, ψ

The wheelchair system modeled in VN software environment was used as a plant and controlled with the developed FLC in the Matlab/Simulink environment. The steering motion introduced takes place after the lifting and stabilizing mechanism has been achieved.


**b. FLC for steering motion** 

Fig. 18. Torque between Link1 and Link2, τ2, FLC2 (Nm)

other motion controls are active at the same time.

(degree) are compared with the target references.




Torque between

Link1 and Link2 (Nm)

0

50

100

This new capacity increased the number of DOF of the two-wheeled wheelchair. Thus, it is noticeable challenge to control the two-wheeled wheelchair where limited actuators are available for different functions. Therefore, suitable controllers are needed, and FLC is adopted. Results show that the FLC strategy works well and gives good system performance.

Fig. 19. Block diagram for steering motion control

Two inputs and two outputs FLC is developed to control the steering motion. The membership functions used are shown in Figure 20. The membership levels for each input

Fig. 20. Membership levels for inputs and outputs of steering control

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 55

0 5 10 15

Time (s)

0 5 10 15

Time (s)

Fig. 21. Final steering position for 30° reference point



Fig. 23. Angular position of Link2, δ2 (degree)



Angular position of Link2 (degree)

0

10

Fig. 22. Angular position of Link1, δ1 (degree)

0

20

40

Angular position of Link1 (degree)

60

80

100

and output comprise Negative Big (NB), Negative Small (NS), Zero (Z), Positive Small (PS) and Positive Big (PB). The two inputs used were the wheelchair rotation error (eψ) and the change of wheelchair rotation error, ∆eψ. The controller outputs are the right and left wheel torques, τR and τL. All membership functions of input and output parameters are normalized for ease of control. Table 3 shows the implemented fuzzy rules for steering motion control (FLC4), where the first row relates to right-wheel torque and the second (shaded) row relates to the left-wheel torque.


Table 3. Fuzzy rules for steering motion

#### *Steering to 30°*

The final position of the wheelchair system can be seen in Figure 21. Figures 22 and Figure 23 show the angular positions of Link1, δ1 and Link2, δ2 respectively when the system was set to steer at 30° causing the two-wheeled wheelchair to rotate to the left from its initial position. Both links settled with small steady state error after the steering settlement was achieved. As noted, they settled in less than 4s. As noted in Figure 24, the wheelchair rotated very near to 30°, with < 0.1° of the steady state error. The output torques from each lifting and stabilizing control of Link1 as well as the steering control are shown in Figures 25 and 26 respectively. Note that the output torques from FLC1 had the same magnitude and direction for both right and left wheels. On the other hand, the output torque from FLC4 had the same magnitude but different in direction representing the fuzzy rules output for steering motion. The torque between Link1 and Link2 can be seen in Figure 27. As noted, it changed between +30Nm and -20Nm to maintain the upright stability of Link2 with human payload during the steering motion. The resultant torques for both fuzzy controllers (FLC1+FLC4) is shown in Figure 28. The system was then tested to rotate at a different angle (negative angle leading to rotation to the right).

and output comprise Negative Big (NB), Negative Small (NS), Zero (Z), Positive Small (PS) and Positive Big (PB). The two inputs used were the wheelchair rotation error (eψ) and the change of wheelchair rotation error, ∆eψ. The controller outputs are the right and left wheel torques, τR and τL. All membership functions of input and output parameters are normalized for ease of control. Table 3 shows the implemented fuzzy rules for steering motion control (FLC4), where the first row relates to right-wheel torque and the second

**NB NS Z PS PB** 

NB NB NB NS Z PB PB PB PS Z

NB NB NS Z PS PB PB PS Z NS

NB NS Z PS PB PB PS Z NS NB

NS Z PS PB PB PS Z NS NB NB

Z PS PB PB PB Z NS NB NB NB

The final position of the wheelchair system can be seen in Figure 21. Figures 22 and Figure 23 show the angular positions of Link1, δ1 and Link2, δ2 respectively when the system was set to steer at 30° causing the two-wheeled wheelchair to rotate to the left from its initial position. Both links settled with small steady state error after the steering settlement was achieved. As noted, they settled in less than 4s. As noted in Figure 24, the wheelchair rotated very near to 30°, with < 0.1° of the steady state error. The output torques from each lifting and stabilizing control of Link1 as well as the steering control are shown in Figures 25 and 26 respectively. Note that the output torques from FLC1 had the same magnitude and direction for both right and left wheels. On the other hand, the output torque from FLC4 had the same magnitude but different in direction representing the fuzzy rules output for steering motion. The torque between Link1 and Link2 can be seen in Figure 27. As noted, it changed between +30Nm and -20Nm to maintain the upright stability of Link2 with human payload during the steering motion. The resultant torques for both fuzzy controllers (FLC1+FLC4) is shown in Figure 28. The system was then tested to rotate at a different angle

(shaded) row relates to the left-wheel torque.

**NB** 

**NS** 

**Z** 

**PS** 

**PB** 

(negative angle leading to rotation to the right).

Table 3. Fuzzy rules for steering motion

*Steering to 30°* 

**e<sup>ψ</sup>**

**∆e<sup>ψ</sup>**

Fig. 21. Final steering position for 30° reference point

Fig. 22. Angular position of Link1, δ1 (degree)

Fig. 23. Angular position of Link2, δ2 (degree)

Modular Fuzzy Logic Controller for Two-Wheeled Wheelchair 57

0 5 10 15

Right torque Left torque

Time (s)

0 5 10 15

Time (s)

Fuzzy logic is one of the control techniques that is very close to human feelings and expressions. It can be easily understood and implemented although the knowledge about classical or conventional control system is not much identified. Nevertheless the general knowledge of the system involved must be generally known otherwise it is difficult to formulate a fuzzy controller for such system. If the system involved is known to be linear, and simple thus it is more worth to start with conventional Proportional-Integral-Differential (PID) controller. Otherwise if the system is known to be very complex, nonlinear and ill-defined type of system, then it is suggested to use one of the computational approaches such as fuzzy logic. This method was successfully implemented in the twowheeled wheelchair system where a modular fuzzy control (MFC) was developed and implemented for controlling lifting and stabilizing mechanism, linear and steering motion control. Note that since a wheelchair is a main means of transport for disabled and elderly people, this two-wheeled wheelchair system would allow the user to achieve a higher level of height without assistance and hence independence. The wheelchair has been modeled as a double inverted pendulum. The integrated two-wheeled wheelchair with a human model



Fig. 28. Resultant wheel torques (Nm)


0

50

Resultant wheel torques (Nm)

**5. Conclusion** 

100

150

Fig. 27. Torque between Link1 and Link2, τ2 (Nm)



Torque between

Link1 and Link2 (Nm)


0

50

Fig. 24. Wheelchair rotation, ψ (degree)

Fig. 25. Wheel torques (τR and τL) from FLC1 (Nm)

Fig. 26. Wheel torques (τR and τL) from steering motion control, FLC4 (Nm)

Fig. 27. Torque between Link1 and Link2, τ2 (Nm)

Fig. 28. Resultant wheel torques (Nm)

#### **5. Conclusion**

56 Fuzzy Logic – Controls, Concepts, Theories and Applications

0 5 10 15

Time (s)

0 5 10 15

Right torque Left torque

Right torque Left torque

Time (s)

0 5 10 15

Time (s)

Fig. 26. Wheel torques (τR and τL) from steering motion control, FLC4 (Nm)


Fig. 24. Wheelchair rotation, ψ (degree)




0

Wheel torques from

steering control (Nm)

50

100

Fig. 25. Wheel torques (τR and τL) from FLC1 (Nm)


0

50

Wheel torques from lifting

and stabilizing of Link1 (Nm)

100

150

0

10

Wheelchair rotation (degree)

20

30

40

Fuzzy logic is one of the control techniques that is very close to human feelings and expressions. It can be easily understood and implemented although the knowledge about classical or conventional control system is not much identified. Nevertheless the general knowledge of the system involved must be generally known otherwise it is difficult to formulate a fuzzy controller for such system. If the system involved is known to be linear, and simple thus it is more worth to start with conventional Proportional-Integral-Differential (PID) controller. Otherwise if the system is known to be very complex, nonlinear and ill-defined type of system, then it is suggested to use one of the computational approaches such as fuzzy logic. This method was successfully implemented in the twowheeled wheelchair system where a modular fuzzy control (MFC) was developed and implemented for controlling lifting and stabilizing mechanism, linear and steering motion control. Note that since a wheelchair is a main means of transport for disabled and elderly people, this two-wheeled wheelchair system would allow the user to achieve a higher level of height without assistance and hence independence. The wheelchair has been modeled as a double inverted pendulum. The integrated two-wheeled wheelchair with a human model

**4** 

Bin Zi1,2

*China* 

**Fuzzy Control System Design and** 

 **Cable-Driven Manipulators** 

*1School of Mechanical and Electrical Engineering,* 

 *Zhejiang University, Hangzhou, Zhejiang* 

**Analysis for Completely Restrained** 

 *China University of Mining and Technology, Xuzhou, Jiangsu, 2The State Key Laboratory of Fluid Power and Mechatronic Systems,* 

Cable-driven manipulators, referred to as the overhead crane and rotary crane are widely used in the manufacturing and construction industries in order to move heavy objects as illustrated in Fig. 1. Cable-driven manipulators are relatively simple form, with multiple cables attached to a mobile platform or end-effector. The end-effector may be equipped with various attachments, including hooks, cameras, robotic grippers and so on. Cable-driven manipulators have several advantages over rigid-link mechanisms, including the following: 1) remote location of motors and controls; 2) rapid deployability; 3) potentially large workspaces; 4) high load capacity; 5) reliability (Borgstrom et al., 2009; Zi et al., 2008). For the preceding reasons, cable-driven manipulators have received attention and have been recently studied since 1980s (Behzadipour & Khajepour, 2005; Ghasemi et al., 2008; Motoji,

**1. Introduction** 

2004; Oh & Agrawal, 2005; Pham et al., 2006).

Fig. 1. Crane-type cable manipulator.

has been imported as the plant into Matlab/Simulink environment for control and evaluation purposes. Therefore, fuzzy logic techniques have been found suitable for control of the two-wheeled wheelchair.

A Modular Fuzzy logic Control (MFC) approach has been adopted, where the control tasks are divided into primary and secondary tasks (subsystems), and FLC modules have been designed and executed for the various control tasks accordingly. Among the control tasks, lifting and stabilizing in the upright position are considered as the primary control system task. Secondary system tasks include linear motion and steering motion. The MFC strategy developed is based on a hierarchical approach whereby the primary subsystem must be executed followed by selection of secondary subsystems. Both linear and steering motions have been successfully controlled independently using a two-input two-output PD-type FLC.

The proposed MFC has been successfully implemented and tested within simulated exercises for two-wheeled wheelchair application. The results presented proved that the MFC approach works very well in controlling highly nonlinear systems such as a wheelchair on two wheels and significantly reduces the number of rules.

## **6. Acknowledgment**

The authors would like to express their appreciation to the International Islamic University Malaysia (IIUM) for sponsoring the publication of this book chapter.

## **7. References**


## **Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators**

Bin Zi1,2

*1School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 2The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, Zhejiang China* 

## **1. Introduction**

58 Fuzzy Logic – Controls, Concepts, Theories and Applications

has been imported as the plant into Matlab/Simulink environment for control and evaluation purposes. Therefore, fuzzy logic techniques have been found suitable for control

A Modular Fuzzy logic Control (MFC) approach has been adopted, where the control tasks are divided into primary and secondary tasks (subsystems), and FLC modules have been designed and executed for the various control tasks accordingly. Among the control tasks, lifting and stabilizing in the upright position are considered as the primary control system task. Secondary system tasks include linear motion and steering motion. The MFC strategy developed is based on a hierarchical approach whereby the primary subsystem must be executed followed by selection of secondary subsystems. Both linear and steering motions have been successfully controlled independently using a two-input two-output PD-type FLC. The proposed MFC has been successfully implemented and tested within simulated exercises for two-wheeled wheelchair application. The results presented proved that the MFC approach works very well in controlling highly nonlinear systems such as a

The authors would like to express their appreciation to the International Islamic University

Ahmad, S., N. H. Siddique and M. O. Tokhi (2011). A modular fuzzy control approach for

Bessacini, A. F. and R. F. Pinkos (1995). A hierarchical fuzzy controller for intercept

Engelbrecht, A. P. (2007). *Computational intelligence: An introduction*. Chichester, England,

Mamdani, E. H. (1974). Application of fuzzy algorithms for control of a simple dynamic

Vries, T. J. A. D., C. V. Heteran and L. Huttenhuis (1999). Modeling and control of a fast

Wong, C.-C., H.-Y. Wang, S.-A. Li and C.-T. Cheng (2007). Fuzzy controller designed by GA for two-wheeled mobile robots. *International Journal of Fuzzy Systems* 9(1).

moving, highly maneuverable wheelchair. *International Biomechatronics Workshop*,

two-wheeled wheelchair. *Journal of Intelligent and Robotic Systems* Springer Journal,

guidance with a forbidden zone. Newport, Naval Undersea Warfare Center

wheelchair on two wheels and significantly reduces the number of rules.

Malaysia (IIUM) for sponsoring the publication of this book chapter.

process. *Proceeding of IEEE* 121(12): 1585-1588.

Siljak, D. (1991) *Decentralized Control* of *Complex Systems,* Academic Press**.**

Zadeh, L. A. (1965). Fuzzy sets. *Information and Control* 8(3): 338 - 353.

Reznik, L. (1997). *Fuzzy Controllers*. Oxford, Newnes.

of the two-wheeled wheelchair.

**6. Acknowledgment**

Division.

Vol. 64(3-4), pp. 401-426.

John Wiley & Sons.

Enschede, Netherlands.

**7. References** 

Cable-driven manipulators, referred to as the overhead crane and rotary crane are widely used in the manufacturing and construction industries in order to move heavy objects as illustrated in Fig. 1. Cable-driven manipulators are relatively simple form, with multiple cables attached to a mobile platform or end-effector. The end-effector may be equipped with various attachments, including hooks, cameras, robotic grippers and so on. Cable-driven manipulators have several advantages over rigid-link mechanisms, including the following: 1) remote location of motors and controls; 2) rapid deployability; 3) potentially large workspaces; 4) high load capacity; 5) reliability (Borgstrom et al., 2009; Zi et al., 2008). For the preceding reasons, cable-driven manipulators have received attention and have been recently studied since 1980s (Behzadipour & Khajepour, 2005; Ghasemi et al., 2008; Motoji, 2004; Oh & Agrawal, 2005; Pham et al., 2006).

Fig. 1. Crane-type cable manipulator.

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 61

design. Results and discussions are presented in Section 5. Finally, concluding remarks are

The CRCM suspends an end-effector (clog) by four cables and restrains all motion degrees of freedom for the object using the cables and gravitational force when the end-effector moves within the workspace. In the design, of each cable in the CRCM, one end is connected to the end-effector, the other end rolls through a pulley fixed on the top of the relative pillar and then is fed into a servo mechanism, with which cable length can be altered. The design of CRCM follows a built-up modular system, as illustrated in Fig.2. The system comprises several components: servo motor, belt pulley drive mechanism, speed reducer, girder,

Reliability, long-distance transmission, high speed and precision are paramount for the CRCM design. The structure of the CRCM is shown in Fig.3, and the end-effector is driven by four sets of servomechanism. Belts are looped over pulleys. In a two pulley system, the belt can either drive the pulleys in the same direction. As a source of motion, a conveyor belt is one application where the belt is adapted to continually carry a load between two distant

A simple schematic of the CRCM representing the coordinate systems is shown in Fig. 4. With the bottom of the pillar corresponding to the point *B*3 as the origin, a Cartesian coordinate system is established. The end-effector is predigested as a particle whose location coordinates are *Axyz* (,,) , and the distance between each pulley center whose coordinates are (,,) *Bxy z iiii* and the end-effector is ( 1,2,3,4) *il i* . Four pillars have the same height and are arrayed in a rectangular on the ground, whose deformation in movement is ignored. In order to simplify the calculation, the cable is treated as a kind of massless rigid body, which

points. Typically, gears and elastic drive belts are applied to transmit motion.

provided in Section 6.

**2. Mechanical design** 

Fig. 2. Model of the CRCM.

**3. Modeling and analysis** 

has no deformation, and can only sustain tension.

windlass, cable pillar, cable, end-effector, and so on.

Cable-driven manipulators can be classified as either incompletely restrained or completely restrained (Bosscher & Ebert-Uphoff, 2006). Cable-driven manipulators are underconstrained if it relies on gravity to determine the pose (position and orientation) of the end-effector, while they are completely restrained if the pose of the end-effector is completely determined by the lengths of the cables. As you know, dynamics is a huge field of study devoted to studying the forces required to cause motion. In order to accelerate the robot from rest, glide at a constant end-effector velocity, and finally decelerate to a stop, a complex set of torque functions must be applied by the joint actuators (Craig, 2005). The motivation for this paper comes directly from the design, mechanics analysis, and control of completely restrained cable-driven manipulators (CRCM) with 3 Degrees of Freedom (DOF). As demonstrated in (Anupoju et al., 2005), servomechanism dynamics constitute an important component of the complete robotic dynamics. Therefore, the dynamics of the servomotors and its gears must be modeled for further control design. However, the literature on the CRCM system including the actuator dynamics is sparse.

CRCM systems are multivariable in nature. The control of the multivariable systems is a complicated problem due to the coupling that exists between the control inputs and the outputs, and the multivariable systems are nonlinear and uncertain, therefore, their control problem becomes more challenging (Chien, 2008; Yousef et al., 2009). In order to achieve a high-precision performance, the controller of the CRCM must effectively and accurately manipulate the motion trajectory. It is well known that up until now, a conventional proportional-integral-derivative (PID) controller has been widely used in industry due to its simple control structure, ease of design, and inexpensive cost (Reznik et al., 2000; Visioli, 2001). However, the CRCM is a multivariable nonlinear coupling dynamic system which suffers from structured and unstructured uncertainties such as payload variation, external disturbances, etc. As a result, the PID controller cannot yield a good control performance for this type of control system. For dealing with nonlinear effects, various control algorithms have been proposed. Among them, adaptive control and fuzzy logic system algorithm draw much attention due to the applicability for typically highly nonlinear systems (Chang, 2000; Soyguder & Alli, 2010; Su & Stepanenko, 1994). The idea of fuzzy set and fuzzy control is introduced by Zadeh in an attempt to control systems that are structurally difficult to model (Feng, 2006; Zadeh, 1965). Fuzzy controllers have been well accepted in control engineering practice. The major advantages in all these fuzzy-based control schemes are that the developed controllers can be employed to deal with increasingly complex systems to implement the controller without any precise knowledge of the structure of entire dynamic model. As a knowledge-based approach, the fuzzy controller usually depends on linguistics-based reasoning in design. However, even though a system is well defined mathematically, the fuzzy controller is still preferred by control engineers since it is relatively more understandable whereas expert knowledge can be incorporated conveniently. Recently, the fuzzy controller of nonlinear systems was studied by many authors and has also been extensively adopted in adaptive control of robot manipulators (Chen et al., 1996; Labiod et al., 2005; Purwar et al., 2005; Yoo & Ham, 1998). It has been proven that adaptive fuzzy control is a powerful technique and being increasingly applied in the discipline of systems control, especially when the controlled system has uncertainties and highly nonlinearities (Yu et al., 2011).

This chapter is organized as follows. First, the mechanical system is designed in Section 2. Then, modeling and analysis of the cable-driven manipulator are described in Section 3. Section 4 presents the developed systematic approach for the adaptive fuzzy controller design. Results and discussions are presented in Section 5. Finally, concluding remarks are provided in Section 6.

## **2. Mechanical design**

60 Fuzzy Logic – Controls, Concepts, Theories and Applications

Cable-driven manipulators can be classified as either incompletely restrained or completely restrained (Bosscher & Ebert-Uphoff, 2006). Cable-driven manipulators are underconstrained if it relies on gravity to determine the pose (position and orientation) of the end-effector, while they are completely restrained if the pose of the end-effector is completely determined by the lengths of the cables. As you know, dynamics is a huge field of study devoted to studying the forces required to cause motion. In order to accelerate the robot from rest, glide at a constant end-effector velocity, and finally decelerate to a stop, a complex set of torque functions must be applied by the joint actuators (Craig, 2005). The motivation for this paper comes directly from the design, mechanics analysis, and control of completely restrained cable-driven manipulators (CRCM) with 3 Degrees of Freedom (DOF). As demonstrated in (Anupoju et al., 2005), servomechanism dynamics constitute an important component of the complete robotic dynamics. Therefore, the dynamics of the servomotors and its gears must be modeled for further control design. However, the

CRCM systems are multivariable in nature. The control of the multivariable systems is a complicated problem due to the coupling that exists between the control inputs and the outputs, and the multivariable systems are nonlinear and uncertain, therefore, their control problem becomes more challenging (Chien, 2008; Yousef et al., 2009). In order to achieve a high-precision performance, the controller of the CRCM must effectively and accurately manipulate the motion trajectory. It is well known that up until now, a conventional proportional-integral-derivative (PID) controller has been widely used in industry due to its simple control structure, ease of design, and inexpensive cost (Reznik et al., 2000; Visioli, 2001). However, the CRCM is a multivariable nonlinear coupling dynamic system which suffers from structured and unstructured uncertainties such as payload variation, external disturbances, etc. As a result, the PID controller cannot yield a good control performance for this type of control system. For dealing with nonlinear effects, various control algorithms have been proposed. Among them, adaptive control and fuzzy logic system algorithm draw much attention due to the applicability for typically highly nonlinear systems (Chang, 2000; Soyguder & Alli, 2010; Su & Stepanenko, 1994). The idea of fuzzy set and fuzzy control is introduced by Zadeh in an attempt to control systems that are structurally difficult to model (Feng, 2006; Zadeh, 1965). Fuzzy controllers have been well accepted in control engineering practice. The major advantages in all these fuzzy-based control schemes are that the developed controllers can be employed to deal with increasingly complex systems to implement the controller without any precise knowledge of the structure of entire dynamic model. As a knowledge-based approach, the fuzzy controller usually depends on linguistics-based reasoning in design. However, even though a system is well defined mathematically, the fuzzy controller is still preferred by control engineers since it is relatively more understandable whereas expert knowledge can be incorporated conveniently. Recently, the fuzzy controller of nonlinear systems was studied by many authors and has also been extensively adopted in adaptive control of robot manipulators (Chen et al., 1996; Labiod et al., 2005; Purwar et al., 2005; Yoo & Ham, 1998). It has been proven that adaptive fuzzy control is a powerful technique and being increasingly applied in the discipline of systems control, especially when the controlled system has uncertainties

This chapter is organized as follows. First, the mechanical system is designed in Section 2. Then, modeling and analysis of the cable-driven manipulator are described in Section 3. Section 4 presents the developed systematic approach for the adaptive fuzzy controller

literature on the CRCM system including the actuator dynamics is sparse.

and highly nonlinearities (Yu et al., 2011).

The CRCM suspends an end-effector (clog) by four cables and restrains all motion degrees of freedom for the object using the cables and gravitational force when the end-effector moves within the workspace. In the design, of each cable in the CRCM, one end is connected to the end-effector, the other end rolls through a pulley fixed on the top of the relative pillar and then is fed into a servo mechanism, with which cable length can be altered. The design of CRCM follows a built-up modular system, as illustrated in Fig.2. The system comprises several components: servo motor, belt pulley drive mechanism, speed reducer, girder, windlass, cable pillar, cable, end-effector, and so on.

Reliability, long-distance transmission, high speed and precision are paramount for the CRCM design. The structure of the CRCM is shown in Fig.3, and the end-effector is driven by four sets of servomechanism. Belts are looped over pulleys. In a two pulley system, the belt can either drive the pulleys in the same direction. As a source of motion, a conveyor belt is one application where the belt is adapted to continually carry a load between two distant points. Typically, gears and elastic drive belts are applied to transmit motion.

Fig. 2. Model of the CRCM.

## **3. Modeling and analysis**

A simple schematic of the CRCM representing the coordinate systems is shown in Fig. 4. With the bottom of the pillar corresponding to the point *B*3 as the origin, a Cartesian coordinate system is established. The end-effector is predigested as a particle whose location coordinates are *Axyz* (,,) , and the distance between each pulley center whose coordinates are (,,) *Bxy z iiii* and the end-effector is ( 1,2,3,4) *il i* . Four pillars have the same height and are arrayed in a rectangular on the ground, whose deformation in movement is ignored. In order to simplify the calculation, the cable is treated as a kind of massless rigid body, which has no deformation, and can only sustain tension.

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 63

11 11

*l xx yy zz l xx yy zz l xx yy zz l xx yy zz*

 

22 2 2

As the pillars are arrayed in a rectangular on the base, according to the geometric

2222

The general dynamic equations of motion can be derived from the Lagrangian method. In the model, the end-effector is assumed to act as a point mass and the cable is treated as a kind of massless rigid body. As a result, the kinetic energy, *K* , and the potential energy, *P* ,

cable in or let it out, therefore, it is desirable to regard the cable lengths as the variables. By substituting the forward kinematic equations (2) into the kinetic energy and potential energy shown in Eqs. (4) and (5), respectively, the Lagrange's Equation can be written in the

> ( ) *<sup>i</sup> i ii dK K P <sup>Q</sup> dt q q q*

where and the variables, *<sup>i</sup> q* (for *i* 1,2,3,4 ), the generalized forces, *Qi* , respectively, can be

22 2 2

( )( )( ) ( )( )( ) ( )( )( ) ( )( )( )

22 22

33 33

44 44

The forward kinematic equations can be found by solving (1) for (,,) *xyz* , which results in

1 2 2 1 21

( ) / 2( ) ( ) / 2( ) ( )( ) *i i ii*

*xl l x x xx y l l y y yy z l xx y y z*

2 3 3 2 32 222

2 22

2 22

2 22

2 22

*l* and the end-effector location *Axyz* (,,) , can be

<sup>4213</sup> *llll* (3)

<sup>1</sup> 2 22 ( ) <sup>2</sup> *K mx y z* (4)

*l* , 2*l* , 3*l* and 4*l* , are directly controlled by rotating the winch to reel the

*P mgz* (5)

(6)

(1)

(2)

The relationship between the cable length *<sup>i</sup>*

of the end-effector can be written in Cartesian coordinates as

where *m* is mass of end-effector, *g* is acceleration of gravity.

relationship, the geometric constraint of the cable length is calculated as

easily obtained as follows:

the following:

The cable lengths, 1

following form

expressed as

Fig. 3. Mechanical structure of the CRCM

Fig. 4. Structure model of the CRCM

Pulley Cable Cable pillar

Girder

Servomotor

Servomotor

Fig. 3. Mechanical structure of the CRCM

Fig. 4. Structure model of the CRCM

Belt-pulley drive mechanism

Speed reducer

End-effector (clog)

Windlass

End-effector (clog)

Girder

Cable

The relationship between the cable length *<sup>i</sup> l* and the end-effector location *Axyz* (,,) , can be easily obtained as follows:

$$\begin{cases} l\_1 = \sqrt{(\mathbf{x} - \mathbf{x}\_1)^2 + \left(y - y\_1\right)^2 + \left(z - z\_1\right)^2} \\ l\_2 = \sqrt{\left(\mathbf{x} - \mathbf{x}\_2\right)^2 + \left(y - y\_2\right)^2 + \left(z - z\_2\right)^2} \\ l\_3 = \sqrt{\left(\mathbf{x} - \mathbf{x}\_3\right)^2 + \left(y - y\_3\right)^2 + \left(z - z\_3\right)^2} \\ l\_4 = \sqrt{\left(\mathbf{x} - \mathbf{x}\_4\right)^2 + \left(y - y\_4\right)^2 + \left(z - z\_4\right)^2} \end{cases} \tag{1}$$

The forward kinematic equations can be found by solving (1) for (,,) *xyz* , which results in the following:

$$\begin{cases} \mathbf{x} = \left(l\_1^{-2} - l\_2^{-2} + \mathbf{x}\_2^{-2} - \mathbf{x}\_1^{-2}\right) / \, 2(\mathbf{x}\_2 - \mathbf{x}\_1) \\ y = \left(l\_2^{-2} - l\_3^{-2} + y\_3^{-2} - y\_2^{-2}\right) / \, 2(y\_3 - y\_2) \\ z = -\sqrt{l\_i^2 - (\mathbf{x} - \mathbf{x}\_i)^2 - (y - y\_i)^2} + z\_i \end{cases} \tag{2}$$

As the pillars are arrayed in a rectangular on the base, according to the geometric relationship, the geometric constraint of the cable length is calculated as

$$l\_4^2 + l\_2^2 = l\_1^2 + l\_3^2\tag{3}$$

The general dynamic equations of motion can be derived from the Lagrangian method. In the model, the end-effector is assumed to act as a point mass and the cable is treated as a kind of massless rigid body. As a result, the kinetic energy, *K* , and the potential energy, *P* , of the end-effector can be written in Cartesian coordinates as

$$K = \frac{1}{2}m(\dot{\mathbf{x}}^2 + \dot{\mathbf{y}}^2 + \dot{\mathbf{z}}^2) \tag{4}$$

$$P = \text{mgz} \tag{5}$$

where *m* is mass of end-effector, *g* is acceleration of gravity.

The cable lengths, 1 *l* , 2*l* , 3*l* and 4*l* , are directly controlled by rotating the winch to reel the cable in or let it out, therefore, it is desirable to regard the cable lengths as the variables. By substituting the forward kinematic equations (2) into the kinetic energy and potential energy shown in Eqs. (4) and (5), respectively, the Lagrange's Equation can be written in the following form

$$\frac{d}{dt}(\frac{\partial K}{\partial \dot{q}\_i}) - \frac{\partial K}{\partial q\_i} + \frac{\partial P}{\partial q\_i} = Q\_i \tag{6}$$

where and the variables, *<sup>i</sup> q* (for *i* 1,2,3,4 ), the generalized forces, *Qi* , respectively, can be expressed as

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 65

In which, 1234 [ ]*<sup>T</sup> T T T T T* ; *ir* is the radius of the windlass, (for 1,2,3,4 *<sup>i</sup>* ). For more

The nominal model of CRCM including servomechanism dynamics is described by the

<sup>2</sup> ( )

*d d nKU K J dt dt*

It is also well known that there is a dual relation between externally applied wrench on the end-effector and the cable tensions required to keep the system in equilibrium. The above dynamic model is valid only for 0 *Ti* , i.e., the cables are in tension. Clearly, the equation (12) is a non-homogeneous linear quaternary equations. The solution of the equations will be multiple. For the sake of this, the suitable solution is found through MATLAB software

In general, a fuzzy logic system consists of four parts: the knowledge base, the fuzzifier, the fuzzy inference engine, and the defuzzifier. There are many different choices for the design of fuzzy system if the mapping is static. In this study, we consider a MIMO fuzzy logic system (Liu, 2008; Yoo & Ham, 2000). Supposing the fuzzy logic system performs a mapping

fuzzy knowledge base consists of a collection of fuzzy IF–THEN rules in the following form

*T*

fuzzy system, respectively, *<sup>l</sup> Fi* and *<sup>l</sup> Cj* (for 1,2, , *l M* ) are linguistic variables, and *M* is the number of fuzzy rules. Based on the fuzzy inference engine working on fuzzy rules, the

The output of the fuzzy control system with singleton fuzzifier, product inference engine,

1 1

*<sup>M</sup> <sup>n</sup> <sup>l</sup>*

*l i j M n*

*l i*

1 1

*<sup>m</sup> VV V R <sup>m</sup>* , *V R <sup>j</sup>* (for *j m* 1,2, , ). For a MIMO system, the

*<sup>l</sup> F* and...and *<sup>n</sup> x* is *<sup>l</sup> Fn*

( )

( )

*x*

*l i*

*F i*

*l i*

*i j F*

*y x*

*d bi*

*mi mi*

2

 

(12)

*<sup>n</sup> UU U R <sup>n</sup>* , *U R <sup>i</sup>* (for

(14)

*<sup>l</sup> <sup>C</sup>* and...and *ym* is *<sup>l</sup> Cm* (13)

*yy y* , *<sup>m</sup> V* are the input and output vectors of the

*mi mi*

details on the specification of the drive transmission system, refer to (Zi et al., 2009).

2 2

*d d KU J K dt dt*

*bi i U C ni*

() (,)

*Dqq Cqq*

from fuzzy sets in *<sup>n</sup> U R* to fuzzy sets in *<sup>m</sup> V R* , where 1

( )*<sup>l</sup> <sup>R</sup>* : IF 1 *<sup>x</sup>* is 1

center average defuzzifier is in the following form (Yoo & Ham, 2000)

*y*

*U C mi*

 

based on the pseudo-inverse method.

THEN 1 *y* is 1

*<sup>n</sup> xx x U* , and <sup>1</sup>

defuzzifier maps fuzzy sets in *U* to a crisp point in *V* .

*T*

**4. Adaptive fuzzy control** 

*i n* 1,2, , ), 1

where <sup>1</sup>

following formulation

$$q\_i = \begin{bmatrix} l\_1 \ l\_2 \ l\_3 \ l\_4 \end{bmatrix}^T \tag{7}$$

$$Q\_i = \left[ -\tau\_1 \left\langle r\_1 - \tau\_2 \left\langle r\_2 - \tau\_3 \right\rangle r\_3 - \tau\_4 \left\langle r\_4 \right\rangle \right]^\dagger \tag{8}$$

The windlass torques, 1 , <sup>2</sup> , <sup>3</sup> and 4 , are the control inputs 1*r* , <sup>2</sup>*r* , <sup>3</sup>*r* and 4*r* , is the radius of the windlass.

Given the equations of motion shown above, using the assumptions along with various substitutions and algebraic manipulations of the CRCM derived, the dynamic equation of the CRCM can be expressed as

$$D(q)\ddot{q} + C(q, \dot{q}) + \tau\_d = \sigma \tag{9}$$

where 4 4 *D q*( ) is the inertia matrix which is symmetric positive define, <sup>4</sup> *Cqq* (,) is a nonlinear Coriolis/centripetal/gravity vector terms, <sup>4</sup> *d* represents the disturbance which is bounded, and <sup>4</sup> is the input torque vector with <sup>1234</sup> *T* . The 4x4 matrix *D q*( ) and the 4x1 vector *Cqq* (,) will be referred to as *D* and *C* respectively. The details of these expressions will be omitted for the sake of brevity.

The dynamic model is presented in two parts: one is directed to the structural model (CRCM) above and the other is related to the actuator dynamics (servo mechanism). We have already developed mechanics equations of the drive transmission system (Zi et al., 2009), and briefly outline here. The extendable actuator of each subsystem of the CRCM system is comprised of an alternating current (AC) servomotor & drive unit, belt pulley drive mechanism, two-level cycloid-gear speed reducer, and windlass. To simplify matters, here without regard to the belt pulley drive mechanism, the next step servomechanism model is developed. Without going into details, the servomechanism dynamic model is briefly described by the following formulation,

$$\begin{cases} \mathcal{K}\_{lI} \mathcal{U}\_{\mathcal{C}} = \mathcal{J}\_{mi} \frac{d^2 \theta\_{mi}}{dt^2} + \mathcal{K}\_{oo} \frac{d \theta\_{mi}}{dt} \\\\ \tau\_{hi} = n\_i (\mathcal{K}\_{lI} \mathcal{U}\_{\mathcal{C}} - \mathcal{K}\_{oo} \frac{d \theta\_{mi}}{dt} - \mathcal{J}\_{mi} \frac{d^2 \theta\_{mi}}{dt^2}) \end{cases} \tag{10}$$

where *bi* (for 1,2,3,4 *i* ) is the torque of the windlass; *ni* is the gear ratio; *UC* is control voltage ; *UC* and *Kw* are positive constant, respectively; *mi J* denotes the moment of inertia of the motor; *ni J* is the equivalent moment of inertia including motor, speed reducer, flywheel and windlass, and *mi* is the rotor angular position.

The driving force of cable *Ti* (for 1,2,3,4 *i* ) can be expressed as

$$\begin{cases} K\_{lI} \mathbf{U}\_{\gets} = \mathbf{J}\_{mi} \frac{d^2 \theta\_{mi}}{dt^2} + \mathbf{K}\_{oo} \frac{d \theta\_{mi}}{dt} \\\\ T\_i = \frac{\mathbf{r}\_{bi}}{r\_i} = \frac{n\_i}{r\_i} (\mathbf{K}\_{lI} \mathbf{U}\_{\gets} - \mathbf{K}\_{oo} \frac{d \theta\_{mi}}{dt} - \mathbf{J}\_{mi} \frac{d^2 \theta\_{mi}}{dt^2}) \end{cases} \tag{11}$$

In which, 1234 [ ]*<sup>T</sup> T T T T T* ; *ir* is the radius of the windlass, (for 1,2,3,4 *<sup>i</sup>* ). For more details on the specification of the drive transmission system, refer to (Zi et al., 2009).

The nominal model of CRCM including servomechanism dynamics is described by the following formulation

$$\begin{cases} \mathcal{K}\_{\rm l} \mathcal{U}\_{\rm C} = J\_{mi} \frac{d^2 \theta\_{mi}}{dt^2} + \mathcal{K}\_{oo} \frac{d \theta\_{mi}}{dt} \\\\ \boldsymbol{\tau}\_{hi} = n\_i (\mathcal{K}\_{\rm l} \mathcal{U}\_{\rm C} - \mathcal{K}\_{oo} \frac{d \theta\_{mi}}{dt} - \mathcal{J}\_{mi} \frac{d^2 \theta\_{mi}}{dt^2}) \\\\ D(q)\ddot{q} + \mathcal{C}(q\_{\prime} \dot{q}) + \boldsymbol{\tau}\_{d} = \boldsymbol{\tau}\_{hi} \end{cases} \tag{12}$$

It is also well known that there is a dual relation between externally applied wrench on the end-effector and the cable tensions required to keep the system in equilibrium. The above dynamic model is valid only for 0 *Ti* , i.e., the cables are in tension. Clearly, the equation (12) is a non-homogeneous linear quaternary equations. The solution of the equations will be multiple. For the sake of this, the suitable solution is found through MATLAB software based on the pseudo-inverse method.

#### **4. Adaptive fuzzy control**

64 Fuzzy Logic – Controls, Concepts, Theories and Applications

<sup>1234</sup>

 11 22 33 44 *<sup>T</sup> Q rrrr <sup>i</sup>* 

Given the equations of motion shown above, using the assumptions along with various substitutions and algebraic manipulations of the CRCM derived, the dynamic equation of

() (,) *Dqq Cqq <sup>d</sup>*

where 4 4 *D q*( ) is the inertia matrix which is symmetric positive define, <sup>4</sup> *Cqq* (,) is a

matrix *D q*( ) and the 4x1 vector *Cqq* (,) will be referred to as *D* and *C* respectively. The

The dynamic model is presented in two parts: one is directed to the structural model (CRCM) above and the other is related to the actuator dynamics (servo mechanism). We have already developed mechanics equations of the drive transmission system (Zi et al., 2009), and briefly outline here. The extendable actuator of each subsystem of the CRCM system is comprised of an alternating current (AC) servomotor & drive unit, belt pulley drive mechanism, two-level cycloid-gear speed reducer, and windlass. To simplify matters, here without regard to the belt pulley drive mechanism, the next step servomechanism model is developed. Without going into details, the servomechanism dynamic model is

> 2 2

*d d KU J K dt dt*

2 2

*d d KU J K dt dt*

*bi i U C ni*

*U C mi*

<sup>2</sup> ( )

*d d nKU K J dt dt*

where *bi* (for 1,2,3,4 *i* ) is the torque of the windlass; *ni* is the gear ratio; *UC* is control voltage ; *UC* and *Kw* are positive constant, respectively; *mi J* denotes the moment of inertia of the motor; *ni J* is the equivalent moment of inertia including motor, speed reducer,

*mi* is the rotor angular position.

*i U C ni*

*n dd T KU K J r r dt dt*

*mi mi*

*bi i mi mi*

 

*mi mi*

 

<sup>2</sup> ( )

which is bounded, and <sup>4</sup> is the input torque vector with <sup>1234</sup>

*d* 

2

 

2

 

*mi mi*

The windlass torques, 1

the CRCM can be expressed as

of the windlass.

 , <sup>2</sup> , <sup>3</sup> and 4 

briefly described by the following formulation,

flywheel and windlass, and

The driving force of cable *Ti* (for 1,2,3,4 *i* ) can be expressed as

*U C mi*

*i i*

nonlinear Coriolis/centripetal/gravity vector terms, <sup>4</sup>

details of these expressions will be omitted for the sake of brevity.

*T*

*<sup>i</sup> q llll* (7)

, are the control inputs 1*r* , <sup>2</sup>*r* , <sup>3</sup>*r* and 4*r* , is the radius

(8)

(9)

represents the disturbance

 *T*

(10)

(11)

. The 4x4

In general, a fuzzy logic system consists of four parts: the knowledge base, the fuzzifier, the fuzzy inference engine, and the defuzzifier. There are many different choices for the design of fuzzy system if the mapping is static. In this study, we consider a MIMO fuzzy logic system (Liu, 2008; Yoo & Ham, 2000). Supposing the fuzzy logic system performs a mapping from fuzzy sets in *<sup>n</sup> U R* to fuzzy sets in *<sup>m</sup> V R* , where 1 *<sup>n</sup> UU U R <sup>n</sup>* , *U R <sup>i</sup>* (for *i n* 1,2, , ), 1 *<sup>m</sup> VV V R <sup>m</sup>* , *V R <sup>j</sup>* (for *j m* 1,2, , ). For a MIMO system, the fuzzy knowledge base consists of a collection of fuzzy IF–THEN rules in the following form

$$\mathcal{R}^{(l)}: \text{IF } \mathbf{x}\_1 \text{ is } F\_1^l \text{ and...and } \mathbf{x}\_n \text{ is } F\_n^l$$

$$\text{THEN } y\_1 \text{ is } \mathbb{C}\_1^{(l)} \text{ and...and } y\_m \text{ is } \mathbb{C}\_m^{(l)} \tag{13}$$

where <sup>1</sup> *T <sup>n</sup> xx x U* , and <sup>1</sup> *T yy y* , *<sup>m</sup> V* are the input and output vectors of the fuzzy system, respectively, *<sup>l</sup> Fi* and *<sup>l</sup> Cj* (for 1,2, , *l M* ) are linguistic variables, and *M* is the number of fuzzy rules. Based on the fuzzy inference engine working on fuzzy rules, the defuzzifier maps fuzzy sets in *U* to a crisp point in *V* .

The output of the fuzzy control system with singleton fuzzifier, product inference engine, center average defuzzifier is in the following form (Yoo & Ham, 2000)

$$\begin{aligned} \boldsymbol{y}\_{j} &= \frac{\sum\_{l=1}^{M} \overline{\boldsymbol{y}}\_{j}^{l} \left( \prod\_{i=1}^{n} \mu\_{\boldsymbol{F}\_{i}^{l}} (\boldsymbol{x}\_{i}) \right)}{\sum\_{l=1}^{M} \left( \prod\_{i=1}^{n} \mu\_{\boldsymbol{F}\_{i}^{l}} (\boldsymbol{x}\_{i}) \right)} \end{aligned} \tag{14}$$

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 67

1

*i ii*

4

*r d i ii i*

1

 (22)

4

*r i ii i*

1

(24)

*D q q C q q Fi D q q K s* (25)

 

1

*T T T T*

 

4

*Fqq*, can be written as

(26)

 (23)

*<sup>n</sup> T T*

*i*

where \* *iii* , *i* (for *i*=1, 2, 3, 4) is the parameter vector, \* *<sup>i</sup>* is the ideal parameter,

*T T*

is nonlinear function. Since the disturbance is related to the position and velocity

*T T*

It is considered that the fuzzy logic compensation control is to approach just for the external

 <sup>ˆ</sup> , , *<sup>T</sup> <sup>F</sup> <sup>i</sup> qq qq* 

<sup>ˆ</sup> () (,) ,

1

4

<sup>ˆ</sup> , , <sup>ˆ</sup> , <sup>ˆ</sup> , ,

*F qq q q Fqq*

2 2 3 3

<sup>ˆ</sup> , ,

*F qq q q*

, <sup>ˆ</sup> ,

*F qq q q q q F qq*

disturbance, and the fuzzy logic system *Fqq* , for the CRCM system is defined as

 

To prove the negative definition of ( ) *V t* , the time derivative of (21) is given as follows

can be written in the form of *Fqq* (,) . Hence, Eq. (22) can be rewritten as

*V t s Dq C F*

*q q*, is fuzzy basis function (for *i*=1,2,3,4).

From the previous results, the control law is given as follows

where *K diag K D i* ( ) , 0 *Ki* (for *<sup>i</sup>* 1,2,3,4 ), and <sup>ˆ</sup>

*V t s Dq C*

 

*<sup>r</sup> sqq* (20)

(21)

Then Eq. (18) can be rewritten as

where *<sup>d</sup>* 

signal, *<sup>d</sup>* 

where 

Let us consider the Lyapunov function candidate

and *i* is a positive definite diagonal matrix.

1 2

*V t s Ds*

where *<sup>l</sup> <sup>j</sup> y R* (for *j m* 1,2, , ) is a criop value at which the membership function *<sup>l</sup> <sup>C</sup>* for output fuzzy set reaches its maximum,and *<sup>l</sup>* ( ) *<sup>i</sup> <sup>F</sup> <sup>i</sup> x* is the membership function of the linguistic variable *<sup>i</sup> x* , defined as

$$\mu\_{F\_i^l}(\mathbf{x}\_i) = \exp\left[-\frac{(\mathbf{x}\_i - \overline{\mathbf{x}\_i^l})^2}{\sigma^2}\right] \tag{15}$$

where *<sup>l</sup> <sup>i</sup> x* and are respectively, the mean and the deviation of the Gaussian membership function. The fuzzy control system inputs are composed of the five linguistic terms: NB (Negative Big), NO (Negative Medium), SS (Zero), PO (Positive Medium), and PB (Positive Big).

As the fixed nonlinear mapping in the hidden layer, ( ) *x* is defined as

$$\sigma\_l(\mathbf{x}) = \frac{\prod\_{i=1}^n \mu\_{\mathbf{f}\_i^l}(\mathbf{x}\_i)}{\sum\_{l=1}^M \left(\prod\_{i=1}^n \mu\_{\mathbf{f}\_i^l}(\mathbf{x}\_i)\right)} \tag{16}$$

In order to maintain the consistent performance of the fuzzy control system in situations where there is uncertainty variation, the fuzzy control system should be adaptive. Therefore, (14) can be rewritten as

$$y\_j = \Theta\_j^T \varepsilon(\mathbf{x}) \tag{17}$$

where <sup>1</sup> ( ) ( ), , ( ) *<sup>T</sup> <sup>M</sup> x x xR <sup>M</sup>* is the fuzzy antecedent function vector, and 1 , , *<sup>T</sup> <sup>M</sup> <sup>M</sup> <sup>j</sup> j j yy R* is the center of the fuzzy subset *Cj* .

In the following analysis, it will be assumed that the dynamic model of the robot manipulator to be controlled is well known, and all the state variables can be measurable. The control system requirements for the CRCM are similar to those of almost all manipulators. In order to follow the desired continuously differentiable and uniformly bounded trajectory *<sup>d</sup> q* and keep the tracking error ( ) *<sup>d</sup> et q q* approach zero, a sliding surface, *s*, is defined in the stable state space (Liu, 2008). The most common sliding surface is chosen as follows

$$s = \dot{e} + \mathcal{A}e\tag{18}$$

where is a positive definite design parameter matrix.

Now introduce the variable *<sup>r</sup> q* , and define

$$
\dot{q}\_r(t) = \dot{q}\_d(t) - \lambda e(t) \tag{19}
$$

Then Eq. (18) can be rewritten as

66 Fuzzy Logic – Controls, Concepts, Theories and Applications

*<sup>j</sup> y R* (for *j m* 1,2, , ) is a criop value at which the membership function *<sup>l</sup> <sup>C</sup>*

*<sup>l</sup>* ( ) exp

*i*

*x*

*F i*

( )

*x*

*<sup>i</sup> <sup>F</sup> <sup>i</sup>* 

*x x*

function. The fuzzy control system inputs are composed of the five linguistic terms: NB (Negative Big), NO (Negative Medium), SS (Zero), PO (Positive Medium), and PB (Positive

1

*i l M n*

*n*

1 1

In order to maintain the consistent performance of the fuzzy control system in situations where there is uncertainty variation, the fuzzy control system should be adaptive. Therefore,

*l i*

*j j y* 

In the following analysis, it will be assumed that the dynamic model of the robot manipulator to be controlled is well known, and all the state variables can be measurable. The control system requirements for the CRCM are similar to those of almost all manipulators. In order to follow the desired continuously differentiable and uniformly bounded trajectory *<sup>d</sup> q* and keep the tracking error ( ) *<sup>d</sup> et q q* approach zero, a sliding surface, *s*, is defined in the stable state space (Liu, 2008). The most common sliding surface

> *se e*

*q t q t et r d*

2 2 ( )

*l i i*

are respectively, the mean and the deviation of the Gaussian membership

( )

*x*

*l i*

( ) *<sup>T</sup>*

*x x xR <sup>M</sup>* is the fuzzy antecedent function vector, and

 

*F i*

( )

*x*

*l i*

*F i*

( ) *x* is defined as

output fuzzy set reaches its maximum,and *<sup>l</sup>* ( )

As the fixed nonlinear mapping in the hidden layer,

linguistic variable *<sup>i</sup> x* , defined as

*x* is the membership function of the

(15)

(16)

*x* (17)

(18)

(19)

for

where *<sup>l</sup>*

where *<sup>l</sup>*

Big).

*<sup>i</sup> x* and

(14) can be rewritten as

1 , ,

is chosen as follows

where

where <sup>1</sup> ( ) ( ), , ( ) *<sup>T</sup> <sup>M</sup>*

*<sup>T</sup> <sup>M</sup> <sup>M</sup>*

Now introduce the variable *<sup>r</sup> q* , and define

 

*<sup>j</sup> j j yy R* is the center of the fuzzy subset *Cj* .

is a positive definite design parameter matrix.

$$s = \dot{q} - \dot{q}\_r \tag{20}$$

Let us consider the Lyapunov function candidate

$$V(t) = \frac{1}{2} \left( \mathbf{s}^T D \mathbf{s} + \sum\_{i=1}^n \tilde{\Theta}\_i^T \Gamma\_i \tilde{\Theta}\_i \right) \tag{21}$$

where \* *iii* , *i* (for *i*=1, 2, 3, 4) is the parameter vector, \* *<sup>i</sup>* is the ideal parameter, and *i* is a positive definite diagonal matrix.

To prove the negative definition of ( ) *V t* , the time derivative of (21) is given as follows

$$\dot{V}\left(t\right) = -\mathbf{s}^{T}\left(D\ddot{\boldsymbol{q}}\_{r} + \mathbf{C} + \boldsymbol{\tau}\_{d} - \boldsymbol{\tau}\right) + \sum\_{i=1}^{4} \tilde{\Theta}\_{i}^{T} \Gamma\_{i} \dot{\tilde{\Theta}}\_{i} \tag{22}$$

where *<sup>d</sup>* is nonlinear function. Since the disturbance is related to the position and velocity signal, *<sup>d</sup>* can be written in the form of *Fqq* (,) . Hence, Eq. (22) can be rewritten as

$$\dot{V}\left(t\right) = -\mathbf{s}^{T}\left(D\ddot{\boldsymbol{\eta}}\_{r} + \mathbf{C} + F - \tau\right) + \sum\_{i=1}^{4} \tilde{\Theta}\_{i}^{T} \Gamma\_{i} \dot{\tilde{\Theta}}\_{i} \tag{23}$$

It is considered that the fuzzy logic compensation control is to approach just for the external disturbance, and the fuzzy logic system *Fqq* , for the CRCM system is defined as

$$\hat{F}\left(q,\dot{q}\middle|\tilde{\Theta}\right) = \Theta\_i^T \varepsilon\left(q,\dot{q}\right) \tag{24}$$

where *q q*, is fuzzy basis function (for *i*=1,2,3,4).

From the previous results, the control law is given as follows

$$\tau = D(q)\ddot{q} + \mathcal{C}(q, \dot{q})\hat{F}\_i\left(q, \dot{q} \middle| \tilde{\Theta}\right) - K\_D s \tag{25}$$

where *K diag K D i* ( ) , 0 *Ki* (for *<sup>i</sup>* 1,2,3,4 ), and <sup>ˆ</sup> *Fqq*, can be written as

$$
\hat{F}(\boldsymbol{q},\dot{\boldsymbol{q}}|\boldsymbol{\Theta}) = \begin{bmatrix}
\hat{F}\_1(\boldsymbol{q},\dot{\boldsymbol{q}}|\boldsymbol{\Theta}) \\
\hat{F}\_2(\boldsymbol{q},\dot{\boldsymbol{q}}|\boldsymbol{\Theta}) \\
\hat{F}\_3(\boldsymbol{q},\dot{\boldsymbol{q}}|\boldsymbol{\Theta}) \\
\hat{F}\_4(\boldsymbol{q},\dot{\boldsymbol{q}}|\boldsymbol{\Theta})
\end{bmatrix} = \begin{bmatrix}
\Theta\_1^T \mathcal{E}(\boldsymbol{q},\dot{\boldsymbol{q}}) \\
\Theta\_2^T \mathcal{E}(\boldsymbol{q},\dot{\boldsymbol{q}}) \\
\Theta\_3^T \mathcal{E}(\boldsymbol{q},\dot{\boldsymbol{q}}) \\
\Theta\_4^T \mathcal{E}(\boldsymbol{q},\dot{\boldsymbol{q}})
\end{bmatrix} \tag{26}
$$

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 69

*x t y t*

Fig. 5 displays the workspace of the end-effector of the CRCM. The spatial helical following trajectory and the spatial circle following trajectory of the end-effector are shown in Fig. 6

Fig. 7, Fig. 8, Fig. 10 and Fig. 11 show the changes in length and the tension of the cables in the two different trajectories tracking, respectively. As can be seen in Figs. 6-11, the above

0.2

0.2

Y coordinates (m) X coordinates (m)

X coordinates (m) Y coordinates (m)

0.4

0.6

0.8 1 0.2 0.4 0.6 0.8 1 1.2

0.4

0.6

0.8

1

0.2 0.05

*z t*

 

and Fig. 9, respectively.

Fig. 5. Workspace of the end-effector.

Z coordinates (m) Z coordinates (m)

Fig. 6. Following trajectory of the end-effector.

0.5 0.3cos(0.1 ) 0.5 0.3sin(0.1 )

(32)

The fuzzy approximation error is defined as

$$w = F(q, \dot{q}) - \hat{F}(q, \dot{q} \vert \tilde{\Theta}) \tag{27}$$

Substituting Eqs. (25)-(27) into Eq. (23), the following equation can be derived

$$\begin{split} \dot{V}\left(t\right) &= -\boldsymbol{s}^{T} \left(D\ddot{\boldsymbol{q}}\_{r} + \boldsymbol{C} + \boldsymbol{F} - \boldsymbol{\tau}\right) + \sum\_{i=1}^{4} \tilde{\Theta}\_{i}^{T} \Gamma\_{i} \dot{\tilde{\Theta}}\_{i} \\ &= -\boldsymbol{s}^{T} \left(\Theta\_{i}^{T} \boldsymbol{\varepsilon}\left(\boldsymbol{q}, \dot{\boldsymbol{q}}\right) + \boldsymbol{w} + \boldsymbol{K}\_{D} \boldsymbol{\dot{s}}\right) + \sum\_{i=1}^{4} \tilde{\Theta}\_{i}^{T} \Gamma\_{i} \dot{\tilde{\Theta}}\_{i} \\ &= -\boldsymbol{s}^{T} \boldsymbol{K}\_{D} \boldsymbol{s} - \boldsymbol{s}^{T} \boldsymbol{w} + \sum\_{i=1}^{4} \left(\tilde{\Theta}\_{i}^{T} \Gamma\_{i} \dot{\tilde{\Theta}}\_{i} - \boldsymbol{s}\_{i} \Theta\_{i}^{T} \boldsymbol{\varepsilon}\left(\boldsymbol{q}, \dot{\boldsymbol{q}}\right)\right) \end{split} \tag{28}$$

Then, the adaptive law is defined as

$$\dot{\Theta}\_i = -\Gamma\_i^{-1} s\_i \varepsilon(\boldsymbol{q}\_\prime \dot{\boldsymbol{q}}) \tag{29}$$

Since the minimum approximation error, *w* , can be sufficiently small through designing the fuzzzy logic system with enough rules, and satisfying <sup>4</sup> 1 , *T T i ii ii i s qq* =0. In addition, *KD* 0 . Consequently, we get

$$\dot{V}\{t\} - \mathbf{s}^T \mathbf{K}\_D \mathbf{s} - \mathbf{s}^T w < \mathbf{0} \tag{30}$$

Based on Lyapunov stability theory, and the result of Eq. (30), it is shown that the closedloop system is asymptotically stable, and the scheduled control object can be realized.

#### **5. Results and analysis**

In order to justify the dynamic modeling the CRCM, we performed a series of simulations. This section presents two motion cases of the end-effector for dynamic simulation. A simulation for the dynamic model of the CRCM was carried out by Matlab 7.0 software. Some parameters of the CRCM are given as follows: the height of the pillar is 2 m, Pillars *B*1~ *B*4 are distributed evenly on the vertices of a square, with the side length of 2 m, and the quality of the end-effector is 5 kg. The acceleration of gravity *g* is 9.8 <sup>2</sup> *m s* / .

The spatial circle trajectory can be expressed as

$$\begin{cases} x = 1 + 0.3 \times \cos(0.2\pi t) \\ y = 1.5 + 0.3 \times \sin(0.2\pi t) \\ z = 1 \end{cases} \tag{31}$$

And the spatial helical trajectory is as follows

$$\begin{cases} x = 0.5 + 0.3 \cos(0.1 \pi t) \\ y = 0.5 + 0.3 \sin(0.1 \pi t) \\ z = 0.2 + 0.05t \end{cases} \tag{32}$$

Fig. 5 displays the workspace of the end-effector of the CRCM. The spatial helical following trajectory and the spatial circle following trajectory of the end-effector are shown in Fig. 6 and Fig. 9, respectively.

Fig. 5. Workspace of the end-effector.

68 Fuzzy Logic – Controls, Concepts, Theories and Applications

Substituting Eqs. (25)-(27) into Eq. (23), the following equation can be derived

*V t s Dq C F*

,

*s qq w K s*

4

*T T T i D i ii*

*T T*

1

 <sup>1</sup> , *i iis qq* 

Since the minimum approximation error, *w* , can be sufficiently small through designing the

Based on Lyapunov stability theory, and the result of Eq. (30), it is shown that the closedloop system is asymptotically stable, and the scheduled control object can be realized.

In order to justify the dynamic modeling the CRCM, we performed a series of simulations. This section presents two motion cases of the end-effector for dynamic simulation. A simulation for the dynamic model of the CRCM was carried out by Matlab 7.0 software. Some parameters of the CRCM are given as follows: the height of the pillar is 2 m, Pillars *B*1~ *B*4 are distributed evenly on the vertices of a square, with the side length of 2 m, and the

> 1 0.3 cos(0.2 ) 1.5 0.3 sin(0.2 )

*x t y t*

quality of the end-effector is 5 kg. The acceleration of gravity *g* is 9.8 <sup>2</sup> *m s* / .

1

 

*z*

fuzzzy logic system with enough rules, and satisfying <sup>4</sup>

*TT T T D i ii ii i*

*sKs sw s qq*

<sup>ˆ</sup> *w Fqq Fqq* , , (27)

,

(29)

, *T T i ii ii*

*s qq* 

=0. In

(31)

1

( ) <sup>0</sup> *T T Vt sK s s w <sup>D</sup>* (30)

*i*

(28)

1

*i*

4

*r i ii i*

1 4

The fuzzy approximation error is defined as

Then, the adaptive law is defined as

addition, *KD* 0 . Consequently, we get

The spatial circle trajectory can be expressed as

And the spatial helical trajectory is as follows

**5. Results and analysis** 

Fig. 6. Following trajectory of the end-effector.

Fig. 7, Fig. 8, Fig. 10 and Fig. 11 show the changes in length and the tension of the cables in the two different trajectories tracking, respectively. As can be seen in Figs. 6-11, the above

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 71

0.8

0 2 4 6 8 10 12 14 16 18 20

Time (s)

1.3 1.4 1.5 1.6 1.7

Y coordinates (m) X coordinates (m)

1

1.2

Fig. 9. Following trajectory of the end-effector.

0.4 0.6 0.8 1 1.2 1.4 1.6

Z coordinates (m)

Fig. 10. Changes in tension of cable for the circle motion

5

10

15

20

Tension (N)

25

30

35

formulation tracks the planned trajectory relatively well. From the above simulation results, it can be concluded that the dynamic modeling is justified.

Fig. 7. Changes in length of cable for the helical motion.

Fig. 8. Changes in tension of cable for the helical motion.

Fig. 9. Following trajectory of the end-effector.

formulation tracks the planned trajectory relatively well. From the above simulation results,

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Time (s)

it can be concluded that the dynamic modeling is justified.

Fig. 7. Changes in length of cable for the helical motion.

1

1.2

1.4

1.6

1.8

Length (m)

2

2.2

2.4

2.6

2.8

Fig. 8. Changes in tension of cable for the helical motion.

0

5

10

15

20

Tension (N)

25

30

35

40

Fig. 10. Changes in tension of cable for the circle motion

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 73

0 0.5 1 1.5 2 2.5 3 3.5 4

*q* and *q* (m)

Fig. 12. Membership function of input variables.

0

0.2

0.4

Degree of membership

0.6

0.8

1

Fig. 13. Simulink model of the CRCM.

Fig. 11. Changes in length of cable for the circle motion.

In order to assess the performance of the adaptive fuzzy control system of the CRCM, simulations in spatial circle trajectory motion have been performed. The initial length configuration of the cables of the CRCM is given as *q*(0) [1.32 1.71 2.22 1.93]T, and the other consequent parameters areinitialized to zero. The nonlinearity *Fqq* (,) is estimated by using five Gaussian fuzzy sets for *q* and *q* , which is constructed, as shown in Fig 12. The disturbance vector is 15sin(20 ) 10sin(20 ) 10sin(20 ) 15sin(20 ) *<sup>T</sup> <sup>d</sup> tttt* . The design parameters of the controller are determined as 10 , 0.001 , *K I <sup>D</sup>* 250 , and *I* is a 4 4 matrix. The resulting fuzzy set must be converted to a signal that can be sent to the process as a control input. Based on S-Function, the Simulink model of the CRCM is shown in Fig 13.

Figs. 14 and 15 display the trajectory tracking of the end-effector of the CRCM, respectively. From Fig. 14, the above formulation tracks the planned trajectory relatively well. Figs. 16 and 17 illustrate the position trajectory and the position errors of the end-effector in x, y, z directions, respectively. The changes in length and the length trajectory tracking errors of the cables 1234 *llll* ,,, are shown in Fig. 18 and Fig. 19, respectively. In Figs. 16 and 18, the desired trajectory is indicated in a red solid line, and the actual output is in a blue dash line, and from Fig. 16 and Fig. 18, it can be seen that the actual and desired trajectories almost overlap each other.

Fig. 12. Membership function of input variables.

In order to assess the performance of the adaptive fuzzy control system of the CRCM, simulations in spatial circle trajectory motion have been performed. The initial length configuration of the cables of the CRCM is given as *q*(0) [1.32 1.71 2.22 1.93]T, and the other consequent parameters areinitialized to zero. The nonlinearity *Fqq* (,) is estimated by using five Gaussian fuzzy sets for *q* and *q* , which is constructed, as shown in Fig 12. The

0 2 4 6 8 10 12 14 16 18 20

Time (s)

4 4 matrix. The resulting fuzzy set must be converted to a signal that can be sent to the process as a control input. Based on S-Function, the Simulink model of the CRCM is shown

Figs. 14 and 15 display the trajectory tracking of the end-effector of the CRCM, respectively. From Fig. 14, the above formulation tracks the planned trajectory relatively well. Figs. 16 and 17 illustrate the position trajectory and the position errors of the end-effector in x, y, z directions, respectively. The changes in length and the length trajectory tracking errors of

desired trajectory is indicated in a red solid line, and the actual output is in a blue dash line, and from Fig. 16 and Fig. 18, it can be seen that the actual and desired trajectories almost

*llll* ,,, are shown in Fig. 18 and Fig. 19, respectively. In Figs. 16 and 18, the

*<sup>d</sup> tttt* . The design

, 0.001 , *K I <sup>D</sup>* 250 , and *I* is a

disturbance vector is 15sin(20 ) 10sin(20 ) 10sin(20 ) 15sin(20 ) *<sup>T</sup>*

Fig. 11. Changes in length of cable for the circle motion.

1.4

1.6

1.8

Length (m)

2

2.2

2.4

2.6

parameters of the controller are determined as 10

in Fig 13.

the cables 1234

overlap each other.

Fig. 13. Simulink model of the CRCM.

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 75

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

Time (s)

Time (s)

Fig. 16. Position trajectory of the end-effector in x, y and z directions

0.5

1

1

0.95


0.01


0.01


0

0

0.01

0

1.05

1.5

Position trajectory (m)

Position errors (m)

2

1

1.5

Fig. 17. Position errors of the end-effector in x, y and z directions.

robustness.

Fig. 20 displays the disturbance *<sup>d</sup>* and its compensator, and the control input torques of the windlass are shown in Fig. 21. From the simulation results, it may be concluded that the adaptive fuzzy control strategy can achieve a favourable control performance and has high

Fig. 14. Following trajectory of the end-effector.

Fig. 15. Following trajectory of the end-effector

0.8

1.2

Y coordinates (m) X coordinates (m)

X coordinates (m)

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

1.4

1.6

1

1.2

1.4

Fig. 14. Following trajectory of the end-effector.

1.8 0.9

0.95

Z coordinates (m)

1

1.05

1.1

Fig. 15. Following trajectory of the end-effector

1.1

1.2

1.3

1.4

1.5

Y coordinates (m)

1.6

1.7

1.8

1.9

Fig. 16. Position trajectory of the end-effector in x, y and z directions

Fig. 20 displays the disturbance *<sup>d</sup>* and its compensator, and the control input torques of the windlass are shown in Fig. 21. From the simulation results, it may be concluded that the adaptive fuzzy control strategy can achieve a favourable control performance and has high robustness.

Fig. 17. Position errors of the end-effector in x, y and z directions.

Fuzzy Control System Design and Analysis for Completely Restrained Cable-Driven Manipulators 77

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

Time (s)

Fig. 20. The disturbance *<sup>d</sup>* and its compensator.



Disturbance and compe

nsator


(Nm)




Control input torques


(Nm)


Fig. 21. The control input torques of the windlass 1234 ,,,

Cable parallel manipulators are a class of robotic mechanisms whose simplicity of design, light weight and ability to support large loads make them useful in many industrial and military settings. This chapter presented in detail a 3-DOF, 4-cable CRCM for its adaptive

Time (s)

0 1 2 3 4 5 6 7 8 9 10

**6. Conclusion** 

Fig. 18. Length tracking of the cables 1234 *llll* ,,,

Fig. 19. Length tracking errors of the cables 1234 *llll* ,,,

Fig. 20. The disturbance *<sup>d</sup>* and its compensator.

Fig. 21. The control input torques of the windlass 1234 ,,,

## **6. Conclusion**

76 Fuzzy Logic – Controls, Concepts, Theories and Applications

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

Time (s)

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

Time (s)

*llll* ,,,

*llll* ,,,

Fig. 18. Length tracking of the cables 1234



Length tracking errors


(m)


1 1.5 2

1 1.5 2

Length tracking (m)

1.5 2 2.5

1.5 2 2.5

Fig. 19. Length tracking errors of the cables 1234

Cable parallel manipulators are a class of robotic mechanisms whose simplicity of design, light weight and ability to support large loads make them useful in many industrial and military settings. This chapter presented in detail a 3-DOF, 4-cable CRCM for its adaptive

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fuzzy control system design and analysis. The mechanical system is designed, and the dynamic formulation of the electromechanical coupling system for the CRCM is studied on the basis of the Lagrange's Equation and equivalent circuit of the servo mechanism, and the inverse kinematic problem and inverse dynamics problem of the CRCM system is resolved on condition that operation path of the end-effector has been planned. Computational examples are provided to demonstrate the validity of the model developed. In addition, according to the established dynamic equation of the CRCM, an adaptive fuzzy control system is designed to track a given trajectory. Based on Lyapunov stability analysis, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the satisfactory performance of the adaptive fuzzy control system. This will make the CRCM used in the more precision production field such as part assembly. Future work will be devoted to the experimental validation of the control system.

#### **7. Acknowledgements**

This work was supported by the National Natural Science Foundation of China (50905179) and the Visiting Scholar Foundation of Key Lab in University (GZKF-201112).

#### **8. References**


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**5** 

 *Spain* 

**Control and Estimation of Asynchronous** 

In the conventional design of controllers, the first step is to obtain the model of the plant. With the plant model, the controller is designed considering aspects such as stability, dynamic response behaviour, performance against disturbances, etc. This type of controller

An asynchronous machine is normally controlled using traditional PI or PID controllers. In practice these conventional controllers are often developed via crude system models that satisfy basic and necessary assumptions before being tuned by using established methods. These techniques are traditionally solved using a mathematical model of the machine with fixed parameters. However, in a real machine, the stator and rotor resistances are altered by temperature and the inductances are altered by the magnetizing current values that change for example when the machine is running in the flux weakening region or by an improper detuning between the flux and torque producing currents. For these reasons, the induction machine shows properties of nonlinear and time-varying systems. Parameter variations degrade the system performance over the full range of motor operation and in extreme conditions this can lead to instability (Vas, 1999). To solve this problem the controller parameters have to be continuously adapted. This adaptation can be achieved using different techniques such as MRAC or model reference adaptive control (Zhen & Xu, 1998), sliding mode (Won & Bose, 1992), or self tuning PIDs (Astrom & Hagglung, 1996). For some of these techniques the motor parameters and load inertia must be calculated in real time, so

In the model-based controller design process, heuristics also enters into the implementation and tuning of the final design. Consequently, successful controller design can in part be attributable to the clever heuristic tuning of a control engineer. An advantage of fuzzy control is that it provides a method of manipulating and implementing a human's heuristic

Because the fuzzy logic approach is based on linguistic rules, the controller design does not need to use any machine parameters to make a controller adjustment, so the controller

**1. Introduction** 

design is called model-based design.

there is a high processing requirement for the used processors.

knowledge to control such a system (Zadeh, 1965).

robustness is high (Li, 1998).

**Machines Using Fuzzy Logic** 

José Antonio Cortajarena, Julián De Marcos,

 *University of the Basque Country (EUITI Eibar),* 

Fco. Javier Vicandi, Pedro Alvarez and Patxi Alkorta


## **Control and Estimation of Asynchronous Machines Using Fuzzy Logic**

José Antonio Cortajarena, Julián De Marcos, Fco. Javier Vicandi, Pedro Alvarez and Patxi Alkorta  *University of the Basque Country (EUITI Eibar), Spain* 

## **1. Introduction**

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In the conventional design of controllers, the first step is to obtain the model of the plant. With the plant model, the controller is designed considering aspects such as stability, dynamic response behaviour, performance against disturbances, etc. This type of controller design is called model-based design.

An asynchronous machine is normally controlled using traditional PI or PID controllers. In practice these conventional controllers are often developed via crude system models that satisfy basic and necessary assumptions before being tuned by using established methods.

These techniques are traditionally solved using a mathematical model of the machine with fixed parameters. However, in a real machine, the stator and rotor resistances are altered by temperature and the inductances are altered by the magnetizing current values that change for example when the machine is running in the flux weakening region or by an improper detuning between the flux and torque producing currents. For these reasons, the induction machine shows properties of nonlinear and time-varying systems. Parameter variations degrade the system performance over the full range of motor operation and in extreme conditions this can lead to instability (Vas, 1999). To solve this problem the controller parameters have to be continuously adapted. This adaptation can be achieved using different techniques such as MRAC or model reference adaptive control (Zhen & Xu, 1998), sliding mode (Won & Bose, 1992), or self tuning PIDs (Astrom & Hagglung, 1996). For some of these techniques the motor parameters and load inertia must be calculated in real time, so there is a high processing requirement for the used processors.

In the model-based controller design process, heuristics also enters into the implementation and tuning of the final design. Consequently, successful controller design can in part be attributable to the clever heuristic tuning of a control engineer. An advantage of fuzzy control is that it provides a method of manipulating and implementing a human's heuristic knowledge to control such a system (Zadeh, 1965).

Because the fuzzy logic approach is based on linguistic rules, the controller design does not need to use any machine parameters to make a controller adjustment, so the controller robustness is high (Li, 1998).

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 83

The proposed controller is a hybrid controller with a fuzzy proportional-integral controller

GCU

cu2 CU2

The proportional gain KP makes the fast corrections when a sudden change occurs in the input e. To eliminate the stationary error an integral action is necessary, so a fuzzy PI is included in the controller. If the error is large and the controller tries to obtain a larger output value than the limits, the integral action will remain in pause until the correction level drops below the saturation level. So, as the error becomes smaller the integral action gains in importance as does the proportional action of the fuzzy PI controller. This second proportional action is used for fine tuning and to correct the response to sudden reference

Where, *GE* , *GCE* and *GCU* are the scaling factors of the error, change of error and output, used to tuning the response of the controller (Patel, 2005). *E*<sup>2</sup> (error) and *CE*<sup>2</sup> (change of error) are the inputs of the fuzzy controller, an 2 *cu* (control action) is its output. Because the inputs of the fuzzy controller are the error and change of error it is useful to configure it as an incremental controller. This incremental controller adds a change to the current control

> <sup>1</sup> 2*n nn n Ts U Kp e e e Ti*

Where, *Kp* is the proportional gain and *Ts* and *Ti* the sample or control period and the

It is an advantage that the controller output 2 *CU <sup>n</sup>* is driven directly from an integrator, as it is then is easier to deal with windup and noise (Jantzen, 1998). The fuzzy PI controller

output, 2 *U* , is called the change in output, and 2 *U <sup>n</sup>* is defined by,

0

2 2 22 *E GE e CE GCE ce CU GCU cu* , , (7)

<sup>1</sup> 22 2 *UU U nn n* (8)

(9)

1 *p*

+ +

*LIMH*

*LIML*

OUT

U2

and a proportional term (FPI+P). The full controller structure is shown in figure 1.

KP

**3. Fuzzy controller** 

*d dt*

signal of 2 *U <sup>n</sup>* .

integral time.

GE GCE

Fig. 1. Hybrid fuzzy controller structure

changes, helping to the proportional controller.

And the 2 *U <sup>n</sup>* value in a PI controller would be,

*E*<sup>2</sup> , *CE*<sup>2</sup> and 2 *cu* are defined according to figure 1 as,

ce CE2

E2

e U1

This chapter is composed of 5 sections. Section 2 begins with a mathematical description of the asynchronous machine. These equations are used to get the appropriate expressions and then use the adequate reference system to realize a good regulation of both asynchronous machines. Section 3 explains the used hybrid fuzzy controller. This hybrid controller will be used in all the applications and can be converted in a fuzzy controller cancelling the proportional term.

Section 4, explains the fuzzy control of the squirrel-cage motor using the indirect vector control strategy. Also, speed estimation for a sensorless control is implemented.

Section 5, explains the control strategy to control a double fed induction generator used mainly in wind turbines. Fuzzy control is implemented and tested in a real system.

Section 6, explains the fuzzy control robustness when the squirrel-cage motor is replaced for a new one with different parameters and when there is noise in the stator current measurement.

#### **2. Induction machine model**

The following equations describe the behaviour of the asynchronous machine in an arbitrary rotating reference frame.

$$
\overline{\boldsymbol{\sigma}}\_{s,dq} = \mathcal{R}\_s \overline{\boldsymbol{i}}\_{s,dq} + \frac{d\overline{\boldsymbol{\nu}}\_{s,dq}}{d\mathbf{t}} + jo\_c \overline{\boldsymbol{\nu}}\_{s,dq} \tag{1}
$$

$$
\overline{\boldsymbol{\sigma}}\_{r,d\boldsymbol{q}} = \mathcal{R}\_r \overline{\dot{\boldsymbol{i}}}\_{r,d\boldsymbol{q}} + \frac{d\overline{\boldsymbol{\nu}}\_{r,d\boldsymbol{q}}}{d\boldsymbol{t}} + j\left(\boldsymbol{\alpha}\_e - \boldsymbol{\alpha}\_r\right) \overline{\boldsymbol{\nu}}\_{r,d\boldsymbol{q}} \tag{2}
$$

$$
\Delta \overline{\varphi}\_{s,dq} = L\_s \overline{\mathbf{i}}\_{s,dq} + L\_m \overline{\mathbf{i}}\_{r,dq} \qquad \mathbf{and} \qquad L\_s \equiv L\_m + L\_{ls} \tag{3}
$$

$$\overline{\mathbf{u}}\_r \overline{\mathbf{v}}\_{r,dq} = \mathbf{L}\_r \overline{\dot{\mathbf{i}}}\_{r,dq} + \mathbf{L}\_m \overline{\dot{\mathbf{i}}}\_{s,dq} \qquad \mathbf{and} \qquad \mathbf{L}\_r \equiv \mathbf{L}\_m + \mathbf{L}\_{lr} \tag{4}$$

$$T\_c = \frac{3}{2} P \frac{L\_m}{L\_r} \left(\wp\_{rl} i\_{sq} - \wp\_{rq} i\_{sd}\right) \tag{5}$$

$$T\_e - T\_L = J \frac{d o o\_m}{dt} + B o\_m \tag{6}$$

Where dq are the axis of the arbitrary reference system. *s d*, *<sup>q</sup> v* , *s d*, *<sup>q</sup> i* and *s d*, *<sup>q</sup>* are the stator voltage, current and flux vectors. *r d*, *<sup>q</sup> v* , *r d*, *<sup>q</sup> i* and *r d*, *<sup>q</sup>* are the rotor voltage, current and flux vectors. *r* , *e* and*<sup>m</sup>* are the rotor electrical speed, arbitrary reference system speed, and rotor mechanical speed. *Lm* , *Ls* and *Lr* are the mutual, stator and rotor inductances. *Lls* and *Llr* are the stator and rotor leakage inductances. *Rs* and *Rr* are the stator and rotor resistances. *Te* and *TL* are the motor and load torque. *J* and *B* are the inertia of the system and friction coefficient. <sup>2</sup> 1 *L LL m rs* is the total leakage coefficient. P is the machine pole pares and *sl e r* is the slip speed.

## **3. Fuzzy controller**

82 Fuzzy Logic – Controls, Concepts, Theories and Applications

This chapter is composed of 5 sections. Section 2 begins with a mathematical description of the asynchronous machine. These equations are used to get the appropriate expressions and then use the adequate reference system to realize a good regulation of both asynchronous machines. Section 3 explains the used hybrid fuzzy controller. This hybrid controller will be used in all the applications and can be converted in a fuzzy controller cancelling the

Section 4, explains the fuzzy control of the squirrel-cage motor using the indirect vector

Section 5, explains the control strategy to control a double fed induction generator used

Section 6, explains the fuzzy control robustness when the squirrel-cage motor is replaced for a new one with different parameters and when there is noise in the stator current

The following equations describe the behaviour of the asynchronous machine in an arbitrary

, , , , *s dq s dq ssdq e sdq d v Ri <sup>j</sup> dt*

 

*s dq s s dq m r dq* ,, , *Li L i L L L*  **= and** *s m ls* (3)

*r dq r r dq m s dq* ,, , *Li L i L L L*  **= and** *r m lr* (4)

,

 

(1)

(2)

(5)

(6)

*r d*, *<sup>q</sup>* are the rotor voltage, current and flux

*s d*, *<sup>q</sup>* are the stator

, , , *r dq r dq rrdq e r rdq d v Ri <sup>j</sup> dt*

<sup>3</sup>

 

*<sup>m</sup>* are the rotor electrical speed, arbitrary reference system speed, and

1 *L LL m rs* is the total leakage coefficient. P is the machine

*<sup>m</sup> <sup>e</sup> rd sq rq sd r <sup>L</sup> TP i i*

> *<sup>m</sup> e L <sup>m</sup> <sup>d</sup> TT J B dt*

rotor mechanical speed. *Lm* , *Ls* and *Lr* are the mutual, stator and rotor inductances. *Lls* and *Llr* are the stator and rotor leakage inductances. *Rs* and *Rr* are the stator and rotor resistances. *Te* and *TL* are the motor and load torque. *J* and *B* are the inertia of the system

2

Where dq are the axis of the arbitrary reference system. *s d*, *<sup>q</sup> v* , *s d*, *<sup>q</sup> i* and

is the slip speed.

*<sup>L</sup>*

control strategy. Also, speed estimation for a sensorless control is implemented.

mainly in wind turbines. Fuzzy control is implemented and tested in a real system.

proportional term.

measurement.

vectors.

*r* , *e* and

pole pares and

**2. Induction machine model** 

voltage, current and flux vectors. *r d*, *<sup>q</sup> v* , *r d*, *<sup>q</sup> i* and

and friction coefficient. <sup>2</sup> 

> *sl e r*

rotating reference frame.

The proposed controller is a hybrid controller with a fuzzy proportional-integral controller and a proportional term (FPI+P). The full controller structure is shown in figure 1.

Fig. 1. Hybrid fuzzy controller structure

The proportional gain KP makes the fast corrections when a sudden change occurs in the input e. To eliminate the stationary error an integral action is necessary, so a fuzzy PI is included in the controller. If the error is large and the controller tries to obtain a larger output value than the limits, the integral action will remain in pause until the correction level drops below the saturation level. So, as the error becomes smaller the integral action gains in importance as does the proportional action of the fuzzy PI controller. This second proportional action is used for fine tuning and to correct the response to sudden reference changes, helping to the proportional controller.

*E*<sup>2</sup> , *CE*<sup>2</sup> and 2 *cu* are defined according to figure 1 as,

$$E\_2 = \text{GE-}e, \quad \text{CE}\_2 = \text{GCE-}\bullet e, \quad \text{CLI}\_2 = \text{GCLI}\bullet \text{cu}\_2 \tag{7}$$

Where, *GE* , *GCE* and *GCU* are the scaling factors of the error, change of error and output, used to tuning the response of the controller (Patel, 2005). *E*<sup>2</sup> (error) and *CE*<sup>2</sup> (change of error) are the inputs of the fuzzy controller, an 2 *cu* (control action) is its output. Because the inputs of the fuzzy controller are the error and change of error it is useful to configure it as an incremental controller. This incremental controller adds a change to the current control signal of 2 *U <sup>n</sup>* .

$$
\mathbb{U}\mathcal{D}\_n = \mathbb{U}\mathcal{D}\_{n-1} + \Delta\mathbb{U}\mathcal{D}\_n \tag{8}
$$

And the 2 *U <sup>n</sup>* value in a PI controller would be,

$$
\Delta UI2\_n = \text{Kp} \cdot \left( e\_n - e\_{n-1} + \frac{\text{Ts}}{T\text{i}} e\_n \right) \tag{9}
$$

Where, *Kp* is the proportional gain and *Ts* and *Ti* the sample or control period and the integral time.

It is an advantage that the controller output 2 *CU <sup>n</sup>* is driven directly from an integrator, as it is then is easier to deal with windup and noise (Jantzen, 1998). The fuzzy PI controller output, 2 *U* , is called the change in output, and 2 *U <sup>n</sup>* is defined by,

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 85

Then the system is ready to be tested to see if the closed-loop specications are met. First simulations will be carried analyzing the dynamic behaviour and the stability of the plant and finally the adjustment will be tested and adjusted again in the real machine control

To get the rule-base of the controller the reference and feedback values are compared and the control action is determined to correct the deviation between reference and feedback. As an example, in the speed loop a positive increase of the speed error because the real speed is lower than the reference, must force to the controller to increase their output or torque reference, Te, to increase the machine speed as detailed in equation 6. Something similar happens with the change of error; if the change of error is positive big, that means that the machine is decelerating, then the controller has to increase the torque to reduce the effect, so the controller has to produce a positive big output to increase the

For another error and change of error combinations, the base-rule of table 1 applied to the fuzzy controller shows a phase trajectory reducing the error as shown in figure 2. This is valid for the speed, flux and current loops. The base-rule of table 1 characterizes the control objectives and it is shown as a matrix with the phase trajectory superimposed. The dynamic behaviour of the controller to make zero the error will depend on the antecedents and consequents position, on the selected inference strategy, on the used defuzzification method

*CE*<sup>2</sup>

The meaning of the linguistic terms used in table I are: NB, negative big; NM, negative medium; NS, negative small; ZE, zero; PS, positive small; PM, positive medium and PB,

*E*2

Reference Feedback

platform.

electromagnetic torque.

and on the scaling factors.

positive big.

*t*

Fig. 2. Fuzzy controller phase diagram when used table 1

Table 1 indicates the use of 49 rules. The first is read as,

**If** *E*<sup>2</sup> is Negative Big and *CE*<sup>2</sup> is Negative Big Then 2 *cu* is Negative Big

$$\mathbf{U}\mathbf{2}\_n = \sum\_{i} \left( c\mathbf{u}\mathbf{2}\_i \cdot \mathbf{G}\mathbf{C}\mathbf{U} \cdot \mathbf{Ts} \right) \tag{10}$$

The integrator will add only if *LIM OUT LIM L nH* and 2 0 *<sup>i</sup> cu* . The value of *cu*2 according to the inputs is,

$$\text{cu2}\_n = f\left(\text{GE} \cdot \text{e}\_{n'} \text{GCE} \cdot \text{ce}\_n\right) \tag{11}$$

The function *f* is the fuzzy input-output map of the fuzzy controller. If it were possible to take the function *f* as a linear approximation, considering equations (8-11), the gains related to the conventional PI would be,

$$Kp = \text{GCE} \cdot \text{GCLI} \tag{12}$$

$$\frac{1}{T i} = \frac{GE}{GCE} \tag{13}$$

These relations had shown the importance of the scaling factors. High values of GE produce a short rise time when a step reference is introduced but also a high overshot and a long settling time could arise. The system may become oscillatory and even unstable. If GE is low the overshot will decrease or disappear and the settling time increases. High values of GCE have the same effect as small values of GE and vice versa.

High values of GCU originate a short rise time and overshot when a step reference is introduced. If GCU is small the system gain is small and the rise time increases.

The global output value of the hybrid fuzzy controller is,

$$\begin{aligned} \text{OLIT}\_{n} &= \text{LIM}\_{H} \quad \text{if} \quad \text{UI}\_{n} + \text{U}\mathbf{2}\_{n} > \text{LIM}\_{H} \\ \text{OLIT}\_{n} &= \text{LIM}\_{L} \quad \text{if} \quad \text{UI}\_{n} + \text{U}\mathbf{2}\_{n} < \text{LIM}\_{L} \end{aligned} \tag{14}$$
 
$$\text{OLIT}\_{n} = \text{KP} \cdot \boldsymbol{\varepsilon}\_{n} + \sum\_{i}^{n} \left( f \left( \mathbf{GE} \cdot \boldsymbol{\varepsilon}\_{n}, \text{GCE} \cdot \boldsymbol{\varepsilon} \mathbf{e}\_{n} \right) \cdot \text{GCU} \cdot \text{Ts} \right) \tag{15} \quad \text{if} \quad \text{LIM}\_{L} < \text{UI}\_{n} + \text{U}\mathbf{2}\_{n} < \text{LIM}\_{H}$$

The output of the controller is limited according to the maximum value of the hybrid fuzzy controller, for example for a speed controller the limit will be the maximum admissible torque and for the current controllers the limit will be the maximum admissible voltage of the machine.

For a practical implementation of the fuzzy controllers on a DSP the fuzzy membership functions of the antecedents and consequents are triangular and trapezoidal types because the calculus complexity is lower than the calculus complexity when are used Gaussian or Bell membership functions.

With the information of the plant model, the fuzzy sets and their linguistic variables are defined for the antecedents and consequents. The control strategy has to be implemented based on the engineer experience and if it is possible using simulation tools. The control strategy is stored in the rule-base in the form If-Then and an inference strategy will be chosen.

2 2 *n i*

The integrator will add only if *LIM OUT LIM L nH* and 2 0 *<sup>i</sup> cu* . The value of

The function *f* is the fuzzy input-output map of the fuzzy controller. If it were possible to take the function *f* as a linear approximation, considering equations (8-11), the gains related

1 *GE*

These relations had shown the importance of the scaling factors. High values of GE produce a short rise time when a step reference is introduced but also a high overshot and a long settling time could arise. The system may become oscillatory and even unstable. If GE is low the overshot will decrease or disappear and the settling time increases. High values of GCE

High values of GCU originate a short rise time and overshot when a step reference is

1 2 1 2

*n H nn H n L nn L*

*n n n n Lnn H*

**if**

, 1 2

introduced. If GCU is small the system gain is small and the rise time increases.

**if if**

*OUT LIM U U LIM OUT LIM U U LIM*

 

*OUT KP e f GE e GCE ce GCU Ts LIM U U LIM*

The output of the controller is limited according to the maximum value of the hybrid fuzzy controller, for example for a speed controller the limit will be the maximum admissible torque and for the current controllers the limit will be the maximum admissible voltage of

For a practical implementation of the fuzzy controllers on a DSP the fuzzy membership functions of the antecedents and consequents are triangular and trapezoidal types because the calculus complexity is lower than the calculus complexity when are used Gaussian or

With the information of the plant model, the fuzzy sets and their linguistic variables are defined for the antecedents and consequents. The control strategy has to be implemented based on the engineer experience and if it is possible using simulation tools. The control strategy is stored in the rule-base in the form If-Then and an inference strategy will be

*U cu GCU Ts* (10)

*cu*2 , *n nn f GE e GCE ce* (11)

*Kp GCE GCU* (12)

*Ti GCE* (13)

(14)

*i*

*cu*2 according to the inputs is,

to the conventional PI would be,

have the same effect as small values of GE and vice versa.

The global output value of the hybrid fuzzy controller is,

*n*

*i*

the machine.

chosen.

Bell membership functions.

Then the system is ready to be tested to see if the closed-loop specications are met. First simulations will be carried analyzing the dynamic behaviour and the stability of the plant and finally the adjustment will be tested and adjusted again in the real machine control platform.

To get the rule-base of the controller the reference and feedback values are compared and the control action is determined to correct the deviation between reference and feedback. As an example, in the speed loop a positive increase of the speed error because the real speed is lower than the reference, must force to the controller to increase their output or torque reference, Te, to increase the machine speed as detailed in equation 6. Something similar happens with the change of error; if the change of error is positive big, that means that the machine is decelerating, then the controller has to increase the torque to reduce the effect, so the controller has to produce a positive big output to increase the electromagnetic torque.

For another error and change of error combinations, the base-rule of table 1 applied to the fuzzy controller shows a phase trajectory reducing the error as shown in figure 2. This is valid for the speed, flux and current loops. The base-rule of table 1 characterizes the control objectives and it is shown as a matrix with the phase trajectory superimposed. The dynamic behaviour of the controller to make zero the error will depend on the antecedents and consequents position, on the selected inference strategy, on the used defuzzification method and on the scaling factors.

Fig. 2. Fuzzy controller phase diagram when used table 1

The meaning of the linguistic terms used in table I are: NB, negative big; NM, negative medium; NS, negative small; ZE, zero; PS, positive small; PM, positive medium and PB, positive big.

Table 1 indicates the use of 49 rules. The first is read as,

**If** *E*<sup>2</sup> is Negative Big and *CE*<sup>2</sup> is Negative Big Then 2 *cu* is Negative Big

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 87

The linguistic variable change of error and their linguistic terms position, figure 4, is also the same for all fuzzy controllers. The change of error value is normalized for every controller.

<sup>1</sup> *NB NM NS ZE PS PM PB*


*c error*

<sup>1</sup> *NB NM NS ZE PS PM PB*


Control action

In figure 6, the fuzzy controller surface can be seen. The used implication method is the AND method or min (minimum), which truncates the output fuzzy set and as aggregation the S-norm max (maximum) has been used. The used defuzzification method is the centroid

The linguistic variable of the control action or consequent and the position of its linguistic terms are shown in figure 5. The values are normalized, where a value of 20 in the real

Fig. 4. Linguistic variable change of error and its linguistic terms

0

control action is normalized to 1.

0

or center of gravity, equation 15.

Fig. 5. Control action linguistic terms

0.2

0.4

0.6

0.8

0.2

0.4

*c error*

Control action

0.6

0.8


Table 1. Rule-base of the fuzzy controller and phase diagram

To adjust the scaling factors and the membership functions a first approximation is to make the controller as close as possible to a conventional PI controller (Jantzen, 1998). Then, the scaling factors and the position of the antecedents and consequents are adjusted making multiples simulations with Matlab/Simulink©.

The linguistic variable error and their linguistic terms position, figure 3, is the same for all fuzzy controllers. The error value is normalized for every controller, as an example when the speed error is 1000 rpm, their normalized value is 1.

Fig. 3. Linguistic variable error and its linguistic terms

*<sup>E</sup>*<sup>2</sup> NB NM NS ZE PS PM PB

NB NB NB NB NM NS ZE

A

ZE

PS

G

PS PM PB PB PB

To adjust the scaling factors and the membership functions a first approximation is to make the controller as close as possible to a conventional PI controller (Jantzen, 1998). Then, the scaling factors and the position of the antecedents and consequents are adjusted making

The linguistic variable error and their linguistic terms position, figure 3, is the same for all fuzzy controllers. The error value is normalized for every controller, as an example when

<sup>1</sup> *NB NM NS ZE PS PM PB*


*error*

C

PM PB

NS

I

NM

E

ZE

PS

NS

J

NM

NB NB

ZE

NS

NM

F

NB

ZE

PS

PB

PM

D

PB

PB

PB

PB

PB

PM

PS

ZE

PS

H

PM

NS

*CE*<sup>2</sup>

NB

NM

NB

NB

NB

B

NM

NS

NS

ZE

PS

PM

PB

multiples simulations with Matlab/Simulink©.

0

0.2

0.4

0.6

*error*

0.8

the speed error is 1000 rpm, their normalized value is 1.

Fig. 3. Linguistic variable error and its linguistic terms

ZE

Table 1. Rule-base of the fuzzy controller and phase diagram

The linguistic variable change of error and their linguistic terms position, figure 4, is also the same for all fuzzy controllers. The change of error value is normalized for every controller.

Fig. 4. Linguistic variable change of error and its linguistic terms

The linguistic variable of the control action or consequent and the position of its linguistic terms are shown in figure 5. The values are normalized, where a value of 20 in the real control action is normalized to 1.

Fig. 5. Control action linguistic terms

In figure 6, the fuzzy controller surface can be seen. The used implication method is the AND method or min (minimum), which truncates the output fuzzy set and as aggregation the S-norm max (maximum) has been used. The used defuzzification method is the centroid or center of gravity, equation 15.

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 89

*r rd*

*sl*

*Lm*

*sq <sup>I</sup> Te* <sup>1</sup>

Fig. 9. Torque, flux and speed control structure in the rotor flux reference system

The speed error is the input of a hybrid fuzzy controller and the output of FPI+P controller will generate the torque producing stator current component command Isq. The flux controller generates the flux producing stator current component Isd according to the fluxspeed profile. Both currents are the input of two controllers to produce the stator voltages in the synchronous reference and then transformed to the stationary reference system to

The real platform to test the asynchronous motor and its main characteristics used also for

<sup>a</sup> , , *b c iii* <sup>a</sup> , , *b c uuu*

*m*

> Rated speed 1440r.p.m.

Rated Torque 50Nm Nominal current 14A Frequency 50Hz

Voltage 380V III-Y

6*xPWM*

Fig. 10. Induction motor rig test and asynchronous motor main characteristics

*r*

*TL*

*e*

*<sup>r</sup>* rotor shaft

*B pJ*

*m*

J = 0.038Kg\*m2 B = 0.008Kg\*m2/s P = 2 pole-pairs Rr = 0.57Ω Rs = 0.81Ω Lm = 0.117774H Lr = 0.121498H Ls = 0.120416H

rotor flux

 *e r*

*d*

*s I*

*sd sq <sup>I</sup> <sup>I</sup>*

*mI*

*q*

Fig. 8. Rotor flux reference system

*sd I*

1 1 *<sup>r</sup> r L p R*

> *m r L P L*

generate in the inverter the voltage vector for the motor.

FPGA and signal conditioning

*TL*

*PMSM IM*

PC with DS1103

the simulation purpose are shown in figure 10.

*dc u*

\* *TL*

3 380 *x V*

*m* 3 2

Fig. 6. Fuzzy controller surface

As it can be seen in figure 3 and 4, the linguistic variables are joined close to zero, showing a higher sensibility in this area. For this reason the slope of the surface in figure 6 is high in a surrounding area around the point (0,0,0).

### **4. Squirrel-cage machine control**

A schematic diagram of the induction motor indirect vector control with the fuzzy PI + P controllers is shown in figure 7. The scheme is obtained after operating with the machine equations and using the rotor flux reference system as shown in figure 8.

Fig. 7. Squirrel cage control structure

The rotor flux reference system makes possible the control of the AC machine as a DC machine, allowing the control of the machine torque with the stator current q component and the flux with the d component of the same current as can be deducted from equations 2 to 6. A scheme showing these equations is shown in figure 9.

Fig. 8. Rotor flux reference system

*T y y <sup>y</sup>*


*c error error*

As it can be seen in figure 3 and 4, the linguistic variables are joined close to zero, showing a higher sensibility in this area. For this reason the slope of the surface in figure 6 is high in a

A schematic diagram of the induction motor indirect vector control with the fuzzy PI + P controllers is shown in figure 7. The scheme is obtained after operating with the machine

*m e rd s sd r <sup>L</sup> L I*

*L*

 

> *d q*

*<sup>s</sup>*

*e*

*e*

 

The rotor flux reference system makes possible the control of the AC machine as a DC machine, allowing the control of the machine torque with the stator current q component and the flux with the d component of the same current as can be deducted from equations 2

*e s sq L I*



equations and using the rotor flux reference system as shown in figure 8.

 

torque

I magnetizing

*d q* 

0

0.5

surrounding area around the point (0,0,0).

\* *Te*

 

*r*

*Te*

*sd I sq I*

to 6. A scheme showing these equations is shown in figure 9.

**4. Squirrel-cage machine control** 

1 -1 -0.5 0 0.5 1

Fig. 6. Fuzzy controller surface

speed

flux

*<sup>r</sup> K*

Fig. 7. Squirrel cage control structure

D acción de control

 *control action*

*m*

\* *m*

> 

*r*

\* *r*


*o*

 *T*

(15)

0

 

*<sup>C</sup> <sup>S</sup>* \* *Vs*

\* *SVPWM Vs*

> 

*I*

*r*

Estimator

*sI*

*SVPWM*

*SVPWM*

*r*

*<sup>r</sup> IM*

*abc*

*B S*

*<sup>m</sup> P*

*<sup>A</sup> S*

0.5

1

*VDC*

*y* 

Fig. 9. Torque, flux and speed control structure in the rotor flux reference system

The speed error is the input of a hybrid fuzzy controller and the output of FPI+P controller will generate the torque producing stator current component command Isq. The flux controller generates the flux producing stator current component Isd according to the fluxspeed profile. Both currents are the input of two controllers to produce the stator voltages in the synchronous reference and then transformed to the stationary reference system to generate in the inverter the voltage vector for the motor.

The real platform to test the asynchronous motor and its main characteristics used also for the simulation purpose are shown in figure 10.

Fig. 10. Induction motor rig test and asynchronous motor main characteristics

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 91

0.95 <sup>1</sup> 1.05 1.1 1.15 1.2 1.25 -20

0.95 <sup>1</sup> 1.05 1.1 1.15 1.2 1.25 -4

t(s)




Change of error

0

1

2

3 x 104

t(s)

When the step reference is -20 amperes the feedback or real stator q current reaches the real value quickly, it takes 2 ms. The trajectory on the fuzzy surface for this step is the green line in the surface showing how the change of error and the error are decreasing to zero in about 2 ms. When the step reference goes from -20 to 20 amperes the feedback or real stator q current reaches the real value in 3 ms. The trajectory on the fuzzy surface for this step is the red line in the surface showing how the change of error and the error are decreasing to zero

Once the current loops have been adjusted, the speed and flux loops will be adjusted. As mentioned and shown in figure 9, the machine speed is regulated adjusting the torque

In a classical speed PI controller the proportional term for a bandwidth of 750 rad/s and a phase margin of 80º with the machine parameters given in figure 10 is 0.5. For the adjustment of the hybrid fuzzy controller KP will be 0.4, a little bit smaller than the proportional term in the PI. The scaling factors adjusted after simulations for the speed controllers are *GE GCE* 2, 0.01 and 300 *GCU* . The regulators maximum and minimum limits are ±50

Figure 13 shows the hybrid fuzzy speed controller surface and the trajectory when a step reference from -1000 rpm to 1000 rpm and again to -1000 rpm as shown in figure 14 is

When the step goes from -1000 to 1000 rpm the trajectory on the fuzzy surface for this step is the green line, showing how the change of error and the error are decreasing to zero in about 180 ms. When the step reference goes from 1000 to -1000 rpm the feedback or real speed reaches the real value in 180 ms. The trajectory on the fuzzy surface for this step is the red line, showing how the change of error and the error are decreasing to zero due to the

Nm, the maximum motor torque or a stator current q component of 20 amperes.

Fig. 12. Stator current q component step reference and feedback, error for the step, and


command and the flux adjusting the stator current d component.

0

10

Error

20

30

40

50

0.95 <sup>1</sup> 1.05 1.1 1.15 1.2 1.25 -25

t(s)

due to the value of the control action.

**4.2 Speed and rotor flux control** 

applied to the speed controller.

value of the control action.


change of error

Isq

Ref Fdbk

The real system is based on a DS1103 board and is programmed using the software Matlab/Simulink©. The board controls the IM inverter generating the SVPWM pulses (dSPACE©, 2005). The speed is measured with a 4096 impulse encoder via a FPGA connected to the DS1103 using the multiple period method (Cortajarena et al., 2006).

#### **4.1 Torque or current control**

As mentioned and shown in figure 9, the torque of the machine is controlled with the stator current q component and the flux with the d component. The relation between the torque Te and the stator current q component is,

$$T\_e = \underbrace{\frac{3}{2} \, P \frac{L\_m}{L\_r} \, \nu\_r \, I\_{sq}}\_{K\_{T\_e}} \tag{16}$$

So first, torque and current magnetizing controllers will be adjusted. In a classical PI controller the proportional term for a bandwidth of 2500 rad/s and a phase margin of 80º with the machine parameters given in figure 10 is 0.05. For the adjustment of the hybrid fuzzy controller KP will be 0.025, half of the proportional term in the PI. The scaling factors adjusted after simulations for the current controllers are *GE GCE* 150, 0.03 and *GCU* 8 . The regulators maximum and minimum limits are ±310V, the maximum motor phase voltage.

Fig. 11. Stator current q component controller fuzzy surface and trajectory after current step of figure 12

Figure 11 shows the hybrid fuzzy stator q current controller surface and the trajectory when a step reference of -20 amperes is produced, and after 200 ms another step of 20 amperes as shown in figure 12 is applied to the torque controller.

The real system is based on a DS1103 board and is programmed using the software Matlab/Simulink©. The board controls the IM inverter generating the SVPWM pulses (dSPACE©, 2005). The speed is measured with a 4096 impulse encoder via a FPGA

As mentioned and shown in figure 9, the torque of the machine is controlled with the stator current q component and the flux with the d component. The relation between the torque Te

*Te*

So first, torque and current magnetizing controllers will be adjusted. In a classical PI controller the proportional term for a bandwidth of 2500 rad/s and a phase margin of 80º with the machine parameters given in figure 10 is 0.05. For the adjustment of the hybrid fuzzy controller KP will be 0.025, half of the proportional term in the PI. The scaling factors adjusted after simulations for the current controllers are *GE GCE* 150, 0.03 and *GCU* 8 . The regulators maximum and minimum limits are ±310V, the maximum motor

Fig. 11. Stator current q component controller fuzzy surface and trajectory after current step

Figure 11 shows the hybrid fuzzy stator q current controller surface and the trajectory when a step reference of -20 amperes is produced, and after 200 ms another step of 20 amperes as

*<sup>m</sup> <sup>e</sup> r sq r K*

(16)

*error*

*<sup>L</sup> TP I <sup>L</sup>*

connected to the DS1103 using the multiple period method (Cortajarena et al., 2006).

3 2

**4.1 Torque or current control** 

phase voltage.

 *control action*

of figure 12

<sup>4</sup> *x*10

*change of error*

shown in figure 12 is applied to the torque controller.

and the stator current q component is,

Fig. 12. Stator current q component step reference and feedback, error for the step, and change of error

When the step reference is -20 amperes the feedback or real stator q current reaches the real value quickly, it takes 2 ms. The trajectory on the fuzzy surface for this step is the green line in the surface showing how the change of error and the error are decreasing to zero in about 2 ms. When the step reference goes from -20 to 20 amperes the feedback or real stator q current reaches the real value in 3 ms. The trajectory on the fuzzy surface for this step is the red line in the surface showing how the change of error and the error are decreasing to zero due to the value of the control action.

#### **4.2 Speed and rotor flux control**

Once the current loops have been adjusted, the speed and flux loops will be adjusted. As mentioned and shown in figure 9, the machine speed is regulated adjusting the torque command and the flux adjusting the stator current d component.

In a classical speed PI controller the proportional term for a bandwidth of 750 rad/s and a phase margin of 80º with the machine parameters given in figure 10 is 0.5. For the adjustment of the hybrid fuzzy controller KP will be 0.4, a little bit smaller than the proportional term in the PI. The scaling factors adjusted after simulations for the speed controllers are *GE GCE* 2, 0.01 and 300 *GCU* . The regulators maximum and minimum limits are ±50 Nm, the maximum motor torque or a stator current q component of 20 amperes.

Figure 13 shows the hybrid fuzzy speed controller surface and the trajectory when a step reference from -1000 rpm to 1000 rpm and again to -1000 rpm as shown in figure 14 is applied to the speed controller.

When the step goes from -1000 to 1000 rpm the trajectory on the fuzzy surface for this step is the green line, showing how the change of error and the error are decreasing to zero in about 180 ms. When the step reference goes from 1000 to -1000 rpm the feedback or real speed reaches the real value in 180 ms. The trajectory on the fuzzy surface for this step is the red line, showing how the change of error and the error are decreasing to zero due to the value of the control action.

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 93

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 <sup>100</sup>

Reference FPI+P PI Fuzzy

> FPI+P Fuzzy PI

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -5

t(s)

Fig. 15. Top, speed step and response when PI, Fuzzy and Fuzzy PI + P controllers are used.

To compare the controllers, table 2 shows time domain specifications and performance criteria, integrated absolute error (IAE), the integral of time-weighted absolute error (ITAE), the integral of the square of the error, ISE, and the integral of time multiply squared error

%

PI 1.4ms 42ms 56ms 3 97470 6754 2.23e7 3.29e5 Fuzzy 3.2ms 77ms 80ms 0 1.28e5 7579 2.86e7 4.8e5 FPI+P 1.4ms 42ms 47ms 0 96270 6000 2.23e7 3.01e5 Table 2. Time domain specifications and performance criteria for three classes of controllers

Very similar results are obtained with the PI and FPI+P controllers, although according to the performance criteria the hybrid fuzzy controller is slightly better. The worst controller is

To check the control of the machine with the hybrid fuzzy controller the machine will be forced to run at a speed higher than the nominal value. In such conditions the machine rotor flux has to decrease because the inverter DC voltage can't be higher, so the torque and stator current q component relation is changing as shown in equation 16 and figure 9. This change should be taken in consideration in a classical PI regulator. In the hybrid fuzzy controller the adjustment done with the linguistic variables and the scaling factors shows that the control works properly. In figure 16, the left signals correspond to the real signals obtained whit the machine of the test rig and the right side signals are the simulated in the same conditions than the real case. Because the speed is higher than nominal value, the flux decreases below the nominal value, to do this the stator current d component decreases and increases when

Overshoot IAE ITAE ISE ITSE

(ITSE).

Bottom, torque current controllers output

Rise time

the fuzzy controller as it is shown in table 2 and figure 15.

Settling time

Delay time

Isq (A)

Speed (rpm)

Fig. 13. Speed controller fuzzy surface and trajectory after speed step of figure 14

Fig. 14. Speed step reference and feedback, error for the step, and change of error

When the change of error is high, the controller output is at its maximum limit, and when the change of error decreases the control action also decreases close to zero as it can be seen in the trajectory of figure 13. The error and change of error trajectory of the surface in figure 13 correspond to the values represented in figure 14. The control action contribution can be obtained from the fuzzy controller surface.

Figure 15 shows the response of the real asynchronous motor of figure 10 when a speed step is applied to the machine and later a load torque of 40 Nm after 0.3 s. Three classes of speed controllers are tested to see the response and compare them. A classical PI controller with a 750 rad/s and a phase margin of 80º, the adjusted hybrid Fuzzy PI + P controller and a Fuzzy controller without the KP term and *GE GCE* 2, 0.06 and 300 *GCU* .

Fig. 13. Speed controller fuzzy surface and trajectory after speed step of figure 14

0.6 0.8 <sup>1</sup> 1.2 -2500

When the change of error is high, the controller output is at its maximum limit, and when the change of error decreases the control action also decreases close to zero as it can be seen in the trajectory of figure 13. The error and change of error trajectory of the surface in figure 13 correspond to the values represented in figure 14. The control action contribution can be

Figure 15 shows the response of the real asynchronous motor of figure 10 when a speed step is applied to the machine and later a load torque of 40 Nm after 0.3 s. Three classes of speed controllers are tested to see the response and compare them. A classical PI controller with a 750 rad/s and a phase margin of 80º, the adjusted hybrid Fuzzy PI + P controller and a

Fig. 14. Speed step reference and feedback, error for the step, and change of error

Fuzzy controller without the KP term and *GE GCE* 2, 0.06 and 300 *GCU* .

t(s)


Error

Ref Fdbk

 *control action*

<sup>4</sup> *x*10

*change of error action*

0.6 0.8 <sup>1</sup> 1.2 -1500

t(s)

obtained from the fuzzy controller surface.



0

Speed (rpm)

500

1000

1500

*error*

0.6 0.8 <sup>1</sup> 1.2 -1.5

t(s)



0

Change of error

0.5

1

1.5 x 104

Fig. 15. Top, speed step and response when PI, Fuzzy and Fuzzy PI + P controllers are used. Bottom, torque current controllers output

To compare the controllers, table 2 shows time domain specifications and performance criteria, integrated absolute error (IAE), the integral of time-weighted absolute error (ITAE), the integral of the square of the error, ISE, and the integral of time multiply squared error (ITSE).


Table 2. Time domain specifications and performance criteria for three classes of controllers

Very similar results are obtained with the PI and FPI+P controllers, although according to the performance criteria the hybrid fuzzy controller is slightly better. The worst controller is the fuzzy controller as it is shown in table 2 and figure 15.

To check the control of the machine with the hybrid fuzzy controller the machine will be forced to run at a speed higher than the nominal value. In such conditions the machine rotor flux has to decrease because the inverter DC voltage can't be higher, so the torque and stator current q component relation is changing as shown in equation 16 and figure 9. This change should be taken in consideration in a classical PI regulator. In the hybrid fuzzy controller the adjustment done with the linguistic variables and the scaling factors shows that the control works properly. In figure 16, the left signals correspond to the real signals obtained whit the machine of the test rig and the right side signals are the simulated in the same conditions than the real case. Because the speed is higher than nominal value, the flux decreases below the nominal value, to do this the stator current d component decreases and increases when

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 95

The second group of techniques is based on the anisotropic properties of the machine. Techniques like rotor slot ripple or main inductance saturation are used in this group.

From equations 2 and 4, considering rotor voltage zero, and after Laplace transformation of

, , ( ) ( )

*s dq <sup>m</sup> m r <sup>s</sup> s dq <sup>s</sup> r e sdq r rdq*

As the feeding voltage vector of the stator approaches zero frequency, the rotor speed

, ,, <sup>0</sup> <sup>2</sup> <sup>0</sup> lim

variations of rotor speed have no influence on the stator equation 18 and this makes impossible to detect a speed variation on the stator current. So the mechanical speed of the rotor becomes not observable. Instead of this, when the magnitude of the induced voltage from the rotor into the stator is substantial, its value can be determined and the rotor state variables are then observable. So, there will be a limitation for very low speed operation due

The minimum stator frequency must be superior to zero to have an appropriate relation between induced voltage from the rotor into the stator and also to reduce the noise and

The rotor speed estimator used, figure 17, is based on the fundamental mathematical model of the machine. The rotor speed is obtained with the derivative of the rotor flux angle minus the slip speed, see figure 8. The precision of the estimator has a great dependence on motor parameters and at low speeds a small error (offset for example) in the stator voltage can

The rotor flux estimator contains two models, the open loop current model, which is supposed to produce an accurate estimation at low speed range, and an adaptive voltage model for a medium high speed range of operation. The transition between both models is adjusted by two hybrid fuzzy controllers, reducing the problems due to stator resistance and

*m r s ss <sup>p</sup> <sup>r</sup>*

*vr vr i*

*L <sup>p</sup> <sup>i</sup> <sup>p</sup> L L p j R R*

*r r*

, ,,

 

*r r r*

2

(19)

*<sup>r</sup>* when stator frequency is close to zero, so the

*L R*

*L*

(17)

(18)

*<sup>e</sup>* =0, and

,

*vr*

*s dq*

*s dq* , *<sup>r</sup> v* .

 

 

*<sup>m</sup> r dq s dq r r e r*

2

*di <sup>L</sup> L R L v R Rj i j dt <sup>L</sup> L L*

approaches zero. If the equation 18 is observed in the stationary reference frame,

*r*

to the dc offset components in the measured stator currents and voltages.

 1

the respective space vectors the rotor flux will be,

,

using equation 17, *s dq* , *<sup>r</sup> v* is calculated when p→0,

The equation 19 is independent of

parameters mismatch influence (Holtz, 1996).

suppose an estimation error.

pure integrators at low speed.

 Operating with equations 1 to 4 the next equation is obtained,

It can be seen the induced voltage from the rotor into the stator as

the flux is increasing to the nominal value. The q component of the stator current related with the torque increases when the machine is accelerating and decreases when the machine decelerates.

The speed regulation in the flux weakening region is good, and real platform signals and simulations corroborate the hybrid fuzzy good performance.

The flux hybrid fuzzy controller scaling factors are *GE GCE* 200, 20 and 100 *GCU* . To evaluate the flux regulation, the rotor flux reference and feedback values could be compared in the flux weakening shown in figure 16. Both are very similar showing a very good flux regulation and the flux controller output corresponds with the stator current d component shown in the same figure.

Fig. 16. Left, real machine signals, speed, flux and stator currents. Right, simulated signals

#### **4.3 Speed estimation**

There are in literature many techniques of sensorless control. The first group is based on the fundamental mathematical model of the machine, that is, the flux density distribution in the air gap is sinusoidal. All these models depend on the machine parameters so the accuracy of the estimators will depend on different manner of the precision of these parameters. It is not possible with these techniques to achieve a stable and precise operation at very low speed.

the flux is increasing to the nominal value. The q component of the stator current related with the torque increases when the machine is accelerating and decreases when the machine

The speed regulation in the flux weakening region is good, and real platform signals and

The flux hybrid fuzzy controller scaling factors are *GE GCE* 200, 20 and 100 *GCU* . To evaluate the flux regulation, the rotor flux reference and feedback values could be compared in the flux weakening shown in figure 16. Both are very similar showing a very good flux regulation and the flux controller output corresponds with the stator current d component

> Ref Fdbk

> Ref Fdbk

Isalfa Isbeta

Fig. 16. Left, real machine signals, speed, flux and stator currents. Right, simulated signals

There are in literature many techniques of sensorless control. The first group is based on the fundamental mathematical model of the machine, that is, the flux density distribution in the air gap is sinusoidal. All these models depend on the machine parameters so the accuracy of the estimators will depend on different manner of the precision of these parameters. It is not possible with these techniques to achieve a stable and precise operation at very low speed.

> 0.4 0.6 0.8 1

Isd Isq

20


0

Is (A)

Isdq (A)

Rotor flux (Wb)

Speed (rpm)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ref Fdbk

Ref Fdbk

Isalfa Isbeta

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

t(s)

simulations corroborate the hybrid fuzzy good performance.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

t(s)

decelerates.

> 0.4 0.6 0.8 1

> > 20


20


0

Is (A)

0

Isd Isq

**4.3 Speed estimation** 

Isdq (A)

Rotor flux (Wb)

Speed (rpm)

shown in the same figure.

The second group of techniques is based on the anisotropic properties of the machine. Techniques like rotor slot ripple or main inductance saturation are used in this group.

From equations 2 and 4, considering rotor voltage zero, and after Laplace transformation of the respective space vectors the rotor flux will be,

$$\overline{\nu}\_{r,dq}(p) = \frac{L\_m}{1 + \frac{L\_r}{R\_r}p + j(\alpha\_\varepsilon - \alpha\_r)\frac{L\_r}{R\_r}}\overline{l}\_{s,dq}(p) \tag{17}$$

Operating with equations 1 to 4 the next equation is obtained,

$$\sigma L\_s \frac{d\overline{\mathbf{i}}\_{s,dq}}{dt} = \overline{\mathbf{v}}\_{s,dq} - \left[R\_s + \left(\frac{L\_m}{L\_r}\right)^2 R\_r + j\alpha\_e\right] \overline{\mathbf{i}}\_{s,dq} + \underbrace{\frac{L\_m}{L\_r} \left(\frac{R\_r}{L\_r} - j\alpha\_r\right)}\_{\overline{\mathbf{v}}\_{s,dq}} \tag{18}$$

It can be seen the induced voltage from the rotor into the stator as *s dq* , *<sup>r</sup> v* .

As the feeding voltage vector of the stator approaches zero frequency, the rotor speed approaches zero. If the equation 18 is observed in the stationary reference frame, *<sup>e</sup>* =0, and using equation 17, *s dq* , *<sup>r</sup> v* is calculated when p→0,

$$\left. \overline{\boldsymbol{\upsilon}} \boldsymbol{r}\_{s,\alpha\beta} \right|\_{\alpha\_r \to 0} = \lim\_{p \to 0} \overline{\boldsymbol{\upsilon}} \boldsymbol{r}\_{s,\alpha\beta} = \frac{\boldsymbol{L}\_m^{-2} \boldsymbol{R}\_r}{\boldsymbol{L}\_r^2} \overline{\dot{\mathbf{i}}}\_{s,\alpha\beta} \tag{19}$$

The equation 19 is independent of *<sup>r</sup>* when stator frequency is close to zero, so the variations of rotor speed have no influence on the stator equation 18 and this makes impossible to detect a speed variation on the stator current. So the mechanical speed of the rotor becomes not observable. Instead of this, when the magnitude of the induced voltage from the rotor into the stator is substantial, its value can be determined and the rotor state variables are then observable. So, there will be a limitation for very low speed operation due to the dc offset components in the measured stator currents and voltages.

The minimum stator frequency must be superior to zero to have an appropriate relation between induced voltage from the rotor into the stator and also to reduce the noise and parameters mismatch influence (Holtz, 1996).

The rotor speed estimator used, figure 17, is based on the fundamental mathematical model of the machine. The rotor speed is obtained with the derivative of the rotor flux angle minus the slip speed, see figure 8. The precision of the estimator has a great dependence on motor parameters and at low speeds a small error (offset for example) in the stator voltage can suppose an estimation error.

The rotor flux estimator contains two models, the open loop current model, which is supposed to produce an accurate estimation at low speed range, and an adaptive voltage model for a medium high speed range of operation. The transition between both models is adjusted by two hybrid fuzzy controllers, reducing the problems due to stator resistance and pure integrators at low speed.

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 97

Figure 18 shows three speed references when the machine is unloaded. The speed reference of the left figure is a square signal from -1000 to 1000 rpm. The estimated speed is used as feedback signal and for check purposes the measured or real speed is also shown. As can be seen the real and estimated speeds are very similar. The speed reference of the middle figure is sinusoidal and the reference, estimated and real signals are very similar, showing a good regulation and speed estimation. The right figure shows a random speed reference crossing during 2 seconds at a speed close to zero rpm, where the speed is poorly observable. The reference, estimated and real signals are very similar even at zero speed for a short time.

> Ref Real Estim.

<sup>0</sup> 0.5 <sup>1</sup> 1.5 -600

Fig. 18. Sensorless control for different speed references when the load torque is cero

Ref Real Estim.

> Ref Real

Fig. 19. Sensorless control for 200 rpm and torque step loads of ±30Nm

t(s)

> -40 -20 0 20

Torque (Nm)

Figure 19 shows the speed estimation when a load perturbation of ±30 Nm is applied to the machine. There is an error between the real speed and the estimated speed when the

Speed (rpm)

0 2 4 6 8 10 12

t(s)

Ref Real Estim.

> Ref Real


<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> <sup>100</sup>

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> -60

t(s)

t(s)


0

Speed (rpm)

500

1000

Ref Real Estim.



0

Speed (rpm)

200

400

600

0 0.5 1 1.5

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> <sup>100</sup>

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> -20

machine is loaded due to parameters mismatch.

t(s)

t(s)

t(s)

Ref Real Estim.


Torque (Nm)

Speed (rpm)


0

Speed (rpm)

500

1000

The stator flux in the fixed reference frame related to the rotor flux and the stator current is,

$$\overline{\boldsymbol{\Psi}}\_{s,\alpha\beta}^{i} = \frac{\mathbf{L}\_m}{\mathbf{L}\_r} \overline{\boldsymbol{\Psi}}\_{r,\alpha\beta}^{i} + \frac{\mathbf{L}\_s \mathbf{L}\_r - \mathbf{L}\_m^2}{\mathbf{L}\_r} \overline{\mathbf{i}}\_{s,\alpha\beta} \tag{20}$$

Fig. 17. Rotor speed estimation using hybrid fuzzy controllers

The stator flux using the voltage model is corrected by a compensation term, generated by two hybrid fuzzy controllers,

$$\overline{\boldsymbol{\varphi}}\_{s,\alpha\beta}^{\upsilon} = \int \left( \overline{\boldsymbol{\upsilon}}\_{s,\alpha\beta} - \boldsymbol{R}\_{s} \overline{\boldsymbol{\imath}}\_{s,\alpha\beta} - \overline{\boldsymbol{\upsilon}}\_{comp} \right) \tag{21}$$

And,

$$\overline{\boldsymbol{\sigma}}\_{\text{conv}\_{n}} = \boldsymbol{K} \boldsymbol{P} \cdot \left( \overline{\boldsymbol{\nu}}\_{s,\alpha\beta}^{\boldsymbol{v}} - \overline{\boldsymbol{\nu}}\_{s,\alpha\beta}^{\boldsymbol{i}} \right) + \sum\_{i}^{n} \Big( \boldsymbol{f} \Big( \boldsymbol{\text{GE}} \cdot \Big( \overline{\boldsymbol{\nu}}\_{s,\alpha\beta}^{\boldsymbol{v}} - \overline{\boldsymbol{\nu}}\_{s,\alpha\beta}^{\boldsymbol{i}} \Big)\_{\boldsymbol{n}} \boldsymbol{\text{GCE}} \cdot \boldsymbol{c} \Big( \overline{\boldsymbol{\nu}}\_{s,\alpha\beta}^{\boldsymbol{v}} - \overline{\boldsymbol{\nu}}\_{s,\alpha\beta}^{\boldsymbol{i}} \Big)\_{\boldsymbol{n}} \Big) \cdot \boldsymbol{\text{GCI}} \cdot \boldsymbol{I} \bar{\boldsymbol{s}} \Big) (22)$$

With the obtained stator flux, the rotor flux and angle according to the voltage model are determined,

$$
\overline{\boldsymbol{\eta}}\_{r,\alpha\beta}^{\upsilon} = \frac{\mathcal{L}\_r}{\mathcal{L}\_m} \overline{\boldsymbol{\eta}}\_{s,\alpha\beta}^{\upsilon} + \frac{\mathcal{L}\_s \mathcal{L}\_r - \mathcal{L}\_m^2}{\mathcal{L}\_m} \overline{\overline{\boldsymbol{i}}}\_{s,\alpha\beta} \tag{23}
$$

And,

$$\theta\_e = \theta\_{\nu\_r} = \tan^{-1} \frac{\nu\_{r\beta}^v}{\nu\_{r\alpha}^v} \tag{24}$$

Finally the rotor speed is obtained,

$$
\rho\_r \alpha\_r = \alpha\_{yr} - \alpha\_{sl} = \frac{d\theta\_{yr}}{dt} - \frac{L\_m R\_r}{L\_r \left(\wp^2 \frac{1}{r\alpha} + \wp^2 \frac{1}{r\beta}\right)} \left(\wp\_{r\alpha} \dot{\imath}\_{s\beta} + \wp\_{r\beta} \dot{\imath}\_{sa}\right) \tag{25}
$$

The scaling factors adjusted after simulations for the hybrid fuzzy controllers are, *KP* 245 , *GE GCE* 105, 1 and 11 *GCU* .

With the adjusted hybrid fuzzy controllers some estimated speed profiles in the real machine are presented.

The stator flux in the fixed reference frame related to the rotor flux and the stator current is,

,, , *i i <sup>m</sup> sr m sr s r r L LL L <sup>i</sup> L L*

 

*i* Voltage

 ,

 

Fig. 17. Rotor speed estimation using hybrid fuzzy controllers

 

 *v s*

 *v v s r eer*

The stator flux using the voltage model is corrected by a compensation term, generated by

, ,, *<sup>v</sup> <sup>s</sup> s s s comp v Ri v*

 , , , , , , , *<sup>n</sup> <sup>n</sup> v i v i v i*

*v KP f GE GCE c GCU Ts*

With the obtained stator flux, the rotor flux and angle according to the voltage model are

,, , *v v <sup>r</sup> sr m rs s m m L LL L <sup>i</sup> L L*

<sup>1</sup> tan *<sup>r</sup>*

*e v*

*<sup>r</sup> m r r r sl rs rs rr r*

The scaling factors adjusted after simulations for the hybrid fuzzy controllers are,

With the adjusted hybrid fuzzy controllers some estimated speed profiles in the real

 

*dt L* 

 

> 

> > 2

*v r*

*<sup>d</sup> L R i i*

 

 

*r* 

2 2

 

*comp s s s s s s n n <sup>i</sup>*

 

 ,

*s*

 , , 

*i s*

Current model

> *e*

*s*,

two hybrid fuzzy controllers,

Finally the rotor speed is obtained,

machine are presented.

 

 

  

*KP* 245 , *GE GCE* 105, 1 and 11 *GCU* .

And,

And,

determined,

 2

model

*r* (20)

(21)

 

(23)

(24)

 

 

 

(22)

(25)

*s*,*v*

Figure 18 shows three speed references when the machine is unloaded. The speed reference of the left figure is a square signal from -1000 to 1000 rpm. The estimated speed is used as feedback signal and for check purposes the measured or real speed is also shown. As can be seen the real and estimated speeds are very similar. The speed reference of the middle figure is sinusoidal and the reference, estimated and real signals are very similar, showing a good regulation and speed estimation. The right figure shows a random speed reference crossing during 2 seconds at a speed close to zero rpm, where the speed is poorly observable. The reference, estimated and real signals are very similar even at zero speed for a short time.

Fig. 18. Sensorless control for different speed references when the load torque is cero

Fig. 19. Sensorless control for 200 rpm and torque step loads of ±30Nm

Figure 19 shows the speed estimation when a load perturbation of ±30 Nm is applied to the machine. There is an error between the real speed and the estimated speed when the machine is loaded due to parameters mismatch.

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 99

the sub-synchronous (slip speed is positive, s>0) and super-synchronous (slip speed is

When the reference system is linked to the stator flux, as it can be seen in figure 21, the stator flux q component is zero, and when operating with equation 3 the next two equations

> **<sup>=</sup>***<sup>s</sup> <sup>m</sup> sd rd s s <sup>L</sup> i i L L*

> > **=** *<sup>m</sup> sq rq s <sup>L</sup> i i*

This means that the stator current can be controlled with the rotor current. Taking into account that the stator resistance is small, the stator flux can be considered constant and its

*s*

3 2 *<sup>m</sup> s es rq*

3 2

used also for the simulation purpose are shown in figure 22.

 

*<sup>L</sup> P i*

*<sup>s</sup> <sup>m</sup> s s rd es s*

Equations 30 and 31 showed that the stator active power is controlled with the q component of the rotor current and the stator reactive power with the rotor current d component. In figure 20 can be seen both hybrid fuzzy controllers to regulate the d and q rotor current

The real platform to test the double feed induction generator and its main characteristics

The real system is based on a DS1103 board and is programmed using the software Matlab/Simulink©. The board controls the inverters in a Back to Back configuration generating the SVPWM pulses (dSPACE©, 2005). The grid connected inverter, is regulated keeping the DC

*<sup>V</sup> <sup>L</sup> QV i L L* 

along the stator flux, so considering that the stator active and reactive power is,

*s*

*e V*

**and** 3 3

*s*

*L*

2 2 *P vi vi Q vi vi s sd sd s <sup>q</sup> sq s sq sd sd sq* (29)

The stator voltage d component is almost zero because the reference system is oriented

(26)

*<sup>L</sup>* (27)

(28)

(30)

(31)

negative, s<0) operating area (Hansen et al., 2007).

are obtained,

value is,

And,

components.

It can be obtained that,

## **5. Doubly fed induction generator control**

A doubly fed induction generator (DFIG) vector control with the fuzzy PI + P controllers is shown in figure 20. The scheme is obtained after operating with the machine equations and using the stator flux reference system shown in figure 21.

Fig. 20. DFIG control structure

Fig. 21. DFIG control reference systems

The converter Back to Back configuration provides to the DFIG the ability of reactive power control. Using the appropriate reference system it is possible to decouple the active and reactive power control by the independent control of the rotor excitation current. Due to the bi-directional power converter in the rotor side, the DFIG is able to work as a generator in the sub-synchronous (slip speed is positive, s>0) and super-synchronous (slip speed is negative, s<0) operating area (Hansen et al., 2007).

When the reference system is linked to the stator flux, as it can be seen in figure 21, the stator flux q component is zero, and when operating with equation 3 the next two equations are obtained,

$$\dot{\mathbf{i}}\_{sd} = \frac{\left| \overline{\boldsymbol{\nu} \boldsymbol{\nu}}\_{s} \right|}{L\_{s}} - \frac{L\_{m}}{L\_{s}} \dot{\mathbf{i}}\_{rd} \tag{26}$$

$$\dot{\mathbf{u}}\_{sq} = -\frac{L\_m}{L\_s}\dot{\mathbf{u}}\_{rq} \tag{27}$$

This means that the stator current can be controlled with the rotor current. Taking into account that the stator resistance is small, the stator flux can be considered constant and its value is,

$$\left|\overline{\boldsymbol{\varphi}}\_{s}\right| \approx \left|\frac{\overline{\boldsymbol{V}}\_{s}}{\boldsymbol{\alpha}\_{\varepsilon}}\right|\tag{28}$$

The stator voltage d component is almost zero because the reference system is oriented along the stator flux, so considering that the stator active and reactive power is,

$$P\_s = \frac{\mathfrak{Z}}{\mathfrak{Z}} (\upsilon\_{sd}\dot{\imath}\_{sd} + \upsilon\_{sq}\dot{\imath}\_{sq}) \quad \textbf{and} \quad Q\_s = \frac{\mathfrak{Z}}{\mathfrak{Z}} (\upsilon\_{sq}\dot{\imath}\_{sd} - \upsilon\_{sd}\dot{\imath}\_{sq}) \tag{29}$$

It can be obtained that,

$$P\_s \approx -\frac{3}{2} \alpha\_e \Psi\_s \frac{L\_m}{L\_s} \mathbf{i}\_{r\eta} \tag{30}$$

And,

98 Fuzzy Logic – Controls, Concepts, Theories and Applications

A doubly fed induction generator (DFIG) vector control with the fuzzy PI + P controllers is shown in figure 20. The scheme is obtained after operating with the machine equations and

Uncoupling

*e*

*r I* 

*V V <sup>s</sup> sq* 

*rq I*

 *r* 

Estimator *s*

> *r I*

The converter Back to Back configuration provides to the DFIG the ability of reactive power control. Using the appropriate reference system it is possible to decouple the active and reactive power control by the independent control of the rotor excitation current. Due to the bi-directional power converter in the rotor side, the DFIG is able to work as a generator in

*s*

*r* *rd I*

*s* 

> *e*

*r I* 

*rd I rq I*

 *e r r rd L I*

 *e r r rq L I*

> *d q*

\* *Vrd*

\* *Vrq*

 

, *<sup>s</sup> <sup>s</sup> I I* 

*r*

Reference system linked to the *<sup>s</sup>*

> Reference system fixed to the stator

Reference system linked to the rotor

*e*

*d*

*Vs* , V*<sup>s</sup>*

*d q*

*s*  

 

, *r r* 

 

*abc*

\* *SVPWM Vr*

*r I* 

Park Clarke

\* *Vr*

> *r I*

*SVPWM*

*abc*

*A S*

*B S C S*

*VDC*

*ra I rb I*

*sa I sb I Vsa Vsb*

Grid

*DFIG*

*s I Vs*

*r I Vr*

**5. Doubly fed induction generator control** 

using the stator flux reference system shown in figure 21.

\* *rq I*

*Vs*

\* *r*

*Vs s*

> Equ. 31 Equ. 30

Pitch control

\* *Q*

\* *P*

\* min 0

P Calculation

*s s I I* 

*s s V V* 

Fig. 20. DFIG control structure

*q*

Fig. 21. DFIG control reference systems

 

\* 

*wv* \* *w r*

\* *Prated*

*v*

\* *rd I*

*s*

$$Q\_s \approx \frac{3}{2} \left| V\_s \right| \left[ \frac{\left| V\_s \right|}{o \rho\_c L\_s} - \frac{L\_m}{L\_s} i\_{rd} \right] \tag{31}$$

Equations 30 and 31 showed that the stator active power is controlled with the q component of the rotor current and the stator reactive power with the rotor current d component. In figure 20 can be seen both hybrid fuzzy controllers to regulate the d and q rotor current components.

The real platform to test the double feed induction generator and its main characteristics used also for the simulation purpose are shown in figure 22.

The real system is based on a DS1103 board and is programmed using the software Matlab/Simulink©. The board controls the inverters in a Back to Back configuration generating the SVPWM pulses (dSPACE©, 2005). The grid connected inverter, is regulated keeping the DC

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 101

regulates the output power modifying the pitch angle to get the rated power from the

Fig. 23. Rotor current q component controller fuzzy surface and trajectory after current step

<sup>0</sup> 0.5 <sup>1</sup> 1.5 -15

Fig. 24. Rotor current q component step reference and feedback, error for the step, and

%

t(s)

Overshoot

PI 1.2ms 1.2ms 4ms 20 8413 4110 11576 5105 FPI+P 1ms 1ms 3.5ms 20 7925 3880 10200 4510 Table 3. Time domain specifications and performance criteria for two classes of controllers


Settling time

The power transmitted to the hub of a wind turbine can be expressed as,


0

Irq error (A)

5

10

15

*error*




Change of Irq error (A)

0

1

2

3 x 104

<sup>0</sup> 0.5 <sup>1</sup> 1.5 -4

IAE ITAE ISE ITSE

t(s)

generator without damage it.

*change of error*

Ref Fdbk

<sup>4</sup> *x*10

<sup>0</sup> 0.5 <sup>1</sup> 1.5 <sup>6</sup>

time

t(s)

Rise Time

change of error

Delay

Irq (A)

 *control action*

of figure 24

bus voltage constant. The speed of the DFIG is measured with a 4096 impulse encoder connected to the DS1103 using the frequency method (Cortajarena et al., 2006).

First, the inner current loops are adjusted. The used hybrid fuzzy controller is the same as have been used in the squirrel cage machine. The scaling factors have been adapted after realizing multiple simulations and finally adjusted in the DFIG test rig.

Fig. 22. DFIG rig test and its main characteristics

To test the performance of the hybrid fuzzy controller it will be compared to a conventional PI controller. In a classical PI controller the proportional term for a bandwidth of 3000 rad/s and a phase margin of 80º with the machine parameters given in figure 22 is 0.015. For both current controllers, the proportional term KP will be 0.015 and the scaling factors are *GE GCE* 300, 0.025 and 0.2 *GCU* . The regulators maximum and minimum limits are ±1, equivalent to ±310 V per phase in the rotor.

Figure 23 shows the hybrid fuzzy rotor q current controller surface and the trajectory when a step reference from 10 to 20 amperes is produced. The feedback or real rotor q current reaches the real value quickly, it takes around 3 ms.

The trajectory on the fuzzy surface for this step shows how the error is moving around the high slope where the error is close to zero. In table 3, the performances of two controllers are summarized. The hybrid fuzzy and the conventional PI have similar dynamic response, showing the fuzzy controller a better performance when IAE, ITAE, ISE and ITSE indexes are used to evaluate the performance.

In a DFIG control there are two operating regions depending on the wind speed. Below the machine rated power, the blade pitch angle is set to zero degrees to get the maximum power. When the wind speed is sufficiently fast to get power from the wind higher than the rated power, enters into the second region. In this region the blade pitch angle controller

bus voltage constant. The speed of the DFIG is measured with a 4096 impulse encoder

First, the inner current loops are adjusted. The used hybrid fuzzy controller is the same as have been used in the squirrel cage machine. The scaling factors have been adapted after

6*xPWM*

ga , , *gb gc iii* ga , , *gb gc iii* ra , , *rb rc iii*

6*xPWM*

*DFIG*

To test the performance of the hybrid fuzzy controller it will be compared to a conventional PI controller. In a classical PI controller the proportional term for a bandwidth of 3000 rad/s and a phase margin of 80º with the machine parameters given in figure 22 is 0.015. For both current controllers, the proportional term KP will be 0.015 and the scaling factors are *GE GCE* 300, 0.025 and 0.2 *GCU* . The regulators maximum and minimum limits are

Figure 23 shows the hybrid fuzzy rotor q current controller surface and the trajectory when a step reference from 10 to 20 amperes is produced. The feedback or real rotor q current

The trajectory on the fuzzy surface for this step shows how the error is moving around the high slope where the error is close to zero. In table 3, the performances of two controllers are summarized. The hybrid fuzzy and the conventional PI have similar dynamic response, showing the fuzzy controller a better performance when IAE, ITAE, ISE and ITSE indexes

In a DFIG control there are two operating regions depending on the wind speed. Below the machine rated power, the blade pitch angle is set to zero degrees to get the maximum power. When the wind speed is sufficiently fast to get power from the wind higher than the rated power, enters into the second region. In this region the blade pitch angle controller

sa *sb sc*

J = 0.045Kg\*m2 B = 0.02Kg\*m2/s P = 2 pole-pairs Rr = 0.275Ω Rs = 0.325Ω Lm = 0.0664H Lr = 0.0678H Ls = 0.0681H

Stator voltage 380V Rotor voltage 190V Frequency 50Hz Rated current 14A Rated Torque 50Nm Rated speed 1440r.p.m.

*i i i*

*i*

3 380 *x V*

*m*

connected to the DS1103 using the frequency method (Cortajarena et al., 2006).

realizing multiple simulations and finally adjusted in the DFIG test rig.

FPGA and signal conditioning

sa , , *sb sc iii*

PC with DS1103

*dc u*

<sup>a</sup> , , *b c uuu*

Fig. 22. DFIG rig test and its main characteristics

±1, equivalent to ±310 V per phase in the rotor.

are used to evaluate the performance.

reaches the real value quickly, it takes around 3 ms.

\* *m*

3 380 *x V*

*PMSM*

*m* regulates the output power modifying the pitch angle to get the rated power from the generator without damage it.

Fig. 23. Rotor current q component controller fuzzy surface and trajectory after current step of figure 24

Fig. 24. Rotor current q component step reference and feedback, error for the step, and change of error


Table 3. Time domain specifications and performance criteria for two classes of controllers

The power transmitted to the hub of a wind turbine can be expressed as,

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 103

Rated power

4m/s 6m/s 8m/s 10m/s 11m/s

Wind speed

Tip speed ratio,  *P*

Pitch angle, 

*Cp*

0 1 2 3 4 5 6 7

wpr(rad/s)

The actuator is modelled in closed loop with saturation of the pitch angle and a pitch rate limitation. This closed loop configuration with integrator, gives similar result as a first order transfer function but with limitation of the pitch rate (Bindner, 1999). If the pitch reference angle is outside the lower and higher limits, the integrator output is prevented from

The pitch control diagram is shown in figure 27, where P is the DFIG real power, Pmax DFIG is the maximum admissible power for the DFIG and P\* is the active power reference.

> 1 *p*

The pitching speed rate is fixed to 10º/s, the pitch angle is limited from 0 to 30º, the KP value and the scaling factors adjusted after simulations ensuring stability for the pitch controller are 0.003 *KP* , *GE GCE* 400, 0.24 and 0.1 *GCU* . The hybrid fuzzy

Figure 28 left, shows the response of the pitch control when a wind speed step from 9m/s to 13m/s is produced. The obtained total power from the wind at 9m/s is 3800w and when the wind speed power is higher than the fixed 7000w, the pitch angle starts the regulation to limit the total power. The figure to the right shows the same signals for a random speed profile. When the wind speed is lower than 10m/s the pitch angle is zero, and all wind power is converted in electric power, but when the speed is higher, the pitch angle is

regulator maximum and minimum limits are 0 to 30º as pitch angle reference limit.

 

regulated limiting the maximum power returned to the grid.

Fig. 26. Obtained wind power for a pitch angle of 0º, depending on wind speed and

0

growing indefinitely.

 

Fig. 27. Pitch control diagram

*P*max*DFIG*

*P*

propeller speed

2000

4000

6000

Power (W)

8000

10000

0º

$$P\_{turb} = \frac{1}{2} \mathcal{C}\_p(\mathcal{A}, \mathcal{J}) \rho\_{air} \pi R^2 v\_w^{-3} \tag{32}$$

Where ρair, is the mass density of the air, R is the radius of the propeller, Cp is the power performance coe4fficient, vw is the wind speed, β is the pitch angle and λ is the blade tip speed ratio and is defined as,

$$
\mathcal{A} = \frac{\mathcal{R} \cdot \mathcal{O}\_{pr}}{\upsilon\_w} \tag{33}
$$

and ωpr is the angular velocity of the propeller.

The power performance coefficient Cp, used according to the tip speed ratio and the pitch angle for the DFIG is shown in figure 25.

Fig. 25. Power performance coefficient depending on tip speed ratio and pitch angle

Figure 26 shows for a pitch angle of 0º the obtained power from the wind according to the propeller speed. The black line indicates the maximum power and the propeller speed to get this power from every wind speed. When the obtained power reaches the machine rated power, the wind energy is wasted changing the pitch angle and getting the rated power.

For a known wind speed and using figure 26, the propeller optimum speed and the power are obtained. Then, with equation 30 the rotor q component is determined as reference.

The inertia of the blades turned by the drive is large and a real pitch actuator has thus limited capabilities. Its dynamics are non-linear with saturation limits on pitch angle (usually from 0 to 30º) and pitching speed rate around 10º/s.

Where ρair, is the mass density of the air, R is the radius of the propeller, Cp is the power performance coe4fficient, vw is the wind speed, β is the pitch angle and λ is the blade tip

> *R v*

The power performance coefficient Cp, used according to the tip speed ratio and the pitch

Fig. 25. Power performance coefficient depending on tip speed ratio and pitch angle

Figure 26 shows for a pitch angle of 0º the obtained power from the wind according to the propeller speed. The black line indicates the maximum power and the propeller speed to get this power from every wind speed. When the obtained power reaches the machine rated power, the wind energy is wasted changing the pitch angle and getting the rated power.

For a known wind speed and using figure 26, the propeller optimum speed and the power are obtained. Then, with equation 30 the rotor q component is determined as reference.

The inertia of the blades turned by the drive is large and a real pitch actuator has thus limited capabilities. Its dynamics are non-linear with saturation limits on pitch angle

speed ratio and is defined as,

Pitch angle,

*Cp*

(usually from 0 to 30º) and pitching speed rate around 10º/s.

and ωpr is the angular velocity of the propeller.

angle for the DFIG is shown in figure 25.

<sup>1</sup> 2 3 (, ) <sup>2</sup> *P C Rv turb <sup>p</sup>* 

> *pr w*

 

*air w* (32)

(33)

Tip speed ratio,

Fig. 26. Obtained wind power for a pitch angle of 0º, depending on wind speed and propeller speed

The actuator is modelled in closed loop with saturation of the pitch angle and a pitch rate limitation. This closed loop configuration with integrator, gives similar result as a first order transfer function but with limitation of the pitch rate (Bindner, 1999). If the pitch reference angle is outside the lower and higher limits, the integrator output is prevented from growing indefinitely.

The pitch control diagram is shown in figure 27, where P is the DFIG real power, Pmax DFIG is the maximum admissible power for the DFIG and P\* is the active power reference.

Fig. 27. Pitch control diagram

The pitching speed rate is fixed to 10º/s, the pitch angle is limited from 0 to 30º, the KP value and the scaling factors adjusted after simulations ensuring stability for the pitch controller are 0.003 *KP* , *GE GCE* 400, 0.24 and 0.1 *GCU* . The hybrid fuzzy regulator maximum and minimum limits are 0 to 30º as pitch angle reference limit.

Figure 28 left, shows the response of the pitch control when a wind speed step from 9m/s to 13m/s is produced. The obtained total power from the wind at 9m/s is 3800w and when the wind speed power is higher than the fixed 7000w, the pitch angle starts the regulation to limit the total power. The figure to the right shows the same signals for a random speed profile. When the wind speed is lower than 10m/s the pitch angle is zero, and all wind power is converted in electric power, but when the speed is higher, the pitch angle is regulated limiting the maximum power returned to the grid.

Control and Estimation of Asynchronous Machines Using Fuzzy Logic 105


Speed (rpm)

Ref

Real

sensor has been replaced for the speed estimator to get a sensorless system.

controllers have been implemented in the real platforms giving good results.

Fig. 29. Speed regulation when there is a big noise in the stator current measurement. A load step of 40Nm is applied to the machine at 0.5s. Left, PI controllers. Right, hybrid fuzzy

Control of asynchronous machines can be made relatively simple if the machine is understood as a DC machine. This is obtained making the appropriate transformations of reference systems. The squirrel cage machine has been used as a motor and hybrid fuzzy controllers have been used to control the speed of the machine. The performance has been compared with classical PI and fuzzy controllers, showing a better performance. Also a speed estimator has been implemented using two hybrid fuzzy controllers. The speed

The control of the double feed induction generator used in wind turbines has been studied. First the main control equations are presented and then, the rotor current controllers are implemented with the hybrid fuzzy controllers. The performance is compared to conventional PI controllers, showing a slightly better performance. Also pitch control is realized to limit the maximum power obtained from the wind. The real system shows how

All the proposed controllers have been simulated and compared to the real system to validate the systems model. With the checked models, the adjustments to guarantee the stability and to get good performance are done. Then, all of simulated hybrid fuzzy


0

Stator current (A)

50

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

t(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ref Real

t(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

t(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

t(s)

the controller limits the maximum power properly.


controllers

**7. Conclusions** 

Speed (rpm)


0

Stator current (A)

50

100

Fig. 28. Fuzzy pitch control performance when a step of wind speed and a random wind speed profile are produced

#### **6. Parameter variations**

As it was commented into the introduction, the fuzzy logic approach is based on linguistic rules, and the controller robustness is high. To verify the above, the squirrel-cage motor is replaced by a different one. The motor parameters change and without realizing any adjustment in the controllers the speed regulation is tested in a motor control with conventional PI controllers and with the proposed hybrid fuzzy controllers. The new motor parameters are: Rr=1.2 Ω, Rs=1.5 Ω, Lm=0.108 H, Lr=0.12 H, Ls=0.12 H, J=0.038 Kg\*m2.

Figure 29 shows the speed of the machine when there is a big noise in the stator alfa and beta components; in fact the noise is very high. The speed reference is 1000 rpm and a load step of 40 Nm is applied to the new machine, without readjusting the controllers, at 0.5s. The left figure shows the response of the machine controlled with PI controllers. The performance of the system becomes wrong when the load changes after 0.5s, the system becomes instable. Instead, in the right figure the motor is controlled with the hybrid fuzzy controllers adjusted in section 4. When the load torque is applied to the machine the speed regulation after that moment is correct. This is an example of the robustness of the fuzzy controller compared with the conventional PI controllers when there is noise in the measurements, in this case stator current measurement.

Fig. 29. Speed regulation when there is a big noise in the stator current measurement. A load step of 40Nm is applied to the machine at 0.5s. Left, PI controllers. Right, hybrid fuzzy controllers

## **7. Conclusions**

104 Fuzzy Logic – Controls, Concepts, Theories and Applications

0


Pitch angle (º)

Fig. 28. Fuzzy pitch control performance when a step of wind speed and a random wind

As it was commented into the introduction, the fuzzy logic approach is based on linguistic rules, and the controller robustness is high. To verify the above, the squirrel-cage motor is replaced by a different one. The motor parameters change and without realizing any adjustment in the controllers the speed regulation is tested in a motor control with conventional PI controllers and with the proposed hybrid fuzzy controllers. The new motor parameters are: Rr=1.2 Ω, Rs=1.5 Ω, Lm=0.108 H, Lr=0.12 H, Ls=0.12 H, J=0.038

Figure 29 shows the speed of the machine when there is a big noise in the stator alfa and beta components; in fact the noise is very high. The speed reference is 1000 rpm and a load step of 40 Nm is applied to the new machine, without readjusting the controllers, at 0.5s. The left figure shows the response of the machine controlled with PI controllers. The performance of the system becomes wrong when the load changes after 0.5s, the system becomes instable. Instead, in the right figure the motor is controlled with the hybrid fuzzy controllers adjusted in section 4. When the load torque is applied to the machine the speed regulation after that moment is correct. This is an example of the robustness of the fuzzy controller compared with the conventional PI controllers when there is noise in the


P (w)

P actual P rated

Wind speed (m/s)

0 10 20 30 40 50 60

t(s)

P actual P rated

0 10 20 30 40 50 60

t(s)

0 10 20 30 40 50 60

t(s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

measurements, in this case stator current measurement.

t(s)

t(s)

t(s)


0

Kg\*m2.

speed profile are produced

**6. Parameter variations** 

5

Pitch angle (º)

10

P (w)

Wind speed (m/s)

Control of asynchronous machines can be made relatively simple if the machine is understood as a DC machine. This is obtained making the appropriate transformations of reference systems. The squirrel cage machine has been used as a motor and hybrid fuzzy controllers have been used to control the speed of the machine. The performance has been compared with classical PI and fuzzy controllers, showing a better performance. Also a speed estimator has been implemented using two hybrid fuzzy controllers. The speed sensor has been replaced for the speed estimator to get a sensorless system.

The control of the double feed induction generator used in wind turbines has been studied. First the main control equations are presented and then, the rotor current controllers are implemented with the hybrid fuzzy controllers. The performance is compared to conventional PI controllers, showing a slightly better performance. Also pitch control is realized to limit the maximum power obtained from the wind. The real system shows how the controller limits the maximum power properly.

All the proposed controllers have been simulated and compared to the real system to validate the systems model. With the checked models, the adjustments to guarantee the stability and to get good performance are done. Then, all of simulated hybrid fuzzy controllers have been implemented in the real platforms giving good results.

**6** 

 *Algeria* 

**Application of Fuzzy Logic in** 

Abdel Ghani Aissaoui1 and Ahmed Tahour2

*1Faculty of Science & Technology, University of Bechar, Bechar, 2Faculty of Science & Technology, University of Mascara, Mascara,* 

**Control of Electrical Machines** 

During the past decades, fuzzy logic control (FLC) has been one of the most active and fruitful areas for research in the application of fuzzy set theory. It has has been an active research topic in automation and control theory, since the work of Mamdani proposed in 1974 based on the fuzzy sets theory of Zadeh (1965), to deal with the system control

The literature in fuzzy control has been growing rapidly in recent years, making it difficult to present a comprehensive survey of the wide variety of applications that have been made. Fuzzy logic, which is the logic on which fuzzy control is based, is much closer in spirit to human thinking and natural language than the traditional logical systems. Basically, it provides an effective means of capturing the approximate and the inexact nature of the real world. The fuzzy logic controller is a set of linguistic control rules related by the dual concepts of fuzzy implication and the compositional rule of inference. The FLC provides an algorithm which can convert the linguistic control strategy based on expert knowledge into

The concept of FLC is to utilize the qualitative knowledge of a system to design a practical controller. For a process control system, a fuzzy control algorithm embeds the intuition and experience of an operator designer and researcher. The fuzzy control method is suitable for systems with non-specific models, and therefore, it suits well to a process where the model is unknown or ill-defined and particularly to systems with uncertain or complex dynamics

The implementation of such control consists of translating the input variables to a language like: positive big, zero, negative small, etc. and to establish control rules so that the decision process can produce the appropriate outputs. Fuzzy control (FC) using linguistic information possesses several advantages such as robustness, model-free, universal approximation theorem and rules-based algorithm [Kim Y.T.& Bien Z. 2000; Lee C.C. 1990;

problems which is not easy to be modeled [Mamdani E.H. 1974].

**1. Introduction** 

an automatic control strategy.

[Yu F. M. et al 2003].

Timothy J. R. 1994].

Also, the robustness of the controlled system with the hybrid fuzzy controllers is demonstrated, compared with the conventional control implemented with conventional PI regulators.

## **8. References**


## **Application of Fuzzy Logic in Control of Electrical Machines**

Abdel Ghani Aissaoui1 and Ahmed Tahour2

*1Faculty of Science & Technology, University of Bechar, Bechar, 2Faculty of Science & Technology, University of Mascara, Mascara, Algeria* 

## **1. Introduction**

106 Fuzzy Logic – Controls, Concepts, Theories and Applications

Also, the robustness of the controlled system with the hybrid fuzzy controllers is demonstrated, compared with the conventional control implemented with conventional PI

Astrom, K.J. ; Hagglung, T. (1996). Automatic tuning of PID controllers. *The Control* 

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Won, C.Y. ; Bose, B.K. (1992). An Induction Motor Servo System with Improved Sliding

Zhen, L. ; Xu, L. (1998). Sensorless Field Oriented Control of Induction Machines Based on a Mutual MRAS Scheme. *IEEE Trans. on Indust. Electonics.* Vol 45. no.5. pp 824-830.

Mode Control. *IEEE Conf. Proceedings of IECON'92*, pp. 60-66. Zadeh, L.A. (1965). Fuzzy sets. *Information and Control*, Vol. 8 pp 338-353.

speed doubly-fed induction generator wind turbine. *Proc. of Wind Power Nordic* 

*Neural, Fuzzy-Neural, and Genetic-Algorithm-Based Techniques*. Oxford University

induction motor speed estimators. *Proceedings of SAAEI06.* Gijón.

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regulators.

**8. References** 

Inc. pp 817-846.

Laboratory, Roskilde, Denmark.

Realese 5.0. GmbH Paderborn, Germany.

AC Motor Drives. *IEEE Press*,pp21-29.

Press, Inc., ISBN 0 19 859397 X, New York.

University of Denmark, Lyngby.

During the past decades, fuzzy logic control (FLC) has been one of the most active and fruitful areas for research in the application of fuzzy set theory. It has has been an active research topic in automation and control theory, since the work of Mamdani proposed in 1974 based on the fuzzy sets theory of Zadeh (1965), to deal with the system control problems which is not easy to be modeled [Mamdani E.H. 1974].

The literature in fuzzy control has been growing rapidly in recent years, making it difficult to present a comprehensive survey of the wide variety of applications that have been made. Fuzzy logic, which is the logic on which fuzzy control is based, is much closer in spirit to human thinking and natural language than the traditional logical systems. Basically, it provides an effective means of capturing the approximate and the inexact nature of the real world. The fuzzy logic controller is a set of linguistic control rules related by the dual concepts of fuzzy implication and the compositional rule of inference. The FLC provides an algorithm which can convert the linguistic control strategy based on expert knowledge into an automatic control strategy.

The concept of FLC is to utilize the qualitative knowledge of a system to design a practical controller. For a process control system, a fuzzy control algorithm embeds the intuition and experience of an operator designer and researcher. The fuzzy control method is suitable for systems with non-specific models, and therefore, it suits well to a process where the model is unknown or ill-defined and particularly to systems with uncertain or complex dynamics [Yu F. M. et al 2003].

The implementation of such control consists of translating the input variables to a language like: positive big, zero, negative small, etc. and to establish control rules so that the decision process can produce the appropriate outputs. Fuzzy control (FC) using linguistic information possesses several advantages such as robustness, model-free, universal approximation theorem and rules-based algorithm [Kim Y.T.& Bien Z. 2000; Lee C.C. 1990; Timothy J. R. 1994].

Application of Fuzzy Logic in Control of Electrical Machines 109

membership function. In fuzzy set terminology, all the possible values that a variable can assume are named universe of discourse, and the fuzzy sets (characterized by membership functions) cover the whole universe of discourse. The shape of fuzzy sets can be triangular,

A fuzzy control essentially embeds the intuition and experience of a human operator, and sometimes those of a designer and researcher. The data base and the rules form the knowledge base which is used to obtain the inference relation R. The data base contains a description of input and output variables using fuzzy sets. The rule base is essentially the control strategy of the system. It is usually obtained from expert knowledge or heuristics, it contains a collection of fuzzy conditional statements expressed as a set of IF-THEN rules,

 R(i) : **If** *x*1 is F1 and *x*2 is F2 …and *xn* is F*<sup>n</sup>* **THEN** Y is G(i), i=1, …, M (1) where : (*x*1, *x*2, …, *xn*) is the input variables vector, Y is the control variable, M is the number

For the given rule base of a control system, the fuzzy controller determines the rule base to be fired for the specific input signal condition and then computes the effective control action

The composition operation is the method by which such a control output can be generated using the rule base. Several composition methods, such as max-min or sup-min and max-dot

The mathematical procedure of converting fuzzy values into crisp values is known as 'defuzzification'. A number of defuzzification methods have been suggested. The choice of

of rules, *n* is the number of fuzzy variables, (F1, F2,… F*n*) are the fuzzy sets.

(the output fuzzy variable) [Bose B. K. 1994 ; Spooner J.T. et al 2002].

have been proposed in the literature.

Fig. 1. The internal configuration of a fuzzy logic controller

trapezoïdale, etc [BOSE B. K. 1994; Bühler H. 1994].

such as:

As an intelligent control technology, fuzzy logic control (FLC) provides a systematic method to incorporate human experience and implement nonlinear algorithms, characterized by a series of linguistic statements, into the controller. In general, a fuzzy control algorithm consists of a set of heuristic decision rules and can be regarded as an adaptive and nonmathematical control algorithm based on a linguistic process, in contrast to a conventional feedback control algorithm [Sousa G.C. D.& Bose B. K. 1994; Yager, R. R. 1997].

The fuzzy control also works as well for complex nonlinear multi-dimensional system, system with parameter variation problem or where the sensor signals are not precise. It is basically nonlinear and adaptive in nature, giving robust performance under parameter variation and load disturbance effect.

In process control applications, recent literature has explored the potentials of fuzzy control for machine drive application [Tang Y. & Xu L. 1994, Heber B. et al 1995 ]. It has been shown that a properly designed direct fuzzy controller can outperform conventional proportional integral derivative (PID) controllers [Heber B. et al 1995 ].

This paper presents an application of fuzzy logic to control the speed of a synchronous machine (SM). Based on the analysis of the SM transient response and fuzzy logic, a fuzzy controller is developed. The fuzzy controller generates the variations of the reference current vector of the SM speed control based on the speed error and its change. Digital simulation results shows that the designed fuzzy speed controller realises a good dynamic behaviour of the motor, a perfect speed tracking with no overshoot and a good rejection of impact loads disturbance. The results of applying the fuzzy logic controller to a SM show best performances and high robustness than those obtained by the application of a conventional controller (PI). In this paper, we propose several controllers based on fuzzy logic, to deduce the best one.

The organization of this paper is as follows: in section 2, the fuzzy logic control principle is described and used to design fuzzy logic controllers; in section 3, vector control principle for synchronous motor drive is presented, the proposed controllers are used to control the synchronous motor speed. In section 4, simulation results are given to show the effectiveness of these controllers and finally conclusions are summarized in the last section.

## **2. Fuzzy logic control**

The structure of a complete fuzzy control system consists of the following main parts:


Figure (1) shows the internal configuration of a fuzzy logic controller.

## **2.1 Fuzzy logic principle**

The fuzzification module converts the crisp values of the control inputs into fuzzy values. A fuzzy variable has values which are defined by linguistic variables (fuzzy sets or subsets) such as low, Medium, high, big, slow… where each one is defined by a gradually varying

As an intelligent control technology, fuzzy logic control (FLC) provides a systematic method to incorporate human experience and implement nonlinear algorithms, characterized by a series of linguistic statements, into the controller. In general, a fuzzy control algorithm consists of a set of heuristic decision rules and can be regarded as an adaptive and nonmathematical control algorithm based on a linguistic process, in contrast to a conventional feedback control

The fuzzy control also works as well for complex nonlinear multi-dimensional system, system with parameter variation problem or where the sensor signals are not precise. It is basically nonlinear and adaptive in nature, giving robust performance under parameter

In process control applications, recent literature has explored the potentials of fuzzy control for machine drive application [Tang Y. & Xu L. 1994, Heber B. et al 1995 ]. It has been shown that a properly designed direct fuzzy controller can outperform conventional proportional

This paper presents an application of fuzzy logic to control the speed of a synchronous machine (SM). Based on the analysis of the SM transient response and fuzzy logic, a fuzzy controller is developed. The fuzzy controller generates the variations of the reference current vector of the SM speed control based on the speed error and its change. Digital simulation results shows that the designed fuzzy speed controller realises a good dynamic behaviour of the motor, a perfect speed tracking with no overshoot and a good rejection of impact loads disturbance. The results of applying the fuzzy logic controller to a SM show best performances and high robustness than those obtained by the application of a conventional controller (PI). In this paper, we propose several controllers based on fuzzy

The organization of this paper is as follows: in section 2, the fuzzy logic control principle is described and used to design fuzzy logic controllers; in section 3, vector control principle for synchronous motor drive is presented, the proposed controllers are used to control the synchronous motor speed. In section 4, simulation results are given to show the effectiveness of these controllers and finally conclusions are summarized in the last section.

The structure of a complete fuzzy control system consists of the following main parts:

The fuzzification module converts the crisp values of the control inputs into fuzzy values. A fuzzy variable has values which are defined by linguistic variables (fuzzy sets or subsets) such as low, Medium, high, big, slow… where each one is defined by a gradually varying

Figure (1) shows the internal configuration of a fuzzy logic controller.

algorithm [Sousa G.C. D.& Bose B. K. 1994; Yager, R. R. 1997].

integral derivative (PID) controllers [Heber B. et al 1995 ].

variation and load disturbance effect.

logic, to deduce the best one.

**2. Fuzzy logic control** 

**2.1 Fuzzy logic principle** 


Fig. 1. The internal configuration of a fuzzy logic controller

membership function. In fuzzy set terminology, all the possible values that a variable can assume are named universe of discourse, and the fuzzy sets (characterized by membership functions) cover the whole universe of discourse. The shape of fuzzy sets can be triangular, trapezoïdale, etc [BOSE B. K. 1994; Bühler H. 1994].

A fuzzy control essentially embeds the intuition and experience of a human operator, and sometimes those of a designer and researcher. The data base and the rules form the knowledge base which is used to obtain the inference relation R. The data base contains a description of input and output variables using fuzzy sets. The rule base is essentially the control strategy of the system. It is usually obtained from expert knowledge or heuristics, it contains a collection of fuzzy conditional statements expressed as a set of IF-THEN rules, such as:

$$\mathbf{R}^{\langle \rangle} \colon \mathbf{If } \mathbf{x}\_1 \text{ is } \mathbf{F}\_1 \text{ and } \mathbf{x}\_2 \text{ is } \mathbf{F}\_2 \dots \text{and } \mathbf{x}\_n \text{ is } \mathbf{F}\_n \text{ THEN } \mathbf{Y} \text{ is } \mathbf{G}^{\langle \rangle}, \mathbf{i} = \mathbf{1}, \dots, \mathbf{M} \tag{1}$$

where : (*x*1, *x*2, …, *xn*) is the input variables vector, Y is the control variable, M is the number of rules, *n* is the number of fuzzy variables, (F1, F2,… F*n*) are the fuzzy sets.

For the given rule base of a control system, the fuzzy controller determines the rule base to be fired for the specific input signal condition and then computes the effective control action (the output fuzzy variable) [Bose B. K. 1994 ; Spooner J.T. et al 2002].

The composition operation is the method by which such a control output can be generated using the rule base. Several composition methods, such as max-min or sup-min and max-dot have been proposed in the literature.

The mathematical procedure of converting fuzzy values into crisp values is known as 'defuzzification'. A number of defuzzification methods have been suggested. The choice of

Application of Fuzzy Logic in Control of Electrical Machines 111


N Z P

*e*

N Z P


*de*

N Z P


*u*


Table 1 shows one of possible control rules based on five membership functions [Aissaoui et

*de e*

Fig. 4. The output surface of the fuzzy inference system for three fuzzy subsets using the



0

0.5

1 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

**2.3 Fuzzy control with five fuzzy subsets** 

*u*

inputs and the output.

al 2007].


0

0.5

1

0 0.5 1 1.5

0 0.5 1 1.5

0 0.5 1 1.5

Fig. 3. Membership functions for input e, *de* and *u*

defuzzification methods usually depends on the application and the available processing power. This operation can be performed by several methods of which center of gravity (or centroïd) and height methods are common [Spooner J.T. et al 2002 ; Rachid A. 1996].

Fig. 2. Basic structure of fuzzy control system

The actual crisp input are approximates to the closer values of the respective universes of discourse. Hence, the fuzzy inputs are described by singleton fuzzy sets.

The elaboration of this controller is based on the phase plan. The control rules are designed to assign a fuzzy set of the control input *u* for each combination of fuzzy sets of *e* and Δ*e* [Aissaoui A. G. et al 2007]. The performances of such controller depend on the quality of rules and the choice of the fuzzy sets that describe number of the inputs and the output of the controller.

### **2.2 Fuzzy control with three fuzzy subsets**

Table 1 shows one of possible control rules based on three membership functions [Aissaoui 2007].


Table 1. Rules Base for speed control

The columns represent the rate of the error change *de* and the rows represent the error *e*. Each pair (*e*, *de*) determines the output level N to P corresponding to *u*.

Here N is negative, Z is zero, P is positive, are labels of fuzzy sets and their corresponding membership functions are depicted in figure (3). Figure (4) shows the corresponding output surface.

defuzzification methods usually depends on the application and the available processing power. This operation can be performed by several methods of which center of gravity (or

The actual crisp input are approximates to the closer values of the respective universes of

The elaboration of this controller is based on the phase plan. The control rules are designed to assign a fuzzy set of the control input *u* for each combination of fuzzy sets of *e* and Δ*e* [Aissaoui A. G. et al 2007]. The performances of such controller depend on the quality of rules and the choice of the fuzzy sets that describe number of the inputs and the output of

Table 1 shows one of possible control rules based on three membership functions [Aissaoui

*de* N Z P

N N N Z Z N Z P P Z P P

The columns represent the rate of the error change *de* and the rows represent the error *e*.

Here N is negative, Z is zero, P is positive, are labels of fuzzy sets and their corresponding membership functions are depicted in figure (3). Figure (4) shows the corresponding output

discourse. Hence, the fuzzy inputs are described by singleton fuzzy sets.

*u*

Each pair (*e*, *de*) determines the output level N to P corresponding to *u*.

*e*

centroïd) and height methods are common [Spooner J.T. et al 2002 ; Rachid A. 1996].

Fig. 2. Basic structure of fuzzy control system

**2.2 Fuzzy control with three fuzzy subsets** 

Table 1. Rules Base for speed control

the controller.

2007].

surface.

Fig. 3. Membership functions for input e, *de* and *u*

Fig. 4. The output surface of the fuzzy inference system for three fuzzy subsets using the inputs and the output.

#### **2.3 Fuzzy control with five fuzzy subsets**

Table 1 shows one of possible control rules based on five membership functions [Aissaoui et al 2007].

Application of Fuzzy Logic in Control of Electrical Machines 113

Fig. 6. The output surface of the fuzzy inference system for five fuzzy subsets using the

Table 3 shows one of possible control rules based on seven membership functions [Aissaoui

**NB NB NB NB NB NM NS <sup>Z</sup>**

**NM NB NB NB NM NS Z PS** 

**NS NB NB NM NS Z PS PM** 

**Z NB NM NS Z PS PM PB** 

**PS NM NS Z PS PM PB PB** 

**PM NS Z PS PM PB PB PB** 

**PB Z PS PM PB PB PB PB** 

Here NS is negative small and PS is positive small. The labels of fuzzy sets and their corresponding membership functions are depicted in figures (7). Figure (8) shows the

**NB NM NS Z PS PM PB** 

inputs and the output.

et al 2011].

**2.4 Fuzzy control with seven fuzzy subsets** 

 **e de u**

Table 3. Rules Base for speed control

corresponding output surface.


Table 2. Rules Base for speed control

Here NB is negative big, NM is negative medium, ZR is zero, PM is positive medium and PB is positive big, are labels of fuzzy sets and their corresponding membership functions are depicted in figures (5). Figure (6) shows the corresponding output surface.

Fig. 5. Membership functions for input e, *de* and *u*

NB NB NB NM NM ZR NM NB NM NM ZR PM ZR NM NM ZR PM PM PM NM ZR PM PM GP PB ZR PM PM GP GP

Here NB is negative big, NM is negative medium, ZR is zero, PM is positive medium and PB is positive big, are labels of fuzzy sets and their corresponding membership functions are

depicted in figures (5). Figure (6) shows the corresponding output surface.

*de*  NB NM ZR PM PB

*u*

*e*

Fig. 5. Membership functions for input e, *de* and *u*

Table 2. Rules Base for speed control

Fig. 6. The output surface of the fuzzy inference system for five fuzzy subsets using the inputs and the output.

## **2.4 Fuzzy control with seven fuzzy subsets**

Table 3 shows one of possible control rules based on seven membership functions [Aissaoui et al 2011].


Table 3. Rules Base for speed control

Here NS is negative small and PS is positive small. The labels of fuzzy sets and their corresponding membership functions are depicted in figures (7). Figure (8) shows the corresponding output surface.

Application of Fuzzy Logic in Control of Electrical Machines 115

The choice of membership functions (MF) is important in the design of fuzzy logic controller. The most MF shapes known and used frequently are: Triangular, Gaussian, Trapezoidal,… Different cases can be subject of our study, following the MF used and their

Fig. 9. Membership functions for input e, *de* and *u* arranged in symmetrical Gaussian shape.


*de e*


Fig. 10. The output surface of the fuzzy inference system for five fuzzy subsets in


0.5

1 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

*u*

symmetrical Gaussian shape.


0

0.5

1

**2.5 Influence of the choice of Membership Function** 

**2.5.1 Symmetrical Gaussian membership functions** 

distribution on the universe of discourse.

Fig. 7. Membership functions for input e, *de* and *u*

Fig. 8. The output surface of the fuzzy inference system for seven fuzzy subsets using the inputs and the output.

The continuity of input membership functions, reasoning method, and defuzzification method for the continuity of the mapping *u ee fuzzy* , is necessary. In this paper, the triangular membership function, the max-min reasoning method, and the center of gravity defuzzification method are used, as those methods are most frequently used in many literatures [Bose B. K. 1994; Rachid A. 1996 ].


*de e*

Fig. 8. The output surface of the fuzzy inference system for seven fuzzy subsets using the

The continuity of input membership functions, reasoning method, and defuzzification method for the continuity of the mapping *u ee fuzzy* , is necessary. In this paper, the triangular membership function, the max-min reasoning method, and the center of gravity defuzzification method are used, as those methods are most frequently used in many




0

0.5

1

Fig. 7. Membership functions for input e, *de* and *u*

0.5

1

literatures [Bose B. K. 1994; Rachid A. 1996 ].


0

*u*

inputs and the output.

0.5

### **2.5 Influence of the choice of Membership Function**

The choice of membership functions (MF) is important in the design of fuzzy logic controller. The most MF shapes known and used frequently are: Triangular, Gaussian, Trapezoidal,… Different cases can be subject of our study, following the MF used and their distribution on the universe of discourse.

#### **2.5.1 Symmetrical Gaussian membership functions**

Fig. 9. Membership functions for input e, *de* and *u* arranged in symmetrical Gaussian shape.

Fig. 10. The output surface of the fuzzy inference system for five fuzzy subsets in symmetrical Gaussian shape.

Application of Fuzzy Logic in Control of Electrical Machines 117

Fig. 13. Membership functions for input e, *de* and *u* arranged in symmetrical triangular

Fig. 14. The output surface of the fuzzy inference system for five fuzzy subsets arranged in

symmetrical triangular shape and with limit recovery of the fuzzy sets.

**2.5.3 Limit recovery of fuzzy sets** 

shape and with limit recovery of the fuzzy sets

#### **2.5.2 Asymmetrical triangular membership functions**

Fig. 11. Membership functions for input e, *de* et *u* arranged in asymmetrical shape.

Fig. 12. The output surface of the fuzzy inference system for five fuzzy subsets arranged in asymmetrical shape..

#### **2.5.3 Limit recovery of fuzzy sets**

116 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 11. Membership functions for input e, *de* et *u* arranged in asymmetrical shape.

Fig. 12. The output surface of the fuzzy inference system for five fuzzy subsets arranged in

asymmetrical shape..

**2.5.2 Asymmetrical triangular membership functions** 

Fig. 13. Membership functions for input e, *de* and *u* arranged in symmetrical triangular shape and with limit recovery of the fuzzy sets

Fig. 14. The output surface of the fuzzy inference system for five fuzzy subsets arranged in symmetrical triangular shape and with limit recovery of the fuzzy sets.

Application of Fuzzy Logic in Control of Electrical Machines 119

In this section, we have based our study on Triangular MF. It gives same results compared to Gaussian MF as it can see in figures (6) and (10) which represent the output surface of the

The symmetry and the recovery of the fuzzy sets (or MF) are important and they significantly affect the performance of FLC. It appears clearly in the surface of fuzzy inference system (figures 6, 12, 14, 16). It is better to choose the MF with a symmetrical shape and the recovery of two to three fuzzy sets is very interest. This comparison is made

The schematic diagram of the speed control system under study is shown in figure (17). The power circuit consists of a continuous voltage supply which can provided by a six rectifier thyristors and a three phase GTO thyristors inverter whose output is connected to the stator of the synchronous machine. The field current *<sup>f</sup> i* of the synchronous machine, which determines the field flux level is controlled by voltage *<sup>f</sup> v* [Aissaoui, A. G. et al 2010;

Fig. 17. System Configuration of Field-Oriented Synchronous Motor Control.

fuzzy inference system of the inputs (*e* and *de*) and the output (*u*).

**2.5.5 Interpretation and discussion** 

using the rules base presented in Table 2.

**3. Description of machine drive** 

Namuduri, C. & Sen,P. C. 1987].

#### **2.5.4 Non recovery of of fuzzy sets**

Fig. 15. The output surface of the fuzzy inference system for five fuzzy subsets arranged in symmetrical triangular shape and with non-recovery of the fuzzy sets

Fig. 16. The output surface of the fuzzy inference system for five fuzzy subsets arranged in symmetrical triangular shape and with non-recovery of the fuzzy sets

#### **2.5.5 Interpretation and discussion**

118 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 15. The output surface of the fuzzy inference system for five fuzzy subsets arranged in

Fig. 16. The output surface of the fuzzy inference system for five fuzzy subsets arranged in

symmetrical triangular shape and with non-recovery of the fuzzy sets

symmetrical triangular shape and with non-recovery of the fuzzy sets

**2.5.4 Non recovery of of fuzzy sets** 

In this section, we have based our study on Triangular MF. It gives same results compared to Gaussian MF as it can see in figures (6) and (10) which represent the output surface of the fuzzy inference system of the inputs (*e* and *de*) and the output (*u*).

The symmetry and the recovery of the fuzzy sets (or MF) are important and they significantly affect the performance of FLC. It appears clearly in the surface of fuzzy inference system (figures 6, 12, 14, 16). It is better to choose the MF with a symmetrical shape and the recovery of two to three fuzzy sets is very interest. This comparison is made using the rules base presented in Table 2.

## **3. Description of machine drive**

The schematic diagram of the speed control system under study is shown in figure (17). The power circuit consists of a continuous voltage supply which can provided by a six rectifier thyristors and a three phase GTO thyristors inverter whose output is connected to the stator of the synchronous machine. The field current *<sup>f</sup> i* of the synchronous machine, which determines the field flux level is controlled by voltage *<sup>f</sup> v* [Aissaoui, A. G. et al 2010; Namuduri, C. & Sen,P. C. 1987].

Fig. 17. System Configuration of Field-Oriented Synchronous Motor Control.

Application of Fuzzy Logic in Control of Electrical Machines 121

field flux, *Te* – electromagnetic torque, *Tl* – external load disturbance, p – pair number of poles, B – is the damping coefficient, J – is the moment of inertia, *ω* – electrical angular

The self-control operation of the inverter-fed synchronous machine results in a rotor field oriented control of the torque and flux in the machine. The principle is to maintain the armature flux and the field flux in an orthogonal or decoupled axis. The flux in the machine is controlled independently by the field winding and the torque is affected by the fundamental component of armature current *qs i* . In order to have an optimal functioning, the direct current *ds i* is maintained equal to zero [Sturtzer G. & Smigiel E. 2000 ;

Substituting (5) in (4), the electromagnetic torque can be rewritten for *<sup>f</sup> i constant* and

 *Tt i t e qs* 

In the same conditions, it appears that the *ds v* and *qs v* equations are coupled. We have to introduce a decoupling system, by introducing the compensation terms *<sup>d</sup> emf* and *<sup>q</sup> emf* in

,

*q ds ds af f*

In order to validate the control strategies as discussed above, digital simulation studies were made on the system described in figure (17). The speed and currents loops of the drive were also designed and simulated respectively with fuzzy control and PI control. The feedback

The speed loop was closed, and transient response was tested with both PI current control and fuzzy speed control. We used several types of fuzzy controller based on the cases presented in section (2.2). The simulation of the starting mode without load is done,

Figures (18), (19) and (20) show the performances of the fuzzy controller using respectively

The simulation is realized using the SIMULINK software in MATLAB environment.

 

*emf L i M i*

*d qs qs*

*emf L i*

control algorithms were iterated until best simulation results were obtained.

followed by reversing the speed reference 100rad/s

is applied at *t*1 = 1 s and eliminated at *t*2 = 1.5 s.

.

(7)

*ref* at *t*3=2s. The load ( 7 . *T Nm <sup>l</sup>* )

– mechanical rotor position,

(6)

*e*

speed of motor. *Ω* – mechanical angular speed of motor,

–electrical rotor position.

Cambronne J. P. et al 1996].

*pM i* .

**4. Simulation results** 

Table (1), (2) and (3).

0 *ds i* as follow:

where *fd <sup>f</sup>* 

which

**3.2 Vector control** 

The parameters of the synchronous machine are:

Rated output power 3HP, Rated phase voltage 60V, Rated phase current 14 A, Rated field voltage *vf*=1.5V, Rated field current *if* =30A, Stator resistance *Rs* =0.325Ω, Field resistance *Rf* =0.05Ω, Direct stator inductance *Lds* =8.4 mH, Quadrature stator inductance *Lqs*=3.5 mH, Field leakage inductance *Lf*=8.1 mH, Mutual inductance between inductor and armature *Mfd*=7.56mH, The damping coefficient *B* =0.005 N.m/s, The moment of inertia *J* =0.05 kg.m2, Pair number of poles *p* = 2.

Figure (17) shows the schematic diagram of the speed control of synchronous motor using fuzzy logic controller.

#### **3.1 Machine equations**

The more comprehensive dynamic performance of a synchronous machine can be studied by synchronously rotating d-q frame model known as Park equations. The dynamic model of synchronous motor in d-q frame can be represented by the following equations [Sturtzer, G. & Smigiel E. 2000; Cambronne, J. P. et al 1996]:

$$\begin{aligned} \upsilon\_{ds} &= \mathbf{R}\_{\rm s} i\_{ds} + \frac{\mathbf{d}}{\mathbf{d}t} \phi\_{\rm ls} - \alpha \phi\_{\rm sp} \\ \upsilon\_{qs} &= \mathbf{R}\_{\rm s} i\_{qs} + \frac{\mathbf{d}}{\mathbf{d}t} \phi\_{\rm ls} + \alpha \phi\_{\rm ls} \\ \upsilon\_{f} &= \mathbf{R}\_{f} i\_{f} + \frac{\mathbf{d}}{\mathbf{d}t} \phi\_{f} \end{aligned} \tag{2}$$

The mechanical equation of synchronous motor can be represented as:

$$\mathbf{J}\frac{\mathbf{d}}{\mathbf{d}t}\boldsymbol{\Omega} = T\_e - T\_l - \mathbf{B}\boldsymbol{\Omega} \tag{3}$$

Where the electromagnetic torque is given in d-q frame:

$$T\_e = \mathbf{p} \left(\phi\_{\rm lss} i\_{qs} - \phi\_{\rm lss} i\_{ds}\right) \tag{4}$$

In which: <sup>d</sup> d *Ω t* , *θ Ω dt* , <sup>d</sup> <sup>p</sup> <sup>d</sup> *<sup>e</sup> θ Ω t* , *θ θ <sup>e</sup>* p .

The flux linkage equations are:

$$\begin{aligned} \phi\_{\rm ls} &= \mathcal{L}\_{\rm cls} i\_{\rm ds} + \mathcal{M}\_{\rm fd} i\_{f} \\ \phi\_{\rm ps} &= \mathcal{L}\_{\rm qs} i\_{\rm qs} \\ \phi\_{\uparrow} &= \mathcal{L}\_{\rm f} i\_{f} + \mathcal{M}\_{\rm fd} i\_{\rm ds} \end{aligned} \tag{5}$$

Where Rs – stator resistance, Rf – field resistance, L ,L – respectively direct and ds qs quadrature stator inductances, Lf – field leakage inductance, Mfd – mutual inductance between inductor and armature, *ds* and *qs* – respectively direct and quadrature flux, *<sup>f</sup>* – field flux, *Te* – electromagnetic torque, *Tl* – external load disturbance, p – pair number of poles, B – is the damping coefficient, J – is the moment of inertia, *ω* – electrical angular speed of motor. *Ω* – mechanical angular speed of motor, – mechanical rotor position, *e* –electrical rotor position.

#### **3.2 Vector control**

120 Fuzzy Logic – Controls, Concepts, Theories and Applications

Rated output power 3HP, Rated phase voltage 60V, Rated phase current 14 A, Rated field voltage *vf*=1.5V, Rated field current *if* =30A, Stator resistance *Rs* =0.325Ω, Field resistance *Rf* =0.05Ω, Direct stator inductance *Lds* =8.4 mH, Quadrature stator inductance *Lqs*=3.5 mH, Field leakage inductance *Lf*=8.1 mH, Mutual inductance between inductor and armature *Mfd*=7.56mH, The damping coefficient *B* =0.005 N.m/s, The moment of inertia *J* =0.05

Figure (17) shows the schematic diagram of the speed control of synchronous motor using

The more comprehensive dynamic performance of a synchronous machine can be studied by synchronously rotating d-q frame model known as Park equations. The dynamic model of synchronous motor in d-q frame can be represented by the following equations [Sturtzer,

s

*v i*

*v i*

*v i*

d

The mechanical equation of synchronous motor can be represented as:

Where the electromagnetic torque is given in d-q frame:

, *θ Ω dt* , <sup>d</sup>

<sup>d</sup> <sup>R</sup> d

*ds ds ds qs*

*t*

  

  (2)

(3)

*qs* – respectively direct and quadrature flux,

*qs qs ds* (4)

(5)

*<sup>f</sup>* –

*qs qs qs ds*

dJ B

*T T e l <sup>t</sup>*

*T ii e ds* p

, *θ θ <sup>e</sup>* p .

qs

L

*qs qs*

<sup>p</sup> <sup>d</sup> *<sup>e</sup> θ Ω t*

*ds* and   

ds fd

*i i*

L M

*ds ds f*

f fd

L M

*i i i*

*f f ds*

Where Rs – stator resistance, Rf – field resistance, L ,L – respectively direct and ds qs quadrature stator inductances, Lf – field leakage inductance, Mfd – mutual inductance

*t*

*t*

<sup>d</sup> <sup>R</sup> d

<sup>d</sup> <sup>R</sup> d

*fff*

s

f

The parameters of the synchronous machine are:

G. & Smigiel E. 2000; Cambronne, J. P. et al 1996]:

kg.m2, Pair number of poles *p* = 2.

fuzzy logic controller.

**3.1 Machine equations** 

In which: <sup>d</sup>

d *Ω t* 

The flux linkage equations are:

between inductor and armature,

The self-control operation of the inverter-fed synchronous machine results in a rotor field oriented control of the torque and flux in the machine. The principle is to maintain the armature flux and the field flux in an orthogonal or decoupled axis. The flux in the machine is controlled independently by the field winding and the torque is affected by the fundamental component of armature current *qs i* . In order to have an optimal functioning, the direct current *ds i* is maintained equal to zero [Sturtzer G. & Smigiel E. 2000 ; Cambronne J. P. et al 1996].

Substituting (5) in (4), the electromagnetic torque can be rewritten for *<sup>f</sup> i constant* and 0 *ds i* as follow:

$$T\_e(t) = \mathcal{X}i\_{qs}(t) \tag{6}$$

where *fd <sup>f</sup> pM i* .

In the same conditions, it appears that the *ds v* and *qs v* equations are coupled. We have to introduce a decoupling system, by introducing the compensation terms *<sup>d</sup> emf* and *<sup>q</sup> emf* in which

$$\begin{aligned} \mathbf{e} \mathbf{e} \mathbf{m} \mathbf{f}\_d &= \alpha \mathbf{L}\_{qs} \mathbf{i}\_{qs}, \\ \mathbf{e} \mathbf{e} \mathbf{m} \mathbf{f}\_q &= -\alpha \mathbf{L}\_{ds} \mathbf{i}\_{ds} - \alpha \mathbf{o} \mathbf{M}\_{af} \mathbf{i}\_f. \end{aligned} \tag{7}$$

#### **4. Simulation results**

In order to validate the control strategies as discussed above, digital simulation studies were made on the system described in figure (17). The speed and currents loops of the drive were also designed and simulated respectively with fuzzy control and PI control. The feedback control algorithms were iterated until best simulation results were obtained.

The speed loop was closed, and transient response was tested with both PI current control and fuzzy speed control. We used several types of fuzzy controller based on the cases presented in section (2.2). The simulation of the starting mode without load is done, followed by reversing the speed reference 100rad/s *ref* at *t*3=2s. The load ( 7 . *T Nm <sup>l</sup>* ) is applied at *t*1 = 1 s and eliminated at *t*2 = 1.5 s.

The simulation is realized using the SIMULINK software in MATLAB environment.

Figures (18), (19) and (20) show the performances of the fuzzy controller using respectively

Table (1), (2) and (3).

Application of Fuzzy Logic in Control of Electrical Machines 123

Fig. 20. The response of the system with fuzzy speed controller using Rules base of Table 3.

Fig. 21. Comparison of the system response for different controller, 1) PI, 2) 3 Fuzzy subsets

3) 5 Fuzzy subsets, 4) 7 Fuzzy subsets.

Fig. 18. The response of the system with fuzzy speed controller using Rules base of Table 1.

Fig. 19. The response of the system with fuzzy speed controller using Rules base of Table 2.

Fig. 18. The response of the system with fuzzy speed controller using Rules base of Table 1.

Fig. 19. The response of the system with fuzzy speed controller using Rules base of Table 2.

Fig. 20. The response of the system with fuzzy speed controller using Rules base of Table 3.

Fig. 21. Comparison of the system response for different controller, 1) PI, 2) 3 Fuzzy subsets 3) 5 Fuzzy subsets, 4) 7 Fuzzy subsets.

Application of Fuzzy Logic in Control of Electrical Machines 125

In order to test the robustness of the used method we have studied the effect of the parameters uncertainties on the performances of the speed control [Aissaoui et al 2007].

To show the effect of the parameters uncertainties, we have simulated the system with different values of the parameter considered and compared to nominal value (real value).

To illustrate the performances of control, we have simulated the starting mode of the motor without load, and the application of the load (*Tl* 7Nm ) at the instance *t*1 = 2 s and its elimination at *t*2 = 3 s; in presence of the variation of parameters considered (the moment of

Figure (23) shows the tests of robustness realized with the fuzzy controller for different

Fig. 23. Test of robustness for different values of the moment of inertia using fuzzy rules of

Figure (24) shows the tests of robustness realized with the fuzzy control for different values

inertia, the stator resistances, the stator inductances) with speed step of +100 rad/s.

**4.1 Robustness** 

Two cases are considered:

1. The moment of inertia ( ±50%).

values of the moment of inertia.

2. The stator and rotor resistances (+50%).

Table 2: 1) – 50%, 2) nominal case, 3) +50%.

of stator and rotor resistances.

The figures (17-21) show the response of SM with using FLC. The FLC presents high quality to achieve the desired trajectory. It rejects the load disturbances rapidly with no overshoot and with a negligible steady state error. The decoupling of torque-flux is maintained in permanent regime.

The reason of superior performance of fuzzy control system is that it is adaptive in nature and the controller is able to realize different control laws for each inputs state (*e* and *de*).

From figure (21), the performances of the FLC can be shown clearly. Compared to PI controller, the FLC give good response to follow the desired trajectory with no overshoot, with a negligible steady state error and with the immediately reject of load disturbances.

The increase of the membership functions in fuzzification and defuzzification improve the quality of the FLC as it is shown in figure (21), however the computation time increase two. It will be better to have a FLC with high performance and with less computation time. The choice of FLC with five Fuzzy-subsets may fulfil these criteria.

Figure (22) shows the influence of the choice of MF on the performance of control.

The choice of MF affects the performances of the FLC, it appears in figure (22) that the triangular or the Gaussian shape doesn't affect the speed control. However, in the presence of asymmetrical distribution the quality of control is bad. The non recovery of fuzzy set gives worst results. It will be better to choose MF with acceptable recovery of fuzzy sets.

Fig. 22. Comparison of the system response for different MF shape: 1) Triangular, 2)Gaussian, 3) Asymmetrical, 4) limit Recovery, 5) Non recovery.

#### **4.1 Robustness**

124 Fuzzy Logic – Controls, Concepts, Theories and Applications

The figures (17-21) show the response of SM with using FLC. The FLC presents high quality to achieve the desired trajectory. It rejects the load disturbances rapidly with no overshoot and with a negligible steady state error. The decoupling of torque-flux is maintained in

The reason of superior performance of fuzzy control system is that it is adaptive in nature and

From figure (21), the performances of the FLC can be shown clearly. Compared to PI controller, the FLC give good response to follow the desired trajectory with no overshoot, with a negligible steady state error and with the immediately reject of load disturbances.

The increase of the membership functions in fuzzification and defuzzification improve the quality of the FLC as it is shown in figure (21), however the computation time increase two. It will be better to have a FLC with high performance and with less computation time. The

The choice of MF affects the performances of the FLC, it appears in figure (22) that the triangular or the Gaussian shape doesn't affect the speed control. However, in the presence of asymmetrical distribution the quality of control is bad. The non recovery of fuzzy set gives worst results. It will be better to choose MF with acceptable recovery of fuzzy sets.

the controller is able to realize different control laws for each inputs state (*e* and *de*).

Figure (22) shows the influence of the choice of MF on the performance of control.

Fig. 22. Comparison of the system response for different MF shape: 1) Triangular,

2)Gaussian, 3) Asymmetrical, 4) limit Recovery, 5) Non recovery.

choice of FLC with five Fuzzy-subsets may fulfil these criteria.

permanent regime.

In order to test the robustness of the used method we have studied the effect of the parameters uncertainties on the performances of the speed control [Aissaoui et al 2007].

To show the effect of the parameters uncertainties, we have simulated the system with different values of the parameter considered and compared to nominal value (real value).

Two cases are considered:


To illustrate the performances of control, we have simulated the starting mode of the motor without load, and the application of the load (*Tl* 7Nm ) at the instance *t*1 = 2 s and its elimination at *t*2 = 3 s; in presence of the variation of parameters considered (the moment of inertia, the stator resistances, the stator inductances) with speed step of +100 rad/s.

Figure (23) shows the tests of robustness realized with the fuzzy controller for different values of the moment of inertia.

Fig. 23. Test of robustness for different values of the moment of inertia using fuzzy rules of Table 2: 1) – 50%, 2) nominal case, 3) +50%.

Figure (24) shows the tests of robustness realized with the fuzzy control for different values of stator and rotor resistances.

Application of Fuzzy Logic in Control of Electrical Machines 127

indicates clearly the superior performance of FLC, because it is adaptive in nature. It appears from the response properties that it has a high performance in presence of the uncertain plant parameters and load disturbances. It is used to control system with unknown model. The control of speed by FLC gives fast dynamic response with no overshoot and negligible steady-state error. The decoupling, stability and convergence to

This study will be very helpful, to design a new controllers based on FLC. With use of FLC

Aissaoui, A. G. 2007. *The use of neural networks and fuzzy logic for control of synchronous machine,* Phd thesis, University Djilali Liabes of Sidi Bel Abbes, Algeria. Aissaoui, A. G.; Abid, M.; Abid, H. And Tahour A. & Zeblah, A.K. (2007). A Fuzzy Logic

Aissaoui, A. G.; Abid, M.; Abid, H. And Tahour A.; Megherbi, A. C. (2010). A Fuzzy Logic

Aissaoui, A. G.; Abid, M. & Tahour A. (2010). Application Of Fuzzy Sliding Mode

Aissaoui, A. G.; Tahour, A.; Essenbouli, N.; Nollet, F. ; Abid M. & Chergui, M.I. (2011). A

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Cambronne, J. P.; Le Moigne Ph. & Hautier J. P. (1996). Synthèse de la commande d'un

Cirstea, M.N.; Dinu, A.; Khor, J.G.; McCormick, M. (2002). *Neural and Fuzzy Logic Control of* 

Heber, B.; Xu, L. & Tang, Y. (1995). Fuzzy logic enhanced speed control of an indirect field

Kim, Y.T.; Bien, Z. (2000). Robust self-learning fuzzy controller design for a class of

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equilibrium point are verified.

VOL. 58, NO. 5, 285–290

22, 2010.

Newjersey.

lausanne.

121, 1585–1588.

**6. References** 

we can reach high quality in control of non linear systems.

Fig. 24. Test of robustness for different values of stator and rotor resistances using fuzzy rules of Table 2: 1) nominal case, 2) +50%.

For the robustness of control, a decrease or increase of the moment of inertia *J* or the resistances doesn't have any effects on the performances of the technique used (figures 23 and 24). An increase of the moment of inertia gives best performances, but it presents a slow dynamic response (figure 23). The fuzzy control gives to our controller a great place towards the control of the system with unknown parameters.

#### **5. Conclusion**

The study describes an application of fuzzy logic system in control of electrical machines. The fuzzy logic control presents a new approach to robust control. The control methodology is described and used to develop a simple robust controller to deal with uncertain parameters and external disturbances. The design of the FLC depends on the structure adopted in fuzzification, defuzzification and rule base. In choice of FLC structure, we have to reach a compromise between the complexity and the precision of controller. The design of the FLC depends on the shape, symmetry and the recovery of MF.

In this study, a complete fuzzy logic control, based on synchronous motor, has been described. The system was analyzed and designed. The performances were studied extensively by simulation to validate the theoretical concept. To avoid the complexity of the FLC and the decrease of its precision, we have adopted five subsets to describe each inputs and output variables. The simulation results show that the proposed controller is superior to conventional controller in robustness and in tracking precision. The simulation study indicates clearly the superior performance of FLC, because it is adaptive in nature. It appears from the response properties that it has a high performance in presence of the uncertain plant parameters and load disturbances. It is used to control system with unknown model. The control of speed by FLC gives fast dynamic response with no overshoot and negligible steady-state error. The decoupling, stability and convergence to equilibrium point are verified.

This study will be very helpful, to design a new controllers based on FLC. With use of FLC we can reach high quality in control of non linear systems.

#### **6. References**

126 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 24. Test of robustness for different values of stator and rotor resistances using fuzzy

For the robustness of control, a decrease or increase of the moment of inertia *J* or the resistances doesn't have any effects on the performances of the technique used (figures 23 and 24). An increase of the moment of inertia gives best performances, but it presents a slow dynamic response (figure 23). The fuzzy control gives to our controller a great place towards

The study describes an application of fuzzy logic system in control of electrical machines. The fuzzy logic control presents a new approach to robust control. The control methodology is described and used to develop a simple robust controller to deal with uncertain parameters and external disturbances. The design of the FLC depends on the structure adopted in fuzzification, defuzzification and rule base. In choice of FLC structure, we have to reach a compromise between the complexity and the precision of controller. The design of

In this study, a complete fuzzy logic control, based on synchronous motor, has been described. The system was analyzed and designed. The performances were studied extensively by simulation to validate the theoretical concept. To avoid the complexity of the FLC and the decrease of its precision, we have adopted five subsets to describe each inputs and output variables. The simulation results show that the proposed controller is superior to conventional controller in robustness and in tracking precision. The simulation study

rules of Table 2: 1) nominal case, 2) +50%.

**5. Conclusion** 

the control of the system with unknown parameters.

the FLC depends on the shape, symmetry and the recovery of MF.


**Part 2** 

**Control Systems** 


**Part 2** 

**Control Systems** 

128 Fuzzy Logic – Controls, Concepts, Theories and Applications

Namuduri, C. & Sen,P. C. (1987). A servo-control system using a self-controlled

Sousa, G.C. D.; Bose, B. K. (1994). Fuzzy set theory based control of a phase-controlled

Spooner, J.T.; Maggiore, M.; Ordonez, R; Passino, K. M. (2002). *Stable adaptative control and* 

Sturtzer, G. & Smigiel E. (2000). Modélisation et commande des moteurs triphasés. Edition

Tang, Y. & Xu, L. (1994). Fuzzy logic application for intelligent control of a variable speed

Timothy, J. R. (1994). Fuzzy logic with engineering application, McGraw-Hill, New York,

Yager, R. R. (1997). Fuzzy logics and artificial intelligence. *Fuzzy Sets and Systems* 90, 193-198. Yu, F. M.; Chung, H. Y.; Chen, S. Y..(2003). Fuzzy sliding mode controller design for

uncertain time-delayed systems with nonlinear input. *Fuzzy Sets Syst*., vol. 140,

*Application*, vol. IA-23, N°2.

drive, *IEEE PES Winter Meet*.

1, 34-44.

Ellipses.

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359–374.

Interscience.

Rachid, A. (1996). *Systèmes de régulation*, Masson, paris.

synchronous motor (SCSM) with sliding mode control. *IEEE Trans. on Industry* 

converter DC machine drive, *IEEE Transaction on Industry Applications*, Vol. 30, NO.

*estimation for nonlinear system, Neural and fuzzy approximator techniques*, Willey-

**0**

**7**

*Spain*

**Fuzzy Logic Control for Multiresolutive Adaptive**

Communication with remote places is a challenge often solved using satellites. However, when trying to reach Antarctic stations, this solution suffers from poor visibility range and high operational costs. In such scenarios, skywave ionospheric communication systems

The Research Group in Electromagnetism and Communications (GRECO) is designing an HF system for long haul digital communication between the Antarctic Spanish Base in Livingston Island (62.6S, 60.4W) and Observatori de l'Ebre in Spain (40.8N,0.5E) (Vilella et al., 2008). The main interest of Observatori de l'Ebre is the transmission of the data collected from the sensors located at the base, including a geomagnetic sensor, a vertical incidence ionosonde, an oblique incidence ionosonde and a GNSS receiver. The geomagnetic sensor, the vertical incidence ionosonde and the GNSS receiver are commercial solutions from third parties. The oblique incidence ionosonde, used to sound the ionospheric channel between Antarctica and Spain,

During the last Antarctic campaign, exhaustive measurements of the HF channel characteristics were performed, which allowed us to determine parameters such as availability, SNR, delay and Doppler spread, etc. In addition to the scientific interest of this sounding, a further objective of the project is the establishment of a backup link for data transmission from the remote sensors in the Antarctica. In this scenario, ionospheric communications appear to be an interesting complementary alternative to geostationary satellite communications since the latter are expensive and not always available from

Research work in the field of fuzzy logics applied to the estimation of the above mentioned channel was first applied in (Alsina et al., 2005a) for serial search acquisition systems in AWGN channels, afterwards applied to the same channel but in the multiresolutive structure (Alsina et al., 2009a; Morán et al., 2001) in papers (Alsina et al., 2007b; 2009b) achieving good results. In this chapter the application of fuzzy logic control trained for Rayleigh fading channels (Proakis, 1995) with Direct-Sequence Spread-Spectrum (DS-SS) is presented, specifically suited for the ionospheric channel Antarctica-Spain. Stability and reliability of the

reception, which are currently being designed, are key factors for the reception.

represent a good alternative to satellite communications.

was developed by the GRECO in the framework of this project.

**1. Introduction**

high-latitudes.

**PN Acquisition Scheme in Time-Varying**

**Multipath Ionospheric Channel**

Rosa Maria Alsina-Pages, Claudia Mateo Segura,

Joan Claudi Socoró Carrié and Pau Bergada

*La Salle - Universitat Ramon Llull*

## **Fuzzy Logic Control for Multiresolutive Adaptive PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel**

Rosa Maria Alsina-Pages, Claudia Mateo Segura, Joan Claudi Socoró Carrié and Pau Bergada *La Salle - Universitat Ramon Llull Spain*

#### **1. Introduction**

Communication with remote places is a challenge often solved using satellites. However, when trying to reach Antarctic stations, this solution suffers from poor visibility range and high operational costs. In such scenarios, skywave ionospheric communication systems represent a good alternative to satellite communications.

The Research Group in Electromagnetism and Communications (GRECO) is designing an HF system for long haul digital communication between the Antarctic Spanish Base in Livingston Island (62.6S, 60.4W) and Observatori de l'Ebre in Spain (40.8N,0.5E) (Vilella et al., 2008). The main interest of Observatori de l'Ebre is the transmission of the data collected from the sensors located at the base, including a geomagnetic sensor, a vertical incidence ionosonde, an oblique incidence ionosonde and a GNSS receiver. The geomagnetic sensor, the vertical incidence ionosonde and the GNSS receiver are commercial solutions from third parties. The oblique incidence ionosonde, used to sound the ionospheric channel between Antarctica and Spain, was developed by the GRECO in the framework of this project.

During the last Antarctic campaign, exhaustive measurements of the HF channel characteristics were performed, which allowed us to determine parameters such as availability, SNR, delay and Doppler spread, etc. In addition to the scientific interest of this sounding, a further objective of the project is the establishment of a backup link for data transmission from the remote sensors in the Antarctica. In this scenario, ionospheric communications appear to be an interesting complementary alternative to geostationary satellite communications since the latter are expensive and not always available from high-latitudes.

Research work in the field of fuzzy logics applied to the estimation of the above mentioned channel was first applied in (Alsina et al., 2005a) for serial search acquisition systems in AWGN channels, afterwards applied to the same channel but in the multiresolutive structure (Alsina et al., 2009a; Morán et al., 2001) in papers (Alsina et al., 2007b; 2009b) achieving good results. In this chapter the application of fuzzy logic control trained for Rayleigh fading channels (Proakis, 1995) with Direct-Sequence Spread-Spectrum (DS-SS) is presented, specifically suited for the ionospheric channel Antarctica-Spain. Stability and reliability of the reception, which are currently being designed, are key factors for the reception.

receiver can then use the same PN sequence to counteract the effect of the PN sequence used

<sup>133</sup> Fuzzy Logic Control for Multiresolutive Adaptive

c[n]

to modulate in the transmitter, in order to reconstruct the information signal.

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

Fig. 1. The DS-SS signal *x*[*n*] is generated through multiplication of the information

more important when dealing with time varying channels with a variable SNR.

manually adjusted, by means of the acquisition system knowledge.

One of the main challenges to be solved by DS-SS systems is to achieve a quick and robust acquisition of the pseudonoise sequences (PN sequences). In time-varying environments this fact becomes even more important, because acquisition and tracking performance can heavily

There are several schemes to deal with this problem, such as serial search and parallel algorithms (Sklar, 1988). Serial search algorithms require a low computational load but they are slow to converge. On the other hand, parallel systems are fast converging but require a high computational load. In our system, the low-complexity fast-converging multiresolutive structure that was previously presented in (Morán et al., 2001) is used. Nevertheless, a proper design of the decisional system is a key factor in the overall system performance. This is even

Several factors contribute to the performance of the acquisition system (Glisic & Vucetic, 1997): uncertainty about the code phase, channel distortion and variations, noise and interference, and data randomness. Therefore, advanced control systems as fuzzy logic (Zadeh, 1965; 1988) are used to solve this complex acquisition problem. The fuzzy logic estimator used in this chapter was first presented by our research group in (Alsina et al., 2005a) and (Alsina et al., 2008; 2007b; 2009b); in this study, a new control system with a new set of If-Then Rules is presented to cope with the multipath time-variant ionospheric channel (Alsina et al., 2009a).

The decision of using fuzzy logic (Zadeh, 1965; 1988) for the acquisition control of the multiresolutive structure (Morán et al., 2001) is based in the high accuracy of fuzzy logic in terms of complex system description. The behavior of the channel is well-known, as a result of several research studies (Vilella et al., 2009; 2008), thus the control performance can be

Fuzzy logic has been widely used to solve engineering problems (Gad & Farouq, 2001). More specifically, (Daffara, 1995) and (Drake & Prasad, 1999) used fuzzy logic to track phase error detectors in synchronization, while (Perez-Neira & Lagunas, 1996) and (Perez-Neira et al., 1997) improved detection results by means of this technique. Finally, (Bas & Perez-Neira, 2003) applied fuzzy logic to interference rejection. These applications are based in the same

base-band signal *b*[*n*] with the (periodic) spreading sequence *c*[*n*]

b[n]

x[n]

degrade communication reliability.

**2.3 Fuzzy logic as an acquisition control**

It is important to note that the fuzzy control design presented in this chapter not only resolves the issue of improving the multiresolutive structure performance presented by (Morán et al., 2001), but also introduces a new option for the control design of many LMS adaptive structures used for PN code acquisition found in the literature. (El-Tarhuni & Sheikh, 1996) presented an LMS-based system to acquire a DS-SS system in Rayleigh channels; years after, (Han et al., 2006) improved the performance of the acquisition system designed by (El-Tarhuni & Sheikh, 1996). And also in other type of channels, LMS filters are used as an acquisition system, even in oceanic transmissions (Stojanovic & Freitag, 2003). Although the fuzzy control system presented in this chapter is compared to the stability control used in (Morán et al., 2001) it also can be used to improve all previous designs performance in terms of stability and robustness. Despite this generalization, the design of every control system should be done according to the requirements of the acquisition system and the specific channel characteristics.

## **2. Background and system requirements**

The design of the transmitter and the receiver, as well as the modulation used to carry out data transmission is severely conditioned to Antarctica constraints. Power restrictions, low bitrate needed and multipath are requirements to be taken into account in the decisions.

#### **2.1 Ionospheric channel and BAE restrictions**

One of the major constraints is that, due to power restrictions in the Antarctic Base, the transmission power is strongly limited. Consequently, a very low SNR is usually expected at the receiver. However, when using DS-SS techniques, signal spectrum is spread over a wide bandwidth, becoming robust against narrowband interferences.

Previous research efforts have been focused on using pseudorandom sequences with good autocorrelation characteristics (m-sequences) to evaluate the four-five hops link (12700km length) from Antarctica to Observatori de l'Ebre (Spain). Channel estimation and impairment characteristics have been obtained from these previous experiments (Vilella et al., 2008). DS-SS has also been previously used as a signaling technique (Deumal et al., 2006), for DS-SS modulation (Alsina et al., 2009a) or for OFDM modulation (Bergadà et al., 2009), achieving good results in terms of spectral efficiency although scarcely decreasing the system performance. These outcomes encouraged us to consider DS-SS a proper candidate to modulate the transmitted data. An advantage of DS-SS modulation (Glisic & Vucetic, 1997; Peterson et al., 1995) is that channel estimation is not essential in the demodulation stage, but it can be used to improve its reliability (i.e. using a RAKE receiver).

#### **2.2 Direct-Sequence Spread-Spectrum transmission**

Direct-Sequence Spread-Spectrum (Peterson et al., 1995) is a modulation technique that, as well as other spread spectrum technologies, increases the transmitted signal bandwidth and occupies a wider bandwidth (see *x*[*n*] in Figure 1) than the information signal (see *b*[*n*] in Figure 1) that is being modulated. DS-SS pseudorandomly modulates the wave with a continuous string of pseudonoise (PN) code symbols (see *c*[*n*] in Figure 1) called *chips*. Chips are of shorter duration than information bits, hence the wider spectrum and the higher chip rate. So, the chip rate is higher than the information signal bit rate (see Figure 1). DS-SS uses a sequence of chips generated by the transmitter, and also known by the receiver; the 2 Will-be-set-by-IN-TECH

It is important to note that the fuzzy control design presented in this chapter not only resolves the issue of improving the multiresolutive structure performance presented by (Morán et al., 2001), but also introduces a new option for the control design of many LMS adaptive structures used for PN code acquisition found in the literature. (El-Tarhuni & Sheikh, 1996) presented an LMS-based system to acquire a DS-SS system in Rayleigh channels; years after, (Han et al., 2006) improved the performance of the acquisition system designed by (El-Tarhuni & Sheikh, 1996). And also in other type of channels, LMS filters are used as an acquisition system, even in oceanic transmissions (Stojanovic & Freitag, 2003). Although the fuzzy control system presented in this chapter is compared to the stability control used in (Morán et al., 2001) it also can be used to improve all previous designs performance in terms of stability and robustness. Despite this generalization, the design of every control system should be done according to the requirements of the acquisition system and the specific channel

The design of the transmitter and the receiver, as well as the modulation used to carry out data transmission is severely conditioned to Antarctica constraints. Power restrictions, low bitrate needed and multipath are requirements to be taken into account in the decisions.

One of the major constraints is that, due to power restrictions in the Antarctic Base, the transmission power is strongly limited. Consequently, a very low SNR is usually expected at the receiver. However, when using DS-SS techniques, signal spectrum is spread over a

Previous research efforts have been focused on using pseudorandom sequences with good autocorrelation characteristics (m-sequences) to evaluate the four-five hops link (12700km length) from Antarctica to Observatori de l'Ebre (Spain). Channel estimation and impairment characteristics have been obtained from these previous experiments (Vilella et al., 2008). DS-SS has also been previously used as a signaling technique (Deumal et al., 2006), for DS-SS modulation (Alsina et al., 2009a) or for OFDM modulation (Bergadà et al., 2009), achieving good results in terms of spectral efficiency although scarcely decreasing the system performance. These outcomes encouraged us to consider DS-SS a proper candidate to modulate the transmitted data. An advantage of DS-SS modulation (Glisic & Vucetic, 1997; Peterson et al., 1995) is that channel estimation is not essential in the demodulation stage, but

Direct-Sequence Spread-Spectrum (Peterson et al., 1995) is a modulation technique that, as well as other spread spectrum technologies, increases the transmitted signal bandwidth and occupies a wider bandwidth (see *x*[*n*] in Figure 1) than the information signal (see *b*[*n*] in Figure 1) that is being modulated. DS-SS pseudorandomly modulates the wave with a continuous string of pseudonoise (PN) code symbols (see *c*[*n*] in Figure 1) called *chips*. Chips are of shorter duration than information bits, hence the wider spectrum and the higher chip rate. So, the chip rate is higher than the information signal bit rate (see Figure 1). DS-SS uses a sequence of chips generated by the transmitter, and also known by the receiver; the

wide bandwidth, becoming robust against narrowband interferences.

it can be used to improve its reliability (i.e. using a RAKE receiver).

**2.2 Direct-Sequence Spread-Spectrum transmission**

characteristics.

**2. Background and system requirements**

**2.1 Ionospheric channel and BAE restrictions**

receiver can then use the same PN sequence to counteract the effect of the PN sequence used to modulate in the transmitter, in order to reconstruct the information signal.

Fig. 1. The DS-SS signal *x*[*n*] is generated through multiplication of the information base-band signal *b*[*n*] with the (periodic) spreading sequence *c*[*n*]

One of the main challenges to be solved by DS-SS systems is to achieve a quick and robust acquisition of the pseudonoise sequences (PN sequences). In time-varying environments this fact becomes even more important, because acquisition and tracking performance can heavily degrade communication reliability.

There are several schemes to deal with this problem, such as serial search and parallel algorithms (Sklar, 1988). Serial search algorithms require a low computational load but they are slow to converge. On the other hand, parallel systems are fast converging but require a high computational load. In our system, the low-complexity fast-converging multiresolutive structure that was previously presented in (Morán et al., 2001) is used. Nevertheless, a proper design of the decisional system is a key factor in the overall system performance. This is even more important when dealing with time varying channels with a variable SNR.

Several factors contribute to the performance of the acquisition system (Glisic & Vucetic, 1997): uncertainty about the code phase, channel distortion and variations, noise and interference, and data randomness. Therefore, advanced control systems as fuzzy logic (Zadeh, 1965; 1988) are used to solve this complex acquisition problem. The fuzzy logic estimator used in this chapter was first presented by our research group in (Alsina et al., 2005a) and (Alsina et al., 2008; 2007b; 2009b); in this study, a new control system with a new set of If-Then Rules is presented to cope with the multipath time-variant ionospheric channel (Alsina et al., 2009a).

#### **2.3 Fuzzy logic as an acquisition control**

The decision of using fuzzy logic (Zadeh, 1965; 1988) for the acquisition control of the multiresolutive structure (Morán et al., 2001) is based in the high accuracy of fuzzy logic in terms of complex system description. The behavior of the channel is well-known, as a result of several research studies (Vilella et al., 2009; 2008), thus the control performance can be manually adjusted, by means of the acquisition system knowledge.

Fuzzy logic has been widely used to solve engineering problems (Gad & Farouq, 2001). More specifically, (Daffara, 1995) and (Drake & Prasad, 1999) used fuzzy logic to track phase error detectors in synchronization, while (Perez-Neira & Lagunas, 1996) and (Perez-Neira et al., 1997) improved detection results by means of this technique. Finally, (Bas & Perez-Neira, 2003) applied fuzzy logic to interference rejection. These applications are based in the same

the step-size parameter that controls the speed of convergence and the robustness of the filter.

<sup>135</sup> Fuzzy Logic Control for Multiresolutive Adaptive

Under ideal conditions, in a non-frequency selective Rayleigh channel with white Gaussian

where *bi*[*n*] is the information bit, *τ* represents the chip-based delay between the input signal PN sequence and the reference one and *γ*[*k*] is the fading coefficient. The algorithm is reseted every symbol period, and a modulus smoothing average algorithm is applied to each LMS filter coefficients solution *Wi*[*n*] to remove the data randomness component *bi*[*n*] of Equation

The exponential smoothing filter and the choice of the proper value of the parameter *β* are fundamental for the good performance of the multiresolutive structure; it is important to note that |·| is the modulus for each coefficient of *Wi*[*n*]. The design of such components of the multiresolutive structure is optimized in order to stabilize the dynamics of the tap filter

s[nͲW@

O[n] tr[ ]c[n]

c[n]

*max*, in the selected filter.

s[n] d[n] **Detection**

**htr <sup>z</sup> (t) <sup>Ͳ</sup>**<sup>W</sup> **<sup>z</sup><sup>Ͳ</sup>**<sup>O</sup> \_ +

+

+

+

A peak detection algorithm is used by the decisional system embedded in the control stage (see Figure 2) which of the acquisition filters has detected the signal (say *Wcon*[*n*]), considering *Wcon*[*n*] is the filter coefficients after the convergence. The coarse estimation of the acquisition

\_ +

*γ*[*k*]*bi*[*n*]*δ*[*k* − *τ*] (4)

*<sup>i</sup>* [*n*].

*<sup>i</sup>* [*n*] + *β*|*Wi*[*n*]| (5)

**PN Seq Generator**

noise, just one of the filters should locally converge to a Dirac delta response like

*<sup>i</sup>*+1[*n*]=(<sup>1</sup> <sup>−</sup> *<sup>β</sup>*)*Wav*

coefficients, avoiding impulsive changes due to SNR variations or fast fading.

**Control**

wi adq[n,i] [n]

...

c[n] wtr[n]

It is a parameter that has been carefully designed.

4, obtaining nonnegative averaged impulsional responses *Wav*

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

*Wav*

Wˆ[*n*]

**Decimation N**

> ...

[

[ ]

**<sup>z</sup><sup>Ͳ</sup><sup>1</sup>** <sup>M</sup> **w2[n]** \_

**<sup>z</sup><sup>Ͳ</sup>M+1** <sup>M</sup> **wM[n]** \_

**z<sup>Ͳ</sup><sup>2</sup>** M **w3[n]**

...

Fig. 2. Multiresolutive structure for acquisition and tracking

point is given by the position of the maximum, say *n<sup>i</sup>*

cdec[n]sdec[n] <sup>M</sup> **w1[n]** \_

principles that the one presented in this chapter; the wide knowledge of a system performance by the designer, which fuzzy logic helps to translate to a closed control system.

#### **3. Multiresolutive structure for acquisition and tracking**

The aim of the multiresolutive scheme (Morán et al., 2001) is to find the correct acquisition point with low latency and simultaneously requiring low computational cost in a DS-SS transmission. The transmitted signal, the base band continuous signal before spectral shaping is:

$$\mathbf{x}(t) = \sum\_{i=1}^{I} b\_i \cdot \mathbf{c}(t - i \cdot T\_s) \tag{1}$$

where *bi* are the information bits, *I* is the total number of transmitted bits and *Ts* is the bit duration in seconds. The received base band signal, after downconversion and filtering is:

$$r(t) = \sum\_{j=1}^{L} \gamma\_j(t) \cdot x(t - \tau\_j(t)) + n(t) \tag{2}$$

where *L* is the number of multipath components, *γ<sup>j</sup>* is the complex fading coefficient of the j*th* component, and *τ<sup>j</sup>* is the delay of the jth component. The input signal for the multiresolutive structure is *<sup>s</sup>*[*n*] = *<sup>r</sup>*(*<sup>n</sup>* · *Tc <sup>N</sup>* ) (see Figure 2), so it is assumed to be sampled at the frequency of *N fc*, where *fc* = 1/*Tc* is the chip frequency (in number of chips per second) and *Tc* is the chip duration in seconds. The PN sequence used as reference in the acquisition scheme is also sampled at *N fc*, so is *<sup>c</sup>*[*n*] = *<sup>c</sup>*(*<sup>n</sup>* · *Tc <sup>N</sup>* ).

As can be shown in Figure 2, in the acquisition part the signal *s*[*n*] is first decimated by a factor *N* (and then *N* is the number of samples per chip). Since the acquisition stage can accept uncertainties lower than the chip period, the computational load is reduced by decimating without affecting the performance.

#### **3.1 Acquisition stage**

The decimated signal, termed as *sdec*[*n*], is fed into the filters of a multiresolutive structure (see Figure 2). There are *M* different branches that work with decimated versions of the input signal, separated in *M* disjoint subspaces. Each branch has an adaptive FIR filter of length *H* = *PG M* , where *PG* is the Processing Gain (corresponding to the length of the PN sequence), trained with a decimated version of the PN modulating sequence (*cdec*), and �·� stands for the ceil operator. FIR filters use the LMS algorithm as adaptive coefficient update procedure and their performance were compared to other adaptive filters; they outstand for being the best in terms of speed of convergence and reliability (Akhter et al., 2010).

LMS filters converge with a steepest descent algorithm (Haykin, 1996), using a convergence parameter *μ* that has to be adjusted according to the system requirements of stability and time convergence. The steepest descent algorithm is detailed in:

$$w\_{k+1} = w\_k + \mu e\_k s\_k^{dec} \tag{3}$$

where *wk*<sup>+</sup><sup>1</sup> is the tap weight vector at (chip-based) sample time index *k* + 1 and *wk* is the tap weight vector at index time *k*, *ek* is the output error at time *k* and *sdec <sup>k</sup>* is the input signal. *μ* is 4 Will-be-set-by-IN-TECH

principles that the one presented in this chapter; the wide knowledge of a system performance

The aim of the multiresolutive scheme (Morán et al., 2001) is to find the correct acquisition point with low latency and simultaneously requiring low computational cost in a DS-SS transmission. The transmitted signal, the base band continuous signal before spectral shaping

where *bi* are the information bits, *I* is the total number of transmitted bits and *Ts* is the bit duration in seconds. The received base band signal, after downconversion and filtering is:

where *L* is the number of multipath components, *γ<sup>j</sup>* is the complex fading coefficient of the j*th* component, and *τ<sup>j</sup>* is the delay of the jth component. The input signal for the multiresolutive

of *N fc*, where *fc* = 1/*Tc* is the chip frequency (in number of chips per second) and *Tc* is the chip duration in seconds. The PN sequence used as reference in the acquisition scheme is also

As can be shown in Figure 2, in the acquisition part the signal *s*[*n*] is first decimated by a factor *N* (and then *N* is the number of samples per chip). Since the acquisition stage can accept uncertainties lower than the chip period, the computational load is reduced by decimating

The decimated signal, termed as *sdec*[*n*], is fed into the filters of a multiresolutive structure (see Figure 2). There are *M* different branches that work with decimated versions of the input signal, separated in *M* disjoint subspaces. Each branch has an adaptive FIR filter of length

trained with a decimated version of the PN modulating sequence (*cdec*), and �·� stands for the ceil operator. FIR filters use the LMS algorithm as adaptive coefficient update procedure and their performance were compared to other adaptive filters; they outstand for being the best in

LMS filters converge with a steepest descent algorithm (Haykin, 1996), using a convergence parameter *μ* that has to be adjusted according to the system requirements of stability and time

*wk*<sup>+</sup><sup>1</sup> = *wk* + *μeks*

where *wk*<sup>+</sup><sup>1</sup> is the tap weight vector at (chip-based) sample time index *k* + 1 and *wk* is the tap

, where *PG* is the Processing Gain (corresponding to the length of the PN sequence),

*dec*

*<sup>k</sup>* (3)

*<sup>k</sup>* is the input signal. *μ* is

*bi* · *c*(*t* − *i* · *Ts*) (1)

*γj*(*t*) · *x*(*t* − *τj*(*t*)) + *n*(*t*) (2)

*<sup>N</sup>* ) (see Figure 2), so it is assumed to be sampled at the frequency

by the designer, which fuzzy logic helps to translate to a closed control system.

*x*(*t*) =

*L* ∑ *j*=1

*<sup>N</sup>* ).

terms of speed of convergence and reliability (Akhter et al., 2010).

weight vector at index time *k*, *ek* is the output error at time *k* and *sdec*

convergence. The steepest descent algorithm is detailed in:

*I* ∑ *i*=1

**3. Multiresolutive structure for acquisition and tracking**

*r*(*t*) =

is:

structure is *<sup>s</sup>*[*n*] = *<sup>r</sup>*(*<sup>n</sup>* · *Tc*

sampled at *N fc*, so is *<sup>c</sup>*[*n*] = *<sup>c</sup>*(*<sup>n</sup>* · *Tc*

without affecting the performance.

**3.1 Acquisition stage**

*H* = *PG M*  the step-size parameter that controls the speed of convergence and the robustness of the filter. It is a parameter that has been carefully designed.

Under ideal conditions, in a non-frequency selective Rayleigh channel with white Gaussian noise, just one of the filters should locally converge to a Dirac delta response like

$$
\gamma[k]b\_i[n]\delta[k-\tau] \tag{4}$$

where *bi*[*n*] is the information bit, *τ* represents the chip-based delay between the input signal PN sequence and the reference one and *γ*[*k*] is the fading coefficient. The algorithm is reseted every symbol period, and a modulus smoothing average algorithm is applied to each LMS filter coefficients solution *Wi*[*n*] to remove the data randomness component *bi*[*n*] of Equation 4, obtaining nonnegative averaged impulsional responses *Wav <sup>i</sup>* [*n*].

$$\mathcal{W}\_{i+1}^{av}[n] = (1 - \beta)\mathcal{W}\_i^{av}[n] + \beta|\mathcal{W}\_i[n]|\tag{5}$$

The exponential smoothing filter and the choice of the proper value of the parameter *β* are fundamental for the good performance of the multiresolutive structure; it is important to note that |·| is the modulus for each coefficient of *Wi*[*n*]. The design of such components of the multiresolutive structure is optimized in order to stabilize the dynamics of the tap filter coefficients, avoiding impulsive changes due to SNR variations or fast fading.

Fig. 2. Multiresolutive structure for acquisition and tracking

A peak detection algorithm is used by the decisional system embedded in the control stage (see Figure 2) which of the acquisition filters has detected the signal (say *Wcon*[*n*]), considering *Wcon*[*n*] is the filter coefficients after the convergence. The coarse estimation of the acquisition point is given by the position of the maximum, say *n<sup>i</sup> max*, in the selected filter.

(Alsina et al., 2007b). The knowledge of the performance of the multiresolutive structure is a key process for both the first channel (fast SNR variation channel) and for the ionospheric

<sup>137</sup> Fuzzy Logic Control for Multiresolutive Adaptive

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

In this Section a detailed explanation of the input variables and their meaning is given. Each input variable is defined and it is chosen according to the information it generates to improve the control performance. Once the four input variables are detailed, they are tested using a family of 10 PN sequences previously designed (Alsina et al., 2005b; 2007a) to improve the multiresolutive structure capabilities. As will be shown (see Section 4.1.2.2), there are substantial differences in the performance of each of the PN sequences in terms of input variables, so a preferred sequence is chosen; the minimization of the values of autocorrelation and crosscorrelation - which contribute to the fitness function of the GA algorithm (Alsina et al., 2007a) - is taken into account. Afterwards, the median and the lower and upper quartiles of the input variables are studied for the preferred sequence; finally the membership functions

Four parameters are defined as inputs in the fuzzy logic control system; three of them refer to

*<sup>i</sup>* [*n*]), especially the LMS

*con*[*n*] (6)

*max*] (7)

*con*[*n<sup>i</sup>*

*<sup>i</sup>* [*n*] (8)

*con*[*n*]), and one

*con*[*n<sup>i</sup> max*])

*con*[*n<sup>i</sup> max*])

*max*]) divided

*<sup>i</sup>* [*n*]):

*max* as the LMS

the values of the four modulus averaged acquisition LMS filters (*Wav*

*tr* [*n*]):

by the mean value of the three other filters (*Wav*

filter adapted and synchronized with the decimated sequence *cdec* (named *Wav*

divided by the mean value of this filter but the maximum (consider *n<sup>i</sup>*

• *Ratio*1: it is computed as the quotient of the peak value of the LMS filter (*Wav*

maximum equivalent to reconstructed acquisition point, named *τ* in Figure 2):

*Ratio*<sup>1</sup> <sup>=</sup> *<sup>W</sup>av*

• *Ratio*2: it is evaluated as the quotient of the peak value of the LMS filter (*Wav*

*Ratio*<sup>2</sup> <sup>=</sup> *<sup>W</sup>av*

• *Ratio*3: it is obtained as the quotient of the peak value of the LMS filter (*Wav*

*Ratio*<sup>3</sup> <sup>=</sup> *<sup>W</sup>av*

1 *M*−1

1 *<sup>M</sup>*−<sup>1</sup> <sup>∑</sup>*<sup>M</sup> i*=1 *i*�=*con*

1 *<sup>H</sup>*−<sup>1</sup> <sup>∑</sup>*<sup>M</sup> i*=1 *i*�=*con*

• *Ratio*1*trac*: it is computed as the quotient of the peak value of the LMS tracking filter

*tr* [*nmax*]), being *nmax* the most precise estimation of the correct acquisition point,

1 *<sup>H</sup>* <sup>∑</sup>*<sup>H</sup> <sup>n</sup>*=<sup>1</sup> *n*�=*ni max*

divided by the average of the value of the same position in the other three filters (*Wav*

*con*[*n<sup>i</sup> max*]

*con*[*n<sup>i</sup> max*]

*<sup>i</sup>* [*n*]):

*con*[*n<sup>i</sup> max*]

*Wav <sup>i</sup>* [*n<sup>i</sup>*

∑*<sup>H</sup> <sup>n</sup>*=<sup>1</sup> *n*�=*ni max* *Wav*

*Wav*

Rayleigh channel currently used.

**4.1 Input variables and fuzzy sets**

are defined.

(*Wav*

**4.1.1 Input variables**

to the tracking filter (*Wav*

#### **3.2 Tracking stage**

Once restored the acquisition point by the decisional system, tracking is solved with another adaptive FIR filter with impulse response *Wtr*[*n*] (of length *H* and also using the LMS algorithm as the coefficient update procedure), which expands the search window around the coarse acquisition point *nmax*, using the full bandwidth input signal *s*[*n*]. The result of the tracking filter is also smoothed using an exponential smoothing as detailed in Section 3.1. Finally, the estimation of the acquisition point is refined by finding the tracking point (see Figure 2, values *τ*ˆ) and the signal can be correctly demodulated.

## **3.3 Control stage**

The control stage of the multiresolutive structure is a key step in this design (Alsina et al., 2009b). The stability and the robustness of the multiresolutive structure are supported by the control system, apart from the quality of the acquisition of the multiresolutive structure. The control system is based on the measurements over the LMS filters used in acquisition and tracking: *i) Wav <sup>i</sup>* [*n*] corresponding to the averaged impulse responses of the tracking filters; *ii) Wav con*[*n*], referring to the current acquisition filter that gives the current acquisition point; and *iii)*, *Wav tr* [*n*] as the tracking filter.

Using this information provided by the acquisition and tracking, the decisional system determines if the system is acquired and demodulation can start, or otherwise the acquisition system must remain in the process of acquisition and tracking of a proper point.

In this project the decisional system is based on fuzzy logic (Zadeh, 1988), due to the deep knowledge of the channel behavior acquired in numerous tests involving different kinds of modulations. These tests did not only provide valuable information about the performance of the LMS adaptive filters both in acquisition and tracking, but also how this performance reflects in the *Acquisition* estimation as is shown in Section 4.

## **4. The acquisition fuzzy control**

The acquisition control is designed using information from the impulsional response of the LMS filters of the multiresolutive structure after being smoothed. Their values give information about the probability of being correctly acquired, and this information feeds the fuzzy decisional system designed for the multiresolutive structure.

Previous work started with the design of a fuzzy control for a serial search algorithm based on a CFAR scheme (Glisic, 1991), work presented in (Alsina et al., 2005a). Afterwards, the fuzzy estimator was adapted to the multiresolutive structure (Morán et al., 2001), in order to improve its performance in channels with fast SNR variations. This design and study was presented in (Alsina et al., 2007b) and in (Alsina et al., 2009b). Then, the fuzzy logic estimator was compared with a neural network based control, work presented in (Alsina et al., 2008).

The input variable definition presented in this paper (corresponding to the four ratios *Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac*) was initialized in (Alsina et al., 2007b). As the design of a fuzzy logic system is highly dependent on the environment where it works, in this paper it has been specifically redesigned and adapted to a ionospheric Rayleigh channel (Proakis, 1995). The number of membership functions and their position have changed, but not the main basis of the variable definition with respect to previous work where fuzzy logic control was used (Alsina et al., 2007b). The knowledge of the performance of the multiresolutive structure is a key process for both the first channel (fast SNR variation channel) and for the ionospheric Rayleigh channel currently used.

## **4.1 Input variables and fuzzy sets**

6 Will-be-set-by-IN-TECH

Once restored the acquisition point by the decisional system, tracking is solved with another adaptive FIR filter with impulse response *Wtr*[*n*] (of length *H* and also using the LMS algorithm as the coefficient update procedure), which expands the search window around the coarse acquisition point *nmax*, using the full bandwidth input signal *s*[*n*]. The result of the tracking filter is also smoothed using an exponential smoothing as detailed in Section 3.1. Finally, the estimation of the acquisition point is refined by finding the tracking point (see

The control stage of the multiresolutive structure is a key step in this design (Alsina et al., 2009b). The stability and the robustness of the multiresolutive structure are supported by the control system, apart from the quality of the acquisition of the multiresolutive structure. The control system is based on the measurements over the LMS filters used in acquisition and

*con*[*n*], referring to the current acquisition filter that gives the current acquisition point; and

Using this information provided by the acquisition and tracking, the decisional system determines if the system is acquired and demodulation can start, or otherwise the acquisition

In this project the decisional system is based on fuzzy logic (Zadeh, 1988), due to the deep knowledge of the channel behavior acquired in numerous tests involving different kinds of modulations. These tests did not only provide valuable information about the performance of the LMS adaptive filters both in acquisition and tracking, but also how this performance

The acquisition control is designed using information from the impulsional response of the LMS filters of the multiresolutive structure after being smoothed. Their values give information about the probability of being correctly acquired, and this information feeds the

Previous work started with the design of a fuzzy control for a serial search algorithm based on a CFAR scheme (Glisic, 1991), work presented in (Alsina et al., 2005a). Afterwards, the fuzzy estimator was adapted to the multiresolutive structure (Morán et al., 2001), in order to improve its performance in channels with fast SNR variations. This design and study was presented in (Alsina et al., 2007b) and in (Alsina et al., 2009b). Then, the fuzzy logic estimator was compared with a neural network based control, work presented in (Alsina et al., 2008). The input variable definition presented in this paper (corresponding to the four ratios *Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac*) was initialized in (Alsina et al., 2007b). As the design of a fuzzy logic system is highly dependent on the environment where it works, in this paper it has been specifically redesigned and adapted to a ionospheric Rayleigh channel (Proakis, 1995). The number of membership functions and their position have changed, but not the main basis of the variable definition with respect to previous work where fuzzy logic control was used

system must remain in the process of acquisition and tracking of a proper point.

*<sup>i</sup>* [*n*] corresponding to the averaged impulse responses of the tracking filters; *ii)*

Figure 2, values *τ*ˆ) and the signal can be correctly demodulated.

reflects in the *Acquisition* estimation as is shown in Section 4.

fuzzy decisional system designed for the multiresolutive structure.

**3.2 Tracking stage**

**3.3 Control stage**

tracking: *i) Wav*

*tr* [*n*] as the tracking filter.

**4. The acquisition fuzzy control**

*Wav*

*iii)*, *Wav*

In this Section a detailed explanation of the input variables and their meaning is given. Each input variable is defined and it is chosen according to the information it generates to improve the control performance. Once the four input variables are detailed, they are tested using a family of 10 PN sequences previously designed (Alsina et al., 2005b; 2007a) to improve the multiresolutive structure capabilities. As will be shown (see Section 4.1.2.2), there are substantial differences in the performance of each of the PN sequences in terms of input variables, so a preferred sequence is chosen; the minimization of the values of autocorrelation and crosscorrelation - which contribute to the fitness function of the GA algorithm (Alsina et al., 2007a) - is taken into account. Afterwards, the median and the lower and upper quartiles of the input variables are studied for the preferred sequence; finally the membership functions are defined.

#### **4.1.1 Input variables**

Four parameters are defined as inputs in the fuzzy logic control system; three of them refer to the values of the four modulus averaged acquisition LMS filters (*Wav <sup>i</sup>* [*n*]), especially the LMS filter adapted and synchronized with the decimated sequence *cdec* (named *Wav con*[*n*]), and one to the tracking filter (*Wav tr* [*n*]):

• *Ratio*1: it is computed as the quotient of the peak value of the LMS filter (*Wav con*[*n<sup>i</sup> max*]) divided by the mean value of this filter but the maximum (consider *n<sup>i</sup> max* as the LMS maximum equivalent to reconstructed acquisition point, named *τ* in Figure 2):

$$Ratio\_1 = \frac{W\_{con}^{av}[n\_{max}^i]}{\frac{1}{H} \sum\_{n=1 \atop n \neq n\_{max}^i}^H W\_{con}^{av}[n]} \tag{6}$$

• *Ratio*2: it is evaluated as the quotient of the peak value of the LMS filter (*Wav con*[*n<sup>i</sup> max*]) divided by the average of the value of the same position in the other three filters (*Wav <sup>i</sup>* [*n*]):

$$Ratio\_2 = \frac{W\_{con}^{av} \left[ n\_{max}^i \right]}{\frac{1}{M-1} \sum\_{\substack{i=1 \\ i \neq con}}^M W\_i^{av} \left[ n\_{max}^i \right]} \tag{7}$$

• *Ratio*3: it is obtained as the quotient of the peak value of the LMS filter (*Wav con*[*n<sup>i</sup> max*]) divided by the mean value of the three other filters (*Wav <sup>i</sup>* [*n*]):

$$Ratio\_3 = \frac{W\_{con}^{av} \left[ n\_{max}^i \right]}{\frac{1}{M-1} \frac{1}{H-1} \sum\_{i=1}^M \sum\_{\substack{i=1 \\ i \neq con}}^H \frac{H}{n \neq n\_{max}^i}} \quad \tag{8}$$

• *Ratio*1*trac*: it is computed as the quotient of the peak value of the LMS tracking filter (*Wav tr* [*nmax*]), being *nmax* the most precise estimation of the correct acquisition point,

Best availability data from (Vilella et al., 2008) is considered for this research work.

<sup>139</sup> Fuzzy Logic Control for Multiresolutive Adaptive

Scenario 0 - - - - - 1.2

Scenario 1 01 -6 63% 9 2 1.25

Scenario 2 21 -6 43% 15 0.7 0.9

Scenario 3 08 -6 36% 15 0.6 0.8

The PN sequence family used to test the four input ratios was designed using evolution strategies (Alsina et al., 2007b; 2005a), in order to satisfy the requirements of the multiresolutive structure (as shown in Figure 2 and in Section 3). This structure uses a decimated PN sequence to estimate the first acquisition point, and therefore it is convenient to obtain good autocorrelation for the decimated sequence, as well as a limited crosscorrelation between the *M* decimated versions of the PN sequence. These requirements have been used in the evolution strategy design, generating a family of PN sequences that not only minimized the autocorrelation and the crosscorrelation, but also these statistical parameters

In Figures 3, 4, 5 and 6 a four-ratio comparison is made using the four simulation scenarios of Table 1. The four top subfigures plot the ratio values for the acquired situation; the four bottom subfigures plot the ratio values for non-acquired situation. This evaluation is made for each ratio (*Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac*) and also for each scenario (scenario 0, scenario 1, scenario 2 and scenario 3) applying at each simulation a different SNR value in

Figure 3 shows a clear difference between the values for *Ratio*<sup>1</sup> in the case of acquisition and in the case of non-acquisition, especially for scenario 0. Scenario 1, scenario 2 and scenario 3 values for acquisition are not so stable, and neither are the values for the non-acquisition situation. This is a behavior that will be repeated for the four ratios: the first scenario is the one that allows a better discrimination between acquisition and non acquisition in terms of ratios, it is the clearest to detect an acquisition. In the other three scenarios, due to the fact that

Figure 4 presents very good results for nearly all the PN sequences of the family. These figures show that *Ratio*<sup>2</sup> can be used for performing an stable estimation of the decision to evaluate. Figure 5 shows a noisy *Ratio*3; but despite its unstable values for the non-acquired situation, values for *Ratio*<sup>3</sup> in acquired scenarios 2 and 3, which are the worst results for the results tests, it exhibits a fairly distinct behavior in acquisition situation with respect to non-acquisition situation. Then *Ratio*<sup>3</sup> information is valuable in the case of severe channel conditions. Finally,

they produce multipath, the values for the ratios are more ambiguous.





, *fk* ∈ *Fl <sup>v</sup>*(*hl*)*Fk* ,*<sup>j</sup>*

, *fk* ∈ *Fk*

**Scenario** *hl SNR Dw*(*hl*)*<sup>f</sup>* ,*<sup>j</sup> fk* = *<sup>f</sup> <sup>τ</sup>*(*hl*)*Fk* ,*<sup>j</sup>*

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

Table 1. Ionospheric simulation scenarios (Vilella et al., 2009; 2008)

4.1.2.2 Ratio values for each sequence and scenario

for the decimated sequences.

order to perform a noise value study.

divided by the mean value of the same filter but the maximum (consider *nmax* as the LMS maximum equivalent to reconstructed tracking point named *λ* in Figure 2).

$$Ratio\_{1trac} = \frac{W\_{tr}^{av} \left[ n\_{max} \right]}{\frac{1}{H} \sum\_{n \neq n\_{max}}^{H} W\_{tr}^{av} \left[ n \right]} \tag{9}$$

*Ratio*<sup>1</sup> gives information about the signal to noise ratio of the channel; in second term it also reflects the mean autocorrelation of the decimated signal used as reference. If the mean values of the tap weights of the converged filter are high, *Ratio*<sup>1</sup> shows a wide dynamic margin to define all membership functions, which means that the autocorrelation for *cdec* is not negligible. *Ratio*<sup>2</sup> shows information about the SNR and about the delay spread of the channel; if the received data is not spread around the contiguous chips of the detected tracking position *Ratio*<sup>2</sup> obtains good dynamic margin. *Ratio*<sup>3</sup> gives information about the SNR at the receiver, and about the crosscorrelation between the four decimated versions of a PN sequence. If the crosscorrelation is high between subsequences, *Ratio*<sup>3</sup> achieves non-discriminative results and does not help acquisition. Finally, *Ratio*1*trac* gives information about the SNR at the receiver in terms of the entire sequence - not the decimated as the three previous ratios - . These parameters have been chosen due to the information they contain about the probability of successful acquisition related to their values; their output dynamic range can be divided into several membership functions referring to their value, in order to help the estimation of the acquisition stage.

#### **4.1.2 Input fuzzy sets**

In this Section the input fuzzy sets for each input variable are described. The input fuzzy sets with their membership functions need a ratio value estimation for each input variable. This studio is made for a family of 10 different PN sequences optimized to work with the multiresolutive structure (Alsina et al., 2007a).

A scenario description is firstly described, in order to detail the channel environment in which the tests are made. The channel or simulation settings are defined according to the information given by (Vilella et al., 2009; 2008), using measurements from real transmission campaigns. Lately, the four ratios curves for each scenario are obtained and explained for both acquisition and non-acquisition situations. This information leads us to choose the appropriate preferred PN sequences. Statistical parameters are computed over the performance of the preferred PN sequence, and membership functions are finally defined.

#### 4.1.2.1 Scenario description

In order to train the system to work with real data, four simulation scenarios have been defined in Table 1. They are absolutely based on analysis of real data (Vilella et al., 2009; 2008), except for scenario 0, that is a simpler version of transmissions throughout ionospheric radiolink, considering only the most powerful path in a multipath scenario.

Table 1 is sorted by *hl*, that is the hour time - during day or night -. For every hour, three SNR values are shown (-9 dB, -6 dB, -3 dB), measured using a transmission bandwidth *Bw* = 3*kHz* around a carrier frequency *fl* (expressed in MHz). *Dwf* ,*<sup>j</sup>* is the availability of each frequency in %. *<sup>τ</sup>*(*hl*)*Fk* ,*<sup>j</sup>* , where *fk* ∈ *Fk*, is the composite multipath spread in ms, and finally, *<sup>v</sup>*(*hl*)*Fk* ,*<sup>j</sup>* , where *fk* ∈ *Fk*, is the Doppler spread in Hertz.

8 Will-be-set-by-IN-TECH

1 *<sup>H</sup>* <sup>∑</sup>*<sup>H</sup> <sup>n</sup>*=<sup>1</sup> *n*� *nmax*

*Ratio*<sup>1</sup> gives information about the signal to noise ratio of the channel; in second term it also reflects the mean autocorrelation of the decimated signal used as reference. If the mean values of the tap weights of the converged filter are high, *Ratio*<sup>1</sup> shows a wide dynamic margin to define all membership functions, which means that the autocorrelation for *cdec* is not negligible. *Ratio*<sup>2</sup> shows information about the SNR and about the delay spread of the channel; if the received data is not spread around the contiguous chips of the detected tracking position *Ratio*<sup>2</sup> obtains good dynamic margin. *Ratio*<sup>3</sup> gives information about the SNR at the receiver, and about the crosscorrelation between the four decimated versions of a PN sequence. If the crosscorrelation is high between subsequences, *Ratio*<sup>3</sup> achieves non-discriminative results and does not help acquisition. Finally, *Ratio*1*trac* gives information about the SNR at the receiver in terms of the entire sequence - not the decimated as the three previous ratios - . These parameters have been chosen due to the information they contain about the probability of successful acquisition related to their values; their output dynamic range can be divided into several membership functions referring to their value, in order to

In this Section the input fuzzy sets for each input variable are described. The input fuzzy sets with their membership functions need a ratio value estimation for each input variable. This studio is made for a family of 10 different PN sequences optimized to work with the

A scenario description is firstly described, in order to detail the channel environment in which the tests are made. The channel or simulation settings are defined according to the information given by (Vilella et al., 2009; 2008), using measurements from real transmission campaigns. Lately, the four ratios curves for each scenario are obtained and explained for both acquisition and non-acquisition situations. This information leads us to choose the appropriate preferred PN sequences. Statistical parameters are computed over the performance of the preferred PN

In order to train the system to work with real data, four simulation scenarios have been defined in Table 1. They are absolutely based on analysis of real data (Vilella et al., 2009; 2008), except for scenario 0, that is a simpler version of transmissions throughout ionospheric

Table 1 is sorted by *hl*, that is the hour time - during day or night -. For every hour, three SNR values are shown (-9 dB, -6 dB, -3 dB), measured using a transmission bandwidth *Bw* = 3*kHz* around a carrier frequency *fl* (expressed in MHz). *Dwf* ,*<sup>j</sup>* is the availability of each frequency

, where *fk* ∈ *Fk*, is the composite multipath spread in ms, and finally, *<sup>v</sup>*(*hl*)*Fk* ,*<sup>j</sup>*

,

radiolink, considering only the most powerful path in a multipath scenario.

maximum equivalent to reconstructed tracking point named *λ* in Figure 2).

help the estimation of the acquisition stage.

multiresolutive structure (Alsina et al., 2007a).

where *fk* ∈ *Fk*, is the Doppler spread in Hertz.

sequence, and membership functions are finally defined.

**4.1.2 Input fuzzy sets**

4.1.2.1 Scenario description

in %. *<sup>τ</sup>*(*hl*)*Fk* ,*<sup>j</sup>*

*Ratio*1*trac* <sup>=</sup> *<sup>W</sup>av*

divided by the mean value of the same filter but the maximum (consider *nmax* as the LMS

*tr* [*nmax*]

*Wav*

*tr* [*n*] (9)


Best availability data from (Vilella et al., 2008) is considered for this research work.

Table 1. Ionospheric simulation scenarios (Vilella et al., 2009; 2008)

4.1.2.2 Ratio values for each sequence and scenario

The PN sequence family used to test the four input ratios was designed using evolution strategies (Alsina et al., 2007b; 2005a), in order to satisfy the requirements of the multiresolutive structure (as shown in Figure 2 and in Section 3). This structure uses a decimated PN sequence to estimate the first acquisition point, and therefore it is convenient to obtain good autocorrelation for the decimated sequence, as well as a limited crosscorrelation between the *M* decimated versions of the PN sequence. These requirements have been used in the evolution strategy design, generating a family of PN sequences that not only minimized the autocorrelation and the crosscorrelation, but also these statistical parameters for the decimated sequences.

In Figures 3, 4, 5 and 6 a four-ratio comparison is made using the four simulation scenarios of Table 1. The four top subfigures plot the ratio values for the acquired situation; the four bottom subfigures plot the ratio values for non-acquired situation. This evaluation is made for each ratio (*Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac*) and also for each scenario (scenario 0, scenario 1, scenario 2 and scenario 3) applying at each simulation a different SNR value in order to perform a noise value study.

Figure 3 shows a clear difference between the values for *Ratio*<sup>1</sup> in the case of acquisition and in the case of non-acquisition, especially for scenario 0. Scenario 1, scenario 2 and scenario 3 values for acquisition are not so stable, and neither are the values for the non-acquisition situation. This is a behavior that will be repeated for the four ratios: the first scenario is the one that allows a better discrimination between acquisition and non acquisition in terms of ratios, it is the clearest to detect an acquisition. In the other three scenarios, due to the fact that they produce multipath, the values for the ratios are more ambiguous.

Figure 4 presents very good results for nearly all the PN sequences of the family. These figures show that *Ratio*<sup>2</sup> can be used for performing an stable estimation of the decision to evaluate. Figure 5 shows a noisy *Ratio*3; but despite its unstable values for the non-acquired situation, values for *Ratio*<sup>3</sup> in acquired scenarios 2 and 3, which are the worst results for the results tests, it exhibits a fairly distinct behavior in acquisition situation with respect to non-acquisition situation. Then *Ratio*<sup>3</sup> information is valuable in the case of severe channel conditions. Finally,





SNR


SNR

trac Scenario 3


SNR


SNR

Ratio3

Scenario 3

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

> 0.2 0.4 0.6 0.8 1 Ratio1

0.2 0.4 0.6 0.8 1

SNR


SNR

trac Scenario 2


SNR


SNR

Ratio3

Scenario 2

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

> 0.2 0.4 0.6 0.8 1 Ratio1

0.2 0.4 0.6 0.8 1

Fig. 5. Performance of the PN sequence ratio values for *Ratio*3. The four upper figures show *Ratio*<sup>3</sup> values for the four scenarios in the acquired situation. The four lower figures show

SNR


SNR

trac Scenario 1


SNR


SNR

Fig. 6. Performance of the PN sequence ratio values for *Ratio*1*trac*. The four upper figures show *Ratio*1*trac* values for the four scenarios in the acquired situation. The four lower figures

Ratio3

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

Scenario 1

<sup>141</sup> Fuzzy Logic Control for Multiresolutive Adaptive

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

> 0.2 0.4 0.6 0.8 1 Ratio1

0.2 0.4 0.6 0.8 1

SNR


SNR

*Ratio*<sup>3</sup> values for the non-acquired situation.

trac Scenario 0


SNR


SNR

show *Ratio*1*trac* values for the non-acquired situation.

Ratio3

Scenario 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

> 0.2 0.4 0.6 0.8 1 Ratio1

0.2 0.4 0.6 0.8 1

Ratio1trac NotAcquired

Ratio1trac Acquired

Ratio3 NotAcquired

Ratio3 Acquired

Fig. 3. Performance of the PN sequence ratio values for *Ratio*1. The four upper figures show *Ratio*<sup>1</sup> values for the four scenarios in the acquired situation. The four lower figures show *Ratio*<sup>1</sup> values for the non-acquired situation.

Fig. 4. Performance of the PN sequence ratio values for *Ratio*2. The four upper figures show *Ratio*<sup>2</sup> values for the four scenarios in the acquired situation. The four lower figures show *Ratio*<sup>2</sup> values for the non-acquired situation.

10 Will-be-set-by-IN-TECH

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Ratio1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.5 1 1.5 2 2.5 3 3.5 4 Ratio2

0.5 1 1.5 2 2.5 3 3.5 4

Fig. 4. Performance of the PN sequence ratio values for *Ratio*2. The four upper figures show *Ratio*<sup>2</sup> values for the four scenarios in the acquired situation. The four lower figures show

Fig. 3. Performance of the PN sequence ratio values for *Ratio*1. The four upper figures show *Ratio*<sup>1</sup> values for the four scenarios in the acquired situation. The four lower figures show



SNR


SNR

Scenario 3


SNR


SNR

Scenario 3

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Ratio1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

> 0.5 1 1.5 2 2.5 3 3.5 4 Ratio2

0.5 1 1.5 2 2.5 3 3.5 4

SNR


SNR

Scenario 2


SNR


SNR

Scenario 2

Scenario 1


SNR


SNR

Scenario 1


SNR


SNR

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Ratio1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.5 1 1.5 2 2.5 3 3.5 4 Ratio2

0.5 1 1.5 2 2.5 3 3.5 4


SNR


SNR

*Ratio*<sup>1</sup> values for the non-acquired situation.

Scenario 0


SNR


SNR

*Ratio*<sup>2</sup> values for the non-acquired situation.

Scenario 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Ratio1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.5 1 1.5 2 2.5 3 3.5 4 Ratio2

0.5 1 1.5 2 2.5 3 3.5 4

Ratio2 NotAcquired

Ratio2 Acquired

Ratio1 NotAcquired

Ratio1 Acquired

Fig. 5. Performance of the PN sequence ratio values for *Ratio*3. The four upper figures show *Ratio*<sup>3</sup> values for the four scenarios in the acquired situation. The four lower figures show *Ratio*<sup>3</sup> values for the non-acquired situation.

Fig. 6. Performance of the PN sequence ratio values for *Ratio*1*trac*. The four upper figures show *Ratio*1*trac* values for the four scenarios in the acquired situation. The four lower figures show *Ratio*1*trac* values for the non-acquired situation.



SNR

trac Acq

Ratio1

Scenario 0 Scenario 1 Scenario 2 Scenario 3


SNR

Ratio2 Acq

Scenario 0 Scenario 1 Scenario 2 Scenario 3

0.5 1 1.5 2 2.5 3 3.5

0.2

0.4

0.6

Ratio1trac Value

0.8

1

Ratio2 Value

<sup>143</sup> Fuzzy Logic Control for Multiresolutive Adaptive

SNR

Ratio3 Acq


SNR

**Probably Not Acquired** and **Probably Acquired**.

goal of the definition of these two fuzzy sets.

first one clearly acquired, and the second one clearly not acquired.

Fig. 7. Values for *Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac* for an Acquired situation

The output parameter is *Acquisition*, which gives a value in the range [0,1], being zero when it is **Not Acquired** and one if it is **Acquired**. In between, two other fuzzy sets are defined:

The parameter *Acquisition* is used to give information to the detection stage about the reliability of the estimation. Notice that the multiresolutive structure gives an estimation of the acquisition point while the *Acquisition* value evaluates the probability of being acquired.

The critical values of the output variable *Acquisition*, around [0.4, 0.6] are divided into two fuzzy sets, the lower one corresponding to **Probably Not Acquired** and the higher one corresponding to **Probably Acquired**. If the output variable obtains a critical value this is a result of non clear acquisition, so the decisional system does not have certainty about the reliability of the results. An additional period of time for acquisition is needed, and this is the

For values over 0.6 and under 0.4 the output variable *Acquisition* is clearly defined, being the

Ratio1 Acq

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

Scenario 0 Scenario 1 Scenario 2 Scenario 3

Scenario 0 Scenario 1 Scenario 2 Scenario 3

**4.2 Output variable and fuzzy sets**

**4.2.1 Output fuzzy sets**

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Ratio3 Value

Ratio1 Value

Figure 6 plots the results for *Ratio*1*trac*; they are the best results given by the system in the four scenarios and considering the four ratios. Nevertheless there is a drawback for *Ratio*1*trac*: the system must be acquired for this value to be reliable, otherwise just a noisy amount of output values is shown.

This information is gathered, and one PN sequence is chosen for its good response to the four ratios in the four scenarios. This sequence is the dotted one in the four Figures (3, 4, 5 and 6). It has been chosen due to its minimization of the Euclidean distance with the best sequence at each ratio evaluation.

#### 4.1.2.3 Selected sequence

The selected PN sequence is not the best one for all the ratios and for all the scenarios. It stands for the best global values, which means that is little noisy when comparing with the other sequences. In most of the results previously shown it reaches the best values (i.e. the values that better discriminates between acquisition and non acquisition).

Once chosen the preferred PN sequence, some statistics have to be computed over the ratios obtained using this sequence. The ratios are computed again for a wider group of values of SNR, and the results for the acquisition situation are shown in Figure 7. Over these results median, lower and upper quartiles are computed in order to fix some thresholds to define the membership functions in the fuzzy input variables. Figure 8 shows the boxplots of the values for *Ratio*<sup>1</sup> when acquired, and also performs the boxplots of the values for *Ratio*<sup>2</sup> when acquired. Figure 8 also gives the boxplots of the values for *Ratio*<sup>3</sup> when acquired and the values for *Ratio*1*trac* when acquired.

In the last figure, the median values for the four ratios simulated in the four scenarios, and the quartiles for these groups of ratios are also shown. Especially the quartiles over the four ratios when the system is acquired can be considered the key to tune the membership functions for the input variables.

### 4.1.2.4 Fuzzy membership functions

Finally, the input variables membership functions are defined. Four fuzzy sets have been defined for each variable; two for the acquisition situation and two for the non-acquisition situation; only for *Ratio*1*trac* is defined with five fuzzy sets, three for acquisition situation and two for the non-acquisition situation. Only four sets have been considered, because the system needs to give the clear idea of whether the receiver is acquired or not, assuming doubts. The four groups are named (from worse to best performance of the system) **Not Acquired**, **Probably Not Acquired (**∼ *NoAcq***)**, **Probably Acquired (**∼ *Acq***)** and **Acquired**. The division between **Not Acquired** and **Probably Not Acquired** is the median value for the non-acquired situation; and the same for **Probably Acquired** and **Acquired**, the threshold is the median value for the acquired situation. The division between **Probably Not Acquired** and **Probably Acquired** is held assuming that the maximum values for each are the low and high, respectively, quartiles for each of the ratios. All values are obtained with the mean value for the four ratios observed, and in case of doubt, always states the worst case. Some of the thresholds for the membership functions follow the worst case studio rule. Figures for the membership functions for *Ratio*1, *Ratio*<sup>2</sup> and *Ratio*<sup>3</sup> are shown in Figure 9, Figure 10 and 11, respectively. The only difference in the design is for membership functions of *Ratio*1*trac*; this ratio gives enough information to affirm that for some very high values (see statistics in Figure 8), not only is acquired, but also is working with only one path, as shown in Figure 12.

12 Will-be-set-by-IN-TECH

Figure 6 plots the results for *Ratio*1*trac*; they are the best results given by the system in the four scenarios and considering the four ratios. Nevertheless there is a drawback for *Ratio*1*trac*: the system must be acquired for this value to be reliable, otherwise just a noisy amount of output

This information is gathered, and one PN sequence is chosen for its good response to the four ratios in the four scenarios. This sequence is the dotted one in the four Figures (3, 4, 5 and 6). It has been chosen due to its minimization of the Euclidean distance with the best sequence at

The selected PN sequence is not the best one for all the ratios and for all the scenarios. It stands for the best global values, which means that is little noisy when comparing with the other sequences. In most of the results previously shown it reaches the best values (i.e. the

Once chosen the preferred PN sequence, some statistics have to be computed over the ratios obtained using this sequence. The ratios are computed again for a wider group of values of SNR, and the results for the acquisition situation are shown in Figure 7. Over these results median, lower and upper quartiles are computed in order to fix some thresholds to define the membership functions in the fuzzy input variables. Figure 8 shows the boxplots of the values for *Ratio*<sup>1</sup> when acquired, and also performs the boxplots of the values for *Ratio*<sup>2</sup> when acquired. Figure 8 also gives the boxplots of the values for *Ratio*<sup>3</sup> when acquired and the

In the last figure, the median values for the four ratios simulated in the four scenarios, and the quartiles for these groups of ratios are also shown. Especially the quartiles over the four ratios when the system is acquired can be considered the key to tune the membership functions for

Finally, the input variables membership functions are defined. Four fuzzy sets have been defined for each variable; two for the acquisition situation and two for the non-acquisition situation; only for *Ratio*1*trac* is defined with five fuzzy sets, three for acquisition situation and two for the non-acquisition situation. Only four sets have been considered, because the system needs to give the clear idea of whether the receiver is acquired or not, assuming doubts. The four groups are named (from worse to best performance of the system) **Not Acquired**, **Probably Not Acquired (**∼ *NoAcq***)**, **Probably Acquired (**∼ *Acq***)** and **Acquired**. The division between **Not Acquired** and **Probably Not Acquired** is the median value for the non-acquired situation; and the same for **Probably Acquired** and **Acquired**, the threshold is the median value for the acquired situation. The division between **Probably Not Acquired** and **Probably Acquired** is held assuming that the maximum values for each are the low and high, respectively, quartiles for each of the ratios. All values are obtained with the mean value for the four ratios observed, and in case of doubt, always states the worst case. Some of the thresholds for the membership functions follow the worst case studio rule. Figures for the membership functions for *Ratio*1, *Ratio*<sup>2</sup> and *Ratio*<sup>3</sup> are shown in Figure 9, Figure 10 and 11, respectively. The only difference in the design is for membership functions of *Ratio*1*trac*; this ratio gives enough information to affirm that for some very high values (see statistics in Figure 8), not only is acquired, but also is working with only one path, as shown in Figure 12.

values that better discriminates between acquisition and non acquisition).

values is shown.

each ratio evaluation. 4.1.2.3 Selected sequence

values for *Ratio*1*trac* when acquired.

4.1.2.4 Fuzzy membership functions

the input variables.

Fig. 7. Values for *Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac* for an Acquired situation

#### **4.2 Output variable and fuzzy sets**

The output parameter is *Acquisition*, which gives a value in the range [0,1], being zero when it is **Not Acquired** and one if it is **Acquired**. In between, two other fuzzy sets are defined: **Probably Not Acquired** and **Probably Acquired**.

The parameter *Acquisition* is used to give information to the detection stage about the reliability of the estimation. Notice that the multiresolutive structure gives an estimation of the acquisition point while the *Acquisition* value evaluates the probability of being acquired.

#### **4.2.1 Output fuzzy sets**

The critical values of the output variable *Acquisition*, around [0.4, 0.6] are divided into two fuzzy sets, the lower one corresponding to **Probably Not Acquired** and the higher one corresponding to **Probably Acquired**. If the output variable obtains a critical value this is a result of non clear acquisition, so the decisional system does not have certainty about the reliability of the results. An additional period of time for acquisition is needed, and this is the goal of the definition of these two fuzzy sets.

For values over 0.6 and under 0.4 the output variable *Acquisition* is clearly defined, being the first one clearly acquired, and the second one clearly not acquired.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

<sup>145</sup> Fuzzy Logic Control for Multiresolutive Adaptive

input variable "Ratio1 "

0 0.5 1 1.5 2 2.5 3 3.5

NoAdq ~NoAdq ~Adq Adq

input variable "Ratio2 "

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

trac"

input variable "Ratio1

input variable "Ratio3 "

NoAdq ~NoAdq~Adq Adq Adq-1path

NoAdq ~NoAdq ~Adq Adq

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

NoAdq ~NoAdq ~Adq Adq

0

0

0

0

0.5

1

0.5

1

0.5

1

Fig. 9. Membership functions for input variable *Ratio*<sup>1</sup>

Fig. 10. Membership functions for input variable *Ratio*<sup>2</sup>

Fig. 11. Membership functions for input variable *Ratio*<sup>3</sup>

Fig. 12. Membership functions for input variable *Ratio*1*trac*

0.5

1

Fig. 8. Median and quartiles for *Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac* for acquisition situation

#### **4.3 If-then rules**

If-then rules have been defined to obtain the best performance (in terms of reliability of the output variable *Acquisition* of the fuzzy estimator) along the full range of measured values for each input parameter. Two examples of the dependence between input variables are shown in Figure 14, where dependence among *Acquisition* and *Ratio*<sup>1</sup> and *Ratio*1*trac*, and also *Ratio*<sup>2</sup> and *Ratio*<sup>3</sup> are depicted.

The most critical estimation for the output variable *Acquisition* is the correspondence to **Probably Not Acquired** and to **Probably Acquired**; this means that the input parameters have no coherent values for **Acquired** or **Not Acquired**. To obtain a precise output value, the fuzzy estimator evaluates the degree of implication of each input parameter to the input variables membership functions and projects this implication to the fuzzy sets of the output variable *Acquisition*, in order to obtain its final value through defuzzyfication.

#### **4.4 Decisional system feedback**

Depending on the value of the output variable *Acquisition*, the multiresolutive acquisition block will perform in four different ways:

14 Will-be-set-by-IN-TECH

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>0</sup>

and *Ratio*<sup>3</sup> are depicted.

**4.4 Decisional system feedback**

block will perform in four different ways:

Sce0,Sce1,Sce2,Sce3

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>0</sup>

Sce0,Sce1,Sce2,Sce3

variable *Acquisition*, in order to obtain its final value through defuzzyfication.

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>0</sup>

Sce0,Sce1,Sce2,Sce3

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>0</sup>

Sce0,Sce1,Sce2,Sce3

0.1

0.2

0.3

0.4

0.5

RATIO1trac

0.6

0.7

0.8

0.9

Sequence Acq

0.01

Fig. 8. Median and quartiles for *Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac* for acquisition situation

If-then rules have been defined to obtain the best performance (in terms of reliability of the output variable *Acquisition* of the fuzzy estimator) along the full range of measured values for each input parameter. Two examples of the dependence between input variables are shown in Figure 14, where dependence among *Acquisition* and *Ratio*<sup>1</sup> and *Ratio*1*trac*, and also *Ratio*<sup>2</sup>

The most critical estimation for the output variable *Acquisition* is the correspondence to **Probably Not Acquired** and to **Probably Acquired**; this means that the input parameters have no coherent values for **Acquired** or **Not Acquired**. To obtain a precise output value, the fuzzy estimator evaluates the degree of implication of each input parameter to the input variables membership functions and projects this implication to the fuzzy sets of the output

Depending on the value of the output variable *Acquisition*, the multiresolutive acquisition

0.02

0.03

0.04

RATIO3

0.05

0.06

0.07

Sequence Acq

0.5

1

1.5

RATIO2

2

2.5

3

Sequence Acq

0.05

**4.3 If-then rules**

0.1

0.15

0.2

RATIO1

0.25

0.3

0.35

Sequence Acq

Fig. 9. Membership functions for input variable *Ratio*<sup>1</sup>

Fig. 10. Membership functions for input variable *Ratio*<sup>2</sup>

Fig. 11. Membership functions for input variable *Ratio*<sup>3</sup>

Fig. 12. Membership functions for input variable *Ratio*1*trac*

the worst place - the one that obtains the acquisition point far from the center of the LMS

<sup>147</sup> Fuzzy Logic Control for Multiresolutive Adaptive

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

These four categories are chosen depending on the *Acquisition* output variable values. This feedback improves the speed of convergence of the acquisition and reduces computational load for the entire structure, by means of stopping the convergence of some of the adaptive

In this Section the results of the performance of the designed fuzzy system are presented. First, an evaluation of the performance of the fuzzy control set designed is shown, evaluating the estimation reliability of the variable *Acquisition* against the true receiver state at every simulation time. The second evaluation devoted to study the whole multiresolutive structure performance. The results for the fuzzy multiresolutive structure are compared with the previously presented multiresolutive structure with a stability control (Morán et al., 2001). Tests have been made using the four scenarios described in Section 4.1.2.1; in all simulations the same 128 chip PN sequence, obtained using an evolutionary strategy has been used (Alsina et al., 2007a). In each test (for a certain SNR and a certain scenario) 600 symbols length data sequences have been used, and ten repetitions have been simulated using different channel

In the evaluation of the control system performance three variables have been measured. The first is the % of correct acquisition estimations, comparing the *Acquisition* value with the a posteriori measured probability of being acquired. The second is the % of incorrect acquisition estimations, but only for the optimistic ones; this means to evaluate when the fuzzy control system estimates the multiresolutive structure is acquired (assuming this is when *Acquisition* variable value is over 0.5), and the system real estimation of the acquisition position is incorrect. The last one is the % of incorrect acquisition estimation, but only for the pessimistic ones; this means to evaluate when the fuzzy control system estimates the multiresolutive structure is not acquired (assuming this is when *Acquisition* variable is under

In Figure 15 these measurements are depicted. As shown in Figure 15.a, the % of correct fuzzy acquisition estimations perform good values, near 100%, except for the range of [-38,-35] dB, where all four scenarios present hit values of around 20%. This is due to a threshold SNR value, where the ratios make confusing evaluations due to the high level of noise. But this fact is temporary, because when the SNR worsens, the ratios evaluated make the fuzzy system converge to the correct evaluation; however, in this case quite a lot of evaluations are for **Not**

The error performance evaluations are shown in Figures 15.b and 15.c. These figures outstand that most of the incorrect evaluations are for the system output indicating **Not Acquired** when the system is really **Acquired**. They also show that the *optimistic* incorrect estimations are really better than those related to the *pessimistic* ones. These results are the main indicators of a good system robustness: the system remotely considers *Acquisition* wrongly, so the information detection process works only for the correct *Acquisition* situations. Although this

initialization; the presented results are the mean of all these evaluations.

0.5), and the system real estimation of the acquisition point is correct.

**5.1 Evaluation of the control system performance**

filters -.

**5. Tests and results**

**Acquired**.

filters when convergence is assured.

Fig. 13. Membership functions of *Acquisition*

(a) *Acquisition* as a function of *Ratio*<sup>1</sup> and *Ratio*1*trac* (b) *Acquisition* as a function of *Ratio*<sup>2</sup> and *Ratio*<sup>3</sup>

Fig. 14. Two examples of the variation of output variable *Acquisition* for all the whole range of values of the two ratios, taken by pairs.


the worst place - the one that obtains the acquisition point far from the center of the LMS filters -.

These four categories are chosen depending on the *Acquisition* output variable values. This feedback improves the speed of convergence of the acquisition and reduces computational load for the entire structure, by means of stopping the convergence of some of the adaptive filters when convergence is assured.

## **5. Tests and results**

16 Will-be-set-by-IN-TECH

NoAdq ~NoAdq ~Adq Adq

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

output variable "adq"

(a) *Acquisition* as a function of *Ratio*<sup>1</sup> and *Ratio*1*trac* (b) *Acquisition* as a function of *Ratio*<sup>2</sup> and *Ratio*<sup>3</sup>

Fig. 14. Two examples of the variation of output variable *Acquisition* for all the whole range

• **Acquired**, it maintains the acquired position, saving computational load by stopping some of the adaptive filters used in the acquisition stage. This helps the structure to reduce its computational load. The ratios are computed only for the active filters, and each pause period (fixed to a certain number of symbol periods) ends with a convergence of all the

• **Probably Acquired**, it keeps the searching procedure to improve acquisition, and of course, evaluations are maintained until the convergence is certain - if this is the case.

evaluate improvements; this pointer movement is used to prevent the system from failing in its purpose due to a bad initial pointer position. Not all the initial values are equally convenient for the multiresolutive structure; the optimum situation is when the acquisition point is found in the middle of any of the four adaptive filters, and this approach helps the convergence if the position is not the optimum, despite convergence is possible at any tap

<sup>2</sup> and evaluate to find changes. The move of *Ts*

the previous case because if the system is in an *not acquired* situation, it means that the acquisition is far to be detected, so the initial data for the acquisition stage can be found in

<sup>4</sup> the beginning of the data for the acquisition stage and

<sup>2</sup> is larger than in

filters, and a recalculation of all the ratios in order to prevent losing acquisition.

0

Fig. 13. Membership functions of *Acquisition*

of values of the two ratios, taken by pairs.

• **Probably Not Acquired**, move *Ts*

of the four LMS filters. • **Not Acquired**, move *Ts*

0.5

1

In this Section the results of the performance of the designed fuzzy system are presented. First, an evaluation of the performance of the fuzzy control set designed is shown, evaluating the estimation reliability of the variable *Acquisition* against the true receiver state at every simulation time. The second evaluation devoted to study the whole multiresolutive structure performance. The results for the fuzzy multiresolutive structure are compared with the previously presented multiresolutive structure with a stability control (Morán et al., 2001).

Tests have been made using the four scenarios described in Section 4.1.2.1; in all simulations the same 128 chip PN sequence, obtained using an evolutionary strategy has been used (Alsina et al., 2007a). In each test (for a certain SNR and a certain scenario) 600 symbols length data sequences have been used, and ten repetitions have been simulated using different channel initialization; the presented results are the mean of all these evaluations.

### **5.1 Evaluation of the control system performance**

In the evaluation of the control system performance three variables have been measured. The first is the % of correct acquisition estimations, comparing the *Acquisition* value with the a posteriori measured probability of being acquired. The second is the % of incorrect acquisition estimations, but only for the optimistic ones; this means to evaluate when the fuzzy control system estimates the multiresolutive structure is acquired (assuming this is when *Acquisition* variable value is over 0.5), and the system real estimation of the acquisition position is incorrect. The last one is the % of incorrect acquisition estimation, but only for the pessimistic ones; this means to evaluate when the fuzzy control system estimates the multiresolutive structure is not acquired (assuming this is when *Acquisition* variable is under 0.5), and the system real estimation of the acquisition point is correct.

In Figure 15 these measurements are depicted. As shown in Figure 15.a, the % of correct fuzzy acquisition estimations perform good values, near 100%, except for the range of [-38,-35] dB, where all four scenarios present hit values of around 20%. This is due to a threshold SNR value, where the ratios make confusing evaluations due to the high level of noise. But this fact is temporary, because when the SNR worsens, the ratios evaluated make the fuzzy system converge to the correct evaluation; however, in this case quite a lot of evaluations are for **Not Acquired**.

The error performance evaluations are shown in Figures 15.b and 15.c. These figures outstand that most of the incorrect evaluations are for the system output indicating **Not Acquired** when the system is really **Acquired**. They also show that the *optimistic* incorrect estimations are really better than those related to the *pessimistic* ones. These results are the main indicators of a good system robustness: the system remotely considers *Acquisition* wrongly, so the information detection process works only for the correct *Acquisition* situations. Although this

design. The stability control gives an output **Acquired** if the adaptive filter structure presents the same results for a certain number of times (in this case, three times). In the work of (Morán et al., 2001) it is shown that the probability of being acquired increases as the acquistion position is more stable, and the stability control is based in this principle. The problems of the performance of this kind of stability control solution are lack of robustness in low SNR environments, interference and fading, and of course, multipath, because it cannot recognize a correct acquisition situation immediately; it was designed for enhance stability, so it keeps a

<sup>149</sup> Fuzzy Logic Control for Multiresolutive Adaptive

% Correct Stability Evaluations

SNR

Fig. 16. Performance of the Stability Control. Measurements about the correct and incorrect

This lack of robustness is improved with the design of the fuzzy control system, because its estimation uses various instantaneous parameters, so reacquisition is faster; the fact of relying on four different parameters ensures the robustness of the system, despite instantaneous non

(a) % Correct Stability evaluations

−0.5 0 0.5 1 1.5 2 2.5 3

Scenario 3 Scenario 2 Scenario 1 Scenario 0

Errors

3.5 0

% Incorrect Stability Evaluations − Pessimistic Estimations

SNR

(c) % Incorrect Stability evaluations - *Pessimistic*

3.5 0

−50 −40 −30 −20 −10

−50 −40 −30 −20 −10

**Not Acquired** output until the acquisition position is stable again.

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

Scenario 3 Scenario 2 Scenario 1 Scenario 0

SNR

convergence situations for the LMS filters.

(b) % Incorrect Stability evaluations - *Optimistic*

3.5 0

−50 −40 −30 −20 −10

% Incorrect Stability Evaluations − Optimistic Estimations

Scenario 3 Scenario 2 Scenario 1 Scenario 0

Errors

evaluations.

−0.5 0 0.5 1 1.5 2 2.5 3 −0.5 0 0.5 1 1.5 2 2.5 3

(a) % Correct Fuzzy evaluations

Errors

Fig. 15. Performance of the Fuzzy Logic Control. Measurements about the correct and incorrect evaluations.

factor, it must be taken into account that some bad estimations (*pessimistic* ones) prevent the system from obtaining better information ratios in certain ranges of SNR [-38,-35] dB.

#### **5.2 Evaluation of the Fuzzy Multiresolutive Acquisition vs. the Multiresolutive Structure**

The evaluation of the Fuzzy Multiresolutive Acquisition structure vs. the Multiresolutive Structure (Morán et al., 2001) is based on the comparison of the *Acquisition* estimation evaluated for both systems, obviously using the same channel conditions for the two systems.

#### **5.2.1 The stability control for the Multiresolutive Structure**

The Multiresolutive Structure presented by (Morán et al., 2001) works with a stability control. This control is based on the robustness of the filter convergence, using it as a premise for its

Errors

18 Will-be-set-by-IN-TECH

% Correct Fuzzy Evaluations

SNR

Fig. 15. Performance of the Fuzzy Logic Control. Measurements about the correct and

system from obtaining better information ratios in certain ranges of SNR [-38,-35] dB.

**5.2 Evaluation of the Fuzzy Multiresolutive Acquisition vs. the Multiresolutive Structure**

factor, it must be taken into account that some bad estimations (*pessimistic* ones) prevent the

The evaluation of the Fuzzy Multiresolutive Acquisition structure vs. the Multiresolutive Structure (Morán et al., 2001) is based on the comparison of the *Acquisition* estimation evaluated for both systems, obviously using the same channel conditions for the two systems.

The Multiresolutive Structure presented by (Morán et al., 2001) works with a stability control. This control is based on the robustness of the filter convergence, using it as a premise for its

(a) % Correct Fuzzy evaluations

−0.5 0 0.5 1 1.5 2 2.5 3

Scenario 3 Scenario 2 Scenario 1 Scenario 0

Errors

3.5 0

% Incorrect Fuzzy Evaluations − Pessimistic Estimations

SNR

(c) % Incorrect Fuzzy evaluations - *Pessimistic*

3.5 0

−50 −40 −30 −20 −10

−50 −40 −30 −20 −10

Scenario 3 Scenario 2 Scenario 1 Scenario 0

SNR

(b) % Incorrect Fuzzy evaluations - *Optimistic*

**5.2.1 The stability control for the Multiresolutive Structure**

3.5 0

−50 −40 −30 −20 −10

% Incorrect Fuzzy Evaluations − Optimistic Estimations

Scenario 3 Scenario 2 Scenario 1 Scenario 0

Errors

incorrect evaluations.

−0.5 0 0.5 1 1.5 2 2.5 3 −0.5 0 0.5 1 1.5 2 2.5 3 design. The stability control gives an output **Acquired** if the adaptive filter structure presents the same results for a certain number of times (in this case, three times). In the work of (Morán et al., 2001) it is shown that the probability of being acquired increases as the acquistion position is more stable, and the stability control is based in this principle. The problems of the performance of this kind of stability control solution are lack of robustness in low SNR environments, interference and fading, and of course, multipath, because it cannot recognize a correct acquisition situation immediately; it was designed for enhance stability, so it keeps a **Not Acquired** output until the acquisition position is stable again.

(a) % Correct Stability evaluations

(b) % Incorrect Stability evaluations - *Optimistic* Errors (c) % Incorrect Stability evaluations - *Pessimistic* Errors

Fig. 16. Performance of the Stability Control. Measurements about the correct and incorrect evaluations.

This lack of robustness is improved with the design of the fuzzy control system, because its estimation uses various instantaneous parameters, so reacquisition is faster; the fact of relying on four different parameters ensures the robustness of the system, despite instantaneous non convergence situations for the LMS filters.

In Figure 17 an analysis of the performance for the correct estimation for both controls is done. In Figure 17.c the comparison for both is made in terms of %. The fuzzy control performs better for each SNR value except for the range [-38,-35] dB, where it performs worse, despite the lowest SNR values back to get into a proper operation. It has to be noticed that the stability

<sup>151</sup> Fuzzy Logic Control for Multiresolutive Adaptive

evaluations

Mean incorrect fuzzy evaluations Mean incorrect stability evaluations

% Incorrect Acquisition Evaluations − System Comparison

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>0</sup>

SNR

(c) Comparison of the incorrect *Optimistic* evaluations for Fuzzy and Stability Controls

Fig. 18. Comparison of the incorrect evaluations for both fuzzy and stability controls, in case

Figure 18 shows the incorrect optimistic evaluations for both fuzzy and stability controls. Optimistic error is very low for fuzzy control at any SNR (see Figure 18.a), and for stability control is just the opposite: it has very high optimistic error, especially for lower SNR (see Figure 18.b, and 18.c for a comparison between the two control systems). Then, the use of the stability control makes the multiresolutive structure be confident in the information

% Optimistic Evaluations

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>0</sup>

% Incorrect Acquisition Evaluations − Stability System

Mean incorrect values Mean incorrect values Sce0 Mean incorrect values Sce1 Mean incorrect values Sce2 Mean incorrect values Sce3

SNR

(b) % Incorrect *Optimistic* Stability Control system

control starts performing bad around -37 dB, and does not recover for worse SNR.

Mean incorrect values Mean incorrect values Sce0 Mean incorrect values Sce1 Mean incorrect values Sce2 Mean incorrect values Sce3

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>0</sup>

% Incorrect Acquisition Evaluations − Fuzzy System

SNR

% Optimistic Evaluations

(a) % Incorrect *Optimistic* Fuzzy Control system

evaluations

that the error is *optimistic*.

% Optimistic Evaluations

The results for the stability control solution are shown in Figures 16. Figure 16.a shows the correct performance of the stability control, and Figures 16.b and 16.c show the performance for the incorrect stability evaluations, the first for the optimistic errors, and the second one for the pessimistic. Figure 16.b depicts high optimistic error, which deal to the multiresolutive structure to assume acquisition when it is not. This fact globally increases the BER at the receiver in terms of confidence in the demodulation of the information.

#### **5.2.2 Comparison results**

In this Section a comparative analysis of the results of the fuzzy and the stability controls is made. Numerical results for the four scenarios are computed, and the mean of these results is taken into account to compare the two control systems.

Fig. 17. Comparison of the correct evaluations for both fuzzy and stability controls.

20 Will-be-set-by-IN-TECH

The results for the stability control solution are shown in Figures 16. Figure 16.a shows the correct performance of the stability control, and Figures 16.b and 16.c show the performance for the incorrect stability evaluations, the first for the optimistic errors, and the second one for the pessimistic. Figure 16.b depicts high optimistic error, which deal to the multiresolutive structure to assume acquisition when it is not. This fact globally increases the BER at the

In this Section a comparative analysis of the results of the fuzzy and the stability controls is made. Numerical results for the four scenarios are computed, and the mean of these results is

% Correct Acquisition Evaluations − System Comparison

% Correct Evaluations

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>10</sup>

(c) Comparison of the correct evaluations for Fuzzy

Fig. 17. Comparison of the correct evaluations for both fuzzy and stability controls.

SNR

Mean correct fuzzy evaluations Mean correct stability evaluations

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>10</sup>

(b) % Correct Stability evaluations

SNR

Mean correct values Mean correct values Sce0 Mean correct values Sce1 Mean correct values Sce2 Mean correct values Sce3

% Correct Acquistion Evaluations − Stability System

receiver in terms of confidence in the demodulation of the information.

Mean correct values Mean correct values Sce0 Mean correct values Sce1 Mean correct values Sce2 Mean correct values Sce3

taken into account to compare the two control systems.

% Correct Acquisition Evaluations − Fuzzy System

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>10</sup>

(a) % Correct Fuzzy evaluations

SNR

and Stability controls

% Correct Evaluations

**5.2.2 Comparison results**

% Correct Evaluations

In Figure 17 an analysis of the performance for the correct estimation for both controls is done. In Figure 17.c the comparison for both is made in terms of %. The fuzzy control performs better for each SNR value except for the range [-38,-35] dB, where it performs worse, despite the lowest SNR values back to get into a proper operation. It has to be noticed that the stability control starts performing bad around -37 dB, and does not recover for worse SNR.

(a) % Incorrect *Optimistic* Fuzzy Control system evaluations (b) % Incorrect *Optimistic* Stability Control system evaluations

(c) Comparison of the incorrect *Optimistic* evaluations for Fuzzy and Stability Controls

Fig. 18. Comparison of the incorrect evaluations for both fuzzy and stability controls, in case that the error is *optimistic*.

Figure 18 shows the incorrect optimistic evaluations for both fuzzy and stability controls. Optimistic error is very low for fuzzy control at any SNR (see Figure 18.a), and for stability control is just the opposite: it has very high optimistic error, especially for lower SNR (see Figure 18.b, and 18.c for a comparison between the two control systems). Then, the use of the stability control makes the multiresolutive structure be confident in the information

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> 0.4

control system. The most important advantage of fuzzy logic vs. a stability control is that the quality of the acquisition can be measured; for high values of *Acquisition*, the performance of

In Figure 20 the mean values of output variable *Acquisition* of the fuzzy control system are shown (each value is computed for a specific scenario and SNR). This figure shows the information that the fuzzy control gives to the decisional system of the multiresolutive structure. At first, it is used to set the convergence (see the details in Section 4.4). If the value of *Acquisition* is higher than 0.75, the convergence is nearly guaranteed, and the system does not need to run all the adaptive filters at each symbol time. If the value of *Acquisition* is between 0.5 and 0.75, the system is **Probably Acquired**, but keeps searching to improve acquisition. But if *Acquisition* is between 0.25 and 0.75, the decisional system moves the data

filters. Finally, if the *Acquisition* value is lower than 0.25, the decisional system moves the data

simulations, although some of the outputs for *Acquisition* were lower than 0.25, the values of

The second advantage of using continuous output values for the *Acquisition* variable is reducing computational load by stopping the search - filters LMS adaptation - during

case of certain acquisition (shown through variable *Acquisition* value over 0.75) for SNR values ranging [-20,0] dB approximately, while this is not possible to be done using a stability control.

In this section, the evaluation results have been shown for the performance of the fuzzy logic controller in the multiresolutive acquisition structure. The fuzzy logic control system shows good performance even for low SNR, except for the values in the range [-38,-35]dB; in this range the estimation error increases due to *pessimistic* errors. In comparison with the stability control, the global behavior is improved because the fuzzy control has better results above

SNR

Scenario 0 Scenario 1 Scenario2 Scenario 3

<sup>4</sup> , and evaluates the improvement of the convergence of the

<sup>2</sup> and evaluates the convergence improvement. In the current

<sup>4</sup> of the computational load of the LMS filters can be reduced in

Mean value for Acquisition output

<sup>153</sup> Fuzzy Logic Control for Multiresolutive Adaptive

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Fig. 20. Mean output *Acquisition* values for the four scenarios

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

the SNR tested mean *Acquisition* were evaluated over 0.4.

the system is better, for lower, the convergence is not guaranteed.

Mean value for Acquisition [0,1]

for the acquisition stage by *Ts*

for the acquisition stage by *Ts*

acquisition state. Nearly <sup>3</sup>

**5.4 Summary**

demodulation of the system when it is really not correctly acquired, and BER increases in the receiver.

(a) % Incorrect *Pessimistic* Fuzzy Control system evaluations (b) % Incorrect *Pessimistic* Stability Control system evaluations

evaluations for Fuzzy and Stability Controls

Fig. 19. Comparison of the incorrect evaluations for both fuzzy and stability controls, in case that the error is *pessimistic*.

In Figure 19 the pessimistic error for both controls is shown. In this case, Figure 19.a depicts a bad performance of the fuzzy control system for values ranging [-38,-35] dB, but its performance becomes better when SNR worsen. Figure 19.b outstands a more constant performance for the stability control in the case of the pessimistic error.

#### **5.3 Multiresolutive structure acquisition feedback**

Finally, the possibilities of improving the performance of the multiresolutive structure (Morán et al., 2001) are shown through visualization of the output *Acquisition* behavior for the fuzzy

Fig. 20. Mean output *Acquisition* values for the four scenarios

control system. The most important advantage of fuzzy logic vs. a stability control is that the quality of the acquisition can be measured; for high values of *Acquisition*, the performance of the system is better, for lower, the convergence is not guaranteed.

In Figure 20 the mean values of output variable *Acquisition* of the fuzzy control system are shown (each value is computed for a specific scenario and SNR). This figure shows the information that the fuzzy control gives to the decisional system of the multiresolutive structure. At first, it is used to set the convergence (see the details in Section 4.4). If the value of *Acquisition* is higher than 0.75, the convergence is nearly guaranteed, and the system does not need to run all the adaptive filters at each symbol time. If the value of *Acquisition* is between 0.5 and 0.75, the system is **Probably Acquired**, but keeps searching to improve acquisition. But if *Acquisition* is between 0.25 and 0.75, the decisional system moves the data for the acquisition stage by *Ts* <sup>4</sup> , and evaluates the improvement of the convergence of the filters. Finally, if the *Acquisition* value is lower than 0.25, the decisional system moves the data for the acquisition stage by *Ts* <sup>2</sup> and evaluates the convergence improvement. In the current simulations, although some of the outputs for *Acquisition* were lower than 0.25, the values of the SNR tested mean *Acquisition* were evaluated over 0.4.

The second advantage of using continuous output values for the *Acquisition* variable is reducing computational load by stopping the search - filters LMS adaptation - during acquisition state. Nearly <sup>3</sup> <sup>4</sup> of the computational load of the LMS filters can be reduced in case of certain acquisition (shown through variable *Acquisition* value over 0.75) for SNR values ranging [-20,0] dB approximately, while this is not possible to be done using a stability control.

#### **5.4 Summary**

22 Will-be-set-by-IN-TECH

demodulation of the system when it is really not correctly acquired, and BER increases in the

2

evaluations

Mean incorrect fuzzy evaluations Mean incorrect stability evaluations

% Incorrect Acquisition Evaluations − System Comparison

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>0</sup>

SNR

(c) Comparison of the incorrect *Pessimistic* evaluations for Fuzzy and Stability Controls

Fig. 19. Comparison of the incorrect evaluations for both fuzzy and stability controls, in case

In Figure 19 the pessimistic error for both controls is shown. In this case, Figure 19.a depicts a bad performance of the fuzzy control system for values ranging [-38,-35] dB, but its performance becomes better when SNR worsen. Figure 19.b outstands a more constant

Finally, the possibilities of improving the performance of the multiresolutive structure (Morán et al., 2001) are shown through visualization of the output *Acquisition* behavior for the fuzzy

performance for the stability control in the case of the pessimistic error.

4

6

% Pessimistic Evaluations

8

10

12

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>0</sup>

% Incorrect Acquisition Evaluations − Stability System

Mean incorrect values Mean incorrect values Sce0 Mean incorrect values Sce1 Mean incorrect values Sce2 Mean incorrect values Sce3

SNR

(b) % Incorrect *Pessimistic* Stability Control system

receiver.

evaluations

% Pessimistic Evaluations

<sup>−</sup><sup>50</sup> <sup>−</sup><sup>45</sup> <sup>−</sup><sup>40</sup> <sup>−</sup><sup>35</sup> <sup>−</sup><sup>30</sup> <sup>−</sup><sup>25</sup> <sup>−</sup><sup>20</sup> <sup>−</sup><sup>15</sup> <sup>−</sup><sup>10</sup> <sup>−</sup><sup>5</sup> <sup>0</sup> <sup>0</sup>

% Incorrect Acquisition Evaluations − Fuzzy System

Mean incorrect values Mean incorrect values Sce0 Mean incorrect values Sce1 Mean incorrect values Sce2 Mean incorrect values Sce3

SNR

10

**5.3 Multiresolutive structure acquisition feedback**

that the error is *pessimistic*.

20

30

% Pessimistic Evaluations

40

50

60

(a) % Incorrect *Pessimistic* Fuzzy Control system

In this section, the evaluation results have been shown for the performance of the fuzzy logic controller in the multiresolutive acquisition structure. The fuzzy logic control system shows good performance even for low SNR, except for the values in the range [-38,-35]dB; in this range the estimation error increases due to *pessimistic* errors. In comparison with the stability control, the global behavior is improved because the fuzzy control has better results above

**7. Acknowledgments**

**8. References**

de l'Ebre throughout the research work.

*Global Research in Computer Science* 1: 49–53.

PN Acquisition Scheme in Time-Varying Multipath Ionospheric Channel

This work has been funded by the Spanish Government under the projects REN2003-08376-C02-02, CGL2006-12437-C02-01/ANT, CTM2008-03236-E/ANT, CTM2009-13843-C02-02 and CTM2010-21312-C03-03. La Salle thanks the *Comissionat per a Universitats i Recerca del DIUE de la Generalitat de Catalunya* for their support under the grant 2009SGR459. We must also acknowledge the support of the scientists of the Observatory

<sup>155</sup> Fuzzy Logic Control for Multiresolutive Adaptive

Akhter, N., Ferdouse, L., Jaigirdar, F. & Nipa, T. (2010). A Performance Analysis of LMS, RLS

Alsina, R., Bernadó, E. & Morán, J. (2005b). Evolution Strategies for DS-CDMA Pseudonoise

Alsina, R. M., Bergadà, P., Socoró, J. C. & Deumal, M. (2009a). Multiresolutive Acquisition

Alsina, R. M., Formiga, L., Socoró, J. C. & Bernadó, E. (2007a). Multiobjective Evolution

Alsina, R. M., Mateo, C., Socoró, J. C. & Deumal, M. (2008). Neural Network Acquistition

Alsina, R., Mateo, C. & Socoró, J. (2007b). Multiresolutive Adaptive PN Acquisition Scheme

Alsina, R., Mateo, C. & Socoró, J. (2009b). *Artificial Intelligence Enciclopaedia*, IGI Global, (EUA), chapter 'F': Fuzzy Logic Estimator for Variant SNR Environments, pp. 719–728. Alsina, R., Morán, J. & Socoró, J. (2005a). Sequential PN Acquisition Scheme Based on a Fuzzy

International Work-conference on Artificial Neural Networks (IWANN). Bas, J. & Perez-Neira, A. (2003). A Fuzzy Logic System for Interference Rejection in Code

Bergadà, P., Deumal, M., Alsina, R. & Pijoan, J. (2009). Time Interleaving Study for an OFDM

Daffara, F. (1995). A Fuzzy Rule Based Phase Error Detector, *Proceedings of URSI International*

Deumal, M., Vilella, C., Socoró, J., Alsina, R. & Pijoan, J. (2006). A DS-SS Signaling

*Conference on Ionospheric Radio Systems and Techniques*, IEEE, London, UK.

*Intelligence Research and Development* 131: 189 – 196. IOS Press.

*Systems and Techniques (IRST)*, IET, Edimburgh (Regne Unit).

*Research and Development* 163: 384 – 391. IOS Press.

onference on Artificial Neural Networks (IWANN).

*Intelligent Systems (HIS)*, Barcelona (Espanya).

*Systems and Techniques*, Edimburgh (UK).

*Symposium on Signals, Systems, and Electronics*.

and Lattice based Algorithms as Applied to the Area of Linear Prediction, *Journal of*

Sequence Design, *Frontiers in Artificial Intelligence and Applications - Artificial*

Technique for DS-SS Long-Haul HF Data Link, *Proceedings of the 11th Ionospheric Radio*

Strategies for DS-CDMA Pseudonoise Sequence Design in a Multiresolutive Acquisition, *Frontiers in Artificial Intelligence and Applications - Artificial Intelligence*

Estimator for Multiresolutive Adaptive PN Acquisition Scheme in Multiuser Non Selective Fast SNR Variation Environments, *8th International Conference on Hybrid*

with a Fuzzy Logic Estimator in Non Selective Fast SNR Variation Environments, *Lecture Notes in Computer Science - Springer Verlag* 4507: 367 – 374. International Work-c

Logic Controller, *Lecture Notes in Computer Science - Springer Verlag* 3512: 1238 – 1245.

Division Multiple Access, *IEEE International Conference on Fuzzy Systems* 2: 996–1001.

Long-Haul HF Radio Link, *in* T. IET (ed.), *Proceedings of the 11th Ionospheric Radio*

Based System Proposal for Low SNR HF Digital Communications, *IEEE International*

the critical margin of [-38,-35]dB, and it behaves really well for lower SNR. Another clear advantage of the fuzzy control against the stability control is the wider range of possible output values. This fact allows the multiresolutive structure to decrease its computational load when the system is clearly acquired, and also to change the acquisition pointer in case of a far acquisition estimated point; this information enhances the receiver performance, not only in terms of reliability, but also in terms of computational load.

## **6. Conclusions**

In this chapter a novel fuzzy control system for a multiresolutive acquisition structure (Morán et al., 2001) is detailed. It can be concluded that the four computed ratios used as input values for the control system (*Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac*) perform coherently with the results of the multiresolutive structure. Therefore, decisions can be made attending to their values. It can be stated that these ratios stand out for the performance of the whole system, and their values for the four simulated scenarios are found in the same range of values. Therefore, we conclude that they might be useful to describe and optimize the system performance.

The fuzzy logic control gives a more precise output acquisition variable allowing the system to conclude whether it is correctly acquired, probably acquired, probably not acquired, and not acquired; then, the control logic can optimize the computational load of the structure depending on these values. If the system is correctly acquired (depending on the value for *Acquisition*), the decisional system reduces the global computational load by stopping the convergence of some LMS adaptive filters (despite the detailed computational load study is not included in this chapter). So, not only the acquisition estimation is improved, but also the global performance of the structure is optimized. The only SNR range where the fuzzy control system performance can significantly be improved is around [-40,-35] dB, where this performance is poor. It is also important to note that the correct estimation of the acquisition for very low SNR values helps the system in terms of confidence about the demodulated information; in case of the stability control, for values worse than -36 dB the information demodulated is notoriously unreliable; and for fuzzy control, *Acquisition* continuous value gives enough information to know whether the system is out of the correct acquistion area, and hence the system not being confident on the information results. Future research is focused in improving the performance of the fuzzy control in the multiresolutive structure, especially at specific levels of SNR where the results behavior is pessimistic, in order to increase the reliability of the system estimation.

The results shown in this chapter stand out for the application of fuzzy control systems to other acquisition schemes found in the literature, and allow us to state that our work represents an interesting proposal to the future research in this field; the LMS adaptive scheme presented by (El-Tarhuni & Sheikh, 1996), lately improved by (Han et al., 2006), and also the adaptive system for ocean acquisition transmission presented by (Stojanovic & Freitag, 2003). We think that the knowledge of the channel characteristics and the behavior of the LMS filter convergence would be the first data to be taken into account to the design a fuzzy control system conceived with the aim of improving the stability and the robustness of any acquisition receiver for a DS-SS communications system. This aspect is highlighted here, because control systems designed to operate within LMS-based adaptive acquisition schemes found in the literature do not consider other information rather than the stability of the acquisition estimation.

## **7. Acknowledgments**

24 Will-be-set-by-IN-TECH

the critical margin of [-38,-35]dB, and it behaves really well for lower SNR. Another clear advantage of the fuzzy control against the stability control is the wider range of possible output values. This fact allows the multiresolutive structure to decrease its computational load when the system is clearly acquired, and also to change the acquisition pointer in case of a far acquisition estimated point; this information enhances the receiver performance, not

In this chapter a novel fuzzy control system for a multiresolutive acquisition structure (Morán et al., 2001) is detailed. It can be concluded that the four computed ratios used as input values for the control system (*Ratio*1, *Ratio*2, *Ratio*<sup>3</sup> and *Ratio*1*trac*) perform coherently with the results of the multiresolutive structure. Therefore, decisions can be made attending to their values. It can be stated that these ratios stand out for the performance of the whole system, and their values for the four simulated scenarios are found in the same range of values. Therefore, we conclude that they might be useful to describe and optimize the system performance.

The fuzzy logic control gives a more precise output acquisition variable allowing the system to conclude whether it is correctly acquired, probably acquired, probably not acquired, and not acquired; then, the control logic can optimize the computational load of the structure depending on these values. If the system is correctly acquired (depending on the value for *Acquisition*), the decisional system reduces the global computational load by stopping the convergence of some LMS adaptive filters (despite the detailed computational load study is not included in this chapter). So, not only the acquisition estimation is improved, but also the global performance of the structure is optimized. The only SNR range where the fuzzy control system performance can significantly be improved is around [-40,-35] dB, where this performance is poor. It is also important to note that the correct estimation of the acquisition for very low SNR values helps the system in terms of confidence about the demodulated information; in case of the stability control, for values worse than -36 dB the information demodulated is notoriously unreliable; and for fuzzy control, *Acquisition* continuous value gives enough information to know whether the system is out of the correct acquistion area, and hence the system not being confident on the information results. Future research is focused in improving the performance of the fuzzy control in the multiresolutive structure, especially at specific levels of SNR where the results behavior is pessimistic, in order to

The results shown in this chapter stand out for the application of fuzzy control systems to other acquisition schemes found in the literature, and allow us to state that our work represents an interesting proposal to the future research in this field; the LMS adaptive scheme presented by (El-Tarhuni & Sheikh, 1996), lately improved by (Han et al., 2006), and also the adaptive system for ocean acquisition transmission presented by (Stojanovic & Freitag, 2003). We think that the knowledge of the channel characteristics and the behavior of the LMS filter convergence would be the first data to be taken into account to the design a fuzzy control system conceived with the aim of improving the stability and the robustness of any acquisition receiver for a DS-SS communications system. This aspect is highlighted here, because control systems designed to operate within LMS-based adaptive acquisition schemes found in the literature do not consider other information rather than the stability of

only in terms of reliability, but also in terms of computational load.

increase the reliability of the system estimation.

the acquisition estimation.

**6. Conclusions**

This work has been funded by the Spanish Government under the projects REN2003-08376-C02-02, CGL2006-12437-C02-01/ANT, CTM2008-03236-E/ANT, CTM2009-13843-C02-02 and CTM2010-21312-C03-03. La Salle thanks the *Comissionat per a Universitats i Recerca del DIUE de la Generalitat de Catalunya* for their support under the grant 2009SGR459. We must also acknowledge the support of the scientists of the Observatory de l'Ebre throughout the research work.

## **8. References**


**8** 

 *Colombia* 

**Fuzzy Control in Power Electronics** 

Harold R. Chamorro and Gustavo A. Ramos

*Universidad de los Andes, Bogotá,* 

 **Converters for Smart Power Systems** 

During the last decade, power systems have experienced continuous challenges due to the increasing of demanded energy and the integration with different Renewable Energy Sources (RES) as a possible reduction option to the pollution around the world, for this reason it is necessary the transition to the new power concept known as "Smart Grid", which has been conceived as the integration of different engineering fields and looks for the application of intelligent controllers with adaptability and interoperability with other

Power electronics plays a key role in the interfaces between the Distributed Generation (DG) sources and the power system or users, but it is necessary to add control loops which brings the possibility to give to the power system the flexibility and reconfiguration under

The technology of power electronics converters has evolved dramatically in the last years based on the semiconductors advances, new configuration proposals and important researches in several applications related with the interconnection of Distributed Energy

The intelligent control is associated to the emulation of human thought processes and involves some well-known techniques such as expert systems, neural networks and fuzzy logic (Bor-Ren, 1993; Zadeh, 1994; Bose, 2006). The use of these control methods in power electronics has been increased in the last decades, based on its simplicity design, the development of new speed multitasking processors and the necessity to add some controllers which demonstrates robustness in presence of the high nonlinear dynamic

The primary task of power electronics is the conversion and control of electric power in its two types, Direct Current (DC) and Alternating Current (AC) and its combinations. Fuzzy Logic Control (FLC) has been tested across the whole power converters classification with different objectives. For example in rectifiers, FLC has been used to regulate the output voltage (Cecati et al, 2003 & 2005), in cycloconverters, with the purpose to improve the power quality and regulate the load voltage (Sivakumar & Jickson, 2011). In DC-DC converters, FLC has been applied to the regulation of load voltage in different operation

disturbances, faults or system requirements (Simoes, 2006; Peng, et al, 2009).

Resources (DER) with the utility grid (Elbuluk & Idris, 2008).

**1. Introduction** 

systems (Bose, 2010; Momoh, 2009).

characteristics of the power converters.


## **Fuzzy Control in Power Electronics Converters for Smart Power Systems**

Harold R. Chamorro and Gustavo A. Ramos *Universidad de los Andes, Bogotá, Colombia* 

## **1. Introduction**

26 Will-be-set-by-IN-TECH

156 Fuzzy Logic – Controls, Concepts, Theories and Applications

Drake, J. & Prasad, N. (1999). Current Trends Towards Using Soft Computing Approaches to

El-Tarhuni, M. & Sheikh, A. (1996). MSE Tracking Performance of DS-SS Code Tracking

Gad, A. & Farouq, M. (2001). Applications of Fuzzy Logic in Engineering Problems, *Proceedings of the Annual Conference of IEEE Industrial Electronics Society*. Glisic, S. G. (1991). Automatic Decision Threshold Level Control in Direct Sequence Spread Spectrum Systems, *IEEE Transactions on Communications* 39(2): 519–527. Glisic, S. & Vucetic, B. (1997). *Spread Spectrum CDMA Systems for Wireless Communications*,

Han, M., Yu, T., Kang, C. & Hong, D. (2006). A New Adaptive Code-Acquisition

Haykin, S. (1996). *Adaptive Filter Theory*, Prentice Hall International, United States of America. Morán, J., Socoró, J., Jové, X., Pijoan, J. & Tarrés, F. (2001). Multiresolution Adaptive Structure

Perez-Neira, A. & Lagunas, M. (1996). High Performance DOA Trackers Derived from Parallel

Perez-Neira, A., Lagunas, M. & Bas, J. (1997). Fuzzy Logic for Robust Detection in Wireless

Peterson, R., Ziemer, R. & Borth, D. (1995). *Introduction to Spread Spectrum Communications*,

Sklar, B. (1988). *Digital Communications, Fundamentals and Applications*, Prentice Hall

Stojanovic, M. & Freitag, L. (2003). Acquisition of Direct Sequence Spread Spectrum Acoustic

Vilella, C., Miralles, D., Altadill, D., Acosta, F., Sole, J., Torta, J. M. & Pijoan, J. (2009). Vertical

Vilella, C., Miralles, D. & Pijoan, J. (2008). An Antarctica-to-Spain HF ionospheric radio link:

Polar to Midlatitudes: Results and Relationships, *Radio Science* 44.

Sounding results, *Radio Sci.* 43(doi:10.1029/2007RS003812). Zadeh, L. (1965). Fuzzy Sets, *IEEE Transactions on Information and Control* 8: 338–353.

and Oblique Ionospheric Soundings over a Very Long Multihop HF Radio Link from

Algorithm Using Parallel Subfilter Structure, *IEEE Transactions on Vehicular Technology*

for acquisition in DS-SS receivers, *International Conference on Acoustics, Speech and*

Communications, *Proceedings of the 8th IEEE International Symposium on Personal,*

Scheme Using an Adaptive Filter, *Electronic Letters* 32: 1543–1545.

Artech House Publishers, United States of America.

Low Resolution Detectors, *IEEE Workshop on SSAP*.

Proakis, J. (1995). *Digital Communications*, McGraw-Hill, Singapore.

*Indoor and Mobile Radio Communications*.

Prentice Hall, United States of America.

International, United States of America.

Zadeh, L. (1988). Fuzzy Logic, *Computer* 21(4): 83–92.

Communication Signals, *Oceans* 1: 279 – 286.

*on Circuits and Systems*.

55(6): 1790–1796.

*Signal Processing* .

Phase Shyncrhonization in Communications Systems, *IEEE 42nd Midwest Symposium*

During the last decade, power systems have experienced continuous challenges due to the increasing of demanded energy and the integration with different Renewable Energy Sources (RES) as a possible reduction option to the pollution around the world, for this reason it is necessary the transition to the new power concept known as "Smart Grid", which has been conceived as the integration of different engineering fields and looks for the application of intelligent controllers with adaptability and interoperability with other systems (Bose, 2010; Momoh, 2009).

Power electronics plays a key role in the interfaces between the Distributed Generation (DG) sources and the power system or users, but it is necessary to add control loops which brings the possibility to give to the power system the flexibility and reconfiguration under disturbances, faults or system requirements (Simoes, 2006; Peng, et al, 2009).

The technology of power electronics converters has evolved dramatically in the last years based on the semiconductors advances, new configuration proposals and important researches in several applications related with the interconnection of Distributed Energy Resources (DER) with the utility grid (Elbuluk & Idris, 2008).

The intelligent control is associated to the emulation of human thought processes and involves some well-known techniques such as expert systems, neural networks and fuzzy logic (Bor-Ren, 1993; Zadeh, 1994; Bose, 2006). The use of these control methods in power electronics has been increased in the last decades, based on its simplicity design, the development of new speed multitasking processors and the necessity to add some controllers which demonstrates robustness in presence of the high nonlinear dynamic characteristics of the power converters.

The primary task of power electronics is the conversion and control of electric power in its two types, Direct Current (DC) and Alternating Current (AC) and its combinations. Fuzzy Logic Control (FLC) has been tested across the whole power converters classification with different objectives. For example in rectifiers, FLC has been used to regulate the output voltage (Cecati et al, 2003 & 2005), in cycloconverters, with the purpose to improve the power quality and regulate the load voltage (Sivakumar & Jickson, 2011). In DC-DC converters, FLC has been applied to the regulation of load voltage in different operation

Fuzzy Control in Power Electronics Converters for Smart Power Systems 159

This chapter gathers together some previous works related with the application of fuzzy logic control in power converters and explain its use in Smart MG. The developments presented in this chapter start from theoretical and mathematical background and are supported in literature and recent contributions in the field exposed. For the rest of this chapter the use of FLC is shown in different power converters as follows: In section II it is presented the application of a FLC in a soft switching converter. In section III it is explained two applications of FLC for a VSC. In section IV it is shown two innovative proposals for MG applying FLC as

With the advent of the deep penetration of renewable energy sources along the power system, the application of new power electronic techniques are becoming a necessity in order to improve the efficiency and to get the maximum power transfer as long as possible. Soft switching topologies and resonant power converters are well known by offering a significant reduction in the switching losses and the components size involved, the decreasing of the thermal requirements, and operating at high frequencies (Rashid, 2001). During the last decades, some important developments have shown the applicability of the soft switching circuits in PV arrays and the interfaces in their power conversion chains as a mean of raising the switch power ratings in the inverters associated (Bellini & et al, 2010;

One of those soft switching topologies is the resonant DC link circuits which are the interfaces between DC power supplies or PV cells and the inverters as it can be seen in Fig. 2. These circuits consist of a front - ended converter to cause the DC link voltage to generate a periodic Zero Voltage Switching (ZVS) condition in which the inverter switches can be turned on or off. However, these kinds of converters require defining previously a timing

Fuzzy Logic Control (FLC) has been applied in different soft switched inverters in order to provide a standalone way of switching with good results (Shireen & et al, 1996). In a previous work it is demonstrated the applicability of the FLC in a DC link circuit interacting with a VSC (Chamorro & Trujillo, 2009), now it is presented the TS approach, its design and

The DC link circuit scheme can be seen in Fig. 3, where is highlighted the tank circuit composed by a *Lr* inductor and a *Cr* capacitor and three controllable switches and diodes. It

program for each switch in order to obtain the expected modes and their resonance.

supervisory/hierarchical control. Finally the obtained conclusions are presented.

**2. Takagi Sugeno approach control for a resonant DC link converter** 

Kasa & et al, 2005).

Fig. 2. DC Link Interface

some relevant tests.

**2.1 DC link circuit under study** 

conditions (Bor-Ren, 1993; Mattavelli et al, 1997) or Power Factor Correction (PFC) taking into account the application (Kolokolov, 2004).

In resonant converters and soft self - switching power circuits, the use of FLC has shown significant contributions obtaining the expected results, that with other techniques might not be obtained with the same simplicity design (Corcau & et al, 2010; Chamorro & Trujillo, 2009).

Moreover, FLC has been applied in inverters, specially in Voltage Source Converters (VSC) assuring phase and voltage magnitude (Ayob & et al, 2006) in the power flow control with the utility grid in different operative regions (Diaz & et al, 2007; Chamorro & et al, 2009).

There are plenty of developments of FLC in power electronics in all the voltage scales and power sectors. In Photo Voltaic (PV) applications, FLC has been proposed to optimize the Maximum Power Point (MPP) with outstanding results compared with other methods (Alajmi et al, 2010; Chaouachi et al, 2010; Shireen et al, 2011).

Another important application has been developed in High Voltage Direct Current (HVDC) in both stations (rectifier and inverter) ensuring an adequate performance despite of the system complexity (Liang, 2009).

In the industrial sector as well, FLC has demonstrated a satisfactory use in Adjustable Speed Drivers (ASD) for three phase induction motors under mechanical loads with good results (Chamorro et al, 2009; Chamorro & Toro, 2010).

One important advantage which offers the FLC is the possibility to use it as a hierarchical layer with the ability to supervise and to coordinate other systems such as electric vehicles (Ferreira et al, 2008), Flexible AC Transmission Systems (FACTS) (Sadeghzadeh & Ansarian, 2006) or even Microgrids (MG) and its interaction with power electronic interfaces (Papadimitriou & Vovos, 2010; Chamorro & Ramos, 2011) which is the main point in this chapter.

A basic conceptual representation of a MG is presented in Fig. 1, where it is depicted the physical layer and involves a high penetration of DG (photovoltaic, fuel cell, fly-wheel storage, micro wind turbine) with power electronic interfaces. The MG is connected to the utility distribution system through a static switch and a transformer.

Fig. 1. Microgrid Structure Concept

conditions (Bor-Ren, 1993; Mattavelli et al, 1997) or Power Factor Correction (PFC) taking

In resonant converters and soft self - switching power circuits, the use of FLC has shown significant contributions obtaining the expected results, that with other techniques might not be obtained with the same simplicity design (Corcau & et al, 2010; Chamorro & Trujillo, 2009). Moreover, FLC has been applied in inverters, specially in Voltage Source Converters (VSC) assuring phase and voltage magnitude (Ayob & et al, 2006) in the power flow control with the utility grid in different operative regions (Diaz & et al, 2007; Chamorro & et al, 2009).

There are plenty of developments of FLC in power electronics in all the voltage scales and power sectors. In Photo Voltaic (PV) applications, FLC has been proposed to optimize the Maximum Power Point (MPP) with outstanding results compared with other methods

Another important application has been developed in High Voltage Direct Current (HVDC) in both stations (rectifier and inverter) ensuring an adequate performance despite of the

In the industrial sector as well, FLC has demonstrated a satisfactory use in Adjustable Speed Drivers (ASD) for three phase induction motors under mechanical loads with good results

One important advantage which offers the FLC is the possibility to use it as a hierarchical layer with the ability to supervise and to coordinate other systems such as electric vehicles (Ferreira et al, 2008), Flexible AC Transmission Systems (FACTS) (Sadeghzadeh & Ansarian, 2006) or even Microgrids (MG) and its interaction with power electronic interfaces (Papadimitriou &

A basic conceptual representation of a MG is presented in Fig. 1, where it is depicted the physical layer and involves a high penetration of DG (photovoltaic, fuel cell, fly-wheel storage, micro wind turbine) with power electronic interfaces. The MG is connected to the

Vovos, 2010; Chamorro & Ramos, 2011) which is the main point in this chapter.

utility distribution system through a static switch and a transformer.

into account the application (Kolokolov, 2004).

system complexity (Liang, 2009).

Fig. 1. Microgrid Structure Concept

(Chamorro et al, 2009; Chamorro & Toro, 2010).

(Alajmi et al, 2010; Chaouachi et al, 2010; Shireen et al, 2011).

This chapter gathers together some previous works related with the application of fuzzy logic control in power converters and explain its use in Smart MG. The developments presented in this chapter start from theoretical and mathematical background and are supported in literature and recent contributions in the field exposed. For the rest of this chapter the use of FLC is shown in different power converters as follows: In section II it is presented the application of a FLC in a soft switching converter. In section III it is explained two applications of FLC for a VSC. In section IV it is shown two innovative proposals for MG applying FLC as supervisory/hierarchical control. Finally the obtained conclusions are presented.

## **2. Takagi Sugeno approach control for a resonant DC link converter**

With the advent of the deep penetration of renewable energy sources along the power system, the application of new power electronic techniques are becoming a necessity in order to improve the efficiency and to get the maximum power transfer as long as possible.

Soft switching topologies and resonant power converters are well known by offering a significant reduction in the switching losses and the components size involved, the decreasing of the thermal requirements, and operating at high frequencies (Rashid, 2001).

During the last decades, some important developments have shown the applicability of the soft switching circuits in PV arrays and the interfaces in their power conversion chains as a mean of raising the switch power ratings in the inverters associated (Bellini & et al, 2010; Kasa & et al, 2005).

One of those soft switching topologies is the resonant DC link circuits which are the interfaces between DC power supplies or PV cells and the inverters as it can be seen in Fig. 2. These circuits consist of a front - ended converter to cause the DC link voltage to generate a periodic Zero Voltage Switching (ZVS) condition in which the inverter switches can be turned on or off. However, these kinds of converters require defining previously a timing program for each switch in order to obtain the expected modes and their resonance.

Fig. 2. DC Link Interface

Fuzzy Logic Control (FLC) has been applied in different soft switched inverters in order to provide a standalone way of switching with good results (Shireen & et al, 1996). In a previous work it is demonstrated the applicability of the FLC in a DC link circuit interacting with a VSC (Chamorro & Trujillo, 2009), now it is presented the TS approach, its design and some relevant tests.

## **2.1 DC link circuit under study**

The DC link circuit scheme can be seen in Fig. 3, where is highlighted the tank circuit composed by a *Lr* inductor and a *Cr* capacitor and three controllable switches and diodes. It

Fuzzy Control in Power Electronics Converters for Smart Power Systems 161

Some special attention is required, in order to establish the specific boundaries of the regions in each subset, specifically the zero region and the high positive and negative levels, which imply some important details in a real hardware application such as the rated values

According to the waveforms obtained, on the antecedent the input membership functions are conformed as it can be seen in Fig. 5 , where the linguistic labels mean Negative (N),

> 0 0.2 0.4 0.6 0.8 1

The Takagi – Sugeno system is employed as inference method, using constants or zero order Sugeno models in the output membership function, which represents the turning off or on action of the switches in the DC link circuit. The positive constants are interpreted as the turning on of the switches and the negative constants like the switches turning off instead, for example to turn on the switch called T1 the constant associated is *5*, or to turn off the switch T2 the correspondent constant is *-10*. In order to present these mentioned changes, a graphic of the rule viewer of FIS toolbox of Matlab® are shown displaying the fuzzy inference. The three small plots across the top of the Fig. 6 represent the antecedent and consequent of the rules.

The complete rule base determines all the decisions of the switch turning on or off. The

Degree of membership


N Z PS PL

Voltage

of the capacitor and inductor and their time response under a fast variability.

Zero (Z), Positive Small (PS), Positive Large (PL).

N Z PS PL


Current

Fig. 5. Input Membership Functions

0 0.2 0.4 0.6 0.8 1

Fig. 6. RuleViewer

decision table is presented next.

Degree of membership

is assumed that a high inductive load represents the inverter as a *Io* current source. The states and detail considerations can be seen in (Shireen & et al, 1994).

Fig. 3. DC Link Circuit

#### **2.2 Takagi Sugeno design**

This approach takes advantage of a previous development originally proposed in (Shireen & et al 1996), where is presented a FLC with the objective to pulsate to zero the DC link, allowing soft switching in an inverter connected and to reduce its switching losses as it is demonstrated in a recent paper (Chamorro & Trujillo, 2009).

The design starting point is the definition and classification of sets according to the voltage and current measurement signals in the capacitor. The definitions of linguistic variables are based on a previous developed knowledge evaluation of the current and voltage waveforms in open loop. These waveforms are presented in Fig. 4

Fig. 4. Current and Voltage Capacitor Waveforms

Some special attention is required, in order to establish the specific boundaries of the regions in each subset, specifically the zero region and the high positive and negative levels, which imply some important details in a real hardware application such as the rated values of the capacitor and inductor and their time response under a fast variability.

According to the waveforms obtained, on the antecedent the input membership functions are conformed as it can be seen in Fig. 5 , where the linguistic labels mean Negative (N), Zero (Z), Positive Small (PS), Positive Large (PL).

Fig. 5. Input Membership Functions

160 Fuzzy Logic – Controls, Concepts, Theories and Applications

is assumed that a high inductive load represents the inverter as a *Io* current source. The

g <sup>C</sup> <sup>E</sup> T1a

D1

g

T3a

3 T3

D2

This approach takes advantage of a previous development originally proposed in (Shireen & et al 1996), where is presented a FLC with the objective to pulsate to zero the DC link, allowing soft switching in an inverter connected and to reduce its switching losses as it is

The design starting point is the definition and classification of sets according to the voltage and current measurement signals in the capacitor. The definitions of linguistic variables are based on a previous developed knowledge evaluation of the current and voltage waveforms

0 0.5 1 1.5

0 0.5 1 1.5

Time(s)

Time(s)

C E

D3

3 DC Bus

<sup>v</sup> <sup>+</sup> - DC Bus1

Io = 20A

x 10-4

x 10-4

states and detail considerations can be seen in (Shireen & et al, 1994).

2 T2

g

T2a

C E

1 T1

1 ICr

demonstrated in a recent paper (Chamorro & Trujillo, 2009).

in open loop. These waveforms are presented in Fig. 4

Fig. 4. Current and Voltage Capacitor Waveforms

Cr

Lr

i + - IC

2 VCr

DC2

Fig. 3. DC Link Circuit




Current Capacitor (A)

Voltage Capacitor (V)

0

50

**2.2 Takagi Sugeno design** 

DC1

<sup>v</sup> <sup>+</sup> - VC

> The Takagi – Sugeno system is employed as inference method, using constants or zero order Sugeno models in the output membership function, which represents the turning off or on action of the switches in the DC link circuit. The positive constants are interpreted as the turning on of the switches and the negative constants like the switches turning off instead, for example to turn on the switch called T1 the constant associated is *5*, or to turn off the switch T2 the correspondent constant is *-10*. In order to present these mentioned changes, a graphic of the rule viewer of FIS toolbox of Matlab® are shown displaying the fuzzy inference. The three small plots across the top of the Fig. 6 represent the antecedent and consequent of the rules.

Fig. 6. RuleViewer

The complete rule base determines all the decisions of the switch turning on or off. The decision table is presented next.

Fuzzy Control in Power Electronics Converters for Smart Power Systems 163

The simulation tests in closed loop with the T-S FLC shows and adequate performance and a similarity with the voltage and current waveforms and the soft switching response, as it can

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time(s)

Time(s)

0 1 2 3 4 5 6 7 8 9

In order to show the adaptability and performance of the DC link circuit and the FLC, another test is done with a current source variation with high and abrupt changes. As it is shown in Fig. 11 the FLC is adaptable even under those several changes and the waveforms conserve their resonant behaviour without instability or not desired transient signals.

x 10-4

x 10-4

x 10-4

x 10-4

x 10-4

x 10-5

be seen in Fig 9.

0

1

0

1

0


2000


Notch Voltage (V)

0

Fig. 10. Obtained Waveforms with FLC

Current Capacitor (A)

Voltage Capacitor (V)

0

100

Fig. 9. Self-Switching Pulses

0.5

Switch 3

0.5

Switch 2

0.5

Switch 1

1


Table 1. Decision Table

The surface control associated it is presented in Fig. 7

#### Fig. 7. Surface Control

The final step of the FLC design is the defuzzification process, in this case it is used the common weight average method.

## **2.3 Simulation results**

The proposed structure of the fuzzy soft switching control is presented in the next Simulink(R) block diagram, where it is shown the DC link with its two outputs as the current and voltage measurements, the FLC embedded and the switching pulses generator.

Fig. 8. Closed Loop System

The simulation tests in closed loop with the T-S FLC shows and adequate performance and a similarity with the voltage and current waveforms and the soft switching response, as it can be seen in Fig 9.

Fig. 9. Self-Switching Pulses

162 Fuzzy Logic – Controls, Concepts, Theories and Applications

vc/ic N Z PS PL N NL NL PM PM Z NL PS PS NM PS PL PL NS NM PL PL PL NS NS

> -100 0 100 200 300 400 500 600

> > Out1

ICr VCr

Mux

Voltage

Table 1. Decision Table

Fig. 7. Surface Control

**2.3 Simulation results** 

Fig. 8. Closed Loop System

The surface control associated it is presented in Fig. 7


Switches

common weight average method.


The final step of the FLC design is the defuzzification process, in this case it is used the

The proposed structure of the fuzzy soft switching control is presented in the next Simulink(R) block diagram, where it is shown the DC link with its two outputs as the current

> 32.97 138.7

ICr & VCr

FLC with Ruleviewer

T1 T2 T3

ICr VCr DC Bus DC Link

T1

T2

T3

DC Bus

and voltage measurements, the FLC embedded and the switching pulses generator.

Current

Switching

T3


FLC Out

T1 T2 T3 Pulses

T1

T2

In order to show the adaptability and performance of the DC link circuit and the FLC, another test is done with a current source variation with high and abrupt changes. As it is shown in Fig. 11 the FLC is adaptable even under those several changes and the waveforms conserve their resonant behaviour without instability or not desired transient signals.

Fuzzy Control in Power Electronics Converters for Smart Power Systems 165

g

C E

g

IGBT/Diode44

IGBT/Diode3

3 IGBT3

4 IGBT4

g

g

C E

control the VSC in both of the cases mentioned above.

**3.2 Three phase induction motor speed control** 

measurements in the closed feedback loop control.

Fig. 13. Voltage Source Converter Interface

IGBT/Diode2

1 IGBT2

DC 2

DC 1

IGBT/Diode1

Fig. 12. Voltage Source Converter

Ilochonwu, 2011).

and easier than in the past.

2 IGBT1

C E

> C E

One of the simple switching techniques applied to VSC is the conventional method known as Sinusoidal Pulse Width Modulation (SPWM), this method is used to manipulate and

Rotating electrical machines, specifically three phase induction motors are the functional units with more electricity consumption in the industry, due to their widely use in manifold applications as diverse as industrial fans, blowers and pumps and machine tools, keeping in mind its advantages like resistance, easy maintenance, low cost and durability (Xiaodong &

Different techniques and improvements have been used to regulate the speed in induction motors such as sliding control (Chung-Yuen & et al, 1992), scalar control (Bose, 1984), vector control (Matsugae & et al, 1990) or direct torque control (Takahashi & Ohmori, 1989) with notable results, nevertheless these methods require the system model or use indirect

With the new developments in power electronics devices and microprocessors, the design and implementation of power converter control circuits based IA it has been made possible

In this section it is presented the application of a FLC in order to regulate the speed in a

three phase induction motor with the VSC as actuator as it is highlighted in Fig. 13.

3 phase C <sup>2</sup>

phase B <sup>1</sup>

phase A

g

g

C E

IGBT/Diode6

6 IGBT6

IGBT/Diode5

5 IGBT5

> C E

Fig. 11. Current Variability

## **3. Fuzzy applications in VSC**

One of the most significant converters which have played and will play an important role in the power networks, industry and traction systems is the Voltage Source Converter (VSC). This converter has been applied in different applications such as High Voltage Direct Current (HVDC) power transmission, Adjustable Speed Drivers (ASD), Active Power Filters (APF), Uninterruptible Power Supplies (UPS), electric vehicle drives and the connection of RES, mainly with, wind farms and Photo Voltaic (PV) arrays to grid.

Voltage Source Converter (VSC), used in Supergrids (SG) and MG, are able to manage the bidirectional power flow with the grid (Diaz & et al, 2007 & 2008) and other MG through the tie lines involved (Chamorro & Ramos, 2011).

On the other hand, most industries around the world use three phase induction motors due their high durability, low maintenance and cost, however, it is necessary to add an extra controller with the purpose of achieving speed regulation under mechanical loads, hence, the VSC has become an important piece in the industrial processes given its versatility as an ASD (Mokrytzki, 1991).

This section presents two applications using fuzzy logic in their control loops demonstrating the easiness of design and its importance in the smart electrical systems.

## **3.1 Voltage source converter operation**

Fig. 12 depicts the main components of a VSC, where it can be seen a three phase fully controllable of six semiconductors, typically Insulated Gate Bipolar Transistors (IGBT), a DC capacitor on the DC side in order to provide constant DC bus voltage with a minimal ripple.

Fig. 12. Voltage Source Converter

0 20 40



> -5000 0 5000

Fig. 11. Current Variability

ASD (Mokrytzki, 1991).

**3. Fuzzy applications in VSC** 

tie lines involved (Chamorro & Ramos, 2011).

**3.1 Voltage source converter operation** 

Current Change (A)

DC Link Voltage (V)

Voltage Capacitor (V)

0 1 2 3 4 5 6

Time(s)

0 1 2 3 4 5 6

Time(s)

0 1 2 3 4 5 6

Time(s)

0 1 2 3 4 5 6

Time(s)

One of the most significant converters which have played and will play an important role in the power networks, industry and traction systems is the Voltage Source Converter (VSC). This converter has been applied in different applications such as High Voltage Direct Current (HVDC) power transmission, Adjustable Speed Drivers (ASD), Active Power Filters (APF), Uninterruptible Power Supplies (UPS), electric vehicle drives and the connection of

Voltage Source Converter (VSC), used in Supergrids (SG) and MG, are able to manage the bidirectional power flow with the grid (Diaz & et al, 2007 & 2008) and other MG through the

On the other hand, most industries around the world use three phase induction motors due their high durability, low maintenance and cost, however, it is necessary to add an extra controller with the purpose of achieving speed regulation under mechanical loads, hence, the VSC has become an important piece in the industrial processes given its versatility as an

This section presents two applications using fuzzy logic in their control loops demonstrating

Fig. 12 depicts the main components of a VSC, where it can be seen a three phase fully controllable of six semiconductors, typically Insulated Gate Bipolar Transistors (IGBT), a DC capacitor on the DC side in order to provide constant DC bus voltage with a minimal ripple.

RES, mainly with, wind farms and Photo Voltaic (PV) arrays to grid.

the easiness of design and its importance in the smart electrical systems.

x 10-4

x 10-4

x 10-4

x 10-4

One of the simple switching techniques applied to VSC is the conventional method known as Sinusoidal Pulse Width Modulation (SPWM), this method is used to manipulate and control the VSC in both of the cases mentioned above.

## **3.2 Three phase induction motor speed control**

Rotating electrical machines, specifically three phase induction motors are the functional units with more electricity consumption in the industry, due to their widely use in manifold applications as diverse as industrial fans, blowers and pumps and machine tools, keeping in mind its advantages like resistance, easy maintenance, low cost and durability (Xiaodong & Ilochonwu, 2011).

Different techniques and improvements have been used to regulate the speed in induction motors such as sliding control (Chung-Yuen & et al, 1992), scalar control (Bose, 1984), vector control (Matsugae & et al, 1990) or direct torque control (Takahashi & Ohmori, 1989) with notable results, nevertheless these methods require the system model or use indirect measurements in the closed feedback loop control.

With the new developments in power electronics devices and microprocessors, the design and implementation of power converter control circuits based IA it has been made possible and easier than in the past.

In this section it is presented the application of a FLC in order to regulate the speed in a three phase induction motor with the VSC as actuator as it is highlighted in Fig. 13.

Fig. 13. Voltage Source Converter Interface

Fuzzy Control in Power Electronics Converters for Smart Power Systems 167

*carrier <sup>a</sup> reference*

A basic scheme of an individual (VSC-Motor) unit it is shown in Fig. 15, where is

VSC

phase A

phase B

phase C

wm m

<Rotor speed (wm)>

Machines Measurement Demux

According to the behaviour shown above, it is designed a FLC speed regulation control. FLC design begins from a previous knowledge of the induction motor speed variations where the modulation index (*Δm*) and frequency (*Δf*) are changed in the SPWM signals in the VSC, so that the motor model is not required, however it is necessary to keep in mind the rated values of power, torque or speed as limits or condition constraints in the control action, the

> *P*

The control designer should know the speed variability when it is applied a mechanical load and the rated values such as the nominal speed, torque and the rotor and stator resistance

FLC strategy can be developed based on classical architectures design conserving its series or parallel topologies. It is common to use the error as an input as well as the error deviation

*<sup>a</sup>* (2)

Vab

B

C

m

Vabc <sup>A</sup>

Three-Phase V-I Measurement

RS Tm

1 HP - 220 V 50 Hz - 1400 rpm

A B C

Tm

(3)

a b c

*m*

highlighted the SPWM generation signals block and the main components involved.

IGBT1 IGBT2 IGBT3 IGBT4 IGBT5 IGBT6


<Rotor speed (wm)>

Out1 Out2 Out3 Out4 Out5 Out6

48 mf

1392

N (rpm)

**3.2.2 Proportional derivative fuzzy speed control** 

power and speed are related by the following expression:

(PD) or the integral error (PI) even with fuzzy controllers.

m

Frecuencia

SPWM

Speed

Fig. 15. Open Loop System

and reactance respectively only.

0.7 ma *a*

#### **3.2.1 Induction motor operation in open loop**

The induction motors have high nonlinear characteristics and a mathematical complex model associated (Carmona & et al, 2010). Although these electrical machines are quite efficient, they require of a speed regulation algorithm under mechanical loads as it is shown in Fig. 14. The speed rate (1400rpm) is not regulated and is changing insofar as the mechanical load is increased or decreased.

Fig. 14. Speed time response of the induction motor studied in open loop

The three phase voltages are provided by the VSC depending on the SPWM signals and their variation.

Any change in the SPWM signals is reflected in speed changes in the induction motor through the VSC action, hence the frequency and amplitude modulation index are selected to achieve this action properly. The first is the frequency modulation index (*mf*), which is the relation between the carrier frequency or triangular signal and the frequency control signal or sinusoidal signal, the latter (*ma*) is the amplitude relation of those signals and are expressed as:

$$\begin{aligned} \, \, \, \mathbf{m}\_f = \frac{f\_{carrier}}{f\_{mod\,\, \,}} \end{aligned} \tag{1}$$

$$m\_a = \frac{a\_{carrier}}{a\_{reference}}\tag{2}$$

A basic scheme of an individual (VSC-Motor) unit it is shown in Fig. 15, where is highlighted the SPWM generation signals block and the main components involved.

Fig. 15. Open Loop System

166 Fuzzy Logic – Controls, Concepts, Theories and Applications

The induction motors have high nonlinear characteristics and a mathematical complex model associated (Carmona & et al, 2010). Although these electrical machines are quite efficient, they require of a speed regulation algorithm under mechanical loads as it is shown in Fig. 14. The speed rate (1400rpm) is not regulated and is changing insofar as the

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>0</sup>

Time(s)

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> -200

The three phase voltages are provided by the VSC depending on the SPWM signals and

Any change in the SPWM signals is reflected in speed changes in the induction motor through the VSC action, hence the frequency and amplitude modulation index are selected to achieve this action properly. The first is the frequency modulation index (*mf*), which is the relation between the carrier frequency or triangular signal and the frequency control signal or sinusoidal signal, the latter (*ma*) is the amplitude relation of those signals and are

> mod *carrier*

*uler*

*<sup>f</sup>* (1)

*f*

*<sup>f</sup> <sup>m</sup>*

Fig. 14. Speed time response of the induction motor studied in open loop

Time(s)

**3.2.1 Induction motor operation in open loop** 

mechanical load is increased or decreased.

0.5 1 1.5 2 2.5 3 3.5 4

Speed (rpm)

their variation.

expressed as:

Torque (Nm)

#### **3.2.2 Proportional derivative fuzzy speed control**

According to the behaviour shown above, it is designed a FLC speed regulation control. FLC design begins from a previous knowledge of the induction motor speed variations where the modulation index (*Δm*) and frequency (*Δf*) are changed in the SPWM signals in the VSC, so that the motor model is not required, however it is necessary to keep in mind the rated values of power, torque or speed as limits or condition constraints in the control action, the power and speed are related by the following expression:

$$P = \tau \varpi$$

The control designer should know the speed variability when it is applied a mechanical load and the rated values such as the nominal speed, torque and the rotor and stator resistance and reactance respectively only.

FLC strategy can be developed based on classical architectures design conserving its series or parallel topologies. It is common to use the error as an input as well as the error deviation (PD) or the integral error (PI) even with fuzzy controllers.

Fuzzy Control in Power Electronics Converters for Smart Power Systems 169

Deviation (SPD), High Positive Deviation (HPD), High Decrease (HD), Medium Decrease (MD), Low Decrease (LD), Not change (NC), Low Increase (LI), Medium Increase (MI), High

The controller outputs are the modulation index deviation (*Δma*) and frequency index deviation (*Δmf*) where the membership outputs have the same fuzzy subsets as it can be

> Error Error Deviation *Δm*, *Δf* HP BPD HD SP SPD MD Z LD N ND NC LI MI HI


HD MD LD NC LI MI HI

m deviation

Speed error and speed error deviation are normalised in order to fit out and process adequately the input systems. It is needed an scale factor according to the induction motor

> ∆e/e N PN Z SP ND HD MD LD LD BPD LD LI LI MI SPD NC NC NC LI

rated speed, in this case 1400 rpm, with the aim to guarantee a proper variability.

The defuzzifier selected is the average of centres as is expressed in (4):

The fuzzy rules basis is shown in Table 3 with a combinatory option of 12 (3x4) rules:

seen in Table 2 and in Fig. 17 is presented these functions.

Table 2. Antecedent and Consequent Variables

0

Table 3. Decision Table

Fig. 17. Consequent Membership Functions

0.2

0.4

0.6

Degree of membership

0.8

1

Increase (HI).

When is implemented a FLC, particularly a PD fuzzy control, it is difficult to specify the gain controller effect in the rise time, overshoot and settling time, where the non-linearities are more frequent, therefore it is necessary to determine an adequate tuning procedure of the controller to obtain an optimal and adaptable response.

PD fuzzy control is selected over other fuzzy control types based on its inherent advantages facing significant disturbances and has been implemented with great success in different power converters (Chamorro & Toro, 2010).

Membership functions are determined by the control designer, taking into account that a large number of functions result in a large rule basis per input. Otherwise a reduced number of functions could introduce a non-operative or undesired operation point.

As it is mentioned above, the inputs are the speed error and the speed error deviation. In Fig. 16 it can be seen these membership functions respectively.

Fig. 16. Antecedent Membership Functions

Speed error is calculated with comparison between reference speed and speed signal feedback. It is established four overlapping fuzzy subsets for speed error, three for speed error deviation and seven for each output. The linguistic labels chosen are: Negative (N), Zero (Z), Small Positive (SP), High Positive (HP), Negative Deviation (ND), Small Positive

When is implemented a FLC, particularly a PD fuzzy control, it is difficult to specify the gain controller effect in the rise time, overshoot and settling time, where the non-linearities are more frequent, therefore it is necessary to determine an adequate tuning procedure of

PD fuzzy control is selected over other fuzzy control types based on its inherent advantages facing significant disturbances and has been implemented with great success in different

Membership functions are determined by the control designer, taking into account that a large number of functions result in a large rule basis per input. Otherwise a reduced number

As it is mentioned above, the inputs are the speed error and the speed error deviation. In

N Z SP HP


Error

ND SPD HPD


Speed error is calculated with comparison between reference speed and speed signal feedback. It is established four overlapping fuzzy subsets for speed error, three for speed error deviation and seven for each output. The linguistic labels chosen are: Negative (N), Zero (Z), Small Positive (SP), High Positive (HP), Negative Deviation (ND), Small Positive

Error Deviation

of functions could introduce a non-operative or undesired operation point.

the controller to obtain an optimal and adaptable response.

Fig. 16 it can be seen these membership functions respectively.

power converters (Chamorro & Toro, 2010).

0

0

Fig. 16. Antecedent Membership Functions

0.2

0.4

0.6

Degree of membership

0.8

1

0.2

0.4

0.6

Degree of membership

0.8

1

Deviation (SPD), High Positive Deviation (HPD), High Decrease (HD), Medium Decrease (MD), Low Decrease (LD), Not change (NC), Low Increase (LI), Medium Increase (MI), High Increase (HI).

The controller outputs are the modulation index deviation (*Δma*) and frequency index deviation (*Δmf*) where the membership outputs have the same fuzzy subsets as it can be seen in Table 2 and in Fig. 17 is presented these functions.


Table 2. Antecedent and Consequent Variables

Fig. 17. Consequent Membership Functions

Speed error and speed error deviation are normalised in order to fit out and process adequately the input systems. It is needed an scale factor according to the induction motor rated speed, in this case 1400 rpm, with the aim to guarantee a proper variability.

The fuzzy rules basis is shown in Table 3 with a combinatory option of 12 (3x4) rules:


Table 3. Decision Table

The defuzzifier selected is the average of centres as is expressed in (4):

Fuzzy Control in Power Electronics Converters for Smart Power Systems 171

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> -200

VSC used as the interface between Renewable Energy Sources (RES) with the utility grid or autonomous systems, has demonstrated the power transfer capability from MG with excess generation to those with power demands. A representation of this application can be seen in

The active and reactive power exchange is possible with the manipulation of the SPWM

The principle of operation of VSC is subjected to the management of phase shift and modulation index variability signals generated by SPWM. The active and reactive power exchange between the VSC and the AC network or another VSC is expressed as follows in

> sin *U Us c <sup>P</sup> <sup>X</sup>*

( cos ) *UUU ssc <sup>Q</sup> <sup>X</sup>* 

(5)

(6)

Fig. 19. Speed time response with speed regulation under mechanical load variability

Time(s)

Reference Speed

Speed (rpm)

**3.3 Power flow control** 

Fig. 20. VSC Interface

(5) and (6).

where,

*P*: active power *Q*: reactive power *Uc*: VSC voltage *Us*: bus voltage

*δ*: phase difference with the voltages *X*: coupling reactance reactor

signals via a small reactor (Guangkai & et al, 2006).

Fig. 20.

$$\mathbf{y}^\* = \frac{\sum\_{n=1}^{M} y\_n w\_n}{\sum\_{n=1}^{M} w\_n} \tag{4}$$

Where *M* is the number of fuzzy sets, *w* are the weights of set defined for its height and *y-1* is the centre of n-esimal fuzzy set.

The control surface associated is shown in Fig. 18.

Fig. 18. Control Surface

A detailed design can be seen in previous works (Chamorro & et al, 2009; Chamorro & Toro, 2010), where is exposed the overall performance and the dynamic prefilters used.

#### **3.2.3 Simulation results**

With the rules explained above, a variability load is evaluated to confirm the performance of the controller proposed, the control action achieves the rated speed regulation even with an abrupt load decrease as it can be seen in Fig. 19.

Fig. 19. Speed time response with speed regulation under mechanical load variability

#### **3.3 Power flow control**

170 Fuzzy Logic – Controls, Concepts, Theories and Applications

*M n n n M n n*

Where *M* is the number of fuzzy sets, *w* are the weights of set defined for its height and *y-1* is


A detailed design can be seen in previous works (Chamorro & et al, 2009; Chamorro & Toro,

With the rules explained above, a variability load is evaluated to confirm the performance of the controller proposed, the control action achieves the rated speed regulation even with an

0 5 10 15

Time(s)


2010), where is exposed the overall performance and the dynamic prefilters used.

Error Error Deviation

0.05

0.1

0.15

abrupt load decrease as it can be seen in Fig. 19.

1.5

2

2.5

Load (Nm)

3

3.5

4

0.2 -0.04

Fig. 18. Control Surface

**3.2.3 Simulation results** 


0

ev o 0.02

0.04

0

0.05

0.1

0.15

0.

1 1

*y w*

*w* 

(4)

\*

*y*

the centre of n-esimal fuzzy set.

The control surface associated is shown in Fig. 18.

VSC used as the interface between Renewable Energy Sources (RES) with the utility grid or autonomous systems, has demonstrated the power transfer capability from MG with excess generation to those with power demands. A representation of this application can be seen in Fig. 20.

Fig. 20. VSC Interface

The active and reactive power exchange is possible with the manipulation of the SPWM signals via a small reactor (Guangkai & et al, 2006).

The principle of operation of VSC is subjected to the management of phase shift and modulation index variability signals generated by SPWM. The active and reactive power exchange between the VSC and the AC network or another VSC is expressed as follows in (5) and (6).

$$P = \frac{\mathcal{U}\_s \mathcal{U}\_c}{X} \sin \delta$$

$$Q = \frac{\mathcal{U}\_s(-\mathcal{U}\_s + \mathcal{U}\_c \cos \delta)}{X} \tag{6}$$

where, *P*: active power *Q*: reactive power *Uc*: VSC voltage *Us*: bus voltage *δ*: phase difference with the voltages *X*: coupling reactance reactor

Fuzzy Control in Power Electronics Converters for Smart Power Systems 173

Fuzzification: in this first step, the crisp inputs are transformed into fuzzy inputs. According to the inputs, error (*e*) and error deviation (*de*), the membership functions are assigned.

The output signals are modulation index (*m*) and shift phase (*φ*), the variability of these

The membership functions have five different values to achieve good power reference tracking, big=B, low=L, zero=Z, negative=N, positive=P, change=C, medium=M, decreasing=D and increasing=I respectively. The letter concatenation represents a variable

The normalisation signals are achieved with some constants in order to get a specific value with the required accuracy, as it is explained below in detail, and then the crisp data is converted into fuzzy sets to be compatible with the fuzzy set representation, by means of a

[ ( ), ( )] ( )^ ( ) *AA A q*

Fig. 24 shows the input and output membership functions and the rule basis where the overall combination for Fuzzy Control of active Power (*FCP*) and Fuzzy Control of reactive

   

*x y x y* (7)

signals implies some changes directly in SWPM, allowing control of the power flow.

**3.3.1 Fuzzy logic control VSC-GRID** 

Power (*FCQ*) can be inferred.

and each variable represents a membership function.

Fig. 24. Membership functions and look – up table

fuzzifier, which in this case the Mandani implication is used:

According to these equations, it should be possible a fully control of the active power by δ and the reactive power by *Uc* deviations respectively (Singh & et al, 2006) and independently (Liu & et al, 2009). The power flow concept is depicted in Fig. 21.

Fig. 21. Power flow equivalent circuit

Fig. 22 represents the four operation regions involved in the MG, which corresponds to the combinations of power imported or exported (Forero & et al, 2009). High non – linearity is experienced when both power references are changed abruptly and the control strategy must adapt to and stabilise the system in order to prevent a critical fault or important damage in any hardware device.

Fig. 22. Division of VSC HVDC Power flow operation zones

A basic MG that consists in one DER, a VSC unit and a low pass LC filter is shown in Fig. 23. A local Fuzzy Logic Control (FLC) which is in charge of the power flow regulation is added too.

Fig. 23. MG block representation with Fuzzy Logic Controller

### **3.3.1 Fuzzy logic control VSC-GRID**

172 Fuzzy Logic – Controls, Concepts, Theories and Applications

According to these equations, it should be possible a fully control of the active power by δ and the reactive power by *Uc* deviations respectively (Singh & et al, 2006) and

Fig. 22 represents the four operation regions involved in the MG, which corresponds to the combinations of power imported or exported (Forero & et al, 2009). High non – linearity is experienced when both power references are changed abruptly and the control strategy must adapt to and stabilise the system in order to prevent a critical fault or important

A basic MG that consists in one DER, a VSC unit and a low pass LC filter is shown in Fig. 23. A local Fuzzy Logic Control (FLC) which is in charge of the power flow regulation is added

independently (Liu & et al, 2009). The power flow concept is depicted in Fig. 21.

Fig. 21. Power flow equivalent circuit

damage in any hardware device.

too.

Fig. 22. Division of VSC HVDC Power flow operation zones

Fig. 23. MG block representation with Fuzzy Logic Controller

Fuzzification: in this first step, the crisp inputs are transformed into fuzzy inputs. According to the inputs, error (*e*) and error deviation (*de*), the membership functions are assigned.

The output signals are modulation index (*m*) and shift phase (*φ*), the variability of these signals implies some changes directly in SWPM, allowing control of the power flow.

The membership functions have five different values to achieve good power reference tracking, big=B, low=L, zero=Z, negative=N, positive=P, change=C, medium=M, decreasing=D and increasing=I respectively. The letter concatenation represents a variable and each variable represents a membership function.

The normalisation signals are achieved with some constants in order to get a specific value with the required accuracy, as it is explained below in detail, and then the crisp data is converted into fuzzy sets to be compatible with the fuzzy set representation, by means of a fuzzifier, which in this case the Mandani implication is used:

$$[\!\!\!\!\!\!\!\!\!\/\mu\_A(\mathbf{x})\!\!\/\mu\_A(\mathbf{y})] = \mu\_A(\mathbf{x})\,^\wedge\mu\_q(\mathbf{y})\tag{7}$$

Fig. 24 shows the input and output membership functions and the rule basis where the overall combination for Fuzzy Control of active Power (*FCP*) and Fuzzy Control of reactive Power (*FCQ*) can be inferred.

Fig. 24. Membership functions and look – up table

Fuzzy Control in Power Electronics Converters for Smart Power Systems 175

Reference Active Power

Reference Reactive Power

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -100

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -40

The combination of RES and power electronics interfaces in MG requires different control strategies and diverse control layers to obtain multiple objectives and an adequate response avoiding voltage unbalances and power quality disturbances (Lasseter, 2001; Binduhewa &

Some of the advantages to implement DC MG in industrial environment systems are the reduction of transmission and distribution losses and ensuring power quality in loads. Another advantage of MG is the versatility of connection related with their two operation modes: in grid connected mode, the power supply is shared with the main grid and, in

This approach is oriented to the induction motors coordination in industry, under a fuzzy supervisory frame where there are imprecise and vagueness data, causing loss of

Fig. 27 depicts a DC MG where are some RES and induction motors. There is a lower control layer that determines the local speed set points and an upper (supervisory) layer that coordinates the whole speed references and synchronise the speed at one if it is necessary. The upper layer control has a fuzzy structure based on the industrial system knowledge base where it has been experienced several damages and important extra costs associated. In this study is taken as example one type of industry, where has been applied or required the

The type of industry is concerned with the necessity of the synchronisation of different induction motors at one speed reference like in textile industries, where the speed unification is an important consideration because of a minimal disturbance can cause an unexpected standstill; besides is necessary to consider the fact that not all the motors have

island mode the local RES supply the load system autonomously (Ding et al, 2010).

Time (s)

Time (s)

Fig. 26. Active and reactive power controller time response

synchronism or changes in the different set points.

**4.1 Induction motor coordination in industrial environments** 

Reactive Power (VAR)

et al, 2008).

use of induction motors.

the same mechanical load.

Active Power (W)

The second step is the fuzzy inference process, in this, the membership functions are combined with the control rules. A possible rule evidenced in this system could be: If the value of error is small but conserves its rate, the SPWM signal requires an increment in the magnitude and angle rigorously.

The linguistic labels are formulated according to the power operation regions and the error and error deviation measurements and limits bordered by the frame system.

In the final step, it is necessary to quantify to get a numerical value, the method of defuzzification used in this section is the Center of gravitity (CoG), based on its fast computation and its wide use (Bai & et al, 2006).

## **3.3.2 Results grid – Connected mode of operation**

Fig. 25 shows the MG – VSC – Grid system implemented in Simpower(R). The green and grey blocks are the (*p*) and (*q*) decoupled fuzzy local controllers respectively.

Fig. 25. Block system of three phase grid connected VSC

The time response of the power flow controller is presented in Fig. 26, as it can be seen, the fuzzy control tracks the reference. An important observation is that each reference is generated only when the previous power reference has been reached.

### **4. Fuzzy hierarchical/supervisory control**

The future power networks will require of innovative alternatives and algorithms that can provide some kind of smartness to achieve an effective coordination, self-healing and diagnose and autonomous operation and automation. In this section, the use of fuzzy hierarchical or supervisory frameworks in these systems is considered and it is proposed two applications related.

The second step is the fuzzy inference process, in this, the membership functions are combined with the control rules. A possible rule evidenced in this system could be: If the value of error is small but conserves its rate, the SPWM signal requires an increment in the

The linguistic labels are formulated according to the power operation regions and the error

In the final step, it is necessary to quantify to get a numerical value, the method of defuzzification used in this section is the Center of gravitity (CoG), based on its fast

Fig. 25 shows the MG – VSC – Grid system implemented in Simpower(R). The green and

phase

mi ps

C B A

A B C

generated only when the previous power reference has been reached.

ref Qsal <sup>m</sup> Q Controller

Microgrid I

The time response of the power flow controller is presented in Fig. 26, as it can be seen, the fuzzy control tracks the reference. An important observation is that each reference is

The future power networks will require of innovative alternatives and algorithms that can provide some kind of smartness to achieve an effective coordination, self-healing and diagnose and autonomous operation and automation. In this section, the use of fuzzy hierarchical or supervisory frameworks in these systems is considered and it is proposed

P Controller

ref Psal ref P

Q ref

P

Q

P&Q Flow

and error deviation measurements and limits bordered by the frame system.

grey blocks are the (*p*) and (*q*) decoupled fuzzy local controllers respectively.

magnitude and angle rigorously.

computation and its wide use (Bai & et al, 2006).

N

Grid

**4. Fuzzy hierarchical/supervisory control** 

two applications related.

Fig. 25. Block system of three phase grid connected VSC

**3.3.2 Results grid – Connected mode of operation** 

Fig. 26. Active and reactive power controller time response

## **4.1 Induction motor coordination in industrial environments**

The combination of RES and power electronics interfaces in MG requires different control strategies and diverse control layers to obtain multiple objectives and an adequate response avoiding voltage unbalances and power quality disturbances (Lasseter, 2001; Binduhewa & et al, 2008).

Some of the advantages to implement DC MG in industrial environment systems are the reduction of transmission and distribution losses and ensuring power quality in loads. Another advantage of MG is the versatility of connection related with their two operation modes: in grid connected mode, the power supply is shared with the main grid and, in island mode the local RES supply the load system autonomously (Ding et al, 2010).

This approach is oriented to the induction motors coordination in industry, under a fuzzy supervisory frame where there are imprecise and vagueness data, causing loss of synchronism or changes in the different set points.

Fig. 27 depicts a DC MG where are some RES and induction motors. There is a lower control layer that determines the local speed set points and an upper (supervisory) layer that coordinates the whole speed references and synchronise the speed at one if it is necessary.

The upper layer control has a fuzzy structure based on the industrial system knowledge base where it has been experienced several damages and important extra costs associated. In this study is taken as example one type of industry, where has been applied or required the use of induction motors.

The type of industry is concerned with the necessity of the synchronisation of different induction motors at one speed reference like in textile industries, where the speed unification is an important consideration because of a minimal disturbance can cause an unexpected standstill; besides is necessary to consider the fact that not all the motors have the same mechanical load.

Fuzzy Control in Power Electronics Converters for Smart Power Systems 177

Reference M4 M3 M2 M1

Reference M4 M3 M2 M1

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -400

Time(s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time(s)

Fig. 28. Supervisory Synchronisation Control Induction Motors in the DC MG and Window

The intentional islanding in MG refers to the condition where it is isolated from the utility grid and operates by itself (Balaguer, 2011), in this situation it is important a hierarchical central control layer to provide power management between the microsources and their

With the integration of a central control in multi – energy generator systems, it is possible to control and to drive the energy to a MG side via the VSC operation. The central control main functions are the synchronization of VSCs in order not to exceed the nominal power limits, to avoid the power flow cancellation and coordinate and decide which VSC is in operation or not, at the same time, for this reason the FLC is chosen as a control method. In Fig. 29 is

1. The decision of power importation and exportation according to the necessity and the coordination of the VSC which is in operation. This could be expressed as a fuzzy rule


**4.2 Microgrids power flow hierarchical control** 

depicted the overview of the power flow in MG.

The fuzzy control levels specify three actions listed as follows:

Time Zoom In.

loads.

as:

Speed (rpm)

Speed (rpm)

Fig. 27. Supervisory Control in Industrial DC Microgrids

In the study reported in this section are considered conditionals and priority statements to form the decision making actions.

The fuzzy supervisory control specifies the next actions listed as follows:

The first priority is to regulate the speed steady state error in each unit (VSC - Motor) according to the speed set point desired and the operation range involved. This could be expressed like a fuzzy rule as:

*if* the speed set point is changed in each unit *n*, then change the *ma* and *mf* applying the fuzzy local control rules explained above.

The speed error and speed error deviation are given by:

$$e\_s = P\_o - P\_s \tag{8}$$

$$
\Delta e\_s = e(k) - e(k-1) \tag{9}
$$

where, *Po*, is the speed measured *Ps*, is the speed required

## **4.1.1 Simulation results**

A desynchronization time is previously defined in order to test the supervisory control layer. In Fig. 27 it is shown the speed response of four units (VSC – three phase induction motors) while it is acting a constant mechanical load of 3 Nm. As it can be seen, immediately the supervisory control starts to apply the weights and two seconds later all the machines reach the rated speed at the same time, it is necessary to do a zoom in the simulation window to see the action mentioned, this effect is shown in Fig. 28 too.

In the study reported in this section are considered conditionals and priority statements to

The first priority is to regulate the speed steady state error in each unit (VSC - Motor) according to the speed set point desired and the operation range involved. This could be

*if* the speed set point is changed in each unit *n*, then change the *ma* and *mf* applying the fuzzy

A desynchronization time is previously defined in order to test the supervisory control layer. In Fig. 27 it is shown the speed response of four units (VSC – three phase induction motors) while it is acting a constant mechanical load of 3 Nm. As it can be seen, immediately the supervisory control starts to apply the weights and two seconds later all the machines reach the rated speed at the same time, it is necessary to do a zoom in the simulation

window to see the action mentioned, this effect is shown in Fig. 28 too.

*s os e PP* (8)

( ) ( 1) *<sup>s</sup> e ek ek* (9)

Fig. 27. Supervisory Control in Industrial DC Microgrids

The speed error and speed error deviation are given by:

The fuzzy supervisory control specifies the next actions listed as follows:

form the decision making actions.

expressed like a fuzzy rule as:

*Po*, is the speed measured *Ps*, is the speed required

**4.1.1 Simulation results** 

where,

local control rules explained above.

Fig. 28. Supervisory Synchronisation Control Induction Motors in the DC MG and Window Time Zoom In.

## **4.2 Microgrids power flow hierarchical control**

The intentional islanding in MG refers to the condition where it is isolated from the utility grid and operates by itself (Balaguer, 2011), in this situation it is important a hierarchical central control layer to provide power management between the microsources and their loads.

With the integration of a central control in multi – energy generator systems, it is possible to control and to drive the energy to a MG side via the VSC operation. The central control main functions are the synchronization of VSCs in order not to exceed the nominal power limits, to avoid the power flow cancellation and coordinate and decide which VSC is in operation or not, at the same time, for this reason the FLC is chosen as a control method. In Fig. 29 is depicted the overview of the power flow in MG.

The fuzzy control levels specify three actions listed as follows:


Fuzzy Control in Power Electronics Converters for Smart Power Systems 179


The system presented in Fig. 30 shows the power flow control between four VSCs, in this case, one of them requires power (in orange), the fuzzy central control decides to disable one

*<sup>p</sup> o s e PP* (16)

*<sup>q</sup> o s eQQ* (17)

Scope

Q\_total

P\_total

QDeliver1

Q

PDeliver1

ref Qsal <sup>m</sup> Q1 Master1

ps <sup>P</sup>

Microgrid 3

mi

mi

C B A

C B A

The results of the simulations can be seen in Fig.31 for Ps= (-100, -40) W and Qs= (-30, -20)

Q M4 P&Q M3

P&Q M2 P&Q M1

ref Psal phase P1 Master1 QDeliver

Q

PDeliver

ref Qsal <sup>m</sup> Q1 Master

ps <sup>P</sup>

Microgrid 1

ref Psal phase P1 Master

( ) ( 1) *<sup>p</sup> e ek ek* ^ ( ) ( 1) *<sup>q</sup> e ek ek* (18)

MG and apply the fuzzy local control rules.

The error and error deviation are given by:

*Po*, *Qo* are the powers measured *Ps*, *Qs* are the powers references

MG and to enable the other two.

RS Tm4

RS Tm3

ref Qsal <sup>m</sup> Q2 Slave

ps <sup>P</sup>

Microgrid 2

ref Psal phase P2 Slave

RS Tm2

Q

Fig. 30. Power flow control in island MG

VAr.

ref Qsal <sup>m</sup> Q2 Slave1

ps <sup>P</sup>

Microgrid 4

mi

mi

C B A

C B A

ref Psal phase P2 Slave1

RS Tm1

Q

where,

Fig. 29. Hierarchical Fuzzy Control

The power flow control in function of this control architecture following the equations (10) and (11) can be mathematically expressed as:

$$P\_{ir} = \frac{U\_i U\_r}{X} \sin \delta \tag{10}$$

$$\mathcal{Q}\_{\nu} = \frac{U\_i(-U\_i + U\_r \cos \delta)}{X} \tag{11}$$

where,


with,

$$r = 1, 2, \ldots, n \tag{12}$$

$$i = 1, 2, \ldots, n \tag{13}$$

N: number of VSC units

and *i r*


$$P\_{sum} = \sum\_{i=1}^{N} P\_i \tag{14}$$

$$\mathcal{Q}\_{sum} = \sum\_{i=1}^{N} \mathcal{Q}\_i \tag{15}$$

1. The regulation of steady – state power error: an important aspect proposed, is the requirement in the coordination of the power reference changes when a MG requires it and involves the primary control level explained above. Based on this desired behaviour, the corresponding fuzzy rule is:


The error and error deviation are given by:

$$e\_p = P\_o - P\_s \tag{16}$$

$$e\_q = Q\_o - Q\_s \tag{17}$$

$$
\Delta e\_p = e(k) - e(k-1) \quad \land \quad \Delta e\_q = e(k) - e(k-1) \tag{18}
$$

where,

178 Fuzzy Logic – Controls, Concepts, Theories and Applications

The power flow control in function of this control architecture following the equations (10)

*X <sup>U</sup> <sup>U</sup> <sup>P</sup> <sup>i</sup> <sup>r</sup>*

*<sup>U</sup> <sup>U</sup> <sup>U</sup> <sup>Q</sup> <sup>i</sup> <sup>i</sup> <sup>r</sup>*


 *N*

 *N*

*i Qsum Qi*

1. The regulation of steady – state power error: an important aspect proposed, is the requirement in the coordination of the power reference changes when a MG requires it and involves the primary control level explained above. Based on this desired

*i Psum Pi* 1

*ir*

1. The power share between VSCs or as a fuzzy rule function:

behaviour, the corresponding fuzzy rule is:

sin

*X*

( cos

*ir* (10)

) (11)

*r* 1,2,.....*n* (12)

*i* 1,2,.....*n* (13)

(14)

<sup>1</sup> (15)

Fig. 29. Hierarchical Fuzzy Control

where,

with,

and *i r*

N: number of VSC units

and (11) can be mathematically expressed as:

*r*= is the VSC unit which requires power, *i*= is the VSC unit which exports power,

*Po*, *Qo* are the powers measured

*Ps*, *Qs* are the powers references

The system presented in Fig. 30 shows the power flow control between four VSCs, in this case, one of them requires power (in orange), the fuzzy central control decides to disable one MG and to enable the other two.

Fig. 30. Power flow control in island MG

The results of the simulations can be seen in Fig.31 for Ps= (-100, -40) W and Qs= (-30, -20) VAr.

Fuzzy Control in Power Electronics Converters for Smart Power Systems 181

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Fig. 31. Power flow control in island MG

## **5. Conclusion**

The smart application schemes studied in this chapter show that the FLC can provide a suitable management for power converters and related developments with RES without an exact mathematical model and just the observed behaviour, due to its important features such as flexibility and adaptability to face high non-linearities and load changes in these kinds of systems.

Due to the local controllers have already been tested in previous developments, the next step in this research is to test the upper layer in an embedded system with the capability of real-time signal management and processing.

The hierarchical fuzzy architecture shown provides the opportunity to increase the autonomous and coordination actions in the converters involved giving a future idea about the low voltage MG to achieve self-healing or diagnose.

The addition of some extra rules in the higher control layer could generate an extensive computational process, however these rules would be necessary in a larger MG system or if it is required to improve other decisions.

If the VSC-Induction motor or VSC-Grid units are increased in large quantities or differ in their characteristics, the system model is increased and the complexity as well. A supervisory fuzzy control is suitable to manage them with the sole requirement to know the entire behaviour.

As a future work, it can be added another coordination targets such as the batteries charging converters, the dc-dc converters involved and the MPPT algorithms.

## **6. References**

Alajmi, B. (2010). Fuzzy Logic Control Approach of a Modified Hill Climbing Method for Maximum Power Point in Microgrid Stand-alone Photovoltaic System. I*EEE Transactions on Power Electronics*, Vol. 26, No. 4, (November 2010), pp. (1022 – 1030), ISSN : 0885-8993

Reference Active Power

Reference Reactive Power

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -100

Time (s)

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -50

The smart application schemes studied in this chapter show that the FLC can provide a suitable management for power converters and related developments with RES without an exact mathematical model and just the observed behaviour, due to its important features such as flexibility and adaptability to face high non-linearities and load changes in these

Due to the local controllers have already been tested in previous developments, the next step in this research is to test the upper layer in an embedded system with the capability of

The hierarchical fuzzy architecture shown provides the opportunity to increase the autonomous and coordination actions in the converters involved giving a future idea about

The addition of some extra rules in the higher control layer could generate an extensive computational process, however these rules would be necessary in a larger MG system or if

If the VSC-Induction motor or VSC-Grid units are increased in large quantities or differ in their characteristics, the system model is increased and the complexity as well. A supervisory fuzzy control is suitable to manage them with the sole requirement to know the entire behaviour.

As a future work, it can be added another coordination targets such as the batteries charging

Alajmi, B. (2010). Fuzzy Logic Control Approach of a Modified Hill Climbing Method for

Maximum Power Point in Microgrid Stand-alone Photovoltaic System. I*EEE Transactions on Power Electronics*, Vol. 26, No. 4, (November 2010), pp. (1022 – 1030),

Time (s)

0

Fig. 31. Power flow control in island MG

real-time signal management and processing.

it is required to improve other decisions.

ISSN : 0885-8993

the low voltage MG to achieve self-healing or diagnose.

converters, the dc-dc converters involved and the MPPT algorithms.

Reactive Power (VAR)

**5. Conclusion** 

kinds of systems.

**6. References** 

50

Active Power (W)


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**9** 

**Synthesis and VHDL Implementation of** 

**Voltage and Frequency Scaling (DVFS)** 

 **Fuzzy Logic Controller for Dynamic** 

Juan Diego Echeverri Escobar and José Pineda de Gyvez

The concept of power consumption is becoming the primary concern in modern high performance processors, and in digital circuits and system on chips (SoCs). While CMOS technology has been scaling towards smaller feature sizes, the performance of digital systems has been exponentially increasing as clock frequency increases. Also the computational workload and hence the activity of a digital circuit may change substantially and it exposes a lot of breakthroughs in the exploitation of adaptive low power methodologies. Dynamic voltage and frequency scaling (DVFS) is a popular system level power management technique that dynamically scales the supply voltage and clock frequency level of device (Rabaey, 2010). A DVFS system can be considered as a closed loop control system: contingent on the observed workload, supply voltage and operational speed gets adjusted. Since the changes in supply voltages do not occur instantaneously due to the fact that some delays are involved the large capacitance on the supply rails, the main real challenge in the design of such a system lies in how to measure and predict the workload of processor to change supply voltage accurately. The efficiency of DVFS strongly depends on the accuracy of the workload estimation, and note that misestimating can substantially

Most previous DVFS methods focused on offline profiling to learn the average case execution time or worst case execution time. Different closed loop adaptive controllers have been proposed to deal with time varying workloads. Most of them are based on conventional PID controllers and their variants e.g. PI controller or I controller. These kinds of configurations need offline profiling to tune the coefficients of the controller to be able to track or predict the workload variations. However, for different shapes of workload variations, it is necessary to do the off-line tuning again and determine the coefficients another time. So they are not considered as general solutions for adjusting voltage and frequency. Some other estimation methods e.g. adaptive filters have proposed for predicting

**1. Introduction** 

reduce the effectiveness of such closed loop systems.

**Goals in Digital Processors** 

 *Eindhoven University of Technology, Eindhoven,* 

Hamid Reza Pourshaghaghi,

*Electronic Systems Group,* 

 *the Netherlands* 


## **Synthesis and VHDL Implementation of Fuzzy Logic Controller for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors**

Hamid Reza Pourshaghaghi,

Juan Diego Echeverri Escobar and José Pineda de Gyvez *Electronic Systems Group, Eindhoven University of Technology, Eindhoven, the Netherlands* 

## **1. Introduction**

184 Fuzzy Logic – Controls, Concepts, Theories and Applications

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*International Conference on Acoustics, Speech, and Signal Processing*, ISBN: 0-7803-1775-

The concept of power consumption is becoming the primary concern in modern high performance processors, and in digital circuits and system on chips (SoCs). While CMOS technology has been scaling towards smaller feature sizes, the performance of digital systems has been exponentially increasing as clock frequency increases. Also the computational workload and hence the activity of a digital circuit may change substantially and it exposes a lot of breakthroughs in the exploitation of adaptive low power methodologies. Dynamic voltage and frequency scaling (DVFS) is a popular system level power management technique that dynamically scales the supply voltage and clock frequency level of device (Rabaey, 2010). A DVFS system can be considered as a closed loop control system: contingent on the observed workload, supply voltage and operational speed gets adjusted. Since the changes in supply voltages do not occur instantaneously due to the fact that some delays are involved the large capacitance on the supply rails, the main real challenge in the design of such a system lies in how to measure and predict the workload of processor to change supply voltage accurately. The efficiency of DVFS strongly depends on the accuracy of the workload estimation, and note that misestimating can substantially reduce the effectiveness of such closed loop systems.

Most previous DVFS methods focused on offline profiling to learn the average case execution time or worst case execution time. Different closed loop adaptive controllers have been proposed to deal with time varying workloads. Most of them are based on conventional PID controllers and their variants e.g. PI controller or I controller. These kinds of configurations need offline profiling to tune the coefficients of the controller to be able to track or predict the workload variations. However, for different shapes of workload variations, it is necessary to do the off-line tuning again and determine the coefficients another time. So they are not considered as general solutions for adjusting voltage and frequency. Some other estimation methods e.g. adaptive filters have proposed for predicting

Synthesis and VHDL Implementation of Fuzzy Logic Controller

determines the prediction accuracy.

with extra latency as buffer utilization is only one measure of workload.

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 187

computational workload were taken into account as well. Like the self-timed variable voltage system of (Nielsen et al., 1994), input data is buffered into a FIFO type of buffer to enable averaging of the workload. Then, the control loop controls the processing rate to avoid queuing overflow and underflow of the FIFOs. The controller in this methodology consists of a voltage regulator, a ring oscillator, a rate-compare block and a programmable look-up table (LUT). The controller block decides to change the voltage and frequency based on the processing rate and existent LUT. Disadvantage of this configuration is that it comes

An evolution to closed loop control configuration, in the estimation of workload and adaptive control methods become main challenge for design efficient DVFS. These techniques aimed at estimating time varying workload using adaptive filters that most of them were based on a conventional proportional, integral and derivative (PID) controller. One famous PID based approach is presented in (Wei & Horowitz, 2003) where voltage samples are used to control a VCO to change the frequency as feedback signal for the buck converter. The reference signal and feedback signal come into the controller as variable frequency clocks, both feed into counters, and the number of transitions is counted for a fixed period of time. A PID controller, based on the calculated error value between its inputs, decides to change the voltage and frequency of the circuit. Some example of using PID controller to estimate workload variations are proposed in (Hughes and Adve, 2003; Gu & Chakraborty, 2008; Wu et al., 2005; Lu et al., 2002, 2003). In (Hughes and Adve, 2003), the PID controller is used to estimate the frame decoding time in multimedia applications and it was used in (Gu & Chakraborty, 2008) for 3-D games. In (Wu et al., 2005) and (Lu et al., 2003), the PI controller, which is a variant of the PID method, is applied to estimate the buffer occupancy for DVS targeting data buffered systems. In (Lu et al., 2002), an integral controller which is also a variant of PID method is designed and used to estimate workload estimation for performing DVS. Despite the PID controller is an adaptive filter, it suffers from possible overshooting and undershooting, depending on the selected coefficients. Also the PID controller for estimating application is useful when the designer select coefficient for specific workload variations and if the shape of workload changes, the coefficient should be defined again based on new workload variations. Hence, the tuning of coefficients critically

Beside PID based controllers, some other estimators and adaptive filters are proposed to forecast workload variations in order to adjust voltage and/or frequency. In (Sinha & Chandrakasan, 2001), an adaptive approach for dynamic voltage scheduling on processors is presented based on workload prediction by filtering a trace history. In this work, they examine some conventional filters and evaluate their accuracy based on power saving amounts. They concluded that adaptive LMS filtering is the most powerful one and can be used to predict workload variations. Also in (Bang et al., 2009), they proposed a Kalmanfilter based on-line estimator to predict and track the workload variation that can be

Compared to previous approaches, the fuzzy logic controller is similar to adaptive filters in the sense of estimating the workload variations. However, the fuzzy logic controller can work as an on-line methodology without updating any parameters during run-time adaptations and also without any other information about the nature of the workload

applicable to periodic applications with soft real-time constrains.

workload and controlling the behavior of the power and energy savings. Unfortunately, most of them need offline profiling and/or the applications are limited to some specific periodic workload variations.

In this chapter, we discuss an on-line adaptive fuzzy logic controller for DVFS that is able to accurately and robustly predict and track the workload variations even when those variations are highly nonstationary or soft. Furthermore, we describe comprehensively how one can build the controller in VHDL and use it as the power management controller unit. We propose a new method to use for the defuzzification part of the fuzzy controller that makes the circuit faster. The fuzzy controller can be applicable to different kinds of workload variations with regards to real-time constraints, and can adaptively change the supply voltage and frequency of a processor. The proposed controller can be easily upgraded by adding new rules or adding new features to improve performance. In this chapter, all the practical limitations and real-time constraints for designing the fuzzy logic controller as the DVFS method will be discussed during design procedure.

## **2. Related works over power management techniques**

So far a lot of research has been done to explore different approaches for performing DVFS. Many of the previous works are categorized in task level algorithms that use offline profiling to obtain the average-case execution time (ACET) or worst-case execution time (WCET) as models for the workloads of the given application. For example, one of the earliest works was presented in (Yao et al., 1995) where they assumed that the arrival time, deadline of workloads, and task execution time based on CPU cycle are given to designers as constants. The works proposed in (Im et al., 2006) and (Jejurikar & Gupta, 2006) are two more examples where in (Im et al., 2006) they proposed a technique to reduce the energy consumption based on WCET workload model using buffers; and in (Jejurikar & Gupta, 2006) a dynamic voltage scaling (DVS) method in the presence of task synchronization based on WCET workload model in multiprocessor environment was proposed. This kind of approaches cannot deal with the time-varying workload especially when the workload shows a large variation with nonstationary property. Another category of researches related to DVFS comprise techniques which require either application or compiler support to perform (Azevedo et al., 2002; Yang et al., 2001; Chung et al., 2002). Generality and offline profiling for different workload variations is still a big drawback existing in these classes of works.

Using adaptive approaches for DVFS leads to save more power and energy in comparison to the conventional techniques. Proposing closed loop system architectures started by introducing self-timed adaptive supply-voltage scaling for asynchronous circuits in (Nielsen et al., 1994) where in their architecture, first input-first output (FIFO) buffers are used in both inputs and outputs of the processor. The FIFO-buffers average the computational workload to adjust the supply voltage and frequency. The feedback is based on actual path delays of the circuit. The feedback signal controls the DC-DC converter based on the information derived from the FIFO's. After this architecture, other researchers used a similar configuration to adapt the power supply voltage to lower the power consumption in digital signal processors DSPs (Gutnik & Chandrakasan, 1997). The structure of the proposed system architecture in (Gutnik & Chandrakasan, 1997) is the same as (Nielsen et al., 1994), but they designed a configuration for synchronous designs, and variations in the

workload and controlling the behavior of the power and energy savings. Unfortunately, most of them need offline profiling and/or the applications are limited to some specific

In this chapter, we discuss an on-line adaptive fuzzy logic controller for DVFS that is able to accurately and robustly predict and track the workload variations even when those variations are highly nonstationary or soft. Furthermore, we describe comprehensively how one can build the controller in VHDL and use it as the power management controller unit. We propose a new method to use for the defuzzification part of the fuzzy controller that makes the circuit faster. The fuzzy controller can be applicable to different kinds of workload variations with regards to real-time constraints, and can adaptively change the supply voltage and frequency of a processor. The proposed controller can be easily upgraded by adding new rules or adding new features to improve performance. In this chapter, all the practical limitations and real-time constraints for designing the fuzzy logic

So far a lot of research has been done to explore different approaches for performing DVFS. Many of the previous works are categorized in task level algorithms that use offline profiling to obtain the average-case execution time (ACET) or worst-case execution time (WCET) as models for the workloads of the given application. For example, one of the earliest works was presented in (Yao et al., 1995) where they assumed that the arrival time, deadline of workloads, and task execution time based on CPU cycle are given to designers as constants. The works proposed in (Im et al., 2006) and (Jejurikar & Gupta, 2006) are two more examples where in (Im et al., 2006) they proposed a technique to reduce the energy consumption based on WCET workload model using buffers; and in (Jejurikar & Gupta, 2006) a dynamic voltage scaling (DVS) method in the presence of task synchronization based on WCET workload model in multiprocessor environment was proposed. This kind of approaches cannot deal with the time-varying workload especially when the workload shows a large variation with nonstationary property. Another category of researches related to DVFS comprise techniques which require either application or compiler support to perform (Azevedo et al., 2002; Yang et al., 2001; Chung et al., 2002). Generality and offline profiling for different workload variations

Using adaptive approaches for DVFS leads to save more power and energy in comparison to the conventional techniques. Proposing closed loop system architectures started by introducing self-timed adaptive supply-voltage scaling for asynchronous circuits in (Nielsen et al., 1994) where in their architecture, first input-first output (FIFO) buffers are used in both inputs and outputs of the processor. The FIFO-buffers average the computational workload to adjust the supply voltage and frequency. The feedback is based on actual path delays of the circuit. The feedback signal controls the DC-DC converter based on the information derived from the FIFO's. After this architecture, other researchers used a similar configuration to adapt the power supply voltage to lower the power consumption in digital signal processors DSPs (Gutnik & Chandrakasan, 1997). The structure of the proposed system architecture in (Gutnik & Chandrakasan, 1997) is the same as (Nielsen et al., 1994), but they designed a configuration for synchronous designs, and variations in the

controller as the DVFS method will be discussed during design procedure.

**2. Related works over power management techniques** 

is still a big drawback existing in these classes of works.

periodic workload variations.

computational workload were taken into account as well. Like the self-timed variable voltage system of (Nielsen et al., 1994), input data is buffered into a FIFO type of buffer to enable averaging of the workload. Then, the control loop controls the processing rate to avoid queuing overflow and underflow of the FIFOs. The controller in this methodology consists of a voltage regulator, a ring oscillator, a rate-compare block and a programmable look-up table (LUT). The controller block decides to change the voltage and frequency based on the processing rate and existent LUT. Disadvantage of this configuration is that it comes with extra latency as buffer utilization is only one measure of workload.

An evolution to closed loop control configuration, in the estimation of workload and adaptive control methods become main challenge for design efficient DVFS. These techniques aimed at estimating time varying workload using adaptive filters that most of them were based on a conventional proportional, integral and derivative (PID) controller. One famous PID based approach is presented in (Wei & Horowitz, 2003) where voltage samples are used to control a VCO to change the frequency as feedback signal for the buck converter. The reference signal and feedback signal come into the controller as variable frequency clocks, both feed into counters, and the number of transitions is counted for a fixed period of time. A PID controller, based on the calculated error value between its inputs, decides to change the voltage and frequency of the circuit. Some example of using PID controller to estimate workload variations are proposed in (Hughes and Adve, 2003; Gu & Chakraborty, 2008; Wu et al., 2005; Lu et al., 2002, 2003). In (Hughes and Adve, 2003), the PID controller is used to estimate the frame decoding time in multimedia applications and it was used in (Gu & Chakraborty, 2008) for 3-D games. In (Wu et al., 2005) and (Lu et al., 2003), the PI controller, which is a variant of the PID method, is applied to estimate the buffer occupancy for DVS targeting data buffered systems. In (Lu et al., 2002), an integral controller which is also a variant of PID method is designed and used to estimate workload estimation for performing DVS. Despite the PID controller is an adaptive filter, it suffers from possible overshooting and undershooting, depending on the selected coefficients. Also the PID controller for estimating application is useful when the designer select coefficient for specific workload variations and if the shape of workload changes, the coefficient should be defined again based on new workload variations. Hence, the tuning of coefficients critically determines the prediction accuracy.

Beside PID based controllers, some other estimators and adaptive filters are proposed to forecast workload variations in order to adjust voltage and/or frequency. In (Sinha & Chandrakasan, 2001), an adaptive approach for dynamic voltage scheduling on processors is presented based on workload prediction by filtering a trace history. In this work, they examine some conventional filters and evaluate their accuracy based on power saving amounts. They concluded that adaptive LMS filtering is the most powerful one and can be used to predict workload variations. Also in (Bang et al., 2009), they proposed a Kalmanfilter based on-line estimator to predict and track the workload variation that can be applicable to periodic applications with soft real-time constrains.

Compared to previous approaches, the fuzzy logic controller is similar to adaptive filters in the sense of estimating the workload variations. However, the fuzzy logic controller can work as an on-line methodology without updating any parameters during run-time adaptations and also without any other information about the nature of the workload

Synthesis and VHDL Implementation of Fuzzy Logic Controller

used. The delay of a CMOS gate can be modeled as

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 189

Since there is a strong correlation between the supply current and the workload of a processor (Benini et al., 1999), the controller is designed based on observing and tracking of the average of current variations. The most important purpose is how to predict and track supply current variations of the processor and to drive it to operate at the lowest possible voltage and corresponding minimum frequency, for which a specific application can meet all of its deadlines under specific timing constraints. If the supply current tracking can perform in a proper way, the supply voltage and clock frequency of the processor can be adjusted w.r.t output predicted current signal. Supply voltage variations are same with variations of the predicted supply current signal. For determining clock frequency in each control time, the proper look up table corresponding to the delay-voltage model can be

� ��

frequency for satisfying all timing deadlines of the circuit can be determined as

Fig. 2. Performance spread of a sample CMOS digital circuit in 65nm Technology.

Imagine a specific application is running with a constant frequency ���� at its nominal supply voltage ����without any voltage scaling. Now suppose that the supply current is such that there is opportunity to save power by reducing the supply voltage. However, observe that when the supply voltage reduces (e.g. to a point between ���� and ���� as shown in Fig. 2), the frequency of operation would reduce as well to�����. If the supply

six different clock frequencies, like ������ ������������ shown in Fig. 2.

��������

where � and � are technological parameters, and ��� is device threshold voltage. The cycle time of a design is modeled as a function of the critical path delay given as �� � ��� where �� is the logic depth in number of (equivalent) gates in the critical path. Therefore, the clock

The relation of the normalized operating frequency versus normalized supply voltage of a sample CMOS digital circuit is shown in Fig. 2. As mentioned before, changing the processor clock frequency can be done by the available PLL in the circuit. PLL can only provide some limited clock frequencies, for instance suppose that a sample PLL can provide

�(�������)� (2)

���(�) � � �� ⁄ (�). (3)

variation. The controller can estimate and track any kind of workload variations accurately and it does not require any coefficient tuning through offline profiling.

### **3. Principles of Dynamic Voltage and Frequency Scaling (DVFS)**

The most important key to save power and energy of a digital circuit or processor is to reduce supply voltage and clock frequency according to the performance requirements. The power consumption of a clocked digital CMOS circuit is given by the well-known formula:

$$Power = \underbrace{a.C.V\_{dd}^2.F\_{ck}}\_{Dynamic\ Power} + \underbrace{I\_{leak\cdot}.V\_{dd}}\_{leakage\ power} \tag{1}$$

where ߙǤ ܥ is the total switched capacitance, ܸௗௗ is the supply voltage, ܨ is the clock frequency and ܫ is the off-state current of the circuit. By reducing the supply voltage and clock frequency, considerable power can be saved while ߙǤ ܥ is generally fixed for a specific application. Over the years, researchers have proposed different hardware adaptive power management infrastructures to construct low power system-on-chip (SoC) integrated circuits. Among all the methods, DVFS methods are the most effective ones to save power consumption in processors. Conceptually, online DVFS problem for a digital CMOS circuit e.g. a processor is to scale voltage and frequency based on performance variation demands. The general block diagram of a dynamic supply voltage and frequency scaled system is shown in Fig. 1(Nielsen et al., 1994; Gutnik & Chandrakasan, 1997).

Fig. 1. General block diagram of a DVFS system

In this block diagram, there are three main components. The first component is a performance sensor that monitors the main specification of the processor e.g. average of supply current, temperature and supply voltage variations. The second component is the controller. This controller block works based on an input data received from the sensors by comparing it with the reference performance received from the power management unit or software to decide the change in supply voltage when necessary. The third block is the supply voltage actuator that can be on-chip or off-chip, e.g. a DC-DC converter and clock frequency actuators that can be a PLL. Since reducing the supply voltage causes increasing the delay of circuits, controlling the voltage and frequency of a processor dramatically depends on the accuracy of the controller.

variation. The controller can estimate and track any kind of workload variations accurately

The most important key to save power and energy of a digital circuit or processor is to reduce supply voltage and clock frequency according to the performance requirements. The power consumption of a clocked digital CMOS circuit is given by the well-known formula:

ᇥ

where ߙǤ ܥ is the total switched capacitance, ܸௗௗ is the supply voltage, ܨ is the clock frequency and ܫ is the off-state current of the circuit. By reducing the supply voltage and clock frequency, considerable power can be saved while ߙǤ ܥ is generally fixed for a specific application. Over the years, researchers have proposed different hardware adaptive power management infrastructures to construct low power system-on-chip (SoC) integrated circuits. Among all the methods, DVFS methods are the most effective ones to save power consumption in processors. Conceptually, online DVFS problem for a digital CMOS circuit e.g. a processor is to scale voltage and frequency based on performance variation demands. The general block diagram of a dynamic supply voltage and frequency scaled system is

In this block diagram, there are three main components. The first component is a performance sensor that monitors the main specification of the processor e.g. average of supply current, temperature and supply voltage variations. The second component is the controller. This controller block works based on an input data received from the sensors by comparing it with the reference performance received from the power management unit or software to decide the change in supply voltage when necessary. The third block is the supply voltage actuator that can be on-chip or off-chip, e.g. a DC-DC converter and clock frequency actuators that can be a PLL. Since reducing the supply voltage causes increasing the delay of circuits, controlling the voltage and frequency of a processor dramatically

 ܫᇣ ᇧᇧᇤǤ ܸᇧᇧௗௗᇥ ௪

(1)

<sup>ଶ</sup> ᇣᇧᇧᇧᇤᇧᇧǤ ܨᇧ

௬௪

and it does not require any coefficient tuning through offline profiling.

**3. Principles of Dynamic Voltage and Frequency Scaling (DVFS)** 

ௗௗܸ Ǥܥ Ǥߙ ൌ ݎ݁ݓܲ

shown in Fig. 1(Nielsen et al., 1994; Gutnik & Chandrakasan, 1997).

Fig. 1. General block diagram of a DVFS system

depends on the accuracy of the controller.

Since there is a strong correlation between the supply current and the workload of a processor (Benini et al., 1999), the controller is designed based on observing and tracking of the average of current variations. The most important purpose is how to predict and track supply current variations of the processor and to drive it to operate at the lowest possible voltage and corresponding minimum frequency, for which a specific application can meet all of its deadlines under specific timing constraints. If the supply current tracking can perform in a proper way, the supply voltage and clock frequency of the processor can be adjusted w.r.t output predicted current signal. Supply voltage variations are same with variations of the predicted supply current signal. For determining clock frequency in each control time, the proper look up table corresponding to the delay-voltage model can be used. The delay of a CMOS gate can be modeled as

$$
\pi = \frac{c\_{gate}\nu\_{dd}}{\kappa(\nu\_{dd} - \nu\_{th})^\beta} \tag{2}
$$

where � and � are technological parameters, and ��� is device threshold voltage. The cycle time of a design is modeled as a function of the critical path delay given as �� � ��� where �� is the logic depth in number of (equivalent) gates in the critical path. Therefore, the clock frequency for satisfying all timing deadlines of the circuit can be determined as

$$f\_{ck}(\mathbf{t}) = \mathbf{1}/T\_c(\mathbf{t}).\tag{3}$$

The relation of the normalized operating frequency versus normalized supply voltage of a sample CMOS digital circuit is shown in Fig. 2. As mentioned before, changing the processor clock frequency can be done by the available PLL in the circuit. PLL can only provide some limited clock frequencies, for instance suppose that a sample PLL can provide six different clock frequencies, like ������ ������������ shown in Fig. 2.

Fig. 2. Performance spread of a sample CMOS digital circuit in 65nm Technology.

Imagine a specific application is running with a constant frequency ���� at its nominal supply voltage ����without any voltage scaling. Now suppose that the supply current is such that there is opportunity to save power by reducing the supply voltage. However, observe that when the supply voltage reduces (e.g. to a point between ���� and ���� as shown in Fig. 2), the frequency of operation would reduce as well to�����. If the supply

Synthesis and VHDL Implementation of Fuzzy Logic Controller

(Lee, 1999).

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 191

frequency of the processor. Actually, by this method, the fuzzy logic controller is tracking the supply current to decide upon the new voltage of the digital circuit. Actuators for supply voltage can be an on-chip or off-chip DC-DC converters. The same procedure can be done for determining the frequency of the processor. But for deciding about the final frequency value, it should be taken into account that the frequency obtained by fuzzy logic controller has to be greater than the frequency obtained by worst case execution time. Also

Based on performing different experiments, the proposed internal structure of fuzzy controller was resulted to have membership functions and fuzzy rules like ones shown in Fig. 4. In this structure, if ܰmembership functions are defined for the supply current and 3 membership functions are defined for its derivative, then ܰൈ͵ rules should define the fuzzy logic rule-base block. The rules should be defined in a way that the supply voltage tracks the variations of the supply current. Therefore, the proposed controller predicts first the supply current variations and then it decides on how to change the voltage and frequency pair. Using fuzzy logic sets, the fuzzy inference system (FIS) formulates the process of getting the output based on the defined input membership functions and the fuzzy if-then rules. Mamdani FIS is the most commonly useful methodology for applying fuzzy logic controllers on practical systems and we recommend using it for DVFS goals

Fig. 4. The defined membership functions of states, A) Supply current as the first input of the fuzzy controller. It has N membership functions named by I(1), I(2),…, I(N) , B) Derivative of supply current as the second input of the fuzzy controller, it has three membership functions named by Negative, Zero, and Positive, C) Supply voltage as the output of the fuzzy controller, it has N membership functions named by Vdd(1), Vdd(2),…,

Several experiments have been conducted to evaluate different aspects of the controller. In the first simulation, we designed a controller and implemented it on a sampled supply current of a processor near to reality. This supply current is shown in Fig. (5.a) and its

and Vdd(N). Fuzzy *if-then* rules are defined in the table.

the frequency can be defined based on a proper predefined look up table.

voltage goes for a value between ܸௗௗଶ andܸௗௗଷ, then the frequency can switch to the݂ଷ value. In this way, adjusting supply voltage to the lowest allowable value together with frequency scaling will ensure that the application is properly executed and the maximum possible power is saved. For switching the supply voltage to different possible values, it is needed to use voltage actuators like on-chip or off-chip DC-DC converters. In most DC-DC converters as voltage regulators, switching between voltage output levels takes a few tens of microseconds. For doing safe voltage and frequency switching, voltage and clock frequency changes may not be done in parallel. While the supply current is going to decrease, the frequency should first be decreased and subsequently the voltage should be lowered to the appropriate value. On the contrary, when the supply current is going to increase, the circuit requires the voltage to be increased first followed by the frequency update. This ensures that the voltage supply to the processor is never lower than the minimum required for the current operating frequency and avoids data corruption due to circuit failure.

## **4. DVFS based on fuzzy logic controller**

The block diagram of the proposed dynamic voltage and frequency scaling configuration is shown in Fig. 3 (Pourshaghaghi & Pineda de Gyvez, 2009).

Fig. 3. Dynamic voltage and frequency scaling configuration based on supply-current tracking by fuzzy logic controller.

In this block diagram, the supply current and also the derivative of the supply current are observed as two inputs of the fuzzy logic block. The reason for using the derivative of the supply current is that it helps to predict the variations of the workload. If one can predict variations of the supply current, then it is easier for the actuators to act sooner. Consequently, the amount of saved power can be increased significantly, not to mention finishing the executing task on time. Given a specific value for the supply current, if the derivative is positive, it implies that the supply current is increasing. Otherwise, the supply current is decreasing. Therefore, the fuzzy *if-then* rules should be defined to follow this concept. It should be taken into account that, for having more precision to predict supply current variations, it is possible to compute the second derivative of the current. Thus, the fuzzy logic block receives two inputs: supply-current and its derivative. Based on these two inputs, the fuzzy logic block, as an expert system, can decide about the voltage and

voltage goes for a value between ܸௗௗଶ andܸௗௗଷ, then the frequency can switch to the݂ଷ value. In this way, adjusting supply voltage to the lowest allowable value together with frequency scaling will ensure that the application is properly executed and the maximum possible power is saved. For switching the supply voltage to different possible values, it is needed to use voltage actuators like on-chip or off-chip DC-DC converters. In most DC-DC converters as voltage regulators, switching between voltage output levels takes a few tens of microseconds. For doing safe voltage and frequency switching, voltage and clock frequency changes may not be done in parallel. While the supply current is going to decrease, the frequency should first be decreased and subsequently the voltage should be lowered to the appropriate value. On the contrary, when the supply current is going to increase, the circuit requires the voltage to be increased first followed by the frequency update. This ensures that the voltage supply to the processor is never lower than the minimum required for the

The block diagram of the proposed dynamic voltage and frequency scaling configuration is

Fig. 3. Dynamic voltage and frequency scaling configuration based on supply-current

In this block diagram, the supply current and also the derivative of the supply current are observed as two inputs of the fuzzy logic block. The reason for using the derivative of the supply current is that it helps to predict the variations of the workload. If one can predict variations of the supply current, then it is easier for the actuators to act sooner. Consequently, the amount of saved power can be increased significantly, not to mention finishing the executing task on time. Given a specific value for the supply current, if the derivative is positive, it implies that the supply current is increasing. Otherwise, the supply current is decreasing. Therefore, the fuzzy *if-then* rules should be defined to follow this concept. It should be taken into account that, for having more precision to predict supply current variations, it is possible to compute the second derivative of the current. Thus, the fuzzy logic block receives two inputs: supply-current and its derivative. Based on these two inputs, the fuzzy logic block, as an expert system, can decide about the voltage and

*I* ∈ *R*

*I* ∈ *R*

current operating frequency and avoids data corruption due to circuit failure.

**4. DVFS based on fuzzy logic controller** 

= *VFf* )(

tracking by fuzzy logic controller.

shown in Fig. 3 (Pourshaghaghi & Pineda de Gyvez, 2009).

∈ min *VVV* max],[ *fff* maxmin ],[ *ck* ∈ frequency of the processor. Actually, by this method, the fuzzy logic controller is tracking the supply current to decide upon the new voltage of the digital circuit. Actuators for supply voltage can be an on-chip or off-chip DC-DC converters. The same procedure can be done for determining the frequency of the processor. But for deciding about the final frequency value, it should be taken into account that the frequency obtained by fuzzy logic controller has to be greater than the frequency obtained by worst case execution time. Also the frequency can be defined based on a proper predefined look up table.

Based on performing different experiments, the proposed internal structure of fuzzy controller was resulted to have membership functions and fuzzy rules like ones shown in Fig. 4. In this structure, if ܰmembership functions are defined for the supply current and 3 membership functions are defined for its derivative, then ܰൈ͵ rules should define the fuzzy logic rule-base block. The rules should be defined in a way that the supply voltage tracks the variations of the supply current. Therefore, the proposed controller predicts first the supply current variations and then it decides on how to change the voltage and frequency pair. Using fuzzy logic sets, the fuzzy inference system (FIS) formulates the process of getting the output based on the defined input membership functions and the fuzzy if-then rules. Mamdani FIS is the most commonly useful methodology for applying fuzzy logic controllers on practical systems and we recommend using it for DVFS goals (Lee, 1999).

Fig. 4. The defined membership functions of states, A) Supply current as the first input of the fuzzy controller. It has N membership functions named by I(1), I(2),…, I(N) , B) Derivative of supply current as the second input of the fuzzy controller, it has three membership functions named by Negative, Zero, and Positive, C) Supply voltage as the output of the fuzzy controller, it has N membership functions named by Vdd(1), Vdd(2),…, and Vdd(N). Fuzzy *if-then* rules are defined in the table.

Several experiments have been conducted to evaluate different aspects of the controller. In the first simulation, we designed a controller and implemented it on a sampled supply current of a processor near to reality. This supply current is shown in Fig. (5.a) and its

Synthesis and VHDL Implementation of Fuzzy Logic Controller

control methods.

**150.2**

**150.1 150.2 150.3 150.4 150.5**

**Current(mA)**

**150.4**

**current(mA)**

**150.6**

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 193

controller. Finally, with a trial and error method we found that with �� = 100, �� = 2 and �� = 1, it can track the supply current very well. The tracking result is shown in Fig. (6.b). But when the shape of the supply current changed, similar to the supply current shown in Fig. (6.c), the PID could not track the variations with the same coefficients and we have to change coefficients again. The output of PID block in the second experiment is shown in Fig. (6.d). It is also important to mention that the fuzzy logic controller works well regardless of the system's inputs, while the PID controller requires the mathematical formulation of the system to adapt its coefficients to be able to work properly. One of the main advantages of the fuzzy logic controller is that the hardware implementation is easy because everything here is digital. Another advantage is that this controller can work on-line to track all workload circumstances with high speed and less error in comparison with other traditional

Fig. 6. Simulation of PID controller on two different input supply current signals. a,b) the supply voltage track supply current variations well. c,d) when the current variations changes as c, then supply voltage cannot track the new variations with old PID coefficients.

**1.036 1.037 1.038 1.039 1.04**

**0.997 0.998 0.999 1 1.001**

**Voltage(V)**

**Voltage(V)**

**<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> 1.035**

**Time(msec)**

**d)Voltage output of PID with changing input to (c)**

**0 0.2 0.4 0.6 0.8 1**

**Time(msec)**

**b)Voltage output of PID regarding to input (a)**

The general architecture of the fuzzy logic controller to track supply current variations of a processor is shown in Fig. 7 where the information flows from left to right. The fuzzy logic controller is designed based on the Mamdani fuzzy inference system (FIS). The first step to implement the controller as a digital circuit is to convert analogue input values, supply current and its derivative, to digital ones. For this purpose an analogue to digital converter (A/D) is necessary to digitize the input crisp values. The resolution of the selected A/D depends on the desired accuracy for supply current, derivative of supply current and supply voltage data. For example, suppose that the supply current variations of a processors change between 0mA and 100mA and one has selected an 8 bit A/D. In this case, the

**5. VHDL implementation of the fuzzy logic controller** 

**<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>150</sup>**

**<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>150</sup>**

**Time(msec)**

**Time(msec)**

**c)Refrence Current in 2nd experiment of PID**

**a)Refrence Input for PID in 1st experiment**

resolution of the supply current samples is as follows:

derivative is shown in Fig. (5.b). Based on the internal fuzzy system structure described in Fig. 4, we have considered nine Triangular membership functions for supply current. These functions are defined between �50�� to �00��, without losing the generality, with a symmetrical shapes and widths. Each supply current membership function has 50% overlaps with its neighbor membership function (functions). We have considered five Triangular membership functions for derivative of supply current from �250 �� ��� � to 250 �� ��� � . Consequently, we defined 27 *if-then* rules based on the rules shown in Fig. 4. Nine symmetrical triangular membership functions for supply voltage have been considered as well. These membership functions have 50% overlap with each other and have same widths too. We used also the centre of area as the defuzzification method. The result of this simulation is shown in Fig. (5.c). As one can see from the supply voltage values, the fuzzy logic can track the variation of supply current very well. The output surface of fuzzy logic controller is shown in Fig. (5.d). In this figure, the entire span of supply voltage based upon the entire span of supply current and its derivative is displayed. It shows pseudo continuity of the output voltage with variations of workload.

Fig. 5. Simulation results of applying fuzzy Logic controller (FLC) on a sampled supply current. a) Supply current of a sample processor, the variation of current is based on different applications, b) Derivative of the supply current, c) Voltage (output) of the FLC that goes to DC-DC converter, d) Output surface of the controller which shows variations rate of the voltage (output) regarding to input variations.

We simulated a PID controller on another supply current signal and compared the results with the fuzzy controller. Suppose that we have a supply current signal like the one shown in Fig. (6.a). We trained the PID controller with some simulation testing to find out what coefficients are the best for the proportional, integration and derivative part of the

derivative is shown in Fig. (5.b). Based on the internal fuzzy system structure described in Fig. 4, we have considered nine Triangular membership functions for supply current. These functions are defined between �50�� to �00��, without losing the generality, with a symmetrical shapes and widths. Each supply current membership function has 50% overlaps with its neighbor membership function (functions). We have considered five

��� � . Consequently, we defined 27 *if-then* rules based on the rules shown in Fig. 4. Nine symmetrical triangular membership functions for supply voltage have been considered as well. These membership functions have 50% overlap with each other and have same widths too. We used also the centre of area as the defuzzification method. The result of this simulation is shown in Fig. (5.c). As one can see from the supply voltage values, the fuzzy logic can track the variation of supply current very well. The output surface of fuzzy logic controller is shown in Fig. (5.d). In this figure, the entire span of supply voltage based upon the entire span of supply current and its derivative is displayed.

**Dcurrent (uA/msec)**

**<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> -200**

**Time(msec)**

**b) Derivative of supply-current of the Processor**

��� � to

Triangular membership functions for derivative of supply current from �250 ��

It shows pseudo continuity of the output voltage with variations of workload.

Fig. 5. Simulation results of applying fuzzy Logic controller (FLC) on a sampled supply current. a) Supply current of a sample processor, the variation of current is based on different applications, b) Derivative of the supply current, c) Voltage (output) of the FLC that goes to DC-DC converter, d) Output surface of the controller which shows variations

We simulated a PID controller on another supply current signal and compared the results with the fuzzy controller. Suppose that we have a supply current signal like the one shown in Fig. (6.a). We trained the PID controller with some simulation testing to find out what coefficients are the best for the proportional, integration and derivative part of the

rate of the voltage (output) regarding to input variations.

**<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>150</sup>**

**<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> 0.8**

**Time(msec)**

**Time(msec)**

**c) Supply Voltage as the Output of the Fuzzy Logic controller**

**a) Supply current of the processor**

250 ��

> **0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25**

**Supply voltage (v)**

**Supply Current (uA)**

controller. Finally, with a trial and error method we found that with �� = 100, �� = 2 and �� = 1, it can track the supply current very well. The tracking result is shown in Fig. (6.b). But when the shape of the supply current changed, similar to the supply current shown in Fig. (6.c), the PID could not track the variations with the same coefficients and we have to change coefficients again. The output of PID block in the second experiment is shown in Fig. (6.d). It is also important to mention that the fuzzy logic controller works well regardless of the system's inputs, while the PID controller requires the mathematical formulation of the system to adapt its coefficients to be able to work properly. One of the main advantages of the fuzzy logic controller is that the hardware implementation is easy because everything here is digital. Another advantage is that this controller can work on-line to track all workload circumstances with high speed and less error in comparison with other traditional control methods.

Fig. 6. Simulation of PID controller on two different input supply current signals. a,b) the supply voltage track supply current variations well. c,d) when the current variations changes as c, then supply voltage cannot track the new variations with old PID coefficients.

## **5. VHDL implementation of the fuzzy logic controller**

The general architecture of the fuzzy logic controller to track supply current variations of a processor is shown in Fig. 7 where the information flows from left to right. The fuzzy logic controller is designed based on the Mamdani fuzzy inference system (FIS). The first step to implement the controller as a digital circuit is to convert analogue input values, supply current and its derivative, to digital ones. For this purpose an analogue to digital converter (A/D) is necessary to digitize the input crisp values. The resolution of the selected A/D depends on the desired accuracy for supply current, derivative of supply current and supply voltage data. For example, suppose that the supply current variations of a processors change between 0mA and 100mA and one has selected an 8 bit A/D. In this case, the resolution of the supply current samples is as follows:

Synthesis and VHDL Implementation of Fuzzy Logic Controller

circuit.

Slope (N): 8

I : input supply current

3 dmf\_I = 0

**1 For** N=1 to I\_MFS **2 IF** I < ܲଵሺܰሻ

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 195

 For each current value as the input, the degree of membership function (dmf) depends on the location of the current value regarding to these four parameters. The pseudo code to calculate the degree of membership function for a specific input current value is presented in Algorithm 1. In this pseudo code, it is supposed that the slopes of all triangular membership functions have value 8. With this assumption, one can avoid using multipliers in the circuit to calculate the degree of membership functions and increase the speed of the

Fig. 8. Triangular membership functions for the supply current variations

derivate of current as slope (MF1) =slope (MF3) =8 and slope (MF2) =16.

ܲଶሺܰሻ: Point 2 of the membership function N (middle point in each MF)

 **Data(** ܲଵ, ܲଶ, slope, ܫ̴ܨܯܵ, ̴݂݀݉ܫ : std\_logic\_vector(7 downto 0))

ܲଵሺܰሻ: Point 1 of the membership function N shown in Fig.8

 *dmf\_I*: Degree of membership functions

**Algorithm 1** – Fuzzification : triangular MFs for supply current and calculate dmf

 *N*: Counter for the Number of membership function for supply current variations

 *I\_MFS*: Number of membership function for supply current variations (here: 9)

To calculate the degree of membership functions of the derivative of supply current, an algorithm similar to Algorithm 1 can be used. The only differences are 1) three MFs are defined (N=3) for the derivative of current, 2) different slopes are defined for the MFs of the

$$2^{\mathfrak{B}} = \frac{I\_{\max} - I\_{\min}}{res.(I)} \to res.(I) \cong 0.4 mA \tag{4}$$

Hence if a voltage actuator e.g. a DC-DC converter has been selected to regulate the processor's voltage between 0.7V and 1.2V, the output supply voltage made by the fuzzy logic controller has steps of 1.95 mV for supply voltage. In this section, we design the controller in VHDL based on an 8 bits resolution for digital values, and without loss of generality one can extend the design to other resolutions.

Fig. 7. Architecture of the Mamdani Fuzzy Inference System (FIS) for the supply voltage computation in VHDL implementation

#### **5.1 Implementation of the fuzzification stage**

After digitizing the input crisp values, the first step is to define membership functions for the current, derivative of the current and the supply voltage. We consider nine membership functions for the supply current variations, three membership function for its derivative, and nine membership functions for the output supply voltage. The numbers of the membership functions are obtained based on executing different experiments and evaluating the accuracy of the controller with different supply current signatures. These functions are defined in the triangular shapes like the ones presented in Fig. 4 combined with the same corresponding table of fuzzy if-then rules. First we start to design the membership functions (MFs) of the supply current. Since we have used an 8 bits resolution for A/D, the input range of current should map between 0(\$0) and 255 (\$FF). Consider defined MFs of the current as the ones shown in Fig. 8. In this figure, the Y axis shows the degree of membership function as a value between 0 and 1 and the X axis shows the supply current universe of discourse. All these parameters need to be mapped between 0 and 255. Each MF in Fig. 8 is represented by four parameters: point1 (P1), the positive slope value, point2 (P2), and the negative slope value.

 For each current value as the input, the degree of membership function (dmf) depends on the location of the current value regarding to these four parameters. The pseudo code to calculate the degree of membership function for a specific input current value is presented in Algorithm 1. In this pseudo code, it is supposed that the slopes of all triangular membership functions have value 8. With this assumption, one can avoid using multipliers in the circuit to calculate the degree of membership functions and increase the speed of the circuit.

To calculate the degree of membership functions of the derivative of supply current, an algorithm similar to Algorithm 1 can be used. The only differences are 1) three MFs are defined (N=3) for the derivative of current, 2) different slopes are defined for the MFs of the derivate of current as slope (MF1) =slope (MF3) =8 and slope (MF2) =16.

**Algorithm 1** – Fuzzification : triangular MFs for supply current and calculate dmf

 **Data(** ܲଵ, ܲଶ, slope, ܫ̴ܨܯܵ, ̴݂݀݉ܫ : std\_logic\_vector(7 downto 0))

 *N*: Counter for the Number of membership function for supply current variations

ܲଵሺܰሻ: Point 1 of the membership function N shown in Fig.8

ܲଶሺܰሻ: Point 2 of the membership function N (middle point in each MF)

Slope (N): 8

194 Fuzzy Logic – Controls, Concepts, Theories and Applications

Hence if a voltage actuator e.g. a DC-DC converter has been selected to regulate the processor's voltage between 0.7V and 1.2V, the output supply voltage made by the fuzzy logic controller has steps of 1.95 mV for supply voltage. In this section, we design the controller in VHDL based on an 8 bits resolution for digital values, and without loss of

������� � ���� ��� � ����� (4)

**dmf\_V(2)**

**dmf\_V(1)**

max

*Vout*

2� <sup>=</sup>���������

∏<sup>1</sup>

Π2

Π3

Π<sup>25</sup> Π<sup>26</sup> Π<sup>27</sup>

Fig. 7. Architecture of the Mamdani Fuzzy Inference System (FIS) for the supply voltage

After digitizing the input crisp values, the first step is to define membership functions for the current, derivative of the current and the supply voltage. We consider nine membership functions for the supply current variations, three membership function for its derivative, and nine membership functions for the output supply voltage. The numbers of the membership functions are obtained based on executing different experiments and evaluating the accuracy of the controller with different supply current signatures. These functions are defined in the triangular shapes like the ones presented in Fig. 4 combined with the same corresponding table of fuzzy if-then rules. First we start to design the membership functions (MFs) of the supply current. Since we have used an 8 bits resolution for A/D, the input range of current should map between 0(\$0) and 255 (\$FF). Consider defined MFs of the current as the ones shown in Fig. 8. In this figure, the Y axis shows the degree of membership function as a value between 0 and 1 and the X axis shows the supply current universe of discourse. All these parameters need to be mapped between 0 and 255. Each MF in Fig. 8 is represented by four parameters: point1 (P1), the positive slope value,

generality one can extend the design to other resolutions.

**dmf\_I(1)**

**dmf\_I(1)**

**dmf\_p**

computation in VHDL implementation

point2 (P2), and the negative slope value.

**5.1 Implementation of the fuzzification stage** 

**dmf\_N**

**dmf\_Z**

*I*

(*I*) *dt d*

 *I\_MFS*: Number of membership function for supply current variations (here: 9)

 *dmf\_I*: Degree of membership functions

I : input supply current

**1 For** N=1 to I\_MFS

**2 IF** I < ܲଵሺܰሻ

3 dmf\_I = 0

Synthesis and VHDL Implementation of Fuzzy Logic Controller

**1** Function Maximum(a, b: std\_logic\_vector(7 downto 0))

**2** variable max: std\_logic\_vector(7 downto 0) := (others => '0');

**Algorithm 3** – Maximum Function

**4** If a > b then

**6** Else

**8** End If; **9** Return max; **10** End Maximum;

**5** max := a;

**7** max := b;

**5.3 Implementation of the defuzzification stage** 

aggregated output fuzzy set is as the one shown in Fig. 9.

memory and how to address and access to data in the LUT.

**3** Begin

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 197

The output value of the minimum function is a value that determines the degree of MF for Vdd(2) in rule 1. For all the defined 27 rules, there may exist different degrees of MF values for each fuzzy voltage set. Therefore, one final value for each MF of the supply voltage should be determined. The min-max Mamdani FIS uses the maximum operator to calculate the final degree of the membership function for Vdd(1) to Vdd(9). The fuzzy maximum operator models one fuzzy set with the maximum values returned by the output fuzzy set of

**-Note**: In this function, a and b represent the dmf\_V values (degree of membership function of the voltage). This function should be called for each dmf\_V(1), …,dmf\_v(9) separately.

The last step is to perform the defuzzification process that converts the obtained fuzzy set into a single number as the output supply voltage. The aggregate output fuzzy set consists of a range of voltage output values and has to be defuzzified to determine a single output supply voltage value. For the defuzzification method, the centroid calculation is used to compute the final value. The centroid method computes the center of area under the curve of the fuzzy output set. From the min-max FIS, nine degrees of membership functions for each voltage set is obtained (dmf\_V(1), …, dmf\_V(9)). For each input value of the current and its derivative, there are a maximum of 3 *dmf* that have a nonzero value. Suppose that the

To compute the output voltage value, as one can see from eq. (5), the following functions are needed to use: summation, multiplier and divider. Since implementing a divider block results in a circuit that occupies more area, we propose to use a look up table (LUT) stored in the memory of processor. This LUT needs to be filled out by the designer. Under this approach, the data stored in the memory estimates the center of gravity of the output fuzzy set obtained by the min-max Mamdani FIS. Here, we explain the required size of the

each rule. In VHDL, one can use the maximum function presented in Algorithm 3.


## **5.2 Rule evaluation: Implementation of fuzzy inference system**

Considering Fig. 7 and since there are 9 MFs for the current and 3 MFs for its derivative, 27 fuzzy if-the rules are defined to correspondingly calculate the fuzzy supply voltage output values. The Mamdani FIS is used to evaluate the fuzzy if-then rules. To design Mamdani FIS in VHDL, let's consider the first fuzzy if-the rules defined in Fig. 7:

**IF** the supply current belongs to I(1) **AND** the derivative of current belongs to P (Positive) **Then** voltage is VDD(2).

For this rule, the AND operator should be applied to obtain one value out of two degree of membership functions (current and its derivative) which represents the result of the antecedent part in rule 1. This value actually represents a weighting factor for this specific rule. In the Mamdani FIS, the AND operator is a fuzzy operator to find the minimum value between two degrees of MFs: current and its derivative. The following minimum function, Algorithm 2, is used to implement the fuzzy AND operator in VHDL. In Fig. 7, this stage is called product layer which is a part of the min-max Mamdani FIS.

**Algorithm 2** – Minimum Function

**1** Function Minimum(a, b: std\_logic\_vector(7 downto 0))

**2** variable min: std\_logic\_vector (7 downto 0) := (others => '0');

**3** Begin **4** If a < b Then **5** min := a; **6** Else **7** min := b; **8** End If; **9** Return min;

**10** End Minimum;


The output value of the minimum function is a value that determines the degree of MF for Vdd(2) in rule 1. For all the defined 27 rules, there may exist different degrees of MF values for each fuzzy voltage set. Therefore, one final value for each MF of the supply voltage should be determined. The min-max Mamdani FIS uses the maximum operator to calculate the final degree of the membership function for Vdd(1) to Vdd(9). The fuzzy maximum operator models one fuzzy set with the maximum values returned by the output fuzzy set of each rule. In VHDL, one can use the maximum function presented in Algorithm 3.

## **Algorithm 3** – Maximum Function

196 Fuzzy Logic – Controls, Concepts, Theories and Applications

Considering Fig. 7 and since there are 9 MFs for the current and 3 MFs for its derivative, 27 fuzzy if-the rules are defined to correspondingly calculate the fuzzy supply voltage output values. The Mamdani FIS is used to evaluate the fuzzy if-then rules. To design Mamdani FIS

**IF** the supply current belongs to I(1) **AND** the derivative of current belongs to P (Positive) **Then** voltage is VDD(2). For this rule, the AND operator should be applied to obtain one value out of two degree of membership functions (current and its derivative) which represents the result of the antecedent part in rule 1. This value actually represents a weighting factor for this specific rule. In the Mamdani FIS, the AND operator is a fuzzy operator to find the minimum value between two degrees of MFs: current and its derivative. The following minimum function, Algorithm 2, is used to implement the fuzzy AND operator in VHDL. In Fig. 7, this stage is

**4 Elseif** I < ܲଶሺܰሻ

**6 Elseif** I < ܲଶሺܰ ͳሻ

**8 Else** I > ܲଶሺܰ ͳሻ **9** dmf\_I = 0

**Algorithm 2** – Minimum Function

**4** If a < b Then

**6** Else

**8** End If;

**9** Return min; **10** End Minimum;

**5** min := a;

**7** min := b;

current) and b represents dmf\_di.

**3** Begin

**10 End** 

**5** dmf\_I = (I - ܲଵሺܰሻ ) \* Slope (N)

**7** dmf\_I = 255 - (I - ܲଵሺܰሻ ) \* Slope (N)

**5.2 Rule evaluation: Implementation of fuzzy inference system** 

in VHDL, let's consider the first fuzzy if-the rules defined in Fig. 7:

called product layer which is a part of the min-max Mamdani FIS.

**1** Function Minimum(a, b: std\_logic\_vector(7 downto 0))

**2** variable min: std\_logic\_vector (7 downto 0) := (others => '0');



**-Note**: In this function, a and b represent the dmf\_V values (degree of membership function of the voltage). This function should be called for each dmf\_V(1), …,dmf\_v(9) separately.

## **5.3 Implementation of the defuzzification stage**

The last step is to perform the defuzzification process that converts the obtained fuzzy set into a single number as the output supply voltage. The aggregate output fuzzy set consists of a range of voltage output values and has to be defuzzified to determine a single output supply voltage value. For the defuzzification method, the centroid calculation is used to compute the final value. The centroid method computes the center of area under the curve of the fuzzy output set. From the min-max FIS, nine degrees of membership functions for each voltage set is obtained (dmf\_V(1), …, dmf\_V(9)). For each input value of the current and its derivative, there are a maximum of 3 *dmf* that have a nonzero value. Suppose that the aggregated output fuzzy set is as the one shown in Fig. 9.

To compute the output voltage value, as one can see from eq. (5), the following functions are needed to use: summation, multiplier and divider. Since implementing a divider block results in a circuit that occupies more area, we propose to use a look up table (LUT) stored in the memory of processor. This LUT needs to be filled out by the designer. Under this approach, the data stored in the memory estimates the center of gravity of the output fuzzy set obtained by the min-max Mamdani FIS. Here, we explain the required size of the memory and how to address and access to data in the LUT.

Synthesis and VHDL Implementation of Fuzzy Logic Controller

controller is shown in Algorithm 5.

address: address of the memory

Vout: output supply voltage value

**3** Counter = Counter + 1

**9** Vout = 32\*(Counter - 1) + LUT(address)

specifications are mentioned in Table 1.

**4 IF** rb(N) = 1

**6** break **7 End IF**

**5.4 Synthesis results** 

**Data** 

**1** Counter = 0

**8 End For** 

**2 For** N = 2 to V\_MFS

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 199

To construct the LUT, we only use the first 3 most significant bits (MSB) of each voltage membership function. Since there is a maximum of three membership functions involved in calculating the final crisp voltage value, one needs to consider 2����� = 512 words of the memory to make the desired LUT. Suppose we want to consider the whole 8 bits of each degree of voltage membership function value, the number of words in the memory changes to 2��. For now, let's assume we have considered 3 MSBs for each degree of MF. Depending on the number of the active voltage membership functions and corresponding degree of membership functions obtained by the Mamdani FIS, one can access the corresponding word in the memory to access the output voltage value stored in it. The VHDL algorithm to access the proper memory address in the defuzzification part of the designed fuzzy

Now each address of the memory should be filled out by a proper value to estimate the centre of gravity accordingly. We simulated all the corresponding possible situations for the aggregated fuzzy output voltage sets in MATLAB and estimate the output voltages. Then

we stored all the corresponding values into the 512 bytes considered memory.

*N[1:9]*: the number of membership function for supply voltage

**5** address = concatenate(r(N-1), r(N), r(N+1))

**Algorithm 5** – How to access the data of the memory in the defuzzification stage

*rb [0 or1]:* a bit to specify which MF is involved in calculating the final voltage value

We have implemented the proposed fuzzy logic controller in a CMOS 90nm technology and synthesized it with Cadence RC compiler to measure its power consumption and area. For benchmarking purposes, the synthesis of the circuit is done with different speeds. Synthesis

Fig. 9. Defuzzication and calculation of the final supply voltage value

If the centroid method for the defuzzification is applied, the output voltage value is as follows:

$$\mathcal{V} = \frac{\sum\_{l=1}^{6} \mathcal{V}l \* dm f\_{-} \mathcal{V}l}{\sum\_{l=1}^{6} dm f\_{-} \mathcal{V}l} \tag{5}$$

To track supply current variations, for each pair of fuzzy inputs (supply current and its derivative) at a specific time, there is a maximum of three adjacent membership functions MFs for the voltage which have degree of membership function *dmf* value distinct from zero. Therefore, one can use Algorithm 4 to first find those involved voltage MFs and then use the LUT to calculate the final voltage value.

**Algorithm 4** – Specifying active voltage membership functions in the defuzzification stage

## **Data**:

 *V\_MFS =9*: Number of membership function for supply voltage (here: 9)

 *N[1:9]*: Counter for the number of membership functions of supply voltage

```
 dmf_V [0:255]: Degree of MF
```
*rb [0 or1]:* a bit to specify which MF is involved in calculating the final voltage value

```
1 For N=1 to V_MFS
```

```
2 IF dmf_V(N) = 0 Then
```

To construct the LUT, we only use the first 3 most significant bits (MSB) of each voltage membership function. Since there is a maximum of three membership functions involved in calculating the final crisp voltage value, one needs to consider 2����� = 512 words of the memory to make the desired LUT. Suppose we want to consider the whole 8 bits of each degree of voltage membership function value, the number of words in the memory changes to 2��. For now, let's assume we have considered 3 MSBs for each degree of MF. Depending on the number of the active voltage membership functions and corresponding degree of membership functions obtained by the Mamdani FIS, one can access the corresponding word in the memory to access the output voltage value stored in it. The VHDL algorithm to access the proper memory address in the defuzzification part of the designed fuzzy controller is shown in Algorithm 5.

Now each address of the memory should be filled out by a proper value to estimate the centre of gravity accordingly. We simulated all the corresponding possible situations for the aggregated fuzzy output voltage sets in MATLAB and estimate the output voltages. Then we stored all the corresponding values into the 512 bytes considered memory.

**Algorithm 5** – How to access the data of the memory in the defuzzification stage

## **Data**

198 Fuzzy Logic – Controls, Concepts, Theories and Applications

If the centroid method for the defuzzification is applied, the output voltage value is as

**V1 V2 V3 V4 V5 V6**

� � <sup>∑</sup> ��������� � ��� ∑ ������ � ���

To track supply current variations, for each pair of fuzzy inputs (supply current and its derivative) at a specific time, there is a maximum of three adjacent membership functions MFs for the voltage which have degree of membership function *dmf* value distinct from zero. Therefore, one can use Algorithm 4 to first find those involved voltage MFs and then

**Algorithm 4** – Specifying active voltage membership functions in the defuzzification stage

*rb [0 or1]:* a bit to specify which MF is involved in calculating the final voltage value

 *V\_MFS =9*: Number of membership function for supply voltage (here: 9)  *N[1:9]*: Counter for the number of membership functions of supply voltage

(5)

**Voltage**

Fig. 9. Defuzzication and calculation of the final supply voltage value

use the LUT to calculate the final voltage value.

 *dmf\_V [0:255]*: Degree of MF

**dmf-V3=dmf-V4**

**dmf-V1=dmf-V2**

**dmf-V5=dmf-V6**

**2 IF** dmf\_V(N) = 0 **Then** 

**1 For** N=1 to V\_MFS

**3** rb(N) = 0 **4 Else** rb(N) = 1

**5 End**

**6 End** 

follows:

**Degree of MF**

 **Data**:

address: address of the memory

*N[1:9]*: the number of membership function for supply voltage

*rb [0 or1]:* a bit to specify which MF is involved in calculating the final voltage value

Vout: output supply voltage value

```
1 Counter = 0
```

```
2 For N = 2 to V_MFS
```


```
7 End IF
```

```
8 End For
```

```
9 Vout = 32*(Counter - 1) + LUT(address)
```
## **5.4 Synthesis results**

We have implemented the proposed fuzzy logic controller in a CMOS 90nm technology and synthesized it with Cadence RC compiler to measure its power consumption and area. For benchmarking purposes, the synthesis of the circuit is done with different speeds. Synthesis specifications are mentioned in Table 1.

Synthesis and VHDL Implementation of Fuzzy Logic Controller

and Matlab simulation

power consumption and area.

**7. Acknowledgment** 

agreement 363120-427.

**8. References** 

**6. Conclusion** 

for Dynamic Voltage and Frequency Scaling (DVFS) Goals in Digital Processors 201

**Supply Current VHDL Output Matlab Output Current [0:255]**

Fig. 11. Comparison between the tracking results of the implemented VHDL fuzzy circuit

**1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81**

**Time (ms)**

In this chapter, a dynamic fuzzy logic controller based on supply-current variation tracking for dynamic voltage and frequency scaling purposes was proposed. In the proposed method, the fuzzy logic controller decides about changing the supply voltage of the circuit under control by observing and predicting the supply-current variations. The simulation results showed the effectiveness of the proposed configuration in comparison to a PID controller. Furthermore, in this chapter, we described how to implement the proposed controller in VHDL. Also a new method for implementing the defuzzification stage in VHDL was proposed. The synthesized results of the implemented fuzzy controller in a CMOS 90nm technology, using Cadence RC compiler, evaluated in this chapter based on its

This work was supported by the Dutch Technical Science Foundation (STW), under the

Azevedo, A.; Issenin, I.; Cornea, R.; Gupta, R.; Dutt, N.; Veidenbaum, A. & Nicolau, A. (2002).

Benini, L.; Bogliolo, A.; Paleologo, G.A. & De Micheli, G. (1999). Policy optimization for

*Integrated Circuits and Systems,* Vol.28, No.9, pp. 1334-1347.

*Circuits and Systems,* Vol.18, No.6, pp. 813-833.

Profile-Based Dynamic Voltage Scheduling Using Program Checkpoints, *Proceedings of the conference on Design, Automation and Test in Europe (DATE 2002)*, pp. 168-175. Bang, S.; Bang, K.; Yoon, S. & Chung, E.Y. (2009). Run-time adaptive workload estimation

for dynamic voltage scaling, *IEEE Transactions on Computer-Aided Design of* 

dynamic power management, *IEEE Trans. On Computer-Aided Design of Integrated* 


Table 1. Library specification for synthesizing the fuzzy logic controller

The synthesis results are shown in Fig. 10. Since the fuzzy logic controller is a digital controller, its circuit does not consume much power and it does not occupy much area as shown in Fig. 10.

The main differences between the proposed VHDL implementation of the fuzzy controller and the other already implemented VHDL fuzzy controllers (Vuong et al., 2006; Vasantha et al., 2005; Sakthivel et all., 2010; Daijin, 2000) is about the speed of the controller. In the proposed implementation strategy, there are no multiplier and divider circuits used, and also we have considered a fixed slope value for the membership functions. For these reasons, the circuit naturally works faster. Since we have used the memory to store the defuzzification data, it is worth to mention that the power consumption of the proposed circuit is probably higher than previously reported ones.

Fig. 10. Synthesis results of the fuzzy logic controller

As way of example, we test the fuzzy logic circuit with the supply current profile of a processor when it executes a MPEG2-decoding application. The output result of the fuzzy logic circuit implemented in VHDL is shown in Fig. 11. The output signal of the fuzzy controller can accurately track the supply current variations. This output signal can be used to scale and adjust the supply voltage of the processor based on current variations for dynamic voltage scaling goals. Also in Fig. 11, the simulation result of the fuzzy controller implemented in Matlab is presented.

Fig. 11. Comparison between the tracking results of the implemented VHDL fuzzy circuit and Matlab simulation

## **6. Conclusion**

200 Fuzzy Logic – Controls, Concepts, Theories and Applications

**Synthesis and the Library specifications:** 

Frequencies : {20, 40,60,80,100,200,333} MHz

The synthesis results are shown in Fig. 10. Since the fuzzy logic controller is a digital controller, its circuit does not consume much power and it does not occupy much area as

The main differences between the proposed VHDL implementation of the fuzzy controller and the other already implemented VHDL fuzzy controllers (Vuong et al., 2006; Vasantha et al., 2005; Sakthivel et all., 2010; Daijin, 2000) is about the speed of the controller. In the proposed implementation strategy, there are no multiplier and divider circuits used, and also we have considered a fixed slope value for the membership functions. For these reasons, the circuit naturally works faster. Since we have used the memory to store the defuzzification data, it is worth to mention that the power consumption of the proposed

As way of example, we test the fuzzy logic circuit with the supply current profile of a processor when it executes a MPEG2-decoding application. The output result of the fuzzy logic circuit implemented in VHDL is shown in Fig. 11. The output signal of the fuzzy controller can accurately track the supply current variations. This output signal can be used to scale and adjust the supply voltage of the processor based on current variations for dynamic voltage scaling goals. Also in Fig. 11, the simulation result of the fuzzy controller

**20 40 60 80 100 200 333**

**Frequency (MHz)**

**area : 8408um2**

CMOS 90 nm HVT-TSMC Supply Voltage: 1.2 V PVT Typical corner Temperature: 25 degree

Table 1. Library specification for synthesizing the fuzzy logic controller

circuit is probably higher than previously reported ones.

**average area: 7582 um2**

**Power(uw)**

Fig. 10. Synthesis results of the fuzzy logic controller

implemented in Matlab is presented.

shown in Fig. 10.

**0**

**50**

**100**

**150**

**200**

**250**

**300**

In this chapter, a dynamic fuzzy logic controller based on supply-current variation tracking for dynamic voltage and frequency scaling purposes was proposed. In the proposed method, the fuzzy logic controller decides about changing the supply voltage of the circuit under control by observing and predicting the supply-current variations. The simulation results showed the effectiveness of the proposed configuration in comparison to a PID controller. Furthermore, in this chapter, we described how to implement the proposed controller in VHDL. Also a new method for implementing the defuzzification stage in VHDL was proposed. The synthesized results of the implemented fuzzy controller in a CMOS 90nm technology, using Cadence RC compiler, evaluated in this chapter based on its power consumption and area.

## **7. Acknowledgment**

This work was supported by the Dutch Technical Science Foundation (STW), under the agreement 363120-427.

## **8. References**


**10** 

*Republic of Korea* 

**Precision Position Control of Servo** 

Jong Shik Kim, Han Me Kim and Seong Ik Han *School of Mechanical Engineering, Pusan National University,* 

**Systems Using Adaptive Back-Stepping** 

To improve product quality in high-tech industrial fields and in precision product processes, high precision position control systems have been developed. However, high precision position control systems have been faced with a friction problem that exists between the contact surfaces of two materials and produces an obstacle to the precise motion, because the friction is very sensitive to nonlinear time-varying effects such as temperature, lubrication condition, material texture, and contamination degree. Thus, the tracking performance of servo systems can be seriously deteriorated because of the

To overcome the friction problem and to obtain high performance of servo control systems, an appropriate friction model (Olsson, 1998) to describe the nonlinear friction characteristics is required. The LuGre model (Canudas de Wit, 1995) is a representative model. Researchers have used this model because it has a simple structure to be implemented in the design of the controller and can represent most of the friction characteristics except the pre-sliding

Model-based control methods for precision position control can be divided into two methods. The first one is the friction feed-forward compensation scheme, which needs the identification of the nonlinear friction phenomena (Olsson, 1998)(Canudas de Wit, 1995). However, it takes a long time and much effort to identify the nonlinear friction. In addition, even with successful completion of the friction identification process, it is difficult to achieve desirable tracking performance due to the nonlinear friction characteristics. Therefore, to achieve desirable tracking performance of servo systems, a robust control scheme should be

The second method is the real time estimation scheme for nonlinear friction coefficients, which is called as the adaptive friction control scheme. This method can actively cope with the variation of the nonlinear friction, which has been proved and studied through experiments (Canudas de Wit, 1997)(Lischinsky, 1999)(Ha, 2000)(Tan, 1999). However, to generate the adaptation rules for the friction coefficients based on the LuGre friction model, a detailed mathematical approach is required. In addition, since the mathematical model of

used simultaneously with the friction feed-forward compensator (Lee, 2004).

**1. Introduction** 

characteristic.

nonlinear friction characteristics.

**and Recurrent Fuzzy Neural Networks** 


## **Precision Position Control of Servo Systems Using Adaptive Back-Stepping and Recurrent Fuzzy Neural Networks**

Jong Shik Kim, Han Me Kim and Seong Ik Han *School of Mechanical Engineering, Pusan National University, Republic of Korea* 

## **1. Introduction**

202 Fuzzy Logic – Controls, Concepts, Theories and Applications

Chung, E.Y.; De Micheli, G. & Benini, L. (2002). Contents provider-assisted dynamic voltage

Gutnik, V. & Chandrakasan, A.P. (1997). Embedded power supply for low-power DSP, *IEEE* 

Hughes, C.J. & Adve, S.V. (2003). A formal approach to frequent energy adaptations for multimedia applications, in *Proc. Int. Conf. Comput. Des.*, pp. 489–496. Im, C.; Kim, H. & Ha, S. (2006). Dynamic voltage scheduling technique for low-power

Jejurikar, R. & Gupta, R. (2006). Energy-aware task scheduling with task synchronization for

Lee, C.-C., (1990) Fuzzy Logic in Control Systems: Fuzzy Logic Controller-Parts 1 and 2, *IEEE Trans.on Systems, Man, and Cybernetics*, Vol.20, No.2, pp. 404-435. Lu, Z.; Hein, J.; Humphrey, M.; Stan, M.; Lach, J. & Skadron, K. (2002). Control-theoretic

Lu, Z.; Lach, J.; Stan, M. & Skadron, K. (2003). Reducing multimedia decode power using

Nielsen, L.S.; Nielssen, C.; Sparsø, J. & Van Berkel, K. (1994). Low-power operation using

Pourshaghaghi, H.R. & Pineda de Gyvez, J., (2009). Dynamic Voltage Scaling Based on

Sakthivel, G.; Anandhi, T.S. & Natarajan, S.P. (2010) Real time implementation of a fuzzy

Vasantha Rani, S.P.J.; Kanagasabapathy, P. & Sathish Kumar, A. (2005). Digital Fuzzy Logic

Vuong, P.T.; Madni, A.M. & Vuong, J.B. (2006). VHDL implementation for a fuzzy logic

Wei, G. & Horowitz, M. (1999). A fully digital energy-efficient adaptive power supply regulator, *IEEE Journal of solid-state Circuits*, Vol.34, No.4, pp. 520-528. Wu, Q.; Juang, P.; Martonosi, M. & Clark, D.W. (2005). Formal control techniques for power-

Yang, P.; Wong, C.; Marchal, P.; Catthoor, F.; Desmet, D.; Verkest, D. & Lauwereins, R.

Yao, F.; Demers, A. & Shenker, S. A. (1995). Scheduling model for reduced CPU energy,

(2001). Energy-Aware Runtime Scheduling for Embedded-Multiprocessor SOCs,

*Journal of Engineering Science and Technology,* Vol.2, No.9, pp. 4511-4519. Sinha, A. & Chandrakasan, A.P. (2001). Dynamic voltage scheduling using adaptive filtering

*Conf. on Electronics, Circuits, and Systems, (ICECS 2009),* pp. 779-782.

Rabaey J, (2010) *Low Power Design Essentials*. Springer, pp. 249-288.

Controller using VHDL, *INDICON2005,* pp. 463-466.

*IEEE Design & Test*, Vol.18, No.5, pp.46-58.

*Proc. Found. Comput. Sci.,* pp. 374-382.

controller, *Automation Congress, 2006. WAC '06. World,* pp. 1-8.

performance management, *IEEE Micro*, Vol.25, No.5, pp. 52–62.

embedded real-time systems*, IEEE Trans. Comput.- Aided Design Integr. Circuits* 

dynamic frequency and voltage scaling for multimedia workloads, in *Proc. Int.* 

self-timed circuits and adaptive scaling of the supply voltage, *IEEE Trans. VLSI* 

Supply Current Tracking Using Fuzzy Logic Controller, *Proc. of the 16th IEEE Int.* 

logic controller on FPGA using VHDL for DC-Motor speed control, *International* 

of workload traces, *Proc. of the 14th International Conference on VLSI Design (VLSID* 

multimedia applications using buffers, *Proc. ISLPED,* pp. 34-39.

*Conf. Compilers, Architecture, Synthesis Embed. Syst.*, pp. 156–163.

feedback control, in *Proc. Int. Conf. Comput. Des.*, pp. 489–496.

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*'01)*, pp.221-226.

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scaling for low energy multimedia applications, *Proc. of the 2002 international symposium on Low power electronics and design*, Monterey, California, USA, pp. 42-47. Daijin, K. (2000) An Implementation of Fuzzy Logic Controller on the Reconfigurable FPGA System, *IEEE Transactions on Industrial Electronic*, Vol.47, No.3, pp. 703 – 715. Gu, Y. & Chakraborty, S., (2008). Control theory-based DVS for interactive 3D games, in

> To improve product quality in high-tech industrial fields and in precision product processes, high precision position control systems have been developed. However, high precision position control systems have been faced with a friction problem that exists between the contact surfaces of two materials and produces an obstacle to the precise motion, because the friction is very sensitive to nonlinear time-varying effects such as temperature, lubrication condition, material texture, and contamination degree. Thus, the tracking performance of servo systems can be seriously deteriorated because of the nonlinear friction characteristics.

> To overcome the friction problem and to obtain high performance of servo control systems, an appropriate friction model (Olsson, 1998) to describe the nonlinear friction characteristics is required. The LuGre model (Canudas de Wit, 1995) is a representative model. Researchers have used this model because it has a simple structure to be implemented in the design of the controller and can represent most of the friction characteristics except the pre-sliding characteristic.

> Model-based control methods for precision position control can be divided into two methods. The first one is the friction feed-forward compensation scheme, which needs the identification of the nonlinear friction phenomena (Olsson, 1998)(Canudas de Wit, 1995). However, it takes a long time and much effort to identify the nonlinear friction. In addition, even with successful completion of the friction identification process, it is difficult to achieve desirable tracking performance due to the nonlinear friction characteristics. Therefore, to achieve desirable tracking performance of servo systems, a robust control scheme should be used simultaneously with the friction feed-forward compensator (Lee, 2004).

> The second method is the real time estimation scheme for nonlinear friction coefficients, which is called as the adaptive friction control scheme. This method can actively cope with the variation of the nonlinear friction, which has been proved and studied through experiments (Canudas de Wit, 1997)(Lischinsky, 1999)(Ha, 2000)(Tan, 1999). However, to generate the adaptation rules for the friction coefficients based on the LuGre friction model, a detailed mathematical approach is required. In addition, since the mathematical model of

Precision Position Control of Servo Systems

Fig. 2. Friction interfaces with bristles between two surfaces

variable *z* as follows (Canudas de Wit, 1997) :

is the generalized velocity, *st*

Also, the friction torque *Tf* was represented as

independent unknown positive constants.

system with friction can be expressed as

of the position servo system, the coefficients

where

and 

where

0 , <sup>1</sup> , and


be represented by bristles.

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 205

The LuGre model is used for modeling the friction in the position servo system. The LuGre model can describe the nonlinear friction characteristics between two contact surfaces in a mechanical system. As shown in Fig. 2, the relative motion between two contact surfaces can

The stiffness and damping of bristles can be modeled with springs and dampers, respectively. Canudas de Wit represented the average deflection of bristles by a state

> <sup>0</sup> *z hz*

> > *g*

<sup>2</sup> (/ ) () ( ) *st c sc g T T Te*

friction parameter, *Ts* is the static friction torque, and *Tc* is the Coulomb friction torque.

viscous damping coefficient, respectively. The function *g*( ) is assumed to be known and to be a positive value, and it depends on some factors such as material properties and temperature. In order to consider the friction torque variations due to the contact condition

Substituting Eqs. (2), (3), and (4) into Eq. (1), the dynamic equation for the position servo

012 

*T zz <sup>f</sup>* 

 

is the Stribeck velocity,

 

0 , <sup>1</sup> , and

<sup>2</sup> are the bristle stiffness coefficient, bristle damping coefficient, and

*h*

( ), (2)

(3)

(4)

0 is the nominal static

2 are assumed to be

the nonlinear friction may include system uncertainties such as unmodeled dynamics, which can cause an undesirable position tracking error of servo systems.

To compensate these system uncertainties and to improve tracking performance, artificial intelligent algorithms such as fuzzy logic and neural networks have been applied because of their advantages to cope with system uncertainties (Wai, 2003)(Leu, 1997)(Peng, 2007)(Lin, 2006). In general, fuzzy logic and neural network algorithms are effective in inferring ambiguous information because of their logicality such as adaptation for learning ability, capacity for experiences, and parallel process ability (Lin, 1996). The fuzzy neural network(FNN) combining the advantages of fuzzy logic and neural network algorithms was presented (Leu, 1997)(Peng, 2007). However, in real applications, the FNN has a static problem due to its feed-forward network characteristics. Therefore, to overcome this static problem of the FNN, the recurrent fuzzy neural network(RFNN) with robust characteristics due to its feed-back structure was presented (Peng, 2007)(Lin, 2006)(Lin, 2004).

In this paper, an adaptive back-stepping control scheme with the RFNN technique is proposed so that servo systems with nonlinear friction uncertainties can achieve higher precision position tracking performance. A dual adaptive friction observer is also designed to observer the internal states of the nonlinear friction model. The position tracking performance of the proposed control system is evaluated through experiments.

The organization of this paper is as follows: In section 2, the dynamic equations for the position servo system with the LuGre friction model are described. In section 3, to estimate the unknown friction coefficients and to overcome system uncertainties in a position servo system, the adaptive back-stepping controller based on the dual friction observer and the recurrent fuzzy neural networks are designed. In section 4, the experimental results of the tracking performance, the observation of the states, and the estimation of the friction coefficients are shown. Finally, the conclusion is given in section 5.

## **2. Modeling of a position servo system**

The layout of a position servo system consists of mass, linear motion guide, ball-screw, and servo motor as shown in Fig. 1. The dynamic equation for the position servo system can be briefly represented as

$$\mathbf{J}\ddot{\boldsymbol{\theta}} = \boldsymbol{\mu} - \mathbf{T}\_f - \mathbf{T}\_d \tag{1}$$

where *J* is the moment of inertia of the servo system, is the angular acceleration of the screw, *u* is the control input torque, *Tf* is the friction torque, and *Td* is the disturbance torque due to system uncertainties.

Fig. 1. Layout of the position servo system

The LuGre model is used for modeling the friction in the position servo system. The LuGre model can describe the nonlinear friction characteristics between two contact surfaces in a mechanical system. As shown in Fig. 2, the relative motion between two contact surfaces can be represented by bristles.

Fig. 2. Friction interfaces with bristles between two surfaces

The stiffness and damping of bristles can be modeled with springs and dampers, respectively. Canudas de Wit represented the average deflection of bristles by a state variable *z* as follows (Canudas de Wit, 1997) :

$$\dot{z} = \dot{\theta} - \sigma\_0 h(\dot{\theta}) z\_\prime \tag{2}$$

$$h(\dot{\theta}) = \frac{|\dot{\theta}|}{\mathcal{g}(\dot{\theta})} \tag{3}$$

where

204 Fuzzy Logic – Controls, Concepts, Theories and Applications

the nonlinear friction may include system uncertainties such as unmodeled dynamics,

To compensate these system uncertainties and to improve tracking performance, artificial intelligent algorithms such as fuzzy logic and neural networks have been applied because of their advantages to cope with system uncertainties (Wai, 2003)(Leu, 1997)(Peng, 2007)(Lin, 2006). In general, fuzzy logic and neural network algorithms are effective in inferring ambiguous information because of their logicality such as adaptation for learning ability, capacity for experiences, and parallel process ability (Lin, 1996). The fuzzy neural network(FNN) combining the advantages of fuzzy logic and neural network algorithms was presented (Leu, 1997)(Peng, 2007). However, in real applications, the FNN has a static problem due to its feed-forward network characteristics. Therefore, to overcome this static problem of the FNN, the recurrent fuzzy neural network(RFNN) with robust characteristics

In this paper, an adaptive back-stepping control scheme with the RFNN technique is proposed so that servo systems with nonlinear friction uncertainties can achieve higher precision position tracking performance. A dual adaptive friction observer is also designed to observer the internal states of the nonlinear friction model. The position tracking

The organization of this paper is as follows: In section 2, the dynamic equations for the position servo system with the LuGre friction model are described. In section 3, to estimate the unknown friction coefficients and to overcome system uncertainties in a position servo system, the adaptive back-stepping controller based on the dual friction observer and the recurrent fuzzy neural networks are designed. In section 4, the experimental results of the tracking performance, the observation of the states, and the estimation of the friction

The layout of a position servo system consists of mass, linear motion guide, ball-screw, and servo motor as shown in Fig. 1. The dynamic equation for the position servo system can be

*<sup>f</sup> <sup>d</sup> J uT T*

screw, *u* is the control input torque, *Tf* is the friction torque, and *Td* is the disturbance

(1)

is the angular acceleration of the

which can cause an undesirable position tracking error of servo systems.

due to its feed-back structure was presented (Peng, 2007)(Lin, 2006)(Lin, 2004).

performance of the proposed control system is evaluated through experiments.

coefficients are shown. Finally, the conclusion is given in section 5.

**2. Modeling of a position servo system** 

where *J* is the moment of inertia of the servo system,

briefly represented as

torque due to system uncertainties.

Fig. 1. Layout of the position servo system

$$\lg(\dot{\theta}) = T\_c + (T\_s - T\_c)e^{-(\theta/\vartheta\_{st})^2}$$

and is the generalized velocity, *st* is the Stribeck velocity, 0 is the nominal static friction parameter, *Ts* is the static friction torque, and *Tc* is the Coulomb friction torque. Also, the friction torque *Tf* was represented as

$$T\_f = \mu\_0 z + \mu\_1 \dot{z} + \mu\_2 \dot{\theta} \tag{4}$$

where 0 , <sup>1</sup> , and <sup>2</sup> are the bristle stiffness coefficient, bristle damping coefficient, and viscous damping coefficient, respectively. The function *g*( ) is assumed to be known and to be a positive value, and it depends on some factors such as material properties and temperature. In order to consider the friction torque variations due to the contact condition of the position servo system, the coefficients 0 , <sup>1</sup> , and 2 are assumed to be independent unknown positive constants.

Substituting Eqs. (2), (3), and (4) into Eq. (1), the dynamic equation for the position servo system with friction can be expressed as

Precision Position Control of Servo Systems

The derivative of 2 *y* can be obtained as

the LCF for Eq. (11) is selected as

The derivative of *V*2 can be represented as

If the last term in Eq. (14) is defined as

a large steady-state error may occur.

selected as

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 207

2 1 *y* 

2 1 03 4 1

From Eq. (12), in order to select a feedback control law that can guarantee system stability,

21 2 1 . 2

2 1 22 11 2 1 03 4 1 <sup>1</sup> [ ( ( ) ) ]. *V V yy ky y y u z h z Td <sup>J</sup>* 

1 03 4 1 22

where 2 *k* ( 0) is a design parameter, then the BSC law as the feedback control law can be

1 22 1 0 3 4 ( ) () . *u J y ky z h z T*

However, in Eq. (16), the internal state *z* of the friction model cannot be measured, and friction parameters and the disturbance torque *Td* cannot be known exactly. In addition, if the friction terms in Eq. (16) cannot be exactly considered in position control servo systems,

In order to select a desired control law, a dual-observer (Tan, 1999) to estimate the

0 0 00 *z hz* ˆ ˆ

1 0 11 *z hz* ˆ ˆ

 

 

 

 

**3.2 Design of adaptive back-stepping controller and dual friction observer** 

unmeasurable internal state *z* in the friction model is applied as follows:

 

( () ) *<sup>d</sup> <sup>y</sup> u z hz T k <sup>y</sup> <sup>J</sup>* 

2

  

(14)

 

 *<sup>d</sup>* (16)

() , (17)

() , (18)

   

(12)

( () ) . *<sup>d</sup> y u z hz T <sup>J</sup>* 

  . (11)

 

*V V y* (13)

 

(15)

 

Step 2. The velocity tracking error is defined by the new state 2 *y* as

1

2

 

1

 

$$\mathbf{J}\ddot{\boldsymbol{\theta}} = \mathbf{u} - \mu\_0 \mathbf{z} + \mu\_3 \mathbf{h}(\dot{\boldsymbol{\theta}}) \mathbf{z} - \mu\_4 \dot{\boldsymbol{\theta}} - \mathbf{T}\_d \tag{5}$$

where

$$
\mu\_3 = \sigma\_0 \mu\_1 \quad \mu\_4 = \mu\_1 + \mu\_2 \dots
$$

#### **3. Design of an adaptive control system**

System uncertainties such as high nonlinear friction characteristics according to the operation condition should be considered in precise position servo systems. Thus, feedback linearization and robust control schemes can be considered to reject system nonlinearity and have robustness to unmodeled dynamics, respectively. However, the robust control schemes may not be appropriate for precise position control because these schemes require some premises on bounded uncertainties and bounded disturbance. In addition, if the information on system uncertainties is not included in the control scheme, the feedback linearization scheme may not achieve high precision position tracking performance and make servo systems unstabilize. To overcome these problems in position control servo systems, it is desirable to apply an adaptive control scheme.

#### **3.1 Design of back-stepping controller**

The back-stepping control(BSC) system can be designed step by step as follows (Krstic, 1995):

Step 1. To achieve the desired tracking performance, the tracking error is defined by the new state 1 *y* as

$$y\_1 = \theta - \theta\_r \tag{6}$$

where *<sup>r</sup>* is the reference input. The derivative of 1 *y* is expressed as

$$
\dot{y}\_1 = \dot{\theta} - \dot{\theta}\_r. \tag{7}
$$

We define a stabilizing function 1 as

$$
\alpha\_1 = \dot{\theta}\_r - k\_1 y\_1 \tag{8}
$$

where 1 *k* is a positive constant. The Lyapunov control function (LCF) *V*1 is selected as

$$V\_1 = \frac{1}{2} y\_1^2 \tag{9}$$

Then, the derivative of *V*1 is expressed as

$$\dot{V}\_{\ 1} = y\_1 \dot{y}\_1 = y\_1(\dot{\theta} - \alpha\_1 - k\_1 y\_1) = y\_1 y\_2 - k\_1 y\_1^2 \tag{10}$$

where 2 1 *y* . Step 2. The velocity tracking error is defined by the new state 2 *y* as

$$y\_2 = \dot{\theta} - \alpha\_1. \tag{11}$$

The derivative of 2 *y* can be obtained as

206 Fuzzy Logic – Controls, Concepts, Theories and Applications

03 4 ( ) *<sup>d</sup> J u z hz T*

System uncertainties such as high nonlinear friction characteristics according to the operation condition should be considered in precise position servo systems. Thus, feedback linearization and robust control schemes can be considered to reject system nonlinearity and have robustness to unmodeled dynamics, respectively. However, the robust control schemes may not be appropriate for precise position control because these schemes require some premises on bounded uncertainties and bounded disturbance. In addition, if the information on system uncertainties is not included in the control scheme, the feedback linearization scheme may not achieve high precision position tracking performance and make servo systems unstabilize. To overcome these problems in position control servo systems, it is

The back-stepping control(BSC) system can be designed step by step as follows (Krstic,

Step 1. To achieve the desired tracking performance, the tracking error is defined by the new

<sup>1</sup> *<sup>r</sup> y* 

<sup>1</sup> .*<sup>r</sup> y* 

1 11 *r*

1 11 1 1 11 12 11 *V yy y* ( ) 

2 1 1 1

*<sup>r</sup>* is the reference input. The derivative of 1 *y* is expressed as

 

where 1 *k* is a positive constant. The Lyapunov control function (LCF) *V*1 is selected as

1 as

 

<sup>412</sup> .

(5)

(6)

(7)

*k y* (8)

<sup>2</sup> *V y* (9)

2

*k y yy k y* (10)

 

**3. Design of an adaptive control system** 

desirable to apply an adaptive control scheme.

**3.1 Design of back-stepping controller** 

We define a stabilizing function

Then, the derivative of *V*1 is expressed as

where 2 1 *y* . 3 01 , 

where

1995):

where 

state 1 *y* as

 

$$
\dot{y}\_2 = \ddot{\theta} - \dot{\alpha}\_1 = \frac{1}{l}(\mu - \mu\_0 z + \mu\_3 h(\dot{\theta}) z - \mu\_4 \dot{\theta} - T\_d) - \dot{\alpha}\_1. \tag{12}
$$

From Eq. (12), in order to select a feedback control law that can guarantee system stability, the LCF for Eq. (11) is selected as

$$V\_2 = V\_1 + \frac{1}{2}y\_2^2. \tag{13}$$

The derivative of *V*2 can be represented as

$$\dot{V}\_2 = \dot{V}\_1 + y\_2 \dot{y}\_2 = -k\_1 y\_1^2 + y\_2 [y\_1 + \frac{1}{J}(\mu - \mu\_0 z + \mu\_3 h(\dot{\theta})z - \mu\_4 \dot{\theta} - T\_d) - \dot{\alpha}\_1].\tag{14}$$

If the last term in Eq. (14) is defined as

$$\dot{y}\_1 + \frac{1}{l}(\mu - \mu\_0 z + \mu\_3 h(\dot{\theta})z - \mu\_4 \dot{\theta} - T\_d) - \dot{\alpha}\_1 = -k\_2 y\_2 \tag{15}$$

where 2 *k* ( 0) is a design parameter, then the BSC law as the feedback control law can be selected as

$$
\mu = \mathbf{J}(-y\_1 - k\_2 y\_2 + \dot{\alpha}\_1) + \mu\_0 z - \mu\_3 \mathbf{h}(\dot{\theta}) z + \mu\_4 \dot{\theta} + T\_d. \tag{16}
$$

However, in Eq. (16), the internal state *z* of the friction model cannot be measured, and friction parameters and the disturbance torque *Td* cannot be known exactly. In addition, if the friction terms in Eq. (16) cannot be exactly considered in position control servo systems, a large steady-state error may occur.

#### **3.2 Design of adaptive back-stepping controller and dual friction observer**

In order to select a desired control law, a dual-observer (Tan, 1999) to estimate the unmeasurable internal state *z* in the friction model is applied as follows:

$$
\dot{\hat{z}}\_0 = \dot{\theta} - \sigma\_0 h(\dot{\theta}) \hat{z}\_0 + \eta\_{0\prime} \tag{17}
$$

$$
\dot{\hat{z}}\_1 = \dot{\theta} - \sigma\_0 \ln(\dot{\theta}) \hat{z}\_1 + \eta\_{1\prime} \tag{18}
$$

Precision Position Control of Servo Systems

The derivative of *V*4 can be obtained as

4

 

 

 

From Eq. (27), the update laws can be determined as

and the observer dynamic terms are expressed as

Then, Eq. (27) can be represented as

Eq. (35), then

From Eq. (34), we can define *W y*( ) as follows:

*VV z z* 

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 209

4 3 00 31 0 3 4

22 2 2 2 2 4 11 22 0 0 0 3 0 1 0 0 0 3 1 3

*<sup>y</sup> y h V ky ky h z h z z <sup>z</sup>*

2 22 2

1 1 <sup>ˆ</sup> ( <sup>ˆ</sup> ) ( ) ( ( ) ) ( ).

*y yy y z zh E E J JJ J*

> 0 0 20 <sup>ˆ</sup> *<sup>y</sup> <sup>z</sup>*<sup>ˆ</sup> , *<sup>J</sup>*

> >

4 4 2 <sup>ˆ</sup> *<sup>y</sup>* , *<sup>J</sup>* 

> 2 <sup>0</sup> , *<sup>y</sup> J*

2 <sup>1</sup> ( ), *<sup>y</sup> <sup>h</sup> J*

<sup>ˆ</sup> <sup>2</sup> . *<sup>y</sup> <sup>E</sup> <sup>J</sup>* 

22 2 2 22 4 11 22 0 0 0 3 0 1 11 22 *V ky ky h z h z ky ky*

 () () 0. (34)

Since *V* 0 , *V* is a non-increasing function. Thus, it has a limit *V* as *t* . Integrating

3 3 21 <sup>ˆ</sup> *<sup>y</sup> h z* () , <sup>ˆ</sup> *<sup>J</sup>* 

 

> 

4 4 0 0 00 1 3 3 1

 

 

 

  22 2 2 2

11 1 1 1 . 222 2 2

034

1 1 ( ) () () ( ˆ ˆ ˆ ˆ ) ( )

 

*J J*

(28)

(29)

(30)

(31)

(33)

11 22 1 2 *Wy k y ky Vy y* ( ) (,) (35)

(32)

 

(26)

0 3

  (27)

 

where 0*z*ˆ and 1*z*ˆ are the estimated values of the internal states in the friction model, and 0 and 1 are the observer dynamic terms which can be obtained from an adaptive rule. The corresponding observation errors are given by

$$\dot{\tilde{z}}\_0 = -\sigma\_0 \hbar (\dot{\theta}) \tilde{z}\_0 - \eta\_{0'} \tag{19}$$

$$
\dot{\tilde{z}}\_1 = -\sigma\_0 h(\dot{\theta}) \tilde{z}\_1 - \eta\_{1'} \tag{20}
$$

where 0 0 *z zz* ˆ and 1 1 *z zz* ˆ . Equations (19) and (20) will be induced from the adaptive rule.

In order to induce the adaptive rule to guarantee stability against unknown parameters and the observer dynamic terms, the reconstruction error *E* is defined as

$$E = T\_d - \hat{T}\_d \tag{21}$$

where ˆ *Td* is the estimated value of *Td* and it is assumed that *E E* , where *E* denotes the bounded value of *E* .

We now select the 3rd LCF as follows:

$$V\_3 = V\_2 + \frac{1}{2\rho}(\hat{E} - E)^2\tag{22}$$

where ( 0) is a positive constant and ˆ *E* is the estimated value of the reconstruction error. The derivative of *V*3 can be represented as

$$\dot{V}\_3 = \dot{V}\_2 + \frac{1}{\rho}(\hat{E} - E)\dot{\hat{E}} = -k\_1 y\_1^2 + y\_2 \left[ y\_1 + \frac{1}{l}(\mu - \mu\_0 z + \mu\_3 h(\dot{\theta})z - \mu\_4 \dot{\theta} - T\_d) - \dot{\alpha}\_1 \right] + \frac{1}{\rho}(\hat{E} - E)\dot{\hat{E}} \tag{23}$$

From Eq. (23), the adaptive back-stepping control(ABSC) law can be selected as

$$
\hat{\mu} = \mathbf{J}(-y\_1 - k\_2 y\_2 + \dot{\alpha}\_1) + \hat{\mu}\_0 \hat{z}\_0 - \hat{\mu}\_3 \hbar (\dot{\theta}) \hat{z}\_1 + \hat{\mu}\_4 \dot{\theta} + \hat{T}\_d + \hat{E} \tag{24}
$$

Substituting Eq. (24) into Eq. (23), then

$$\dot{V}\_3 = -k\_1 y\_1^2 - k\_2 y\_2^2 + \frac{y\_2}{\rho} [-\mu\_0 \tilde{z}\_0 - \tilde{\mu}\_0 \hat{\boldsymbol{z}}\_0 + \mu\_3 \ln(\dot{\theta}) \tilde{z}\_1 + \tilde{\mu}\_3 \ln(\dot{\theta}) \hat{\boldsymbol{z}}\_1 - \tilde{\mu}\_4 \dot{\theta}) + \hat{T}\_d - T\_d + \dot{\hat{E}}] + \frac{1}{\rho} (\hat{\mathbf{E}} - \mathbf{E}) \dot{\hat{\mathbf{E}}} \tag{25}$$

where 000 ˆ , 333 ˆ , and 444 ˆ are the unknown parameter estimate errors. The 4th LCF *V*4 is selected as

$$V\_4 = V\_3 + \frac{1}{2}\mu\_0\tilde{z}\_0^2 + \frac{1}{2}\mu\_3\tilde{z}\_1^2 + \frac{1}{2\gamma\_0}\tilde{\mu}\_0^2 + \frac{1}{2\gamma\_3}\tilde{\mu}\_3^2 + \frac{1}{2\gamma\_4}\tilde{\mu}\_4^2. \tag{26}$$

The derivative of *V*4 can be obtained as

208 Fuzzy Logic – Controls, Concepts, Theories and Applications

1 are the observer dynamic terms which can be obtained from an adaptive rule. The

 () , 

 () , 

 

 

(19)

(20)

<sup>ˆ</sup> *ET T d d* (21)

(22)

*E* is the estimated value of the reconstruction error.

 

ˆ are the unknown parameter estimate

 

0

where 0*z*ˆ and 1*z*ˆ are the estimated values of the internal states in the friction model, and

0 0 00 *z hz* 

1 0 11 *z hz* 

where 0 0 *z zz* ˆ and 1 1 *z zz* ˆ . Equations (19) and (20) will be induced from the adaptive

In order to induce the adaptive rule to guarantee stability against unknown parameters and

*Td* is the estimated value of *Td* and it is assumed that *E E* , where *E* denotes the

<sup>1</sup> <sup>ˆ</sup> ( ) <sup>2</sup>

2

the observer dynamic terms, the reconstruction error *E* is defined as

3 2

3 2 11 2 1 03 4 1

From Eq. (23), the adaptive back-stepping control(ABSC) law can be selected as

 

 

*J*

*V V EE* 

11 1 ˆ ˆ ˆ ˆ ( ) [ ( () ) ] ( ) *V V E EE k <sup>d</sup> y yy u z h z T E EE*

1 2 2 1 00 3 1 4 ˆ ˆ ( ) () ˆˆ ˆ ˆ ˆ *u J y ky z h z T E*

 

(25)

*<sup>y</sup> V k <sup>y</sup> <sup>k</sup> <sup>y</sup> z z h z h z T T E E EE*

 ˆ , and 444 

(23)

 

<sup>1</sup> ˆ ˆ ˆˆ [ ˆ ˆ () () ) ] ( ) *d d*

 

 *<sup>d</sup>* (24)

 

and 

rule.

where ˆ

where 

bounded value of *E* .

We now select the 3rd LCF as follows:

( 0) is a positive constant and ˆ

2

3 11 2 2 00 00 3 1 3 1 4

 

The derivative of *V*3 can be represented as

Substituting Eq. (24) into Eq. (23), then

*J* 

errors. The 4th LCF *V*4 is selected as

ˆ , 333 

2 2 2

where 000 

corresponding observation errors are given by

$$\begin{split} \dot{V}\_{4} &= -k\_{1}y\_{1}^{2} - k\_{2}y\_{2}^{2} - \mu\_{0}\sigma\_{0}h(\dot{\theta})\hat{z}\_{0}^{2} - \mu\_{3}\sigma\_{0}h(\dot{\theta})\hat{z}\_{1}^{2} + \tilde{\mu}\_{0}(-\frac{y\_{2}}{l}\hat{z}\_{0} - \frac{1}{\chi\_{0}}\dot{\mu}\_{0}) + \tilde{\mu}\_{3}(\frac{y\_{2}h(\dot{\theta})}{l}\hat{z}\_{1} - \frac{1}{\chi\_{3}}\dot{\mu}\_{3}) \\ &+ \tilde{\mu}\_{4}(-\frac{y\_{2}}{l}\dot{\theta} - \frac{1}{\chi\_{4}}\dot{\mu}\_{4}) + \tilde{z}\_{0}(-\mu\_{0}\frac{y\_{2}}{l} - \mu\_{0}\eta\_{0}) + \tilde{z}\_{1}(\mu\_{3}\frac{y\_{2}}{l}h(\dot{\theta}) - \mu\_{3}\eta\_{1}) + \tilde{E}(\frac{y\_{2}}{l} + \frac{1}{\rho}\dot{\bar{E}}). \end{split} \tag{27}$$

From Eq. (27), the update laws can be determined as

$$
\dot{\mu}\_0 = -\frac{\mathcal{Y}\_0}{J} y\_2 \hat{z}\_{0'} \tag{28}
$$

$$
\dot{\hat{\mu}}\_3 = \frac{\mathcal{Y}\_3}{\mathcal{Y}} y\_2 h(\dot{\theta}) \hat{z}\_1. \tag{29}
$$

$$
\dot{\hat{\mu}}\_4 = -\frac{\mathcal{Y}\_4}{J} y\_2 \dot{\theta}\_{\prime} \tag{30}
$$

and the observer dynamic terms are expressed as

$$
\eta\_0 = -\frac{y\_2}{J},
\tag{31}
$$

$$
\eta\_1 = \frac{y\_2}{l} h(\dot{\theta}),
\tag{32}
$$

$$
\dot{\hat{E}} = -\rho \frac{y\_2}{\mathcal{J}}.\tag{33}
$$

Then, Eq. (27) can be represented as

$$\dot{V}\_4 = -k\_1 y\_1^2 - k\_2 y\_2^2 - \mu\_0 \sigma\_0 \hbar (\dot{\theta}) \tilde{z}\_0^2 - \mu\_3 \sigma\_0 \hbar (\dot{\theta}) \tilde{z}\_1^2 \le -k\_1 y\_1^2 - k\_2 y\_2^2 \le 0. \tag{34}$$

From Eq. (34), we can define *W y*( ) as follows:

$$\mathcal{W}(y) = k\_1 y\_1 + k\_2 y\_2 \le -\dot{V}(y\_{1'}, y\_2) \tag{35}$$

Since *V* 0 , *V* is a non-increasing function. Thus, it has a limit *V* as *t* . Integrating Eq. (35), then

Precision Position Control of Servo Systems

where <sup>1</sup>

iterations.

For the *j* th node,

where *mij* and

where <sup>3</sup>

with the kth rule. <sup>4</sup>

**3.3.2 On-line learning algorithm** 

term of the ith input linguistic variable <sup>2</sup>

1 1 *x y* , <sup>1</sup>

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 211

*Layer 2, Membership layer*: For each node, the Gaussian membership values are calculated.

( ) net ( ) ( )

*Layer 3, Rule layer*: Each node k in this layer is denoted by ∏. In addition, the input signals in

<sup>3</sup> 3 3 net ( ) ( ), *<sup>k</sup> jk j j*

membership layer and the rule layer. ( / )*<sup>i</sup> l ni* is the number of rules with complete rule

*Layer 4, Output layer*: The single node o in this layer is labeled as , which computes the

<sup>4</sup> 4 4 net ( ) ( ), *<sup>o</sup> ko k k*

where the connecting weight <sup>4</sup> *wko* is the output action strength of the oth output associated

In the learning algorithm, it is important to select parameters for the membership functions and weights to decide network performance. In order to train the RFNN effectively, on-line

*<sup>k</sup> <sup>x</sup>* represents the kth input to the node of layer 4, and <sup>4</sup> <sup>ˆ</sup> *o d <sup>y</sup> <sup>T</sup>* .

*<sup>j</sup> x* represents the jth input to the node of layer 3, <sup>3</sup> *wjk* is the weights between the

this layer are multiplied each other and then the result of the product is generated.

2

*N*

*j*

number of the linguistic variables with respect to the input nodes.

connection, if each input node has the same linguistic variables.

overall output as the summation of all input signals:

1 1 11 net ( 1), *i i ii x w yN* (38)

(40)

*<sup>i</sup> x* to the node of layer 2, respectively. *n* is the total

*N wx N* (42)

*N wx N* (44)

4 44 4 ( ) (net ( )) net ( ) *o oo o y N f N N* (45)

1 11 1 ( ) (net ( )) net ( ), 1, 2 *i ii i yN f N Ni* (39)

<sup>2</sup> *x y* , <sup>1</sup> *wi* is the recurrent weights, and *N* denotes the number of

2 2

*i ij*

*x m*

*ij*

2

*ij* are the mean and standard deviation of the Gaussian function in the jth

2 22 <sup>2</sup> ( ) (net ( )) exp(net ( )), 1,..., *j jj <sup>j</sup> y N f N Nj n* (41)

3 33 3 ( ) (net ( )) net ( ), 1, ... , *k kk k y N f N Nk l* (43)

$$\lim\_{t \to \infty} \int\_{t\_0}^t \mathcal{W}(y(\tau))d\tau \le -\lim\_{t \to \infty} \int\_{t\_0}^t \dot{V}(y\_1, y\_2)d\tau = \lim\_{t \to \infty} \left\{ V(y(t\_0), t\_0) - V(y(t), t) \right\} = V(y(t\_0), t\_0) - V\_{\infty} \tag{36}$$

which means that 0 ( ( )) *<sup>t</sup> <sup>t</sup> Wy d* exists and is finite. Since *W y*( ) is also uniformly continuous, the following result can be obtained from Barbalat lemma (Krstic, 1995)(Slotine, 1991) as

$$\lim\_{t \to \ast \ast} \mathcal{W}(y) = 0.\tag{37}$$

Since 1 *y* and 2 *y* are converged to zero as *t* , and approach to *r* and *r* , respectively, as *t* . Therefore, the ABSC system can be asymptotically stable in spite of the variation of system parameters and external disturbance.

#### **3.3 Design of recurrent fuzzy neural networks**

To determine the lumped uncertainty *Td* , a RFNN observer of a 4-layer structure is proposed, which is shown in Fig. 3. Layer 1 is the input layer with the recurrent loop, which accepts the two input variables. Layer 2 represents the fuzzy rules for calculating the Gaussian membership values. Layer 3 is the rule layer, which represents the preconditions and consequence for the links before and after layer 3, respectively. Layer 4 is the output layer. The interaction and learning algorithms for the layers are given as follows:

Fig. 3. A general four-layer RFNN

#### **3.3.1 Description of the RFNN**

*Layer 1, Input layer*: For each node i, the net input and output are represented, respectively, as

 (36)

continuous, the following result can be obtained from Barbalat lemma (Krstic, 1995)(Slotine,

respectively, as *t* . Therefore, the ABSC system can be asymptotically stable in spite of

To determine the lumped uncertainty *Td* , a RFNN observer of a 4-layer structure is proposed, which is shown in Fig. 3. Layer 1 is the input layer with the recurrent loop, which accepts the two input variables. Layer 2 represents the fuzzy rules for calculating the Gaussian membership values. Layer 3 is the rule layer, which represents the preconditions and consequence for the links before and after layer 3, respectively. Layer 4 is the output

*Layer 1, Input layer*: For each node i, the net input and output are represented, respectively, as

layer. The interaction and learning algorithms for the layers are given as follows:

*W y*

*W y d Vy y d Vyt t Vyt t Vyt t V*

0 0 1 2 0 0 0 0 lim ( ( )) lim ( , ) lim ( ( ), ) ( ( ), ) ( ( ), ) *t t*

*t t t tt*

( ( )) *<sup>t</sup> <sup>t</sup> Wy d* 

lim ( ) 0. *<sup>t</sup>*

Since 1 *y* and 2 *y* are converged to zero as *t* ,

**3.3 Design of recurrent fuzzy neural networks** 

Fig. 3. A general four-layer RFNN

**3.3.1 Description of the RFNN** 

the variation of system parameters and external disturbance.

 

which means that 0

1991) as

exists and is finite. Since *W y*( ) is also uniformly

 and 

(37)

approach to

*r* and *r* ,

$$\mathbf{i}\,\mathbf{net}\_i^1 = \mathbf{x}\_i^1 + w\_i^1 \cdot y\_i^1 (\mathbf{N} - \mathbf{1})\_\prime \tag{38}$$

$$y\_i^1(N) = f\_i^1(\text{net}\_i^1(N)) = \text{net}\_i^1(N), i = 1, 2 \tag{39}$$

where <sup>1</sup> 1 1 *x y* , <sup>1</sup> <sup>2</sup> *x y* , <sup>1</sup> *wi* is the recurrent weights, and *N* denotes the number of iterations.

*Layer 2, Membership layer*: For each node, the Gaussian membership values are calculated. For the *j* th node,

$$\text{rect}\_{\dot{f}}^2(\text{N}) = -\frac{\left(\text{x}\_i^2 - m\_{ij}\right)^2}{\left(\sigma\_{ij}\right)^2} \tag{40}$$

$$\text{tr}\,\,\mathbf{y}\_{j}^{2}(\text{N}) = f\_{j}^{2}(\text{net}\_{j}^{2}(\text{N})) = \exp(\text{net}\_{j}^{2}(\text{N})), \,\, j = 1, \ldots, n \tag{41}$$

where *mij* and *ij* are the mean and standard deviation of the Gaussian function in the jth term of the ith input linguistic variable <sup>2</sup> *<sup>i</sup> x* to the node of layer 2, respectively. *n* is the total number of the linguistic variables with respect to the input nodes.

*Layer 3, Rule layer*: Each node k in this layer is denoted by ∏. In addition, the input signals in this layer are multiplied each other and then the result of the product is generated.

$$\text{net}\_k^3(\text{N}) = \prod\_j w\_{jk}^3 x\_j^3(\text{N})\_\prime \tag{42}$$

$$\text{l.}\,y\_k^3(N) = f\_k^3(\text{net}\_k^3(N)) = \text{net}\_k^3(N), \,k = 1, \dots, l \tag{43}$$

where <sup>3</sup> *<sup>j</sup> x* represents the jth input to the node of layer 3, <sup>3</sup> *wjk* is the weights between the membership layer and the rule layer. ( / )*<sup>i</sup> l ni* is the number of rules with complete rule connection, if each input node has the same linguistic variables.

*Layer 4, Output layer*: The single node o in this layer is labeled as , which computes the overall output as the summation of all input signals:

$$\text{rect}\_o^4(\text{N}) = \sum\_k w\_{kv}^4 x\_k^4(\text{N})\_\prime \tag{44}$$

$$f\_o^4(N) = f\_o^4(\text{net}\_o^4(N)) = \text{net}\_o^4(N) \tag{45}$$

where the connecting weight <sup>4</sup> *wko* is the output action strength of the oth output associated with the kth rule. <sup>4</sup> *<sup>k</sup> <sup>x</sup>* represents the kth input to the node of layer 4, and <sup>4</sup> <sup>ˆ</sup> *o d <sup>y</sup> <sup>T</sup>* .

#### **3.3.2 On-line learning algorithm**

In the learning algorithm, it is important to select parameters for the membership functions and weights to decide network performance. In order to train the RFNN effectively, on-line

Precision Position Control of Servo Systems

where 

following equations:

**4. Experiment results** 

shown in Fig. 5.

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 213

The weight, mean, and standard deviation of the hidden layer can be updated by using the

( 1) ( )

 *ij N N* 

Figure 4 shows the servo position tracking control system to evaluate the performance of control schemes. The angular position was measured with an incremental rotary encoder whose counts per encoder was 4 times of 10000 pulses per revolution. A data acquisition board with D/A 12-bit resolution was used to supply the driving voltage to the motor. The sampling rate of the servo system was selected as 500Hz. The control algorithms were programmed with C-language. The parameters of the servo system and friction model for experiment are shown in Table 1. The block diagram of the ABSC system with RFNN is

Fig. 4. Photograph of the servo position tracking control system

*<sup>s</sup>* is the learning-rate parameter of the standard deviation of the Gaussian functions.

4 44 ( 1) *wN w w ko ko ko* (52)

( 1) ( ) *mN mN m ij ij ij* (53)

*ij ij* (54)

 

parameter learning is executed by the gradient decent method. There are four adjustable parameters. Our goal is to minimize the error function *e* represented as

$$\varepsilon = \frac{1}{2}(\theta\_r - \theta)^2 = \frac{1}{2}(y\_1)^2 \,. \tag{46}$$

By using the gradient descent method, the weight in each layer is updated as follows: *Layer 4*: The weight is updated by an amount

$$
\Delta w\_{ko}^4 = -\eta\_w \frac{\partial c}{\partial w\_{ko}^4} = \left( -\eta\_w \frac{\partial c}{\partial u} \frac{\partial u}{\partial \text{net}\_o^4} \right) \left( \frac{\partial \text{net}\_o^4}{\partial w\_{ko}^4} \right) = \eta\_w y\_1 \mathbf{x}\_k^4 \tag{47}
$$

where 1 <sup>4</sup> net*<sup>o</sup> e u y u* and *<sup>w</sup>* is the learning-rate parameter of the connecting weights of the RFNN.

*Layer 3*: Since the weights in this layer are unified, the approximated error term needs to be calculated and propagated to calculate the error term of layer 2 as follows:

$$\boldsymbol{\delta}\_{k}^{3} = -\frac{\boldsymbol{\partial}e}{\boldsymbol{\partial}\boldsymbol{\text{net}}\_{k}^{3}} = -\frac{\partial e}{\partial u}\frac{\partial u}{\partial \mathbf{net}\_{o}^{4}}\frac{\partial \mathbf{net}\_{o}^{4}}{\partial y\_{k}^{3}}\frac{\partial y\_{k}^{3}}{\partial \mathbf{net}\_{k}^{3}} = \boldsymbol{y}\_{1}\boldsymbol{w}\_{ko}^{4} \tag{48}$$

*Layer 2*: The multiplication operation is executed in this layer by using Eq. (46). To update the mean of the Gaussian function, the error term is computed as follows:

$$\boldsymbol{\delta}\_{j}^{2} = -\frac{\partial \boldsymbol{e}}{\partial \boldsymbol{n} \boldsymbol{e}\_{j}^{2}} = -\frac{\partial \boldsymbol{e}}{\partial \boldsymbol{u}} \frac{\partial \boldsymbol{u}}{\partial \boldsymbol{n} \boldsymbol{e}\_{o}^{4}} \frac{\partial \boldsymbol{n} \mathbf{e}\_{o}^{4}}{\partial \boldsymbol{y}\_{k}^{3}} \frac{\partial \boldsymbol{y}\_{k}^{3}}{\partial \boldsymbol{n} \boldsymbol{e}\_{k}^{3}} \frac{\partial \boldsymbol{n} \mathbf{e}\_{k}^{3}}{\partial \boldsymbol{y}\_{j}^{2}} \frac{\partial \boldsymbol{y}\_{j}^{2}}{\partial \boldsymbol{n} \boldsymbol{e}\_{j}^{2}} = \sum\_{k} \boldsymbol{\delta}\_{k}^{3} \boldsymbol{y}\_{k}^{3} \tag{49}$$

and then the update law of *mij* is

$$
\Delta m\_{\rm ij} = -\eta\_m \frac{\partial \varepsilon}{\partial m\_{\rm ij}} = -\eta\_m \frac{\partial \varepsilon}{\partial y\_j^2} \frac{\partial y\_j^2}{\partial \text{net}\_j^2} \frac{\partial \text{net}\_j^2}{\partial m\_{\rm ij}} = \eta\_m \delta\_j^2 \frac{2(\mathbf{x}\_i^2 - m\_{\rm ij})}{\sigma\_{\rm ij}^2} \tag{50}
$$

where *<sup>m</sup>* is the learning-rate parameter of the mean of the Gaussian functions. The update law of *ij* is

$$\Delta\sigma\_{\vec{\eta}} = -\eta\_s \frac{\partial \mathbf{e}}{\partial \sigma\_{\vec{\eta}}} = -\eta\_s \frac{\partial \mathbf{e}}{\partial y\_j^2} \frac{\partial y\_j^2}{\partial \mathbf{net}\_j^2} \frac{\partial \mathbf{net}\_j^2}{\partial \sigma\_{\vec{\eta}}} = \eta\_s \delta\_j^2 \frac{\mathbf{2}(\mathbf{x}\_i^2 - m\_{\vec{\eta}})^2}{\sigma\_{\vec{\eta}}^3} \tag{51}$$

where *<sup>s</sup>* is the learning-rate parameter of the standard deviation of the Gaussian functions.

The weight, mean, and standard deviation of the hidden layer can be updated by using the following equations:

$$w\_{k\flat}^4 \text{(N+1)} = w\_{k\flat}^4 + \Delta w\_{k\flat}^4 \tag{52}$$

$$
\Delta m\_{\vec{\eta}} (\text{N} + \text{1}) = m\_{\vec{\eta}} (\text{N}) + \Delta m\_{\vec{\eta}} \tag{53}
$$

$$
\sigma\_{ij}(N+1) = \sigma\_{ij}(N) + \Delta\sigma\_{ij} \tag{54}
$$

## **4. Experiment results**

212 Fuzzy Logic – Controls, Concepts, Theories and Applications

parameter learning is executed by the gradient decent method. There are four adjustable

1 1 ( ) () 2 2 *<sup>r</sup> e y* 

4 4

*Layer 3*: Since the weights in this layer are unified, the approximated error term needs to be

3 4 3 43 3 1 net

*k ko k ok k e eu <sup>y</sup> <sup>y</sup> <sup>w</sup> u y*

*Layer 2*: The multiplication operation is executed in this layer by using Eq. (46). To update

2 3 3 2 43 32 2

*e eu y y*

*j k k j ok kj j k*

net

net

*ij j j ij ij e e y x m*

*<sup>m</sup>* is the learning-rate parameter of the mean of the Gaussian functions. The update

*ij j j ij ij e e y x m*

*ij m m m j*

 

*my m*

*ij s s s j*

*y*

 

net net net net net

*<sup>y</sup> net <sup>u</sup> y y*

net net net

4 4 4 1

net *<sup>o</sup> ko w <sup>w</sup> w k ko o ko*

By using the gradient descent method, the weight in each layer is updated as follows:

*e eu w y x w w u*

2 2 1

. (46)

4

*<sup>w</sup>* is the learning-rate parameter of the connecting weights of

 

net

(47)

4 3

*o k*

3 2 4 3

*j o k k*

(49)

22 2

 

2 2 2

2 2 3

(51)

(50)

2

*j j i ij*

22 22 2

*j j i ij*

 

net 2( )

net 2( )

(48)

 

parameters. Our goal is to minimize the error function *e* represented as

calculated and propagated to calculate the error term of layer 2 as follows:

the mean of the Gaussian function, the error term is computed as follows:

*Layer 4*: The weight is updated by an amount

 and 

where 1 <sup>4</sup> net*<sup>o</sup>*

*y*

the RFNN.

where 

law of *ij* is *e u*

and then the update law of *mij* is

*m*

*u*  Figure 4 shows the servo position tracking control system to evaluate the performance of control schemes. The angular position was measured with an incremental rotary encoder whose counts per encoder was 4 times of 10000 pulses per revolution. A data acquisition board with D/A 12-bit resolution was used to supply the driving voltage to the motor. The sampling rate of the servo system was selected as 500Hz. The control algorithms were programmed with C-language. The parameters of the servo system and friction model for experiment are shown in Table 1. The block diagram of the ABSC system with RFNN is shown in Fig. 5.

Fig. 4. Photograph of the servo position tracking control system

Precision Position Control of Servo Systems

where *m*<sup>1</sup> *<sup>j</sup>* and

the reference input 1

reference input 1

*r*

ABSC system with RFNN for the reference input 1

system does not have the update rule for 0

1,( 1,2,3,4) *<sup>i</sup>*

*i* .

*m*<sup>2</sup> *<sup>j</sup>* and

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 215

2 2 [ 0.2, 0.1, 0.0, 0.1, 0.2 ] *m <sup>j</sup>*

1 3 [0.003, 0.003, 0.003, 0.003, 0.003]

2 4 [0.3, 0.3, 0.3, 0.3, 0.3]

Figure 6 shows the error of the BSC system, ABSC system, and ABSC system with RFNN for

system is 0.0054. While the ABSC system is operating, its maximum error tends to

the update rules which are given by Eqs. (52), (53), and (54). The angular displacement rms error of the ABSC system is 0.0027. In the operating range of the ABSC system with RFNN, the angular displacement error converges to a steady state value after experiencing a transient state for about 1 second because of the switch from the ABSC system to the ABSC system with RFNN. The angular displacement rms error is 0.0005. The tracking performance of the ABSC system compared with it of the BSC system is improved by 2 times and it of the ABSC system with RFNN compared with it of the ABSC system is improved by 5.4 times. The performance improvement of the ABSC system with RFNN implies that the control input of the RFNN

exponentially decrease and then converge to a steady state value due to 0

including the reconstruction estimation compensates system uncertainties.

Fig. 6. Error of the BSC system, ABSC system, and ABSC system with RFNN for the

ˆ , 3 

Figure 7 shows the estimation and the observation of the BSC system, ABSC system, and

shown in Fig. 7(a). The BSC system estimates the friction parameter to be 0, because the BSC

to the servo system, the update rules estimates the friction parameters, which converge to

ˆ , and 4 

*<sup>j</sup>*

*<sup>j</sup>*

,

<sup>1</sup> *<sup>j</sup>* indicate the mean and standard deviation vectors of 1 *y* , respectively,

*<sup>r</sup>* . The angular displacement rms(root mean square) error of the BSC

<sup>2</sup> *<sup>j</sup>* indicate the mean and standard deviation vectors of 2 *y* , respectively, and

,

> ˆ , 3

*<sup>r</sup>* . The estimations by the update rule are

ˆ . When the ABSC system is applied

ˆ , and 4 ˆ by


Table 1. Parameters of the servo and friction model

Fig. 5. Block diagram of the ABSC system with RFNN

In order to evaluate the performance of the servo system with the proposed control scheme, two reference inputs were applied as follows:

$$\theta\_{r\_1} = 0.1 \sin(0.4 \,\pi \, t) \text{ [rad]}.$$

$$
\theta\_{r\_2} = 0.1 \sin(0.125 \,\pi \, t) \sin(0.75 \,\pi \, t) \text{ [rad]}
$$

To compare the tracking performances of the BSC system, ABSC system, ABSC system with RFNN, the reference input 1 *<sup>r</sup>* was continuously used for experiment as follows: the BSC system was applied during the initial 20 seconds, the ABSC system during the 40 seconds after the application of the BSC system, and the ABSC system with RFNN during the 40 seconds after the application of the ABSC system. The reference input 2 *<sup>r</sup>* was independently experimented for the ABSC system and the ABSC system with RFNN, respectively. In addition, the structure of the RFNN is defined to two neurons at inputs of which each has the recurrent loop, five neurons at the membership layer, five neurons at the rule layer, and one neuron at the output layer. The fuzzy sets at the membership layer, which have the mean ( *mij* ) and standard deviation ( *ij* ), were determined according to the maximum variation boundaries of 1 *y* and 2 *y* of the ABSC system without RFNN. *mij* and *ij* vectors applied to experiment are selected as follows:

$$\mathbf{m}\_{1\circ} = [-0.002, -0.001, 0.0, 0.001, 0.002] \times \mathbf{x}\_{1\circ} \; . $$

Parameter Notation Value Moment of inertia *J* 5 2 2.3 10 kgm

*st*

Coulomb friction *Tc* <sup>3</sup> 1.97 10 Nm Static friction *Ts* <sup>3</sup> 2.6 10 Nm

In order to evaluate the performance of the servo system with the proposed control scheme,

*t* [rad],

 *t t* [rad]

*<sup>r</sup>* was continuously used for experiment as follows: the BSC

*<sup>r</sup>* was

*ij* ), were determined according to the

,

<sup>1</sup> 0.1sin(0.4 ) *<sup>r</sup>*

<sup>2</sup> 0.1sin(0.125 ) sin(0.75 ) *<sup>r</sup>*

seconds after the application of the ABSC system. The reference input 2

To compare the tracking performances of the BSC system, ABSC system, ABSC system with

system was applied during the initial 20 seconds, the ABSC system during the 40 seconds after the application of the BSC system, and the ABSC system with RFNN during the 40

independently experimented for the ABSC system and the ABSC system with RFNN, respectively. In addition, the structure of the RFNN is defined to two neurons at inputs of which each has the recurrent loop, five neurons at the membership layer, five neurons at the rule layer, and one neuron at the output layer. The fuzzy sets at the membership layer,

maximum variation boundaries of 1 *y* and 2 *y* of the ABSC system without RFNN. *mij* and

1 1 [ 0.002, 0.001, 0.0, 0.001, 0.002 ] *m <sup>j</sup>*

 <sup>0</sup> 0.15 Nm

0.013 rad/s

Bristles stiffness coefficient

Stribeck velocity

Table 1. Parameters of the servo and friction model

Fig. 5. Block diagram of the ABSC system with RFNN

which have the mean ( *mij* ) and standard deviation (

*ij* vectors applied to experiment are selected as follows:

two reference inputs were applied as follows:

RFNN, the reference input 1

$$\begin{aligned} m\_{2j} &= [-0.2, -0.1, 0.0, 0.1, 0.2] \times \kappa\_{2j} \\\\ \sigma\_{1j} &= [0.003, 0.003, 0.003, 0.003, 0.003, 0.003] \times \kappa\_{3j} \\\\ \sigma\_{2j} &= [0.3, 0.3, 0.3, 0.3, 0.3, 0.3] \times \kappa\_{4} \end{aligned}$$

where *m*<sup>1</sup> *<sup>j</sup>* and <sup>1</sup> *<sup>j</sup>* indicate the mean and standard deviation vectors of 1 *y* , respectively, *m*<sup>2</sup> *<sup>j</sup>* and <sup>2</sup> *<sup>j</sup>* indicate the mean and standard deviation vectors of 2 *y* , respectively, and 1,( 1,2,3,4) *<sup>i</sup> i* .

Figure 6 shows the error of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *<sup>r</sup>* . The angular displacement rms(root mean square) error of the BSC system is 0.0054. While the ABSC system is operating, its maximum error tends to exponentially decrease and then converge to a steady state value due to 0 ˆ , 3 ˆ , and 4 ˆ by the update rules which are given by Eqs. (52), (53), and (54). The angular displacement rms error of the ABSC system is 0.0027. In the operating range of the ABSC system with RFNN, the angular displacement error converges to a steady state value after experiencing a transient state for about 1 second because of the switch from the ABSC system to the ABSC system with RFNN. The angular displacement rms error is 0.0005. The tracking performance of the ABSC system compared with it of the BSC system is improved by 2 times and it of the ABSC system with RFNN compared with it of the ABSC system is improved by 5.4 times. The performance improvement of the ABSC system with RFNN implies that the control input of the RFNN including the reconstruction estimation compensates system uncertainties.

Fig. 6. Error of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *r*

Figure 7 shows the estimation and the observation of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *<sup>r</sup>* . The estimations by the update rule are shown in Fig. 7(a). The BSC system estimates the friction parameter to be 0, because the BSC system does not have the update rule for 0 ˆ , 3 ˆ , and 4 ˆ . When the ABSC system is applied to the servo system, the update rules estimates the friction parameters, which converge to

Precision Position Control of Servo Systems

RFNN for the reference input 1

the reference input 1

*r*

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 217

Fig. 8. Estimated friction torque of the BSC system, ABSC system, and ABSC system with

(a) Estimated torque of the RFNN including the reconstruction error

(b) Control input torque applied to the servo system Fig. 9. Control inputs of the BSC system, ABSC system, and ABSC system with RFNN for

applied to the servo system at 80 seconds as shown in Fig. 9(a), a little more control input than before that is required to compensate system uncertainties as shown in Fig. 9(b). In

*r*

some values; this convergence stabilizes the servo position system. When the ABSC system is switched to the ABSC system with RFNN, the estimations of the friction parameters do not vary because the angular displacement error is largely decreased by the RFNN. Therefore, the friction estimation values can maintain steady state in the operating range where the RFNN is used. Figure 7(b) shows the observations of the dual observer. The spike phenomenon of 0*z*ˆ among both observation values is occurred to a changing point of velocity, because 2 *y* corresponds to the velocity error, which directly affects 0*z*ˆ , as described in Eq. (31). However, in the case of the ABSC system with RFNN, the spike phenomenon of 0*z*ˆ is largely removed, which means that the RFNN compensates system uncertainties such as nonlinear friction including Coulomb friction, static friction, Stribeck velocity, and unmodeled dynamics.

Fig. 7. Estimation and observation of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *r*

Figure 8 shows the estimated friction torque of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *<sup>r</sup>* . The estimated friction torques of the BSC system, ABSC system, and ABSC system with RFNN reflect the results of Fig. 7. Figure 9 shows the control input of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *<sup>r</sup>* . When the RFNN including reconstruction error estimation is

some values; this convergence stabilizes the servo position system. When the ABSC system is switched to the ABSC system with RFNN, the estimations of the friction parameters do not vary because the angular displacement error is largely decreased by the RFNN. Therefore, the friction estimation values can maintain steady state in the operating range where the RFNN is used. Figure 7(b) shows the observations of the dual observer. The spike phenomenon of 0*z*ˆ among both observation values is occurred to a changing point of velocity, because 2 *y* corresponds to the velocity error, which directly affects 0*z*ˆ , as described in Eq. (31). However, in the case of the ABSC system with RFNN, the spike phenomenon of 0*z*ˆ is largely removed, which means that the RFNN compensates system uncertainties such as nonlinear friction

including Coulomb friction, static friction, Stribeck velocity, and unmodeled dynamics.

(a) Estimations of the update rule

(b) 0*z* and 1*z* of the dual observer Fig. 7. Estimation and observation of the BSC system, ABSC system, and ABSC system with

Figure 8 shows the estimated friction torque of the BSC system, ABSC system, and ABSC

system, ABSC system, and ABSC system with RFNN reflect the results of Fig. 7. Figure 9 shows the control input of the BSC system, ABSC system, and ABSC system with RFNN for

*<sup>r</sup>* . When the RFNN including reconstruction error estimation is

*<sup>r</sup>* . The estimated friction torques of the BSC

RFNN for the reference input 1

the reference input 1

system with RFNN for the reference input 1

*r*

Fig. 8. Estimated friction torque of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *r*

(a) Estimated torque of the RFNN including the reconstruction error

(b) Control input torque applied to the servo system

Fig. 9. Control inputs of the BSC system, ABSC system, and ABSC system with RFNN for the reference input 1 *r*

applied to the servo system at 80 seconds as shown in Fig. 9(a), a little more control input than before that is required to compensate system uncertainties as shown in Fig. 9(b). In

Precision Position Control of Servo Systems

for the reference input 2

reference input 2

*r* *r*

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 219

(a) Estimation of the adaptive rule of the ABSC system

(b) Estimation of the adaptive rule of the ABSC system with RFNN Fig. 11. Friction parameter estimations of the ABSC system and ABSC system with RFNN

Fig. 12. Estimated friction torques of the ABSC system and ABSC system with RFNN for the

addition, the deflection of the control input removes the deflection of the error for the BSC and ABSC systems, which is shown in Fig. 6.

Figure 10 shows the errors of the ABSC system and ABSC system with RFNN for the reference input 2 *<sup>r</sup>* . The reference input 2 *<sup>r</sup>* reflects a real situation and includes more system uncertainties because of the time varying amplitude sinusoidal input. In addition, the experiment conditions of the ABSC system and ABSC system with RFNN are all the same. The tracking error rms values of the ABSC system with RFNN and ABSC system are 0.0007 and 0.003, respectively. Therefore, the tracking rms error of the ABSC system with RFNN is four times less than that of the ABSC system, which implies that the RFNN is suitable for compensating system uncertainties.

Fig. 10. Errors of the ABSC system, and ABSC system with RFNN for the reference input 2 *r*

Figure 11 shows the friction parameter estimations for the ABSC system and ABSC system with RFNN for the reference input 2 *<sup>r</sup>* . The estimations of the friction parameters converge

to steady state values in about 20 seconds as shown in Fig. 11(a). The estimation values of the friction parameters for the ABSC system with RFNN are much smaller than those for the ABSC system, as shown in Fig. 11(b), because the RFNN and the reconstruction error estimator rapidly decrease the tracking error by reducing system uncertainties.

Figure 12 shows the estimated friction torques of the ABSC system and ABSC system with RFNN for the reference input 2 *<sup>r</sup>* . The parameters of the ABSC system with RFNN were estimated to be approximately 0, because the RFNN compensated system uncertainties including nonlinear friction. Therefore, the effectiveness of the RFNN was clearly demonstrated from the above results.

Figure 13 shows the control input of the ABSC system and ABSC system with RFNN for the reference input 2 *<sup>r</sup>* . The estimated torque of the RFNN including the reconstruction error and the control input torque applied to the servo motor are shown in Figs. 13(a) and (b), respectively. The ABSC system with RFNN generated a little more control input than the ABSC system due to the estimation result of the RFNN including the reconstruction error, as shown in Fig. 13(a). This implies that the ABSC system with RFNN compensates system uncertainties such as nonlinear friction and unmodeled dynamics, satisfactorily.

addition, the deflection of the control input removes the deflection of the error for the BSC

Figure 10 shows the errors of the ABSC system and ABSC system with RFNN for the

system uncertainties because of the time varying amplitude sinusoidal input. In addition, the experiment conditions of the ABSC system and ABSC system with RFNN are all the same. The tracking error rms values of the ABSC system with RFNN and ABSC system are 0.0007 and 0.003, respectively. Therefore, the tracking rms error of the ABSC system with RFNN is four times less than that of the ABSC system, which implies that the RFNN is

Fig. 10. Errors of the ABSC system, and ABSC system with RFNN for the reference input 2

Figure 11 shows the friction parameter estimations for the ABSC system and ABSC system

to steady state values in about 20 seconds as shown in Fig. 11(a). The estimation values of the friction parameters for the ABSC system with RFNN are much smaller than those for the ABSC system, as shown in Fig. 11(b), because the RFNN and the reconstruction error

Figure 12 shows the estimated friction torques of the ABSC system and ABSC system with

estimated to be approximately 0, because the RFNN compensated system uncertainties including nonlinear friction. Therefore, the effectiveness of the RFNN was clearly

Figure 13 shows the control input of the ABSC system and ABSC system with RFNN for the

and the control input torque applied to the servo motor are shown in Figs. 13(a) and (b), respectively. The ABSC system with RFNN generated a little more control input than the ABSC system due to the estimation result of the RFNN including the reconstruction error, as shown in Fig. 13(a). This implies that the ABSC system with RFNN compensates system

*<sup>r</sup>* . The estimated torque of the RFNN including the reconstruction error

estimator rapidly decrease the tracking error by reducing system uncertainties.

uncertainties such as nonlinear friction and unmodeled dynamics, satisfactorily.

*<sup>r</sup>* reflects a real situation and includes more

*<sup>r</sup>* . The estimations of the friction parameters converge

*<sup>r</sup>* . The parameters of the ABSC system with RFNN were

*r*

and ABSC systems, which is shown in Fig. 6.

suitable for compensating system uncertainties.

with RFNN for the reference input 2

RFNN for the reference input 2

reference input 2

demonstrated from the above results.

*<sup>r</sup>* . The reference input 2

reference input 2

(a) Estimation of the adaptive rule of the ABSC system

(b) Estimation of the adaptive rule of the ABSC system with RFNN

Fig. 11. Friction parameter estimations of the ABSC system and ABSC system with RFNN for the reference input 2 *r*

Fig. 12. Estimated friction torques of the ABSC system and ABSC system with RFNN for the reference input 2 *r*

Precision Position Control of Servo Systems

function in the RFNN need to be carefully selected.

on the error output of the servo system. Finally, *mij* and

can conclude that *mij* and

Using Adaptive Back-Steppingand Recurrent Fuzzy Neural Networks 221

small as shown in Fig. 14(c) compared with their estimated friction torque of the ABSC system as shown in Fig. 12, which reflects the result of Fig. 14(b). At this time, the ratio of the maximum friction torque in Fig. 12 to it in Fig. 14(c) is approximately 30 times. Thus, we

(a) Error of the ABSC system with RFNN

(b) Estimation of the adaptive rule of the ABSC system with RFNN

(c) Estimated friction torque of the ABSC system with RFNN

*ij* in RFNN for the

Fig. 14. Results of the ABSC system with the variation of *mij* and

reference input 2

*r* *ij* of the Gaussian membership function in the RFNN depend

*ij* of the Gaussian membership

(a) Estimated torque of the RFNN including the reconstruction error

Fig. 13. Control input of the ABSC system and ABSC system with RFNN for the reference input 2 *r*

In order to show an influence of the RFNN parameters on control performance, two main parameters, which are *mij* and *ij* of the Gaussian fuzzy membership function in Layer 2, are changed. Initial values of these values are selected by investigating the range and magnitude of 1 *y* and 2 *y* , and then there are on-line updated through Eqs. (53) and (54). On the other hand, the change in the weight factors is not considered to experimental condition because of using initial random values.

Figure 14 shows the results of the ABSC system with the variation of *mij* and *ij* in RFNN for the reference input 2 *<sup>r</sup>* . The changed conditions of the mean and standard deviation are 0.5 *<sup>i</sup>* and 1.5 *<sup>i</sup>* . For 0.5 *<sup>i</sup>* , the results of the error, estimation, and estimated friction torque of the ABSC system with RFNN are diverged due to the reduction of *mij* and *ij* in 7.5 seconds as shown in Fig. 14 (a), (b), and (c). On the other hand, although the error state of the ABSC system with RFNN for 1.5 *<sup>i</sup>* is stable as shown in Fig. 14(a), the angular displacement rms error of compared system with the ABSC system with RFNN in Fig. 10 is minutely increased to 1.25 times. In addition, although the estimations of the adaptive rule of the ABSC system with RFNN as shown in Fig. 14(b) compared with their estimation values as shown in Fig. 11(b) is increased, their effect for the estimated friction torque is very

(a) Estimated torque of the RFNN including the reconstruction error

(b) Control input torque applied to the servo system Fig. 13. Control input of the ABSC system and ABSC system with RFNN for the reference

In order to show an influence of the RFNN parameters on control performance, two main

are changed. Initial values of these values are selected by investigating the range and magnitude of 1 *y* and 2 *y* , and then there are on-line updated through Eqs. (53) and (54). On the other hand, the change in the weight factors is not considered to experimental condition

*ij* of the Gaussian fuzzy membership function in Layer 2,

*<sup>r</sup>* . The changed conditions of the mean and standard deviation are

*<sup>i</sup>* , the results of the error, estimation, and estimated friction

*<sup>i</sup>* is stable as shown in Fig. 14(a), the angular

*ij* in RFNN

*ij* in

Figure 14 shows the results of the ABSC system with the variation of *mij* and

torque of the ABSC system with RFNN are diverged due to the reduction of *mij* and

7.5 seconds as shown in Fig. 14 (a), (b), and (c). On the other hand, although the error state

displacement rms error of compared system with the ABSC system with RFNN in Fig. 10 is minutely increased to 1.25 times. In addition, although the estimations of the adaptive rule of the ABSC system with RFNN as shown in Fig. 14(b) compared with their estimation values as shown in Fig. 11(b) is increased, their effect for the estimated friction torque is very

input 2 *r*

parameters, which are *mij* and

for the reference input 2

 *<sup>i</sup>* and 1.5 

0.5

because of using initial random values.

 *<sup>i</sup>* . For 0.5 

of the ABSC system with RFNN for 1.5

small as shown in Fig. 14(c) compared with their estimated friction torque of the ABSC system as shown in Fig. 12, which reflects the result of Fig. 14(b). At this time, the ratio of the maximum friction torque in Fig. 12 to it in Fig. 14(c) is approximately 30 times. Thus, we can conclude that *mij* and *ij* of the Gaussian membership function in the RFNN depend on the error output of the servo system. Finally, *mij* and *ij* of the Gaussian membership function in the RFNN need to be carefully selected.

(c) Estimated friction torque of the ABSC system with RFNN

Fig. 14. Results of the ABSC system with the variation of *mij* and *ij* in RFNN for the reference input 2 *r*

**11** 

**Operation of Compressor and Electronic** 

**Expansion Valve via Different Controllers** 

The most critical problem in the world is to meet the energy demand, because of steadily increasing energy consumption. Refrigeration systems` electricity consumption has big portion in overall consumption. Therefore, considerable attention has been given to refrigeration capacity modulation system in order to decrease electricity consumption of these systems. Capacity modulation is used to meet exact amount of load at partial load and lowered electricity consumption by avoiding over capacity using. Variable speed refrigeration systems are the most common capacity modulation method for commercially and household purposes. Although the vapor compression refrigeration designed to satisfy the maximum load, they work at partial load conditions most of their life cycle and they are generally regulated as on/off controlled. The experimental chiller system contains four main components: compressor, condenser, expansion device, and evaporator in Fig.1 where this study deals with effects of different control methods on variable speed compressor (VSC) and electronic expansion valve (EEV). This chiller system has a scroll type VSC and a

There are electronic parts in the control system: DAQ (data acquisition), Controllers, and Inverter. Data acquisition part reads distinct temperature values of the water outlet (Two), evaporator input (Tei), and the evaporator output (Teo) points from the evaporator. Controllers drive both expansion valve and compressor, which are named Controller #1 and Controller #2 throughout the paper, respectively. Inverter, which is commanded by controller #1, drives the compressor speed frequency (f) using *f(V)*. Common controllers are on-off, proportional (P), proportional-integral (PI), and PID respectively. "On-off" control method is the most used conventional technique to control refrigeration systems. This method has a big drawback of undesired current peaks during its state transitions (Aprea et

**1. Introduction** 

stepper motor controlled EEV.

Orhan Ekren1, Savas Sahin2 and Yalcin Isler3

*Mechanical Engineering Department, Edwardsville,* 

 *Department of Control and Automation, Bornova, Izmir,* 

*Department of Electrical and Electronics Engineering,* 

*1Southern Illinois University,* 

 *Incivez, Zonguldak* 

*1USA 2,3Turkey* 

*2Ege University, Ege Technical College,* 

*3Zonguldak Karaelmas University,* 

## **5. Conclunsion**

The tracking performance of servo systems is deteriorated by nonlinear friction and system uncertainties, especially in the region where the direction of velocity of servo systems is changed. In order to reduce the effects of the friction and system uncertainties, a robust adaptive precision position control scheme is proposed. Unmeasurable state and parameters of the dynamic friction model are observed and estimated by the dual observer and the adaptive back-stepping controller, respectively. In order to actively cope with system uncertainties, the RFNN scheme is applied to the servo system. Experiments showed that the servo system with the dual observer, adaptive back-stepping controller, and RFNN including the reconstruction error estimator can achieve desired tracking performance and robustness. In addition, the influence of the mean and standard deviation of the RFNN parameters on control performance is shown through experiment.

## **6. References**


## **Operation of Compressor and Electronic Expansion Valve via Different Controllers**

Orhan Ekren1, Savas Sahin2 and Yalcin Isler3

*1Southern Illinois University, Mechanical Engineering Department, Edwardsville, 2Ege University, Ege Technical College, Department of Control and Automation, Bornova, Izmir, 3Zonguldak Karaelmas University, Department of Electrical and Electronics Engineering, Incivez, Zonguldak 1USA 2,3Turkey* 

## **1. Introduction**

222 Fuzzy Logic – Controls, Concepts, Theories and Applications

The tracking performance of servo systems is deteriorated by nonlinear friction and system uncertainties, especially in the region where the direction of velocity of servo systems is changed. In order to reduce the effects of the friction and system uncertainties, a robust adaptive precision position control scheme is proposed. Unmeasurable state and parameters of the dynamic friction model are observed and estimated by the dual observer and the adaptive back-stepping controller, respectively. In order to actively cope with system uncertainties, the RFNN scheme is applied to the servo system. Experiments showed that the servo system with the dual observer, adaptive back-stepping controller, and RFNN including the reconstruction error estimator can achieve desired tracking performance and robustness. In addition, the influence of the mean and standard deviation of the RFNN

C. Canudas de Wit and P. Lischinsky (1997), Adaptive Friction Compensation with Partially Known Dynamic Friction Model, *Int. J. Adaptive Control and Signal Processing*, 11, 65-80. C. Canudas de Wit, H. Olsson, and P. Lischinsky (1995), A New Model for Control of Systems with Friction. *IEEE Trans. Automatic Control*, 40(3), 419-425. C. H. Lin (2004), Adaptive Recurrent Fuzzy Neural Network Control for Synchronous Reluctance Motor Servo Drive, *IEE Proc. Electr. Power Appl*., 151(6), 711-724. C. T. Lin, and C. S. Greorge (1996), Neural Fuzzy Systems, *Prentice-Hall PTR*, New Jersey, USA. F. J. Lin, S. L. Yang and P. H. Shen(2006), Self-Constructing Recurrent Fuzzy Neural

Network for DSP-Based Permanent-Magnet Linear-Synchronous-Motor

Recurrent Fuzzy Cerebellar Model Articulation Controller, *Neural Inform Process-*

Controller with a Friction Compensator for Motion Control of a Ball-Screw System, *Proc. ImechE Part-I, Journal of Systems and Control Engineering*, 218 (5), 369-380. M. Krstic, I. Kanellakopoulos and P. Kokotovic (1995), Nonlinear and Adaptive Control

to Friction Estimation and Compensation. *Proc. of IEEE, Int. Control on Robot. &* 

Adaptive Control of Nonlinear Dynamic Systems, *IEEE Trans. System Man Cybern*,

H. Olsson, K. J. Astrom, C. C. Wit, M. Gafvert and P. Lischinsky (1998), Friction Models and

J. J. Slotine and W. Li (1991), Applied Nonlinear Control, *Pearson Education*, New Jersey, USA. J. Z. Peng, Y. N. Wang, W. Sun (2007), Trajectory-Tracking Control for Mobile Robot Using

K. J. Lee, H. M. Kim, and J. S. Kim (2004), Design of a Chattering-Free Sliding Mode

P. Lischinsky, C. Canudas de Wit, and G. Morel (1999), Friction Compensation for an

Q. R. Ha, D. C. Rye, and H. F. Durrant-Whyte(2000), Variable Structure Systems Approach

R. J. Wai (2003), Robust Fuzzy Neural Network Control for Nonlinear Motor-Toggle

Y. G. Leu, T. T. Lee and W. Y. Wang(1997), On-Line Turning of Fuzzy-Neural Networks for

Y. Tan, and I. Kanellakopoulos (1999), Adaptive Nonlinear Friction Compensation with

Industrial Hydraulic Robot, *IEEE Contr. Syst. Mag*., 19, 25-32.

Servomechanism, *Fuzzy Sets and Systems*, 139, 185-208.

Parametric Uncertainties. *Proc. AACC*, 2511-2515.

parameters on control performance is shown through experiment.

Servodrive, *IEE Proc. Electr. Power Appl*., 153(2), 236-246.

Friction Compensation, *Eur. J. Control,* 4(3), 176–185.

Design, *Wiley Interscience*, New York, USA.

*Letters & Rev*, 11(1), 15-23.

*Auto*, 3543-3548.

27(6), 1034-1043.

**5. Conclunsion** 

**6. References** 

The most critical problem in the world is to meet the energy demand, because of steadily increasing energy consumption. Refrigeration systems` electricity consumption has big portion in overall consumption. Therefore, considerable attention has been given to refrigeration capacity modulation system in order to decrease electricity consumption of these systems. Capacity modulation is used to meet exact amount of load at partial load and lowered electricity consumption by avoiding over capacity using. Variable speed refrigeration systems are the most common capacity modulation method for commercially and household purposes. Although the vapor compression refrigeration designed to satisfy the maximum load, they work at partial load conditions most of their life cycle and they are generally regulated as on/off controlled. The experimental chiller system contains four main components: compressor, condenser, expansion device, and evaporator in Fig.1 where this study deals with effects of different control methods on variable speed compressor (VSC) and electronic expansion valve (EEV). This chiller system has a scroll type VSC and a stepper motor controlled EEV.

There are electronic parts in the control system: DAQ (data acquisition), Controllers, and Inverter. Data acquisition part reads distinct temperature values of the water outlet (Two), evaporator input (Tei), and the evaporator output (Teo) points from the evaporator. Controllers drive both expansion valve and compressor, which are named Controller #1 and Controller #2 throughout the paper, respectively. Inverter, which is commanded by controller #1, drives the compressor speed frequency (f) using *f(V)*. Common controllers are on-off, proportional (P), proportional-integral (PI), and PID respectively. "On-off" control method is the most used conventional technique to control refrigeration systems. This method has a big drawback of undesired current peaks during its state transitions (Aprea et

Operation of Compressor and Electronic Expansion Valve via Different Controllers 225

In this chapter, different control algorithms, based on proportional-integral-derivative (PID), fuzzy logic (FL), artificial neural network (ANN) for compressor speed and opening percentage of electronic expansion valve, were compared by means of achieving their

There are three parts in a closed-loop control system: error calculation, controller, and plant (Fig. 2). Error calculation part calculates the difference between the desired output, r(k), and the actual output, y(k), of the system. This difference is called error signal, e(k). A controller finds out a control signal, u(k), by considering this error signal. A plant, the system itself under investigation, generates the actual output, y(k), in reply to the u(k). The most important problem is generating the most suitable control signal that derives the plant to minimize the error, which means that the actual output and the desired output are almost

<sup>+</sup> Controller Plant *kr* )( *ke* )( *ku* )( *ky* )(

In the variable speed refrigeration system (VSRS), which is a typical closed-loop control system, contains VSC and EEV controllable components. The frequency of the compressor and the opening amount of the expansion valve are control parameters in order to drive the water outlet temperature and the degree of superheat respectively to desired values in VSRS (Ekren et al., 2010). By considering controllable parts in the experimental setup, after adapting closed-loop control system into the setup, a detailed block diagram of controllers

In the following subsections, certain control methods are given in control refrigeration systems. These methods are itemized two main groups: i) linear controller such as PID and

PID is the most commonly used control technique for industrial applications since it is very simple to design, to implement, and to use (Astrom and Hagglund, 1995). It has also been widely used in Heating Ventilation Air Conditioning and Refrigeration (HVAC&R) systems (Jiangjiang et al., 2006). This controller is tuned by its three variables: proportional (*Kp*), integral (*Ki*) and derivative (*Kd*) parameters. The control action *u t*( ) in time domain can be

desired output and energy demands.

**2. Control methods of the VSRS** 

equal in the closed-loop control system.

Fig. 2. A general closed-loop control system

and system parts for the VSRS are also shown in Fig. 1.

ii) nonlinear controllers such as FL and ANN controllers.

**2.1 PID control** 

calculated as

al., 2009). PID controller has been found wide usage in industrial applications since it is very simple to design, to implement, and to use (Katsuhiko, 2002; Astrom and Hagglund, 1995). Therefore, it has been widely used in Heating Ventilation Air Conditioning and Refrigeration (HVAC&R) systems (Jiangjiang et al., 2006). Recently, energy consuming is a strict issue in designing new refrigeration system (Aprea and Renno, 2009; Ekren et al., 2010, 2011; Nasutin and Hassan, 2006, Sahin et al., 2010). EEV and VSC have important effect on efficiency of system energy consumption. Hence designing an eligible controller for these parts will improve energy consuming. Conventional controllers cannot deal with nonlinear behaviors including uncertainties in system parameters, time delays and limited operation point of refrigeration systems, which may reduce the energy efficiency. Nonlinear controllers based on Fuzzy Logic (FL) and Artificial Neural Network (ANN) may overcome these issues (Aprea et al., 2006a,b). The most important advantage of these algorithms is to enable solving control problems without any already-known mathematical model (Narendra and Parthasarathy, 1990; Narendra, 1993; Aprea et al., 2004; Ross, 2004).

Fig. 1. Schematic of the refrigeration and control system

In this chapter, different control algorithms, based on proportional-integral-derivative (PID), fuzzy logic (FL), artificial neural network (ANN) for compressor speed and opening percentage of electronic expansion valve, were compared by means of achieving their desired output and energy demands.

## **2. Control methods of the VSRS**

224 Fuzzy Logic – Controls, Concepts, Theories and Applications

al., 2009). PID controller has been found wide usage in industrial applications since it is very simple to design, to implement, and to use (Katsuhiko, 2002; Astrom and Hagglund, 1995). Therefore, it has been widely used in Heating Ventilation Air Conditioning and Refrigeration (HVAC&R) systems (Jiangjiang et al., 2006). Recently, energy consuming is a strict issue in designing new refrigeration system (Aprea and Renno, 2009; Ekren et al., 2010, 2011; Nasutin and Hassan, 2006, Sahin et al., 2010). EEV and VSC have important effect on efficiency of system energy consumption. Hence designing an eligible controller for these parts will improve energy consuming. Conventional controllers cannot deal with nonlinear behaviors including uncertainties in system parameters, time delays and limited operation point of refrigeration systems, which may reduce the energy efficiency. Nonlinear controllers based on Fuzzy Logic (FL) and Artificial Neural Network (ANN) may overcome these issues (Aprea et al., 2006a,b). The most important advantage of these algorithms is to enable solving control problems without any already-known mathematical model

(Narendra and Parthasarathy, 1990; Narendra, 1993; Aprea et al., 2004; Ross, 2004).

Fig. 1. Schematic of the refrigeration and control system

There are three parts in a closed-loop control system: error calculation, controller, and plant (Fig. 2). Error calculation part calculates the difference between the desired output, r(k), and the actual output, y(k), of the system. This difference is called error signal, e(k). A controller finds out a control signal, u(k), by considering this error signal. A plant, the system itself under investigation, generates the actual output, y(k), in reply to the u(k). The most important problem is generating the most suitable control signal that derives the plant to minimize the error, which means that the actual output and the desired output are almost equal in the closed-loop control system.

Fig. 2. A general closed-loop control system

In the variable speed refrigeration system (VSRS), which is a typical closed-loop control system, contains VSC and EEV controllable components. The frequency of the compressor and the opening amount of the expansion valve are control parameters in order to drive the water outlet temperature and the degree of superheat respectively to desired values in VSRS (Ekren et al., 2010). By considering controllable parts in the experimental setup, after adapting closed-loop control system into the setup, a detailed block diagram of controllers and system parts for the VSRS are also shown in Fig. 1.

In the following subsections, certain control methods are given in control refrigeration systems. These methods are itemized two main groups: i) linear controller such as PID and ii) nonlinear controllers such as FL and ANN controllers.

## **2.1 PID control**

PID is the most commonly used control technique for industrial applications since it is very simple to design, to implement, and to use (Astrom and Hagglund, 1995). It has also been widely used in Heating Ventilation Air Conditioning and Refrigeration (HVAC&R) systems (Jiangjiang et al., 2006). This controller is tuned by its three variables: proportional (*Kp*), integral (*Ki*) and derivative (*Kd*) parameters. The control action *u t*( ) in time domain can be calculated as

Operation of Compressor and Electronic Expansion Valve via Different Controllers 227

Although there are some other methods to find out the PID parameters, Ziegler Nichols' methods are still the most used and preferred methods in the literature. In this study, Ziegler Nichols' step response method is used to find out the PID parameters by regarding

FL controllers consist of certain rules and membership functions. The certain rules is to determine the decision process and the membership functions is to bring up the relation between linguistic and the precise numeric values. These membership functions define input-output variables of any system and formulate control rules. A membership function can be defined by a geometric shape such as triangular, trapezoidal, etc. The selection of the membership functions depends on expert's knowledge about the process (Aprea et al., 2004;

The operation procedure of the FL controller can be itemized into three main steps: i) fuzzification, ii) inference, and iii) defuzzification (Zadeh, 1965; Ross, 2004). In the fuzzification step, system inputs-outputs and membership functions are well defined. In the inference step, a rules table is prepared according to the human expertise and these rules calculate the outputs (Ross, 2004). In the last step, defuzzification transforms fuzzy outputs into real world values. A detailed explanation of these steps and their implementation details can be found in the literature (Ross, 2004). In this study, the minimum-maximum method and the center of gravity method were used in the inference and the defuzzification

EEV is the first controllable equipment in VSRS (Aprea et al., 2006a,b; Lazzarin and Noro, 2008, Ekren et al., 2010, 2011). For this controller, two inputs and one output variable were

The first input was the difference between desired and actual superheat (SH) values, of which linguistics were marked as negative high (NH), negative medium (NM), zero (Z), positive medium (PM), positive high (PH). The second one was the previous value of the EEV opening. The output was the value of EEV opening (EEVO). The second input and the output of the system had similar membership functions where linguistics were marked as very closed (VC), closed (C), medium (M), opened (O) and very opened (VO). The

the plot of the system output.

**2.2 Fuzzy logic control** 

Ross, 2004).

steps, respectively.

defined (Ekren et al., 2010) in Fig. 4.

Fig. 4. Inputs and output of the first controller in VSRS.

membership functions can be seen in Fig. 5.

$$u(t) = K\_p e(t) + K\_i \int\_0^t e(t)dt + K\_d \dot{e}(t)\tag{6}$$

by means of the error, which is the difference between the desired and the actual output of the plant (*e*), and the derivative of this error ( *e* ). PID parameters can be determined in using either the step response or the self-oscillation methods from Ziegler-Nichols (Ziegler and Nichols, 1942) are widely used in the literature (Astrom and Hagglund, 1995). In the step response method, if the output response of the plant can be obtained in time domain, PID parameters can be determined. This output response can be approximated as a first-order system

$$H(\mathbf{s}) = \frac{\mathbf{K}}{T\mathbf{s} + 1}e^{-Ls} \tag{7}$$

where *T* is time constant, *L* is delay time and *K* is gain. The *T* and *L* give the PID controller design parameters (Katsuhiko, 2002; Astrom and Hagglund, 1995).

The template plot is represented in Fig.3 to find out L and T values. The parameters can be determined from the output plots with respect to step input. The constant gain *K* indicates the amount of output variation from one steady-state to another, with respect to the input variation. *L* represents the past time to observe the initial response changes after applying the input. In addition, *T* denotes the time necessary to reach the output equal to 63.2% of its final value for the first-order systems.

Fig. 3. Output response plots with respect to step function input

In the self-oscillation method, PID controller design parameters are calculated by critical gain and critical period variables. These variables are computed when a stable limit cycle of the closed-loop system is satisfied by using only the proportional gain. This gain is increased slowly, and then the PID parameters are determined. This method possesses very important advantage for the plant because self-oscillation experiment could be in reasonable operating bounds of the plant (Yuksel, 2006; Katsuhiko, 2002; Astrom and Hagglund, 1995).

Although there are some other methods to find out the PID parameters, Ziegler Nichols' methods are still the most used and preferred methods in the literature. In this study, Ziegler Nichols' step response method is used to find out the PID parameters by regarding the plot of the system output.

## **2.2 Fuzzy logic control**

226 Fuzzy Logic – Controls, Concepts, Theories and Applications

0 () () () () *t*

by means of the error, which is the difference between the desired and the actual output of the plant (*e*), and the derivative of this error ( *e* ). PID parameters can be determined in using either the step response or the self-oscillation methods from Ziegler-Nichols (Ziegler and Nichols, 1942) are widely used in the literature (Astrom and Hagglund, 1995). In the step response method, if the output response of the plant can be obtained in time domain, PID parameters can be determined. This output response can be approximated as a first-order

> ( ) <sup>1</sup> *<sup>K</sup> Ls Hs e Ts*

design parameters (Katsuhiko, 2002; Astrom and Hagglund, 1995).

Fig. 3. Output response plots with respect to step function input

final value for the first-order systems.

where *T* is time constant, *L* is delay time and *K* is gain. The *T* and *L* give the PID controller

The template plot is represented in Fig.3 to find out L and T values. The parameters can be determined from the output plots with respect to step input. The constant gain *K* indicates the amount of output variation from one steady-state to another, with respect to the input variation. *L* represents the past time to observe the initial response changes after applying the input. In addition, *T* denotes the time necessary to reach the output equal to 63.2% of its

In the self-oscillation method, PID controller design parameters are calculated by critical gain and critical period variables. These variables are computed when a stable limit cycle of the closed-loop system is satisfied by using only the proportional gain. This gain is increased slowly, and then the PID parameters are determined. This method possesses very important advantage for the plant because self-oscillation experiment could be in reasonable operating bounds of the plant (Yuksel, 2006; Katsuhiko, 2002; Astrom and Hagglund, 1995).

system

*u t K e t K e t dt K e t pi d* (6)

(7)

FL controllers consist of certain rules and membership functions. The certain rules is to determine the decision process and the membership functions is to bring up the relation between linguistic and the precise numeric values. These membership functions define input-output variables of any system and formulate control rules. A membership function can be defined by a geometric shape such as triangular, trapezoidal, etc. The selection of the membership functions depends on expert's knowledge about the process (Aprea et al., 2004; Ross, 2004).

The operation procedure of the FL controller can be itemized into three main steps: i) fuzzification, ii) inference, and iii) defuzzification (Zadeh, 1965; Ross, 2004). In the fuzzification step, system inputs-outputs and membership functions are well defined. In the inference step, a rules table is prepared according to the human expertise and these rules calculate the outputs (Ross, 2004). In the last step, defuzzification transforms fuzzy outputs into real world values. A detailed explanation of these steps and their implementation details can be found in the literature (Ross, 2004). In this study, the minimum-maximum method and the center of gravity method were used in the inference and the defuzzification steps, respectively.

EEV is the first controllable equipment in VSRS (Aprea et al., 2006a,b; Lazzarin and Noro, 2008, Ekren et al., 2010, 2011). For this controller, two inputs and one output variable were defined (Ekren et al., 2010) in Fig. 4.

Fig. 4. Inputs and output of the first controller in VSRS.

The first input was the difference between desired and actual superheat (SH) values, of which linguistics were marked as negative high (NH), negative medium (NM), zero (Z), positive medium (PM), positive high (PH). The second one was the previous value of the EEV opening. The output was the value of EEV opening (EEVO). The second input and the output of the system had similar membership functions where linguistics were marked as very closed (VC), closed (C), medium (M), opened (O) and very opened (VO). The membership functions can be seen in Fig. 5.

Operation of Compressor and Electronic Expansion Valve via Different Controllers 229

control unit. The output for this controller was the frequency change of the supply voltage of the compressor electric motor, *f(V)*. The second input and the output of the system had similar membership functions where linguistics were marked as very small (VS), small (S), medium (M), big (B) and very big (VB). The membership functions can be seen in Fig. 7.

Fig. 7. Membership functions for (a) water temperature error input, (b) for the previous

Fuzzy rules for the compressor control were experimentally verified by using some trials,

*Water Temperature Error VS S M B VB* 

The most important features of the ANN developed by inspiring from biological neural networks are learning, generalizing and making a decision. ANNs are widely used in many industrial applications such as identification, control, data and signal processing area since 1980s. Since ANNs define, in general, a nonlinear algebraic function, they can cope with nonlinearities inherent in control systems possessing complex dynamics. As in the general ANN literature, the mostly widely used ANN model in identification and control is the Multi Layer Perceptron (MLP) due to its function approximation capability and the existence of an efficient learning algorithm (Ahmed, 2000; Lightbody & Irwin, 1995; Meireles et al., 2003; Noriega & Wang, 1998; Omidvar & Elliott, 1997). MLP is a multilayer, algebraic neural network of neurons, called as perceptrons, which are multi-input, single-output functional units taking firstly a weighted sum of their inputs and then pass it through a

*NH S M B VB VB NM S M B VB VB Z VS S M B VB PM VS VS S M B PH VS VS S M B* 

*Previous Change of Frequency* 

change of frequency input and the frequency change output.

Table 2. Compressor fuzzy logic control rules

sigmoidal nonlinearity to produce its output shown in Fig. 8.

and it is given in Table 2.

**2.3 ANN Control** 

Fig. 5. Membership functions of (a) the superheat error input, (b) the previous opening value of EEV input and the EEV opening amount output.

Fuzzy rules for the EEV control were experimentally verified by using some trials, and it is given in Table 1.


Table 1. EEV Fuzzy logic control rules

For the second controller, two inputs and one output variable were defined (Ekren et al., 2010) in Fig. 6.

Fig. 6. Inputs and output of the second controller in VSRS.

The first input was the temperature difference between the desired temperature and actual temperature at outlet of the evaporator (Two), of which linguistics were marked as negative high (NH), negative medium (NM), zero (Z), positive medium (PM), and positive high (PH). The second input was the previous change of frequency value, sent to the inverter by the control unit. The output for this controller was the frequency change of the supply voltage of the compressor electric motor, *f(V)*. The second input and the output of the system had similar membership functions where linguistics were marked as very small (VS), small (S), medium (M), big (B) and very big (VB). The membership functions can be seen in Fig. 7.

Fig. 7. Membership functions for (a) water temperature error input, (b) for the previous change of frequency input and the frequency change output.

Fuzzy rules for the compressor control were experimentally verified by using some trials, and it is given in Table 2.


Table 2. Compressor fuzzy logic control rules

#### **2.3 ANN Control**

228 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 5. Membership functions of (a) the superheat error input, (b) the previous opening value

Fuzzy rules for the EEV control were experimentally verified by using some trials, and it is

*Superheat Error VO O M C VC* 

For the second controller, two inputs and one output variable were defined (Ekren et al.,

The first input was the temperature difference between the desired temperature and actual temperature at outlet of the evaporator (Two), of which linguistics were marked as negative high (NH), negative medium (NM), zero (Z), positive medium (PM), and positive high (PH). The second input was the previous change of frequency value, sent to the inverter by the

*NH O M C VC VC NM O M C VC VC Z VO O M C VC PM VO VO O M C PH VO VO O M C* 

*Previous Opening Value of EEV* 

of EEV input and the EEV opening amount output.

Table 1. EEV Fuzzy logic control rules

Fig. 6. Inputs and output of the second controller in VSRS.

given in Table 1.

2010) in Fig. 6.

The most important features of the ANN developed by inspiring from biological neural networks are learning, generalizing and making a decision. ANNs are widely used in many industrial applications such as identification, control, data and signal processing area since 1980s. Since ANNs define, in general, a nonlinear algebraic function, they can cope with nonlinearities inherent in control systems possessing complex dynamics. As in the general ANN literature, the mostly widely used ANN model in identification and control is the Multi Layer Perceptron (MLP) due to its function approximation capability and the existence of an efficient learning algorithm (Ahmed, 2000; Lightbody & Irwin, 1995; Meireles et al., 2003; Noriega & Wang, 1998; Omidvar & Elliott, 1997). MLP is a multilayer, algebraic neural network of neurons, called as perceptrons, which are multi-input, single-output functional units taking firstly a weighted sum of their inputs and then pass it through a sigmoidal nonlinearity to produce its output shown in Fig. 8.

Operation of Compressor and Electronic Expansion Valve via Different Controllers 231

*ky* )( *ke* )( *ku* )( *kr* )(

MLP-ANN Controller

delays

delays

(Inverse Plant)

Fig. 10. Feed-forward inverse control system using MLP-ANN.

the supply voltage of compressor electric motor (*f*).

**3. Applications of the controllers** 

were examined in the VSRS.

Plant <sup>+</sup> -

MLP-ANN Identification

delays

delays

One of the most important problems in real world applications is the delay time defined the time required before observing the output change after applying a control input. To overcome delay time problem, Smith compensator structure can be used in ANN-based controllers (Ekren et al., 2010; Huang and Lewis, 2003; Lin et al., 2008; Slanvetpan et al., 2003). Inverse system MLP-ANN controller with Smith predictor was used for compensation of the delay time of the plant in Fig. 11. The MLP in both EEV and compressor controllable parts are trained with the gradient algorithm. The number of neurons in the hidden layer of MLP was selected as 20 experimentally. The EEV was controlled using an inverse system ANN controller with Smith compensator. Inputs of the first controller were EEV opening values and SH error with their 15 past values. The output of this controller was EEVO. On the other hand, compressor was controlled using an inverse system ANN controller. Inputs of this controller were compressor frequency and *TWO* error values with their 15 past values. The output of this controller was the frequency change of

In this study, the controllers are designed as decoupled ones without interfering loops (Li et al., 2008). In the experimental setup used in this study, there were some limitations of the equipment. EEV opening value is restricted between 0% and 20% since its limits are 15% and 35% to prevent the low pressure alert and to avoid liquid entrance into the compressor. Instantaneous frequency change is restricted between 0 Hz and 20 Hz to prevent system from the vibration and the unsuitable lubrication since the frequency limits are 30 Hz and 50 Hz. By considering these limitations, three different controllers such as PID, FL, and ANN

ˆ *ky* )(

Fig. 8. Perceptron as a hidden neuron

Although MLP-ANNs are algebraic models, MLP-ANNs can define nonlinear discrete-time dynamical system due to the fact that its inputs can be connected with delayed outputs. As shown in Fig. 9, a multi-input, multi-output MLP with one hidden layer can be used as a Nonlinear Auto-Regressive-Moving-Array (NARMA) model. Input vector of this NARMA model *x yk yk n uk k n* [ ( 1),..., ( ), ( 1),...,( )] where *n* is the finite value and *v* and *w* are weights of the layers.

Fig. 9. MLP implementing NARMA model

In most industrial cases, an ANN is an adaptive system that changes its internal information in the learning phase. A general feed-forward inverse control system contains two MLP-ANNs such as identification and control structures, which are shown in Fig. 10 (Narendra and Parthasarathy, 1990). In this study, for the identification stage, serial-parallel identification is used for inputs of ANN. These inputs are the actual input with its past values ( ( ) [ ( 1),..., ( 15]) *uk uk uk* and the actual output with its past values ( ( ) [ ( 1),..., ( 15)]) *yk yk yk* . The output of ANN identification block is *y*ˆ( ) *k* . After ANN identification is completed, ANN controller weights are tuned with respect to overall closed-loop error function (Narendra and Parthasarathy,1990).

*i v*

*<sup>x</sup>*

Fig. 8. Perceptron as a hidden neuron

y(k-1)

y(k-2)

u(k-1)

.

closed-loop error function (Narendra and Parthasarathy,1990).

u(k-2)

Fig. 9. MLP implementing NARMA model

weights of the layers.

Input Layer Hidden Layer Output Layer

Although MLP-ANNs are algebraic models, MLP-ANNs can define nonlinear discrete-time dynamical system due to the fact that its inputs can be connected with delayed outputs. As shown in Fig. 9, a multi-input, multi-output MLP with one hidden layer can be used as a Nonlinear Auto-Regressive-Moving-Array (NARMA) model. Input vector of this NARMA model *x yk yk n uk k n* [ ( 1),..., ( ), ( 1),...,( )] where *n* is the finite value and *v* and *w* are

Input Layer Hidden Layer Output Layer

In most industrial cases, an ANN is an adaptive system that changes its internal information in the learning phase. A general feed-forward inverse control system contains two MLP-ANNs such as identification and control structures, which are shown in Fig. 10 (Narendra and Parthasarathy, 1990). In this study, for the identification stage, serial-parallel identification is used for inputs of ANN. These inputs are the actual input with its past values ( ( ) [ ( 1),..., ( 15]) *uk uk uk* and the actual output with its past values ( ( ) [ ( 1),..., ( 15)]) *yk yk yk* . The output of ANN identification block is *y*ˆ( ) *k* . After ANN identification is completed, ANN controller weights are tuned with respect to overall

vji

(.) *w*

wkj

*u y* (.)

y(k)

Fig. 10. Feed-forward inverse control system using MLP-ANN.

One of the most important problems in real world applications is the delay time defined the time required before observing the output change after applying a control input. To overcome delay time problem, Smith compensator structure can be used in ANN-based controllers (Ekren et al., 2010; Huang and Lewis, 2003; Lin et al., 2008; Slanvetpan et al., 2003). Inverse system MLP-ANN controller with Smith predictor was used for compensation of the delay time of the plant in Fig. 11. The MLP in both EEV and compressor controllable parts are trained with the gradient algorithm. The number of neurons in the hidden layer of MLP was selected as 20 experimentally. The EEV was controlled using an inverse system ANN controller with Smith compensator. Inputs of the first controller were EEV opening values and SH error with their 15 past values. The output of this controller was EEVO. On the other hand, compressor was controlled using an inverse system ANN controller. Inputs of this controller were compressor frequency and *TWO* error values with their 15 past values. The output of this controller was the frequency change of the supply voltage of compressor electric motor (*f*).

### **3. Applications of the controllers**

In this study, the controllers are designed as decoupled ones without interfering loops (Li et al., 2008). In the experimental setup used in this study, there were some limitations of the equipment. EEV opening value is restricted between 0% and 20% since its limits are 15% and 35% to prevent the low pressure alert and to avoid liquid entrance into the compressor. Instantaneous frequency change is restricted between 0 Hz and 20 Hz to prevent system from the vibration and the unsuitable lubrication since the frequency limits are 30 Hz and 50 Hz. By considering these limitations, three different controllers such as PID, FL, and ANN were examined in the VSRS.

Operation of Compressor and Electronic Expansion Valve via Different Controllers 233

Fig. 12. Superheat change according to control method (the first case).

Fig. 13. Water outlet temperature change according to control method.

dotted line in the Fig. 14 shows the moment of the disturbance.

The system was tested with the set value for SH degree of 7°C and Two of 9°C using all controller combinations. Results for SH can be seen in Fig. 14. Since the Two results were similar to results obtained in Fig. 13, Two graphs were not re-plotted here. The vertical

**3.3 Both compressor and EEV control** 

Fig. 11. Smith delay time compensator configuration using MLP-ANN.

Control experiments, conducted during the study, have been classified in three groups. The first was controlling EEV opening, the second one was controlling compressor frequency, and the last one was controlling both together. For the first and second groups, the other controllable part was operated at a constant value. All cases were tested using three different control algorithms of PID, FL and ANN. In addition, the cooling load was decreased 40% of full load to simulate a disturbance input in all cases. This is presumed to be by a change in water flow.

All controller algorithms were implemented using the most famous software of Matlab version 2011a. No ready-made toolbox routines were used throughout the study. The personal computer with a dual-core processor, 2 GB DDR Ram, and a special internal data acquisition board were used to implement controllers and to read system outputs.

## **3.1 EEV opening control with fixed compressor frequency**

EEV opening amount was controlled to drive SH degree to a desired value. Scroll compressor frequency was fixed at 50 Hz and desired SH value was set to 6°C in order to test only EEV control algorithm. Variations of the SH degree at the outlet of the evaporator were compared and visualized in Fig. 12. The vertical dotted line in this figure shows the moment of the disturbance.

## **3.2 Compressor frequency control with fixed EEV opening**

Compressor speed was controlled to drive water temperature at the outlet of the evaporator. EEV opening amount was fixed at 30% to obtain effects of the compressor control algorithm alone. This value was chosen since it gives better COP value for this system (Ekren and Kücüka, 2010). Water temperature variations can be seen in Fig. 13. The vertical dotted line in this figure shows the moment of the disturbance.

MLP-ANN Controller

(Inverse Plant)

Fig. 11. Smith delay time compensator configuration using MLP-ANN.

*kr* )( *ku* )(

delays

delays

<sup>+</sup> - <sup>+</sup> -

*ke* )( *ke* )(

be by a change in water flow.

moment of the disturbance.

Plant

MLP-ANN Identification

delays

delays

Control experiments, conducted during the study, have been classified in three groups. The first was controlling EEV opening, the second one was controlling compressor frequency, and the last one was controlling both together. For the first and second groups, the other controllable part was operated at a constant value. All cases were tested using three different control algorithms of PID, FL and ANN. In addition, the cooling load was decreased 40% of full load to simulate a disturbance input in all cases. This is presumed to

All controller algorithms were implemented using the most famous software of Matlab version 2011a. No ready-made toolbox routines were used throughout the study. The personal computer with a dual-core processor, 2 GB DDR Ram, and a special internal data

EEV opening amount was controlled to drive SH degree to a desired value. Scroll compressor frequency was fixed at 50 Hz and desired SH value was set to 6°C in order to test only EEV control algorithm. Variations of the SH degree at the outlet of the evaporator were compared and visualized in Fig. 12. The vertical dotted line in this figure shows the

Compressor speed was controlled to drive water temperature at the outlet of the evaporator. EEV opening amount was fixed at 30% to obtain effects of the compressor control algorithm alone. This value was chosen since it gives better COP value for this system (Ekren and Kücüka, 2010). Water temperature variations can be seen in Fig. 13. The vertical dotted line

acquisition board were used to implement controllers and to read system outputs.

**3.1 EEV opening control with fixed compressor frequency** 

**3.2 Compressor frequency control with fixed EEV opening** 

in this figure shows the moment of the disturbance.


*Ls e*

*ke* )(

*ky* )(

Fig. 12. Superheat change according to control method (the first case).

Fig. 13. Water outlet temperature change according to control method.

#### **3.3 Both compressor and EEV control**

The system was tested with the set value for SH degree of 7°C and Two of 9°C using all controller combinations. Results for SH can be seen in Fig. 14. Since the Two results were similar to results obtained in Fig. 13, Two graphs were not re-plotted here. The vertical dotted line in the Fig. 14 shows the moment of the disturbance.

Operation of Compressor and Electronic Expansion Valve via Different Controllers 235

stable SH and Two values in the steady state. ANN controller pair was selected to achieve minimum power consumption and more stable SH and Two values in the transient behavior and better rising time performance (reach to the desired value rapidly). In the second case, ANN controller showed 8.1 percent and 6.6 percent lower power consumption than both PID and Fuzzy controllers, respectively. In addition, Fuzzy controller showed 1.4 percent lower power consumption than PID controller. While a chiller system is being operated at a lower water flow rate, which means less cooling load, compressor speed decreases. Hence, power consumption of the compressor decreases. It can be seen from Figs. 12-14 that ANN control algorithm gave more robust response to the disturbance effect in the system. On the other hand, other control algorithms needed longer response time to eliminate the disturbance effect. Since most consumer electronics products are under the influence of disturbance effects, control algorithms whose transient response is robust against to the disturbance effect should be used to provide consumer comfort. Although controller design based on ANN is an expensive method in the manner of hardware and software, using such

Ahmed, M. S., 2000. Neural-Net-Based Direct Adaptive Control for a Class of Nonlinear

Aprea, C., Renno, C., 2009. Experimental modelling of variable speed system. Int. J. Energy

Aprea, C., Mastrullo, R., Renno, C., 2004. Fuzzy control of the compressor speed in a

Aprea, C., Mastrullo, R., Renno, C., 2006a. Experimental analysis of the scroll compressor

Aprea, C., Mastrullo, R., Renno, C., 2006b. Performance of thermostatic and electronic expansion valves controlling the compressor. Int. J. Energy Res. 30, 1313-1322. Aprea, C.,Mastrullo, R.,Renno, C., 2009.Determinationof theoptimal working of compressor.

Astrom, K., Hagglund, T., 1995. PID Controllers: Theory, Design, and Tuning, second ed.

Ekren, O., Kucuka, S. 2010. Energy saving potential of chiller system with fuzzy logic

Ekren, O., Sahin, S., Isler, Y. 2010. Comparison of Different Controllers for Variable Speed

Ekren, O., Sahin, S., Isler, Y. 2011. Experimental Development of Transfer Functions for

Jiangjiang, W., Dawei, A., Chengzhi, L., 2006. Application of fuzzy-PID controller in heating

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Katsuhiko, O., 2002. Modern Control Engineering. Prentice Hall, NJ.

Compressor and Electronic Expansion Valve, International Journal of Refrigeration,

Variable Speed Chiller System, Proceedings of the IMechE Part E: Journal of Process Mechanical Engineering, article in pres, DOI: 10.1177/0954408911414805. Huang, J.Q., Lewis, F.L., 2003. Neural-network predictive control for nonlinear dynamic

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a controller seems necessary if the system has much disturbance.

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33(6), 1161–1168.

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**5. References** 

Res. 33, 29-37.

Fig. 14. Superheat change according to control method (the second case).

In addition, power consumptions were measured using wattmeter for the same duty, which can be seen in Fig. 15. Lower power consumption was obtained via ANN control algorithm.

Fig. 15. Power consumptions of the compressor.

#### **4. Conclusion**

In this study, effects of different control methods (PID, FL, and ANN) on variable speed compressor (VSC) and electronic expansion valve (EEV) in a VSRS were examined. Two different procedures were applied to control EEV and VSC: controlling each part individually while the other was set to a constant value and controlling both parts together using the same algorithm. In both cases, the results of the three controllers satisfied for the set values of SH and Two. PID controller presented reasonable control solution for more stable SH and Two values in the steady state. ANN controller pair was selected to achieve minimum power consumption and more stable SH and Two values in the transient behavior and better rising time performance (reach to the desired value rapidly). In the second case, ANN controller showed 8.1 percent and 6.6 percent lower power consumption than both PID and Fuzzy controllers, respectively. In addition, Fuzzy controller showed 1.4 percent lower power consumption than PID controller. While a chiller system is being operated at a lower water flow rate, which means less cooling load, compressor speed decreases. Hence, power consumption of the compressor decreases. It can be seen from Figs. 12-14 that ANN control algorithm gave more robust response to the disturbance effect in the system. On the other hand, other control algorithms needed longer response time to eliminate the disturbance effect. Since most consumer electronics products are under the influence of disturbance effects, control algorithms whose transient response is robust against to the disturbance effect should be used to provide consumer comfort. Although controller design based on ANN is an expensive method in the manner of hardware and software, using such a controller seems necessary if the system has much disturbance.

### **5. References**

234 Fuzzy Logic – Controls, Concepts, Theories and Applications

Fig. 14. Superheat change according to control method (the second case).

Fig. 15. Power consumptions of the compressor.

**4. Conclusion** 

In addition, power consumptions were measured using wattmeter for the same duty, which can be seen in Fig. 15. Lower power consumption was obtained via ANN control algorithm.

In this study, effects of different control methods (PID, FL, and ANN) on variable speed compressor (VSC) and electronic expansion valve (EEV) in a VSRS were examined. Two different procedures were applied to control EEV and VSC: controlling each part individually while the other was set to a constant value and controlling both parts together using the same algorithm. In both cases, the results of the three controllers satisfied for the set values of SH and Two. PID controller presented reasonable control solution for more


**12** 

*Iran* 

**Intelligent Neuro-Fuzzy Application** 

 **in Semi-Active Suspension System** 

*Sharif University of Technology, School of Science and Engineering,* 

In the field of artificial intelligence, Neuro-Fuzzy (NF) refers to combinations of artificial neural networks and fuzzy logic and first time introduced in 1990s. Neuro-fuzzy results in a intelligent system that synergizes these two techniques by combining the human-like reasoning style of fuzzy systems with the learning and connectionist structure of neural networks. NF is widely termed as Fuzzy Neural Network (FNN) or Neuro-Fuzzy System (NFS) in the literature. NFS (the more popular term is used henceforth) incorporates the human-like reasoning style of fuzzy systems through the use of fuzzy sets and a linguistic model consisting of a set of IF-THEN fuzzy rules. The main strength of neuro-fuzzy systems is that they are universal approximations with the ability to solicit interpretable IF-THEN rules. The strength of neuro-fuzzy systems involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy. In practice, one of the two properties prevails. The neuro-fuzzy in fuzzy modeling research field is divided into two areas: linguistic fuzzy modeling that is focused on interpretability, mainly the Mamdani model; and precise fuzzy

modeling that is focused on accuracy, mainly the Takagi-Sugeno-Kang (TSK) model.

The previous studies made full use of the advantages of the neural-network and the fuzzy logic controller and solved the different problems in suspension systems. Few researches involved combination of the two techniques to solve the time-delay and the inherent nonlinear nature of the Magneto-Rheological (MR) dampers in semi-active strategy for full car model with high degrees of freedom. In this chapter, four MR dampers are added in a suspension system between body and wheels parallel with passive dampers. For the intelligent system, fuzzy controller which inputs are relative velocities across MR dampers that are excited by road profile for predicting the force of MR damper to receive a desired passenger's displacement is applied. When predicting the displacement and velocity of MR dampers, a four-layer feed forward neural network, trained on-line under the Levenberg– Marquardt (LM) algorithm, is adopted. In order to verify the effectiveness of the proposed neuro-fuzzy control strategy, the uncontrolled system and the clipped optimal controlled suspension system are compared with the neuro-fuzzy controlled system. Through a numerical example under actual road profile excitation, it can be concluded that the control strategy is very important for semi-active control, the neuro-fuzzy control strategy can

**1. Introduction** 

Seiyed Hamid Zareh, Atabak Sarrafan,

Meisam Abbasi and Amir Ali Akbar Khayyat


## **Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System**

Seiyed Hamid Zareh, Atabak Sarrafan, Meisam Abbasi and Amir Ali Akbar Khayyat *Sharif University of Technology, School of Science and Engineering, Iran* 

## **1. Introduction**

236 Fuzzy Logic – Controls, Concepts, Theories and Applications

Lazzarin, R., Noro, M., 2008. Experimental comparison of electronic and thermostatic

Li, H., Jeong, S.K., Yoon, J.I., You, S.S., 2008. An empirical model for independent control of variable speed refrigeration system. Appl. Therm. Eng. 28, 1918-1924. Lightbody, G., Irwin, G.W., 1995. Direct Neural Model Reference Adaptive Control. *IEE* 

Lin, C.L., Chen, C.H., Shiu, B.M., 2008. A neural net-based timedelay compensation scheme and disturbance rejection for pneumatic systems. J. Intell. Manuf., 19,407-19,419. Meireles, M.R.G., Almeida, P.E.M., Simoes, M.G., 2003. A comprehensive review for

Narendra, K.S., 1993. Hierarchical neural network models for identification and control. In:

Narendra, K.S., Parthasarathy, K., 1990. Identification and control of dynamical systems

Nasutin, H., Hassan, M.N.W., 2006. Potential electricity savings by variable speed control of

Noriega, J. R., Wang, H., 1998. A Direct Adaptive Neural-Network Control for Unknown

Omidvar, O. M., Elliott, D. L. 1997. *Neural Systems for Control*. Elsevier Science & Technology

Ross, T.J., 2004. Fuzzy Logic with Engineering Applications. John Wiley and Sons, USA. Sahin, S., Ekren, O., Isler, Y., Güzeliş, C. 2010. Design and Implementation of Artificial

Refrigeration Systems Journal of Engineers and Machinery, 51(603), 8–15. Slanvetpan, T., Barat, R.B., Stevens, J.G., 2003. Process control of a laboratory combustor using artificial neural networks. Comput. Chem. Eng. 27, 1605-1616.

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*Proceeding Control Theory Applications*, 142(1), 31-43.

International Conference of the IEEE, vol. 287.

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using neural networks. IEEE Trans. Neural Netw. 1, 4-27.

113-118.

585-601.

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759-765.

expansion valves performance in an air conditioning plant. Int. J. Refrigeration 31,

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compressor for air conditioning systems. Clean Technol. Environ. Policy 8, 105-111.

Nonlinear Systems and Its Application. *IEEE Transactions on Neural Networks*, 9(1),

Neural Networks Controller via a Real-Time Simulator for Variable Speed

In the field of artificial intelligence, Neuro-Fuzzy (NF) refers to combinations of artificial neural networks and fuzzy logic and first time introduced in 1990s. Neuro-fuzzy results in a intelligent system that synergizes these two techniques by combining the human-like reasoning style of fuzzy systems with the learning and connectionist structure of neural networks. NF is widely termed as Fuzzy Neural Network (FNN) or Neuro-Fuzzy System (NFS) in the literature. NFS (the more popular term is used henceforth) incorporates the human-like reasoning style of fuzzy systems through the use of fuzzy sets and a linguistic model consisting of a set of IF-THEN fuzzy rules. The main strength of neuro-fuzzy systems is that they are universal approximations with the ability to solicit interpretable IF-THEN rules.

The strength of neuro-fuzzy systems involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy. In practice, one of the two properties prevails. The neuro-fuzzy in fuzzy modeling research field is divided into two areas: linguistic fuzzy modeling that is focused on interpretability, mainly the Mamdani model; and precise fuzzy modeling that is focused on accuracy, mainly the Takagi-Sugeno-Kang (TSK) model.

The previous studies made full use of the advantages of the neural-network and the fuzzy logic controller and solved the different problems in suspension systems. Few researches involved combination of the two techniques to solve the time-delay and the inherent nonlinear nature of the Magneto-Rheological (MR) dampers in semi-active strategy for full car model with high degrees of freedom. In this chapter, four MR dampers are added in a suspension system between body and wheels parallel with passive dampers. For the intelligent system, fuzzy controller which inputs are relative velocities across MR dampers that are excited by road profile for predicting the force of MR damper to receive a desired passenger's displacement is applied. When predicting the displacement and velocity of MR dampers, a four-layer feed forward neural network, trained on-line under the Levenberg– Marquardt (LM) algorithm, is adopted. In order to verify the effectiveness of the proposed neuro-fuzzy control strategy, the uncontrolled system and the clipped optimal controlled suspension system are compared with the neuro-fuzzy controlled system. Through a numerical example under actual road profile excitation, it can be concluded that the control strategy is very important for semi-active control, the neuro-fuzzy control strategy can

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 239

The clipped optimal control strategy for an MR damper usually involves two steps. The first step is to assume an ideal actively–controlled device and construct an optimal controller for this active device. In the second step, a secondary controller finally determines the input

That is, the secondary controller clips the optimal force in a manner consistent with the dissipative nature of the device. The block diagram of the clipped optimal algorithm is

The clipped optimal control approach is to append a force feedback loop to induce the MR damper to produce approximately a desired control force fc. The Linear Quadratic Regulator (LQR) algorithm has been employed both for active control and for semi-active control. Using this algorithm, the optimal control force fc for f, which is force generated by an MR damper. (Zareh et al) utilized clipped optimal algorithm for semi-active full car model.

**2.1 Clipped optimal algorithm** 

voltage of the MR damper.

Fig. 2. Clipped optimal algorithm block diagram

dynamics of the MR damper and suspension system.

electronics to the automobile industry.

**3. Neuro-fuzzy strategy using in semi-active vibration control** 

Unfortunately, due to the inherent nonlinear nature of the MR damper to generate a force, a similar model for its inverse dynamics is difficult to obtain mathematically and also due to the nonlinearity of suspension system, its equations are complicated. Because of these reasons, a neural network with fuzzy logic controller is constructed to copy the inverse

Neuro-fuzzy controller is an artificial neural network, which is used to aggregate rules and to provide control result for the designed fuzzy logic controller. Application of fuzzy inference systems as a Fuzzy Logic Controller (FLC) has gradually been recognized as the most significant and fruitful application for fuzzy logic and fuzzy set theory. In the past few years, advances in microprocessors and hardware technologies have created an even more diversified application domain for fuzzy logic controllers, which range from consumer

shown in Fig. 2.

determine voltage of the MR damper quickly and accurately, and the control effect of the neuro-fuzzy control strategy is better than that of the other control strategies. First have brief reviewed on modelling of a full car model and third section clearly reveals more detailed information about neuro-fuzzy strategy for the full-car model. Finally in sections 4 and 5 the results will be presented and discussed.

## **2. Full car model**

 In the full-car model, 11-DOFs is assumed, all wheels and passengers are dependent on each other and on the car's body. It is assumed that each wheel has an effect on the spring and damper of other wheels, and two axles of vehicle are dependent. MR actuator is utilized to damp the effect of road profile on the passengers. Note that MR shock absorber is added between the axel and car's body. In the full-car model, the effects of the rotations of the body around the roll and pitch axes are simulated. The suspension system using a full-car model has 11-DOFs, four of them for the four wheels, three for body displacement and its rotations and the last four for the passengers. Schematic of the full-car model with 11-DOFs and addition of the MR damper is shown in Fig. 1.

Fig. 1. Full-car model with 11-DOFs

where Mb, m1, m2, m3, m4, m5, m6, m7 and m8 stand for the mass of the car's body, mass of four wheels and mass of passengers, respectively. I1 and I2 are the moments of inertia of the car's body around two axes. The terms k1, k2, k3, k4, k5, k6, k7 and k8 are stiffness of the springs of the suspension system and stiffness of the springs of passengers seat, respectively. The terms kt1, kt2, kt3 and kt4 are stiffness of the tires. The terms b1, b2, b3, b4, b5, b6, b7 and b8 are coefficients of car and passenger's seat dampers. Then, br1, br2, br3 and br4 are passive coefficients of the MR dampers, respectively. x1, x2, x3, x4, x5, x6, x7, x8, x9, φ and θ indicate the DOFs of the suspension system model. The terms xi1, xi2, xi3 and xi4 indicate load profile disturbance, respectively. These parameters are used to clipped optimal strategy which is considered as a desire to train neural network and tuning fuzzy memberships. Here optimal force is depending on all state variables (Zareh et al); therefore model with detail information is necessary.

## **2.1 Clipped optimal algorithm**

238 Fuzzy Logic – Controls, Concepts, Theories and Applications

determine voltage of the MR damper quickly and accurately, and the control effect of the neuro-fuzzy control strategy is better than that of the other control strategies. First have brief reviewed on modelling of a full car model and third section clearly reveals more detailed information about neuro-fuzzy strategy for the full-car model. Finally in sections 4

 In the full-car model, 11-DOFs is assumed, all wheels and passengers are dependent on each other and on the car's body. It is assumed that each wheel has an effect on the spring and damper of other wheels, and two axles of vehicle are dependent. MR actuator is utilized to damp the effect of road profile on the passengers. Note that MR shock absorber is added between the axel and car's body. In the full-car model, the effects of the rotations of the body around the roll and pitch axes are simulated. The suspension system using a full-car model has 11-DOFs, four of them for the four wheels, three for body displacement and its rotations and the last four for the passengers. Schematic of the full-car model with 11-DOFs and

where Mb, m1, m2, m3, m4, m5, m6, m7 and m8 stand for the mass of the car's body, mass of four wheels and mass of passengers, respectively. I1 and I2 are the moments of inertia of the car's body around two axes. The terms k1, k2, k3, k4, k5, k6, k7 and k8 are stiffness of the springs of the suspension system and stiffness of the springs of passengers seat, respectively. The terms kt1, kt2, kt3 and kt4 are stiffness of the tires. The terms b1, b2, b3, b4, b5, b6, b7 and b8 are coefficients of car and passenger's seat dampers. Then, br1, br2, br3 and br4 are passive coefficients of the MR dampers, respectively. x1, x2, x3, x4, x5, x6, x7, x8, x9, φ and θ indicate the DOFs of the suspension system model. The terms xi1, xi2, xi3 and xi4 indicate load profile disturbance, respectively. These parameters are used to clipped optimal strategy which is considered as a desire to train neural network and tuning fuzzy memberships. Here optimal force is depending on all state variables (Zareh et al); therefore model with

and 5 the results will be presented and discussed.

addition of the MR damper is shown in Fig. 1.

Fig. 1. Full-car model with 11-DOFs

detail information is necessary.

**2. Full car model** 

The clipped optimal control strategy for an MR damper usually involves two steps. The first step is to assume an ideal actively–controlled device and construct an optimal controller for this active device. In the second step, a secondary controller finally determines the input voltage of the MR damper.

That is, the secondary controller clips the optimal force in a manner consistent with the dissipative nature of the device. The block diagram of the clipped optimal algorithm is shown in Fig. 2.

The clipped optimal control approach is to append a force feedback loop to induce the MR damper to produce approximately a desired control force fc. The Linear Quadratic Regulator (LQR) algorithm has been employed both for active control and for semi-active control. Using this algorithm, the optimal control force fc for f, which is force generated by an MR damper. (Zareh et al) utilized clipped optimal algorithm for semi-active full car model.

Fig. 2. Clipped optimal algorithm block diagram

## **3. Neuro-fuzzy strategy using in semi-active vibration control**

Unfortunately, due to the inherent nonlinear nature of the MR damper to generate a force, a similar model for its inverse dynamics is difficult to obtain mathematically and also due to the nonlinearity of suspension system, its equations are complicated. Because of these reasons, a neural network with fuzzy logic controller is constructed to copy the inverse dynamics of the MR damper and suspension system.

Neuro-fuzzy controller is an artificial neural network, which is used to aggregate rules and to provide control result for the designed fuzzy logic controller. Application of fuzzy inference systems as a Fuzzy Logic Controller (FLC) has gradually been recognized as the most significant and fruitful application for fuzzy logic and fuzzy set theory. In the past few years, advances in microprocessors and hardware technologies have created an even more diversified application domain for fuzzy logic controllers, which range from consumer electronics to the automobile industry.

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 241

The neural network is trained to generate the one step ahead prediction of the displacement

ẋk+3, ẋk+2, ẋk+1, ẋk), the delayed force which is predicted by fuzzy controller (fk+1), and the disturbance input (dk). At the initial time, the inputs of the network will be assigned the value of zero in accordance with the actual initial circumstance. Before online training, the network is trained off-line so as to obtain the weights that are as near to the desired value as

The second part is the fuzzy controller, whose input is the measured relative velocity across MR dampers. The disturbance can be calculated by road profile model. The output of the fuzzy controller is the control force of the MR dampers. The main aim of this part is to determine the control force of the MR dampers quickly in accordance with the input excitation. How to design the fuzzy controller will be explained in the following subsection. In order to reach this aim, it is required to predict the responses of passengers in accordance

The third part is the feedforward neural network to be trained on-line to generate the required voltage of MR damper v. In fact, this part is the inverse dynamics model of MR damper.

This block diagram is designed by authors using of combination of advanced works. In this strategy there are three neural networks. First is to mapping of suspension system. Second is inverse model of MR damper and third is forward model of MR damper. The difference between inverse and forward model is their inputs and outputs where the inputs of inverse model is outputs of forward model and vice-versa. All data that are used to training, testing

As mentioned, due to the inherent non-linear nature of the MR damper, a model for inverse dynamics of MR damper is difficult to obtain mathematically. Because of this reason, a feedforward back propagation neural network is constructed to copy the inverse dynamics of the MR damper. This neural network model is trained using input-output data generated analytically using the simulated MR model based on clipped algorithm. Using this inverse

and validating are LQR results because, they are optimal and our desired.

*<sup>k</sup> <sup>x</sup>* . Inputs to this network are the delayed outputs (xk+3, xk+2, xk+1, xk,

Fig. 3. Architecture of the neuro-fuzzy control strategy

ˆ

<sup>1</sup> ˆ

*<sup>k</sup> <sup>x</sup>* and the velocity <sup>1</sup>

possible (Yildirim et al).

with the optimal responses.

Indeed, for complex and/or ill-defined systems that are not easily subjected to conventional automatic control methods, FLCs provide a feasible alternative since they can capture the approximate, qualitative aspects of human reasoning and decision-making processes. However, without adaptive capability, the performance of FLCs relies exclusively on two factors: the availability of human experts, and the knowledge acquisition techniques to convert human expertise into appropriate fuzzy if-then rules and membership functions. These two factors substantially restrict the application domain of FLCs.

Consequently, a neural control design approach can usually be carried over directly to the design of fuzzy controllers, unless the design method depends directly on the specific architecture of the neural networks used. This portability endows us with a number of design methods for fuzzy controllers which can easily take advantage of a priori human information and expertise in the form of fuzzy if-then rules. The result of the above methodology is called Neuro-Fuzzy Control method. Neural and fuzzy logic controllers have been successfully implemented in the control of linear and nonlinear systems.

Unlike conventional controllers, such controllers do not require mathematical model and they can easily deal with the nonlinearities and uncertainties of the controlled systems. Also, a Levenberg-Marquardt (LM) neural controller has been designed for variable geometry suspension systems with MR actuators.

In the present research, an optimal controller Linear Quadratic Regulator (LQR) is designed for control of a semi-active suspension system for a full-model vehicle, using a neuro-fuzzy along with Levenberg-Marquardt learning and the results compared with Linear Quadratic Gaussian (LQG) (Zareh et al). The purpose in a vehicle suspension system is reduction of transmittance of vibrational effects from the road to the vehicle's passengers, hence providing ride comfort. To accomplish this, one can first design a LQR controller for the suspension system, using an optimal control method and use it to train a neuro-fuzzy controller. This controller can be trained using the LQR controller output error on an online manner.

Once trained, the LQR controller is automatically removed from the control loop and the neuro-fuzzy controller takes on. In case of a change in the parameters of the system under control or excitations, the LQR controller enters the control loop again and the neural network gets trained again for the new condition therefore it can ensure the robustness of strategy due to changes in excitations (Sadati et al). An important characteristic of the proposed controller is that no mathematical model is needed for the system components, such as the non-linear actuator, spring, or shock absorbers.

The basic idea of the proposed neuro-fuzzy control strategy is that the forces of the MR dampers are determined by a fuzzy controller, whose inputs are the measured velocity response predicted by a neural network (Zh et al). The architecture of this strategy is shown in Fig. 3, which consists of two parts to perform different tasks. The first part is for the neural network to be trained on-line. The numbers of the sample data pairs are 3500, the training data pairs increase step by step during the entrance disturbance from road profile.

To select the network architecture, it is required to determine the numbers of inputs, outputs, hidden layers, and nodes in the hidden layers; this is usually done by trial and error. Therefore, one hidden layer, with six nodes, was adopted as one of the best suitable topologies for neural network.

Indeed, for complex and/or ill-defined systems that are not easily subjected to conventional automatic control methods, FLCs provide a feasible alternative since they can capture the approximate, qualitative aspects of human reasoning and decision-making processes. However, without adaptive capability, the performance of FLCs relies exclusively on two factors: the availability of human experts, and the knowledge acquisition techniques to convert human expertise into appropriate fuzzy if-then rules and membership functions.

Consequently, a neural control design approach can usually be carried over directly to the design of fuzzy controllers, unless the design method depends directly on the specific architecture of the neural networks used. This portability endows us with a number of design methods for fuzzy controllers which can easily take advantage of a priori human information and expertise in the form of fuzzy if-then rules. The result of the above methodology is called Neuro-Fuzzy Control method. Neural and fuzzy logic controllers

Unlike conventional controllers, such controllers do not require mathematical model and they can easily deal with the nonlinearities and uncertainties of the controlled systems. Also, a Levenberg-Marquardt (LM) neural controller has been designed for variable geometry

In the present research, an optimal controller Linear Quadratic Regulator (LQR) is designed for control of a semi-active suspension system for a full-model vehicle, using a neuro-fuzzy along with Levenberg-Marquardt learning and the results compared with Linear Quadratic Gaussian (LQG) (Zareh et al). The purpose in a vehicle suspension system is reduction of transmittance of vibrational effects from the road to the vehicle's passengers, hence providing ride comfort. To accomplish this, one can first design a LQR controller for the suspension system, using an optimal control method and use it to train a neuro-fuzzy controller. This

Once trained, the LQR controller is automatically removed from the control loop and the neuro-fuzzy controller takes on. In case of a change in the parameters of the system under control or excitations, the LQR controller enters the control loop again and the neural network gets trained again for the new condition therefore it can ensure the robustness of strategy due to changes in excitations (Sadati et al). An important characteristic of the proposed controller is that no mathematical model is needed for the system components,

The basic idea of the proposed neuro-fuzzy control strategy is that the forces of the MR dampers are determined by a fuzzy controller, whose inputs are the measured velocity response predicted by a neural network (Zh et al). The architecture of this strategy is shown in Fig. 3, which consists of two parts to perform different tasks. The first part is for the neural network to be trained on-line. The numbers of the sample data pairs are 3500, the training data pairs increase step by step during the entrance disturbance from road profile. To select the network architecture, it is required to determine the numbers of inputs, outputs, hidden layers, and nodes in the hidden layers; this is usually done by trial and error. Therefore, one hidden layer, with six nodes, was adopted as one of the best suitable

have been successfully implemented in the control of linear and nonlinear systems.

controller can be trained using the LQR controller output error on an online manner.

such as the non-linear actuator, spring, or shock absorbers.

These two factors substantially restrict the application domain of FLCs.

suspension systems with MR actuators.

topologies for neural network.

Fig. 3. Architecture of the neuro-fuzzy control strategy

The neural network is trained to generate the one step ahead prediction of the displacement <sup>1</sup> ˆ *<sup>k</sup> <sup>x</sup>* and the velocity <sup>1</sup> ˆ *<sup>k</sup> <sup>x</sup>* . Inputs to this network are the delayed outputs (xk+3, xk+2, xk+1, xk, ẋk+3, ẋk+2, ẋk+1, ẋk), the delayed force which is predicted by fuzzy controller (fk+1), and the disturbance input (dk). At the initial time, the inputs of the network will be assigned the value of zero in accordance with the actual initial circumstance. Before online training, the network is trained off-line so as to obtain the weights that are as near to the desired value as possible (Yildirim et al).

The second part is the fuzzy controller, whose input is the measured relative velocity across MR dampers. The disturbance can be calculated by road profile model. The output of the fuzzy controller is the control force of the MR dampers. The main aim of this part is to determine the control force of the MR dampers quickly in accordance with the input excitation. How to design the fuzzy controller will be explained in the following subsection. In order to reach this aim, it is required to predict the responses of passengers in accordance with the optimal responses.

The third part is the feedforward neural network to be trained on-line to generate the required voltage of MR damper v. In fact, this part is the inverse dynamics model of MR damper.

This block diagram is designed by authors using of combination of advanced works. In this strategy there are three neural networks. First is to mapping of suspension system. Second is inverse model of MR damper and third is forward model of MR damper. The difference between inverse and forward model is their inputs and outputs where the inputs of inverse model is outputs of forward model and vice-versa. All data that are used to training, testing and validating are LQR results because, they are optimal and our desired.

As mentioned, due to the inherent non-linear nature of the MR damper, a model for inverse dynamics of MR damper is difficult to obtain mathematically. Because of this reason, a feedforward back propagation neural network is constructed to copy the inverse dynamics of the MR damper. This neural network model is trained using input-output data generated analytically using the simulated MR model based on clipped algorithm. Using this inverse

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 243

where wjk is the weight between the jth neuron in the previous layer and the kth neuron in the current layer, Oj is the output of the jth neuron in the previous layer, f(.) is the neuron's activation function which can be a linear function, a radial basis function, and a sigmoid function, and yk is the bias of the kth neuron. Feed forward neural network often has one or more hidden layers of sigmoid neurons followed by an output layer of linear neurons. Multiple layers of neurons with nonlinear transfer functions allow the network to learn nonlinear and linear relationships between input and output vectors. In the neural network architecture as shown in Fig. 4, the logarithmic sigmoid transfer function is chosen as the

Ok= f(netk+θk)=1/(1+e-( netk+θk)) (3)

 Ok=f(netk+θk)= netk+θk (4) We note that neural network needs to be trained before it can predict any responses. As the inputs are applied to the neural network, the network outputs (.̂ ) are compared with the targets (.). The difference or error between both is processed back through the network to update the weights and biases of the neural network so that the network outputs match

The input and output data are usually represented by vectors called training pairs. The process as mentioned above is repeated for all the training pairs in the data set, until the network error converges to a threshold minimum defined by a corresponding performance function. In this research, the Mean Square Error (MSE) function is adopted (desired MSE is 1e-5). LM algorithm is adapted to train the neural network (Zh et al), which can be written

The linear transfer function is chosen as the activation function of the output layer.

Fig. 4. The neural network architecture

activation function of the hidden layer.

closer with the targets.

as a following equation:

dynamics of MR damper, the required voltage signal v is calculated based on the desired control force fc, the velocity of MR dampers 1 ˆ *<sup>k</sup> <sup>x</sup>* , and the displacement of MR damper xk+1.

The fourth part is the feedforward back propagation neural network to be trained on-line in order to generate the MR damper forces fMR. The inputs of this neural network are voltage signal v, the velocity of MR damper <sup>1</sup> ˆ *<sup>k</sup> <sup>x</sup>* , and the displacement of MR damper xk+1. The difference between inverse and forward model is in inputs and outputs. The outputs of inverse model are the inputs of forward model.

The third and fourth part of the proposed neuro-fuzzy control strategy which is a threelayer feedforward neural network consists of an input layer with 3 nodes, a hidden layer with 6 nodes, and output layer with one node. Determining the numbers of inputs, outputs, hidden layers, and nodes in hidden layers of these three neural networks is done by trial and error. For all neural parts some of the corresponded results that are obtained by LQR are used as a desire data and some others are used as a testing data.

At the same time, the actual responses will feed back to the neural network and the weights and bias will be revised in real time. In this research, results from the optimal control history analysis method are used to simulate the actual measured responses. The errors between the predicted responses and the actual responses are used to update the weights of the neural network on-line.

### **3.1 The neural network based on Levenberg-Marquardt (LM) algorithm**

The MR damper model discussed earlier in this research estimates the damper forces based on the inputs of the reactive velocity. In such case, it is essential to develop an inverse dynamic model that predicts the corresponding control force which is to be generated by dampers.

Neural network is a simplified model of the biological structure which is found in human brains. This model consists of elementary processing units (also called neurons). It is the large amount of interconnections between these neurons and their capability to learn from data which makes neural network as a strong predicting and classification tool. In this study, a three-layer feed forward neural network, which consists of an input layer, one hidden layer, and an output layer ,as shown in Fig. 4, is selected to predict the responses with MR dampers.

Here the networks are trained by LQR results (as a sample data). For example displacements, velocity and forces that are obtained by LQR are selected as a sample data for training and testing. Also target of networks are LQR results. For example in the second network (Inverse model of MR damper) the targets are voltages that obtained by LQR part of clipped method.

The net input value netk of the neuron k in some layer and the output value Ok of the same neuron can be calculated by the following equations:

$$\mathsf{net}\_{\mathsf{k}} \equiv \sum \mathsf{w}\_{\mathsf{jk}} \, \mathsf{O}\_{\mathsf{l}} \tag{1}$$

$$\mathbf{O}\_{\mathbf{k}} = \mathbf{f}(\text{net}\_{\mathbf{k}} \nrightarrow \theta\_{\mathbf{k}}) \tag{2}$$

Fig. 4. The neural network architecture

dynamics of MR damper, the required voltage signal v is calculated based on the desired

The fourth part is the feedforward back propagation neural network to be trained on-line in order to generate the MR damper forces fMR. The inputs of this neural network are voltage

difference between inverse and forward model is in inputs and outputs. The outputs of

The third and fourth part of the proposed neuro-fuzzy control strategy which is a threelayer feedforward neural network consists of an input layer with 3 nodes, a hidden layer with 6 nodes, and output layer with one node. Determining the numbers of inputs, outputs, hidden layers, and nodes in hidden layers of these three neural networks is done by trial and error. For all neural parts some of the corresponded results that are obtained by LQR

At the same time, the actual responses will feed back to the neural network and the weights and bias will be revised in real time. In this research, results from the optimal control history analysis method are used to simulate the actual measured responses. The errors between the predicted responses and the actual responses are used to update the weights of the neural

The MR damper model discussed earlier in this research estimates the damper forces based on the inputs of the reactive velocity. In such case, it is essential to develop an inverse dynamic model that predicts the corresponding control force which is to be generated by

Neural network is a simplified model of the biological structure which is found in human brains. This model consists of elementary processing units (also called neurons). It is the large amount of interconnections between these neurons and their capability to learn from data which makes neural network as a strong predicting and classification tool. In this study, a three-layer feed forward neural network, which consists of an input layer, one hidden layer, and an output layer ,as shown in Fig. 4, is selected to predict the responses

Here the networks are trained by LQR results (as a sample data). For example displacements, velocity and forces that are obtained by LQR are selected as a sample data for training and testing. Also target of networks are LQR results. For example in the second network (Inverse model of MR damper) the targets are voltages that obtained by LQR part

The net input value netk of the neuron k in some layer and the output value Ok of the same

netk=∑ wjk Oj (1)

Ok=f(netk+θk) (2)

*<sup>k</sup> <sup>x</sup>* , and the displacement of MR damper xk+1.

*<sup>k</sup> <sup>x</sup>* , and the displacement of MR damper xk+1. The

ˆ

ˆ

are used as a desire data and some others are used as a testing data.

**3.1 The neural network based on Levenberg-Marquardt (LM) algorithm** 

control force fc, the velocity of MR dampers 1

inverse model are the inputs of forward model.

signal v, the velocity of MR damper <sup>1</sup>

network on-line.

dampers.

with MR dampers.

of clipped method.

neuron can be calculated by the following equations:

where wjk is the weight between the jth neuron in the previous layer and the kth neuron in the current layer, Oj is the output of the jth neuron in the previous layer, f(.) is the neuron's activation function which can be a linear function, a radial basis function, and a sigmoid function, and yk is the bias of the kth neuron. Feed forward neural network often has one or more hidden layers of sigmoid neurons followed by an output layer of linear neurons. Multiple layers of neurons with nonlinear transfer functions allow the network to learn nonlinear and linear relationships between input and output vectors. In the neural network architecture as shown in Fig. 4, the logarithmic sigmoid transfer function is chosen as the activation function of the hidden layer.

$$\mathbf{O}\_{\mathbf{k}} = \mathbf{f}(\mathbf{net}\_{\mathbf{k}} + \mathbf{0}\_{\mathbf{k}}) = \mathbf{1} \left/ \left( \mathbf{1} + \mathbf{e} \cdot (\mathbf{net}\_{\mathbf{k}} \ast \mathbf{0}\_{\mathbf{k}}) \right) \right. \tag{3}$$

The linear transfer function is chosen as the activation function of the output layer.

$$\mathbf{O}\_{\mathbf{k}} \equiv \mathbf{f}(\mathbf{net}\_{\mathbf{k}} + \mathbf{O}\_{\mathbf{k}}) = \mathbf{net}\_{\mathbf{k}} + \mathbf{O}\_{\mathbf{k}} \tag{4}$$

We note that neural network needs to be trained before it can predict any responses. As the inputs are applied to the neural network, the network outputs (.̂ ) are compared with the targets (.). The difference or error between both is processed back through the network to update the weights and biases of the neural network so that the network outputs match closer with the targets.

The input and output data are usually represented by vectors called training pairs. The process as mentioned above is repeated for all the training pairs in the data set, until the network error converges to a threshold minimum defined by a corresponding performance function. In this research, the Mean Square Error (MSE) function is adopted (desired MSE is 1e-5). LM algorithm is adapted to train the neural network (Zh et al), which can be written as a following equation:

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 245

Fig. 6. Membership function of front-right damper velocity

Fig. 7. Membership function of back-left damper velocity

Fig. 8. Membership function of back-right damper velocity

Here, Sugeno inference engine with linear output is used, the main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant. It has led to reduction of computational cost because it does not need any defuzzification procedure. A Sugeno fuzzy model is computationally efficient platform that is well suited for implementation of non-linear associations through the construction of many piecewise linear relationships (Yen et al) .A typical rule in a Sugeno fuzzy model has the form:

If X is A1 and Y is B1 then Z = p1\*x + q1\*y + r1,

If X is A2 and Y is B2 then Z = p2\*x + q2\*y + r2,

$$\mathbf{w}^{i+1} = \mathbf{w}^i \mathbf{I} \left[ (\ $2\text{E}/\$ \text{w}^{i}\text{-}2) + \text{μI} \right] \mathbf{i} \left( \ $\text{E}/\$ \text{w}^{i}\right) \tag{5}$$

where i is the iteration index, δE/δwi is the gradient descent of the performance function E with respect to the parameter matrix wi , μ≥0 is the learning factor, and I is the unity matrix. During the vibration process, the neural network updates the weights and bias of neurons in real time in accordance with sampling pairs till the objective error is satisfied, i.e. the property of the system is acquired.

As we know, the main aim of the neural network is to predict the dynamic responses of the system, and to provide inputs to the fuzzy controller and also data for calculating the control force of MR dampers. Thus outputs of the neural network are predictions of displacement 1 <sup>ˆ</sup> *<sup>k</sup> <sup>x</sup>* and velocity <sup>1</sup> ˆ *<sup>k</sup> <sup>x</sup>* . In order to predict the dynamic responses of the system accurately, the most direct and important factors which affect the predicted dynamic responses are considered, i.e. the delayed outputs (xk+3, xk+2, xk+1, xk, ẋk+3, ẋk+2, ẋk+1, ẋk), the predicted force (fk+1), and the disturbance input (dk). LM algorithm is encoded in Neural Networks Toolbox in MATLAB software.

## **3.2 Design of fuzzy controller**

The first step of designing a fuzzy controller is determining the basic domains of inputs and outputs. The desired displacement and velocity responses are chosen as inputs of the fuzzy controller. The output of fuzzy controller is the control force of the MR damper, whose basic domain is -700N – 300N same as the working force of the MR damper calculated using LQR (Zareh et al).

The membership functions are usually chosen in accordance with their characters and design experience.

For simplifying the calculation, triangular or trapezoidal functions are usually adopted as the membership functions. The triangular membership function is more sensitive to inputs than the trapezoidal form (Zh et al), in expectation that the control forces of the MR dampers are sensitive to excitations and responses, but in this case Gaussian and triangular forms are used because they have demonstrated better responses through trial and error. In this research, gaussian and triangular functions are adopted as the membership functions of velocity. The membership function curves of the velocity are shown in Figs. 5-8. (Relative velocity across dampers)

Fig. 5. Membership function of front-left damper velocity

During the vibration process, the neural network updates the weights and bias of neurons in real time in accordance with sampling pairs till the objective error is satisfied, i.e. the

As we know, the main aim of the neural network is to predict the dynamic responses of the system, and to provide inputs to the fuzzy controller and also data for calculating the control force of MR dampers. Thus outputs of the neural network are predictions of

accurately, the most direct and important factors which affect the predicted dynamic responses are considered, i.e. the delayed outputs (xk+3, xk+2, xk+1, xk, ẋk+3, ẋk+2, ẋk+1, ẋk), the predicted force (fk+1), and the disturbance input (dk). LM algorithm is encoded in Neural

The first step of designing a fuzzy controller is determining the basic domains of inputs and outputs. The desired displacement and velocity responses are chosen as inputs of the fuzzy controller. The output of fuzzy controller is the control force of the MR damper, whose basic domain is -700N – 300N same as the working force of the MR damper calculated using LQR

The membership functions are usually chosen in accordance with their characters and

For simplifying the calculation, triangular or trapezoidal functions are usually adopted as the membership functions. The triangular membership function is more sensitive to inputs than the trapezoidal form (Zh et al), in expectation that the control forces of the MR dampers are sensitive to excitations and responses, but in this case Gaussian and triangular forms are used because they have demonstrated better responses through trial and error. In this research, gaussian and triangular functions are adopted as the membership functions of velocity. The membership function curves of the velocity are shown in Figs. 5-8. (Relative


) (5)

is the gradient descent of the performance function E

*<sup>k</sup> <sup>x</sup>* . In order to predict the dynamic responses of the system

, μ≥0 is the learning factor, and I is the unity matrix.

wi+1=wi

where i is the iteration index, δE/δwi

property of the system is acquired.

displacement 1 <sup>ˆ</sup>

(Zareh et al).

design experience.

velocity across dampers)

Fig. 5. Membership function of front-left damper velocity

with respect to the parameter matrix wi

*<sup>k</sup> <sup>x</sup>* and velocity <sup>1</sup>

Networks Toolbox in MATLAB software.

**3.2 Design of fuzzy controller** 

ˆ

Fig. 6. Membership function of front-right damper velocity

Fig. 7. Membership function of back-left damper velocity

Fig. 8. Membership function of back-right damper velocity

Here, Sugeno inference engine with linear output is used, the main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant. It has led to reduction of computational cost because it does not need any defuzzification procedure. A Sugeno fuzzy model is computationally efficient platform that is well suited for implementation of non-linear associations through the construction of many piecewise linear relationships (Yen et al) .A typical rule in a Sugeno fuzzy model has the form:

> If X is A1 and Y is B1 then Z = p1\*x + q1\*y + r1, If X is A2 and Y is B2 then Z = p2\*x + q2\*y + r2,

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 247

The membership function curves of the force for front-left damper as a fuzzy output (force

Fig. 11. Membership function of back-right damper velocity (force on vertical axis vs.

The rule base used in the semi-active suspension system shown in Table 1 with fuzzy terms derived by the designer's knowledge and experience (because of shortage of space some of

> Front-left Front-right Back-left Back-right Force 1 mf3 1 2 1 1 mf3 1 3 1 1 mf4 2 3 6 1 mf2 2 5 4 2 mf6 1 5 6 2 mf5 3 6 6 3 mf6 2 1 8 3 mf2 1 1 10 4 mf5 3 1 1

The full-car model with MR damper and disturbance is modeled by the dynamic equations and state space matrices. One of the desired points of this study is to decrease the amplitude of passenger's displacement, when the suspension system excited from the road profile. Therefore the effect of LQR and LQG controllers and neuro-fuzzy strategy are simulated for road excitation with calculated their amplitude, and then compared with each other. The

vs. velocity) is shown in Fig. 11.

velocity on horizontal axis)

them are presented).

Table 1. Rule base

**4. Results** 

z2 =p2\*x+q2\*y+r2 (7)

Z=[w1\*z1+w2\*z2]/[ w1+w2] (8)

where q1 and q2 are constant. One of the main advantages of Sugeno method is well suited to mathematical analysis and is also computationally efficient, but Mamdani method is well suited to human input and it is intuitive. The basic idea of the fuzzy rules is that the control force increases with the increasing velocity responses. In this research, OR function is MAX, AND function is MIN and the defuzzification method is chosen as the Weighted Average (wtaver) method. The structure of considered fuzzy controller is shown in Fig. 9.

Fig. 9. The structure of fuzzy controller

For defuzzification we apply centre of gravity for singletons (COGS). Since we are implementing a Sugeno type controller, the combined activation, accumulation, and defuzzification operation simplifies to weighted average, with the activation strengths weighting the singleton positions (Jantzen 2007). Weighted Average defuzzifier is illustrated in Fig. 10.

Fig. 10. Sugeno-style rule evaluation

$$\mathbf{z}\mathbf{1} \mathbf{=} \mathbf{p}\mathbf{1}^\*\mathbf{x} + \mathbf{q}\mathbf{1}^\*\mathbf{y} + \mathbf{r}\mathbf{1} \tag{6}$$

$$\mathbf{z}\mathbf{z} \mathbf{=} \mathbf{p} 2^\* \mathbf{x} + \mathbf{q} 2^\* \mathbf{y} + \mathbf{r} \mathbf{2} \tag{7}$$

$$\mathbf{Z} \equiv [\mathbf{w} \mathbf{1}^{\ast} \mathbf{z} \mathbf{1} + \mathbf{w} \mathbf{2}^{\ast} \mathbf{z} \mathbf{2}] / [\mathbf{w} \mathbf{1} + \mathbf{w} \mathbf{2}] \tag{8}$$

The membership function curves of the force for front-left damper as a fuzzy output (force vs. velocity) is shown in Fig. 11.

Fig. 11. Membership function of back-right damper velocity (force on vertical axis vs. velocity on horizontal axis)

The rule base used in the semi-active suspension system shown in Table 1 with fuzzy terms derived by the designer's knowledge and experience (because of shortage of space some of them are presented).


Table 1. Rule base

#### **4. Results**

246 Fuzzy Logic – Controls, Concepts, Theories and Applications

where q1 and q2 are constant. One of the main advantages of Sugeno method is well suited to mathematical analysis and is also computationally efficient, but Mamdani method is well suited to human input and it is intuitive. The basic idea of the fuzzy rules is that the control force increases with the increasing velocity responses. In this research, OR function is MAX, AND function is MIN and the defuzzification method is chosen as the Weighted Average

For defuzzification we apply centre of gravity for singletons (COGS). Since we are implementing a Sugeno type controller, the combined activation, accumulation, and defuzzification operation simplifies to weighted average, with the activation strengths weighting the singleton positions (Jantzen 2007). Weighted Average defuzzifier is illustrated

z1 =p1\*x+q1\*y+r1 (6)

(wtaver) method. The structure of considered fuzzy controller is shown in Fig. 9.

Fig. 9. The structure of fuzzy controller

Fig. 10. Sugeno-style rule evaluation

in Fig. 10.

The full-car model with MR damper and disturbance is modeled by the dynamic equations and state space matrices. One of the desired points of this study is to decrease the amplitude of passenger's displacement, when the suspension system excited from the road profile. Therefore the effect of LQR and LQG controllers and neuro-fuzzy strategy are simulated for road excitation with calculated their amplitude, and then compared with each other. The

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 249

One of the main advantages of using neuro-fuzzy, the control effort of dampers is less than LQR and LQG responses. Forces of neuro-fuzzy cannot follow optimal controller; because, optimal forces depend on twenty two state variables and the forces obtained by fuzzy part of neuro-fuzzy strategy depend on four state variables (relative velocity across MR

The voltages are calculated using of neuro-fuzzy has a less oscillations, therefore it cause of

dampers). The requirement voltage to receive optimal forces is shown in Fig. 14.

Fig. 14. Requirement voltages to front right MR damper from front left wheel excited

Usual suspension systems are utilized in the vehicle, and damped the vibration from road profile.Unfortunately, due to the inherent nonlinear nature of the MR damper to generate

Fig. 15. Performance of the network

**5. Conclusion** 

save energy and cost. Performance of the network is shown in Fig. 15.

displacement trajectories for front-right passenger's seat that is excited by bumper under front left wheel are shown in Fig. 12. Notice that, in all graphs, time duration is selected for the best resolution and critical responses are happened when car strikes with bumper.

The trajectories of neuro-fuzzy strategy show that this strategy reduces the amplitude of vibration lower than the passive system and also to some extent as well as optimal controllers; because displacement is predicted by feed forward neural networks.

Fig. 12. Displacement of front right seat from front left wheel excite

The primary oscillations are due to the less number of network input to train, on the other hand, there are not strong history in transient, therefore the transient part of response not as well as steady state part. The trajectory for the optimal force which produces the desired displacement is shown in Fig. 13.

Fig. 13. Generated force by front right MR damper from front left wheel excited

displacement trajectories for front-right passenger's seat that is excited by bumper under front left wheel are shown in Fig. 12. Notice that, in all graphs, time duration is selected for the best resolution and critical responses are happened when car strikes with bumper.

The trajectories of neuro-fuzzy strategy show that this strategy reduces the amplitude of vibration lower than the passive system and also to some extent as well as optimal

The primary oscillations are due to the less number of network input to train, on the other hand, there are not strong history in transient, therefore the transient part of response not as well as steady state part. The trajectory for the optimal force which produces the desired

Fig. 13. Generated force by front right MR damper from front left wheel excited

controllers; because displacement is predicted by feed forward neural networks.

Fig. 12. Displacement of front right seat from front left wheel excite

displacement is shown in Fig. 13.

One of the main advantages of using neuro-fuzzy, the control effort of dampers is less than LQR and LQG responses. Forces of neuro-fuzzy cannot follow optimal controller; because, optimal forces depend on twenty two state variables and the forces obtained by fuzzy part of neuro-fuzzy strategy depend on four state variables (relative velocity across MR dampers). The requirement voltage to receive optimal forces is shown in Fig. 14.

The voltages are calculated using of neuro-fuzzy has a less oscillations, therefore it cause of save energy and cost. Performance of the network is shown in Fig. 15.

Fig. 14. Requirement voltages to front right MR damper from front left wheel excited

Fig. 15. Performance of the network

#### **5. Conclusion**

Usual suspension systems are utilized in the vehicle, and damped the vibration from road profile.Unfortunately, due to the inherent nonlinear nature of the MR damper to generate

Intelligent Neuro-Fuzzy Application in Semi-Active Suspension System 251

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Fuzzy Controller Application with Bingham Modified Model in Semi Active

force and suspension system, a model like that for its inverse dynamics is difficult to obtain mathematically. Because of this reason, a neural network with fuzzy logic controller is constructed to copy the inverse dynamics of the MR damper.

In the proposed control system, a dynamic-feedback neural network has been employed to model non-linear dynamic system and the fuzzy logic controller has been used to determine the control forces of MR dampers. Required voltages and actual forces of MR dampers have been obtained by use of two feedforward neural networks, in which the first neural network and second one have acted as the inverse and forward dynamics models of the MR dampers, respectively.

The most important characteristic of the proposed intelligent control strategy is its inherent robustness and its ability to handle the non-linear behavior of the system. Besides, no mathematical model is needed for calculating forces produced by MR dampers.

The performance of the proposed neuro-fuzzy control system has been compared with that of a traditional semi-active control strategy, i.e., clipped optimal control system with LQR and LQR, through computer simulations, while the uncontrolled system response has been used as the baseline.

According to the graphs that show above, the trajectories of neuro-fuzzy strategy can reduce the amplitude of vibration to some extent as well as optimal controllers with less control effort and oscillation. In addition, the neuro-fuzzy control system is more robust to process/sensing noises.

## **6. Acknowledgment**

Seiyed Hamid Zareh deeply indebted to his Supervisor, Dr. Amir Ali Akbar Khayyat, from the Sharif University of Technology whose help, sincere suggestions and encouragement helped him in all the time of research for and writing of this chapter. His insight and enthusiasm for research have enabled him to accomplish this work and are truly appreciated.

The authors are particularly pleased to thank Dr. Abolghassem Zabihollah, Dr. Kambiz Ghaemi Osgouie, Mr. Atabak Sarrafan, Mr. Meisam Abbasi and Mr. Ali Fellahjahromi for their true friendships, supports, invaluable suggestions, and sharing their knowledge and expertises with us. And our special thanks go to the international campus of Sharif University of Technology for the support provided for this research.

## **7. References**


force and suspension system, a model like that for its inverse dynamics is difficult to obtain mathematically. Because of this reason, a neural network with fuzzy logic controller is

In the proposed control system, a dynamic-feedback neural network has been employed to model non-linear dynamic system and the fuzzy logic controller has been used to determine the control forces of MR dampers. Required voltages and actual forces of MR dampers have been obtained by use of two feedforward neural networks, in which the first neural network and second one have acted as the inverse and forward dynamics models of the MR

The most important characteristic of the proposed intelligent control strategy is its inherent robustness and its ability to handle the non-linear behavior of the system. Besides, no

The performance of the proposed neuro-fuzzy control system has been compared with that of a traditional semi-active control strategy, i.e., clipped optimal control system with LQR and LQR, through computer simulations, while the uncontrolled system response has been

According to the graphs that show above, the trajectories of neuro-fuzzy strategy can reduce the amplitude of vibration to some extent as well as optimal controllers with less control effort and oscillation. In addition, the neuro-fuzzy control system is more robust to

Seiyed Hamid Zareh deeply indebted to his Supervisor, Dr. Amir Ali Akbar Khayyat, from the Sharif University of Technology whose help, sincere suggestions and encouragement helped him in all the time of research for and writing of this chapter. His insight and enthusiasm for research have enabled him to accomplish this work and are truly

The authors are particularly pleased to thank Dr. Abolghassem Zabihollah, Dr. Kambiz Ghaemi Osgouie, Mr. Atabak Sarrafan, Mr. Meisam Abbasi and Mr. Ali Fellahjahromi for their true friendships, supports, invaluable suggestions, and sharing their knowledge and expertises with us. And our special thanks go to the international campus of Sharif

Atray V. S.; Roschke P. N. (2004). Neuro-Fuzzy Control of Railcar Vibrations Using Semi

Biglarbegian M.; Melek W.; Golnaraghi F. (2006). Intelligent control of vehicle semi-active

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mathematical model is needed for calculating forces produced by MR dampers.

constructed to copy the inverse dynamics of the MR damper.

dampers, respectively.

used as the baseline.

process/sensing noises.

**6. Acknowledgment** 

appreciated.

**7. References** 

81-92


**13** 

*Brazil* 

Vanilson G. Pereira,

*Federal University of Pará,* 

Roberto C.L. De Oliveira and Fábio M. Soares

**Fuzzy Control Applied to Aluminum Smelting** 

Aluminum is a modern and new metal, since it has been produced for industry no earlier than 1886, when Hall and Héroult concurrently found out a method to produce free Aluminum through electrolysis (Beck, 2008). In 1900, the Aluminum production worldwide had reached a thousand tons. Nevertheless, at the beginning of the 21st century, global production reached 32 million tons encompassed by 24 million of primary Aluminum and 8 million of recycled material. This fact puts Aluminum at the second place in the list of the most used metals on earth. The world without Aluminum became inacceptable: the businessmen, the tourists, the delivery offices fly over the world in airplanes made of Aluminum, as well as many enterprises and industries are strongly dependent of this metal.

This metal has contributed to low fuel consumption in cars and trucks, as well as allowing high speeds for trains and ships due to their weight reduction. Since it is a light metal, Aluminum eases the construction of buildings resistant to corrosion and low need for maintenance. Everywhere in the world, the electricity transmission lines for great distances are made of Aluminum, in part or whole. Food quality is preserved by Aluminum packages, reducing waste and giving comfort to users. This metal protects food, cosmetics and pharmaceutical products from ultraviolet rays, bad smells and bacteria. Food waste is

Aluminum is a global commodity; its industry employs directly at least one million people, and indirectly more than four million. It is a slight compact industry, provided that around

Figure 1 shows in a widely perspective where Aluminum is most used.

Fig. 1. Fields where Aluminum is most used (source: IAI, 2010)

avoided 30% when Aluminum packages are used.

**1. Introduction** 

Vibration Control of 11-DOFs Full Car Suspension System. International Journal on Computing, Vol. 1, No. 3, pp. 39-44


## **Fuzzy Control Applied to Aluminum Smelting**

Vanilson G. Pereira,

Roberto C.L. De Oliveira and Fábio M. Soares *Federal University of Pará, Brazil* 

## **1. Introduction**

252 Fuzzy Logic – Controls, Concepts, Theories and Applications

Zareh S. H.; Sarrafan A.; Khayyat A. A. A. (2011). Clipped Optimal Control of 11-DOFs of a

Zareh S. H.; Sarrafan A.; Khayyat A. A. A.; Fellahjahromi A. (2011). Linear Quadratic

Zh. D. X.; Guo Y. Q. (2008). Neuro-Fuzzy control strategy for earthquake-excited nonlinear

Zhou L.; Chang C. C.; Wang L. X. (2003). Adaptive Fuzzy Control for Non-Linear Building-

Computing, Vol. 1, No. 3, pp. 39-44

Issue on Structural Control, Vol. 7, pp. 905–913

167

Turkey, pp. 122-127

pp. 717-727

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Passenger Car Using Magnetorheological Damper. IEEE International Conference on Computer Control and Automation , Korea, ISBN: 978-1-4244-9767-6, pp. 162-

Gaussian Application and Clipped Optimal Algorithm Using for Semi Active Vibration of Passenger Car. IEEE International Conference on Mechatronics,

magnetorheological structures. Soil Dynamics and Earthquake Engineering, Vol.28,

Magnetorheological Damper System. Journal of Structural Engineering: Special

Aluminum is a modern and new metal, since it has been produced for industry no earlier than 1886, when Hall and Héroult concurrently found out a method to produce free Aluminum through electrolysis (Beck, 2008). In 1900, the Aluminum production worldwide had reached a thousand tons. Nevertheless, at the beginning of the 21st century, global production reached 32 million tons encompassed by 24 million of primary Aluminum and 8 million of recycled material. This fact puts Aluminum at the second place in the list of the most used metals on earth. The world without Aluminum became inacceptable: the businessmen, the tourists, the delivery offices fly over the world in airplanes made of Aluminum, as well as many enterprises and industries are strongly dependent of this metal. Figure 1 shows in a widely perspective where Aluminum is most used.

Fig. 1. Fields where Aluminum is most used (source: IAI, 2010)

This metal has contributed to low fuel consumption in cars and trucks, as well as allowing high speeds for trains and ships due to their weight reduction. Since it is a light metal, Aluminum eases the construction of buildings resistant to corrosion and low need for maintenance. Everywhere in the world, the electricity transmission lines for great distances are made of Aluminum, in part or whole. Food quality is preserved by Aluminum packages, reducing waste and giving comfort to users. This metal protects food, cosmetics and pharmaceutical products from ultraviolet rays, bad smells and bacteria. Food waste is avoided 30% when Aluminum packages are used.

Aluminum is a global commodity; its industry employs directly at least one million people, and indirectly more than four million. It is a slight compact industry, provided that around

Fuzzy Control Applied to Aluminum Smelting 255

Inside these pots, also often called cells, Alumina is fed through silo and it is electrically consumed by the carbon anodes (Solheim, 2005), and as shown in the equation (1), the

> *Al O NaF C AlF CO Na e* 2 3 3 2 1 33 <sup>3</sup> 3 3

At the bottom part of the cell, there is a thermal isolated steel covering made of refractory material, named cathode block. The liquid Aluminum is formed above the cathode, and under the anode the electrolytic bath is formed. The cathode, in an electrochemical sense, is an interface between liquid Aluminum and the electrolytic bath, according to equation (2).

> *Al O C Al CO* 2 3 <sup>2</sup> 13 3 24 4

The pure electrolytic bath, i.e. cryolite, has a melting point at 1,011ºC. In order to lower this point, called *liquidus* temperature, some additives are added into the bath, from which the main are Aluminum Fluoride (AlF3) and Calcium Fluoride (CaF2). The chemical composition of the bath in the reduction pot is 6-13% of AlF3, 4-6% of CaF2 and 2-4% of Al2O3. With a low liquidus temperature, pot operation is performed with low bath temperature, allowing reducing alumina solubility inside the bath. Therefore a good alumina concentration control system is required. Usually an aluminum reduction pot is

Bath is not consumed during the process, but part of it is lost, during vaporization, constituted of NaAlF4. Moreover, part of bath is lost by drops dragging, by water present in fed alumina and the air aspired from inside the cell to form HF. In order to protect the environment, the gas is collected and cleared by a gas washing system. More than 98% of AlF3 is retrieved in the gas washing system (Hyland et al, 2001), and recycled back to the pot. Moreover, Sodium Oxide (Na2O) and Calcium Fluoride (CaF2) at alumina feeding neutralizes AlF3. The neutralized amount is also dependent on sodium penetration into the

At the cathode sidewall there is a cool layer called ledge, which protects the sidewall from erosion. The ledge is composed of Na3AlF6 and CaF2 (Thonstad & Rolseth, 1983). The ledge thickness is dependent on the heat flux through the cell sides, which is dependent on the bath temperature and liquidus temperature (that difference is called superheat). Once it is established that ledge composition is basically Na3AlF6, that means the total cryolite mass varies, while AlF3 and Al2O3 mass do not vary with the ledge thickness. In addition, once the additive concentration is the additive mass divided by the total bath mass, the ledge thickness variation triggers variation in the additives' concentrations. Then, changes in concentrations triggers changes in liquidus temperature, which in turn triggers changes in superheat, affecting ledge thickness. Thus, the challenge is to guarantee a stable pot operation which

means a stable protection ledge minimizing energy input and maximizing production.

(1)

*AlF Na e Al NaF* <sup>3</sup> 33 3 (2)

(3)

2 44

The full reaction inside the reduction pot is shown in equation (3).

operated under temperatures from 940ºC to 970ºC.

cathode which is, the pot age.

anode is also consumed during the electrolytic process.

20 smelters are responsible for 65% or world production. Most companies work only with Aluminum, but 20% of them work with Aluminum with other metals or mines. Half of Aluminum production is done by companies vertically integrated, from bauxite mining to metal recycling (IAI, 2010).

For all these reasons, the Aluminum can be considered a highly important metal, and therefore, its production is a target for many research activities. Researchers all around the world make efforts in making Aluminum production a less costly process, since it spends a lot of energy, and is very complex. In this chapter, we are going to present the whole context, and why and where fuzzy control is important to assist plant operators.

The impact and consequences of this work is the use of rules defined by process operators indirectly through the huge database which provides historic information including control decisions made by them. Since this strategy emulates process operator, it can be said that an expert system can provide this personnel more time to concentrate on other activities. Moreover, this technique will be continually improved by revising its rules and evaluation, provided that fuzzy decisions will also have an impact, and this should be analysed and adjusted.

## **1.1 Aluminum production process**

Aluminum has been produced through the Hall-Héroult process, named after its inventors. So far, this is the only industrial way to produce this metal. Primary Aluminum is produced in a liquid form, through an electrolytic reduction of alumina (Al2O3) in a cryolite bath (Na3AlF6). This reaction takes place in electrolytic pots, as shown in Figure 2.

Fig. 2. Sketch of an Alumina reduction pot of prebake type (adapted from Kola & Store, 2009).

20 smelters are responsible for 65% or world production. Most companies work only with Aluminum, but 20% of them work with Aluminum with other metals or mines. Half of Aluminum production is done by companies vertically integrated, from bauxite mining to

For all these reasons, the Aluminum can be considered a highly important metal, and therefore, its production is a target for many research activities. Researchers all around the world make efforts in making Aluminum production a less costly process, since it spends a lot of energy, and is very complex. In this chapter, we are going to present the whole

The impact and consequences of this work is the use of rules defined by process operators indirectly through the huge database which provides historic information including control decisions made by them. Since this strategy emulates process operator, it can be said that an expert system can provide this personnel more time to concentrate on other activities. Moreover, this technique will be continually improved by revising its rules and evaluation, provided that fuzzy decisions will also have an impact, and this should be analysed and

Aluminum has been produced through the Hall-Héroult process, named after its inventors. So far, this is the only industrial way to produce this metal. Primary Aluminum is produced in a liquid form, through an electrolytic reduction of alumina (Al2O3) in a cryolite bath

Fig. 2. Sketch of an Alumina reduction pot of prebake type (adapted from Kola & Store, 2009).

(Na3AlF6). This reaction takes place in electrolytic pots, as shown in Figure 2.

context, and why and where fuzzy control is important to assist plant operators.

metal recycling (IAI, 2010).

**1.1 Aluminum production process** 

adjusted.

Inside these pots, also often called cells, Alumina is fed through silo and it is electrically consumed by the carbon anodes (Solheim, 2005), and as shown in the equation (1), the anode is also consumed during the electrolytic process.

$$
\frac{1}{2}Al\_2O\_3 + 3NaF + \frac{3}{4}C \rightarrow AlF\_3 + \frac{3}{4}CO\_2 + 3Na^+ + 3e\tag{1}
$$

At the bottom part of the cell, there is a thermal isolated steel covering made of refractory material, named cathode block. The liquid Aluminum is formed above the cathode, and under the anode the electrolytic bath is formed. The cathode, in an electrochemical sense, is an interface between liquid Aluminum and the electrolytic bath, according to equation (2).

$$AlF\_3 + \Im Na^+ + \Im e \to Al + \Im NaF \tag{2}$$

The full reaction inside the reduction pot is shown in equation (3).

$$
\frac{1}{2}Al\_2O\_3 + \frac{3}{4}C \to Al + \frac{3}{4}CO\_2\tag{3}
$$

The pure electrolytic bath, i.e. cryolite, has a melting point at 1,011ºC. In order to lower this point, called *liquidus* temperature, some additives are added into the bath, from which the main are Aluminum Fluoride (AlF3) and Calcium Fluoride (CaF2). The chemical composition of the bath in the reduction pot is 6-13% of AlF3, 4-6% of CaF2 and 2-4% of Al2O3. With a low liquidus temperature, pot operation is performed with low bath temperature, allowing reducing alumina solubility inside the bath. Therefore a good alumina concentration control system is required. Usually an aluminum reduction pot is operated under temperatures from 940ºC to 970ºC.

Bath is not consumed during the process, but part of it is lost, during vaporization, constituted of NaAlF4. Moreover, part of bath is lost by drops dragging, by water present in fed alumina and the air aspired from inside the cell to form HF. In order to protect the environment, the gas is collected and cleared by a gas washing system. More than 98% of AlF3 is retrieved in the gas washing system (Hyland et al, 2001), and recycled back to the pot. Moreover, Sodium Oxide (Na2O) and Calcium Fluoride (CaF2) at alumina feeding neutralizes AlF3. The neutralized amount is also dependent on sodium penetration into the cathode which is, the pot age.

At the cathode sidewall there is a cool layer called ledge, which protects the sidewall from erosion. The ledge is composed of Na3AlF6 and CaF2 (Thonstad & Rolseth, 1983). The ledge thickness is dependent on the heat flux through the cell sides, which is dependent on the bath temperature and liquidus temperature (that difference is called superheat). Once it is established that ledge composition is basically Na3AlF6, that means the total cryolite mass varies, while AlF3 and Al2O3 mass do not vary with the ledge thickness. In addition, once the additive concentration is the additive mass divided by the total bath mass, the ledge thickness variation triggers variation in the additives' concentrations. Then, changes in concentrations triggers changes in liquidus temperature, which in turn triggers changes in superheat, affecting ledge thickness. Thus, the challenge is to guarantee a stable pot operation which means a stable protection ledge minimizing energy input and maximizing production.

Fuzzy Control Applied to Aluminum Smelting 257

balance (Drenstig et al, 1998), the use of LQR (Linear Quadratic Gaussian) to perform cell multivariable control by identifying dynamic models (McFadden et al, 2006); the use of regression models for bath temperature along with IF-THEN rules to add Aluminum fluoride into the cell (Yongbo et al, 2008), and PID (Proportional, Integral and Derivative) control along with a feed-forward loop for Aluminum fluoride addition and a PI (Proportional and Integral) control for bath temperature (Kola & Store, 2009). The use of fuzzy controllers in the cell is also often used (Meghlaoui&Aljabri, 2003; Yan &Taishan, 2006; Shuiping&Jinhong, 2008; Shuiping et al. 2010; Xiaodong et al, 2010; Dan Yang et al., 2011). However these works have not exploited any operational experience stored in process database, and the existing data mining works in the Aluminum Industry (Zhuo et al., 2008)

In this chapter we propose a data-oriented fuzzy-based strategy applied to one of the Aluminum smelting sub-processes. Aluminum industries usually maintain huge databases which provide historic information regarding the process, including control decisions made by process operators. It can be said that these information contain the system's dynamics and the process team's knowledge. This knowledge can be exploited to develop an expert system, provided that most of process decision makers control the plant based on their own experience in a fuzzy approach. This work shows the whole design of the fuzzy system, their rules formation and fuzzy sets selection, and its results. This work was performed in a Brazilian company whose aim was to develop a fuzzy controller based on an expert system whose rules were generated from the company's process database and interviews with process operators. This work is also fully based on the literature of Gomes et al, 2010. The control system is aimed at adding Aluminum fluoride into alumina reduction cells. The

The inaccuracy and uncertainty are two aspects that may be part of the information. There are two theories used to deal with inaccuracy and uncertainty: classic sets (crisp) theory and probabilities theory, respectively. However, these theories do not always capture the information content provided by humans in natural language. The classic sets theory cannot deal with the fuzzy aspect of information while the probabilities theory is more suited to

The fuzzy sets theory, developed by LoftiZadeh in 1965 (Zadeh, 1965), aimed at dealing with the fuzzy aspect of information, while, in 1978, Zadeh also developed the probabilities theory that deals with information uncertainty (Zadeh, 1978). These theories have been used in systems that use human-provided information. These theories are closely linked with each other. When the fuzzy sets theory is used in a logic context, as knowledge-based systems, it is known as fuzzy logic (term used in this chapter). The fuzzy logic is currently one of the most successful technologies for the development of process control systems, due to low implementation cost, easy maintenance and the fact that complex requirements may

results show more stability on bath temperature and AlF3 concentration.

**2. Fuzzy controllers and systems: An overview** 

handle frequency information than those provided by humans.

be implemented in simple controllers.

are not addressed to the fluoride addition problem.

**1.4 The novelty proposed in this work** 

#### **1.2 Current control systems**

Regarding pot control, there are three main variables to be controlled: bath temperature, AlF3 concentration and Al2O3 concentration. For that, there are three control inputs: anode beam moves (controlling energy input, by means of anode-to-cathode distance (ACD), AlF3 addition and Al2O3 addition). The AlF3 mass reduction dynamic process is slow, the AlF3 concentration control system should deal with long response times (long delays) to control inputs which in this case are the changes to AlF3 concentration. On the other hand, the Al2O3 mass reduction process is faster, and the Al2O3 concentration control system should deal with fast responses to the control inputs which in this case are the Al2O3 concentration changes. Usually, the Al2O3 concentration control system is considered an isolate problem, decoupled from the other control systems.

Bath temperature is measured manually, once a day or at least once a week. The AlF3 concentration (acidity) is typically measured manually once or twice a week, while Al2O3 concentration is not normally measured, except in special situations when process engineers need exceptionally. The only real time measurement is the bath pseudo-resistance (Rb), defined by equation (4),

$$R\_b = \frac{\mathcal{U}\_f - 1, 7}{I} \quad (\mu \,\, \Omega) \tag{4}$$

where *Uf* is cell voltage in Volts, and I is potline current in KA, these variables are also measured continually. The Rb measurement is used as input for anode-to-cathode distance adjustment, and acts as a control variable along with energy input into the cell.

Due to the fact that there is a strong relation between energy balance and mass balance through the ledge (see, e.g., Drenstig, 1997, Chapter 5), the reduction cell control must be considered as a multivariable non-linear control. A raise in the bath temperature causes acidity decrease and increases bath conductivity (Hives et al, 1993). According to Drenstig (1997, Chapter 5), acidity variation is ruled by bath temperature variation. Likewise, the control system logic should be bath temperature control through the additives (with negative or positive effects), around a setpoint, and Aluminum fluoride (AlF3) constant addition. While this seems to be obvious and reasonable, there is a long way to go to transform this idea into a viable application in an alumina reduction cell.

#### **1.3 Usage of fuzzy logic in aluminum industry**

One easy and cheap method to perform a non-linear control system in an alumina reduction cell is to use fuzzy systems. With a qualitative approach, fuzzy systems offer a methodology to simulate a human expert operational behaviour and allow using available data from these experts' knowledge. Fuzzy expert systems have been largely used in control systems (Benyakhlef&Radouane, 2008; Chiu &Lian, 2009; Yu et al., 2010; Feng, 2010; Wang et al., 2011), since when Mamdani and Assilian developed a fuzzy controller for a boiler (Mamdani&Assilan, 1975).

In Aluminum industry, control strategies involve alumina addition neural control by cell states estimation (Meghlaoui et al., 1997), bath Aluminum fluoride control by mass balance differential equations and algebraic equations that deal with mass balance and thermal

Regarding pot control, there are three main variables to be controlled: bath temperature, AlF3 concentration and Al2O3 concentration. For that, there are three control inputs: anode beam moves (controlling energy input, by means of anode-to-cathode distance (ACD), AlF3 addition and Al2O3 addition). The AlF3 mass reduction dynamic process is slow, the AlF3 concentration control system should deal with long response times (long delays) to control inputs which in this case are the changes to AlF3 concentration. On the other hand, the Al2O3 mass reduction process is faster, and the Al2O3 concentration control system should deal with fast responses to the control inputs which in this case are the Al2O3 concentration changes. Usually, the Al2O3 concentration control system is considered an isolate problem,

Bath temperature is measured manually, once a day or at least once a week. The AlF3 concentration (acidity) is typically measured manually once or twice a week, while Al2O3 concentration is not normally measured, except in special situations when process engineers need exceptionally. The only real time measurement is the bath pseudo-resistance (Rb),

*f*

*R ( ) <sup>I</sup>* 1,7

where *Uf* is cell voltage in Volts, and I is potline current in KA, these variables are also measured continually. The Rb measurement is used as input for anode-to-cathode distance

Due to the fact that there is a strong relation between energy balance and mass balance through the ledge (see, e.g., Drenstig, 1997, Chapter 5), the reduction cell control must be considered as a multivariable non-linear control. A raise in the bath temperature causes acidity decrease and increases bath conductivity (Hives et al, 1993). According to Drenstig (1997, Chapter 5), acidity variation is ruled by bath temperature variation. Likewise, the control system logic should be bath temperature control through the additives (with negative or positive effects), around a setpoint, and Aluminum fluoride (AlF3) constant addition. While this seems to be obvious and reasonable, there is a long way to go to

One easy and cheap method to perform a non-linear control system in an alumina reduction cell is to use fuzzy systems. With a qualitative approach, fuzzy systems offer a methodology to simulate a human expert operational behaviour and allow using available data from these experts' knowledge. Fuzzy expert systems have been largely used in control systems (Benyakhlef&Radouane, 2008; Chiu &Lian, 2009; Yu et al., 2010; Feng, 2010; Wang et al., 2011), since when Mamdani and Assilian developed a fuzzy controller for a boiler

In Aluminum industry, control strategies involve alumina addition neural control by cell states estimation (Meghlaoui et al., 1997), bath Aluminum fluoride control by mass balance differential equations and algebraic equations that deal with mass balance and thermal

(4)

*b U*

adjustment, and acts as a control variable along with energy input into the cell.

transform this idea into a viable application in an alumina reduction cell.

**1.3 Usage of fuzzy logic in aluminum industry** 

(Mamdani&Assilan, 1975).

**1.2 Current control systems** 

defined by equation (4),

decoupled from the other control systems.

balance (Drenstig et al, 1998), the use of LQR (Linear Quadratic Gaussian) to perform cell multivariable control by identifying dynamic models (McFadden et al, 2006); the use of regression models for bath temperature along with IF-THEN rules to add Aluminum fluoride into the cell (Yongbo et al, 2008), and PID (Proportional, Integral and Derivative) control along with a feed-forward loop for Aluminum fluoride addition and a PI (Proportional and Integral) control for bath temperature (Kola & Store, 2009). The use of fuzzy controllers in the cell is also often used (Meghlaoui&Aljabri, 2003; Yan &Taishan, 2006; Shuiping&Jinhong, 2008; Shuiping et al. 2010; Xiaodong et al, 2010; Dan Yang et al., 2011). However these works have not exploited any operational experience stored in process database, and the existing data mining works in the Aluminum Industry (Zhuo et al., 2008) are not addressed to the fluoride addition problem.

### **1.4 The novelty proposed in this work**

In this chapter we propose a data-oriented fuzzy-based strategy applied to one of the Aluminum smelting sub-processes. Aluminum industries usually maintain huge databases which provide historic information regarding the process, including control decisions made by process operators. It can be said that these information contain the system's dynamics and the process team's knowledge. This knowledge can be exploited to develop an expert system, provided that most of process decision makers control the plant based on their own experience in a fuzzy approach. This work shows the whole design of the fuzzy system, their rules formation and fuzzy sets selection, and its results. This work was performed in a Brazilian company whose aim was to develop a fuzzy controller based on an expert system whose rules were generated from the company's process database and interviews with process operators. This work is also fully based on the literature of Gomes et al, 2010. The control system is aimed at adding Aluminum fluoride into alumina reduction cells. The results show more stability on bath temperature and AlF3 concentration.

## **2. Fuzzy controllers and systems: An overview**

The inaccuracy and uncertainty are two aspects that may be part of the information. There are two theories used to deal with inaccuracy and uncertainty: classic sets (crisp) theory and probabilities theory, respectively. However, these theories do not always capture the information content provided by humans in natural language. The classic sets theory cannot deal with the fuzzy aspect of information while the probabilities theory is more suited to handle frequency information than those provided by humans.

The fuzzy sets theory, developed by LoftiZadeh in 1965 (Zadeh, 1965), aimed at dealing with the fuzzy aspect of information, while, in 1978, Zadeh also developed the probabilities theory that deals with information uncertainty (Zadeh, 1978). These theories have been used in systems that use human-provided information. These theories are closely linked with each other. When the fuzzy sets theory is used in a logic context, as knowledge-based systems, it is known as fuzzy logic (term used in this chapter). The fuzzy logic is currently one of the most successful technologies for the development of process control systems, due to low implementation cost, easy maintenance and the fact that complex requirements may be implemented in simple controllers.

Fuzzy Control Applied to Aluminum Smelting 259

and m(t) is a semantic function that assigns each linguistic term *t T* its meaning, what is a

Given fuzzy sets A and B contained in a universe of µA and µB, respectively, their operation are defined as sets theoretic operation (union, intersection and complement) as follows:

**Union:** This operation is similar to the union between two classic sets *A B* . The union between fuzzy sets may be written with membership functions of sets A and B, as follows:

> 

**Intersection:** This operation is similar to the intersection between two classic sets *A B* . The intersection between fuzzy sets may be written with membership functions of sets A

*x B x A x A B*

**Complement:** The complement set of A, named as *A* , is defined by the membership

*<sup>A</sup> <sup>A</sup>*

**s-Norms:** These are combinations of membership functions of two fuzzy sets A and B,

*sx x x*

**t-Norms:** These are combinations of membership functions of two fuzzy sets A and B,

*tx x x*

 

 

> 

 ,

*A B x x* , then the set A is equal to set B.

*A B x xx* max , *A B* (8)

*x x* 1 (10)

*A B AB* , (11)

*A B AB* , (12)

(9)

*A B x x* , then the set B contains set A.

fuzzy set in X (that is, m: T→(X) where (X) is the fuzzy sets space).

resulting in the union *A B* of set membership functions:

The combination s should match these properties:

The combination t should match these properties:

3. s[a,b] ≤ s[a',b'], if a < a' and b < b'

min

resulting in the intersection *A B* of two set membership functions:

 

 

**2.1.3 Fuzzy sets operation** 

**Equality:** If for every *x U* ,

**Subset:** If for every *x U* ,

and B, as follows:

1. s[1,1]=1,s[a,0]=a 2. s[a,b] = s[b,a]

1. t[1,1]=1,t[a,0]=a 2. t[a,b] = t[b,a]

4. s[s[a,b],c]=s[a,s[b,c]]

function:

In the broad sense, a fuzzy controller is a rule-based fuzzy system, composed of a set of inference rules of the type If <Condition> Then <Action>, that define the control actions according to several ranges the controlled variables in the problem may assume. These ranges (usually poor defined) are modeled by fuzzy sets and named as linguistic terms. In this section, we present all the theoretic aspects for the development of the fuzzy controller.

#### **2.1 Theoretic aspects**

#### **2.1.1 Fuzzy sets**

Crisp sets have hard defined membership functions (either 0 or 1), while fuzzy set have soft defined membership functions. Given a set A in a universe U, the elements of this universe just belong or not to that set. That is, the element x is true *f x <sup>A</sup>* 1 , or false *f x <sup>A</sup>* 0 . This can be expressed as

$$f\_A(\mathbf{x}) = \begin{cases} 1 & \text{if } & \mathbf{x} \in A; \\ 0 & \text{if } & \mathbf{x} \notin A \end{cases} \tag{5}$$

Zadeh(Zadeh, 1965) proposed a more general approach, so the characteristic function could yield float point values in the interval [0,1]. A fuzzy set A in a universe U is defined by a membership function *<sup>A</sup> x* 0,1, that amounts the element x for the fuzzy set. Fuzzy sets can be defined in continuous or discrete universes. If the universe U is discrete and finite, the fuzzy set A is usually denoted by expression:

$$A = \sum\_{i=1}^{m} \frac{\mu\_A(\mathbf{x}\_i)}{\mathbf{x}\_i}$$

$$A = \frac{\mu\_A(\mathbf{x}\_i)}{\mathbf{x}\_i} + \dots + \frac{\mu\_A(\mathbf{x}\_m)}{\mathbf{x}\_m} \tag{6}$$

If U is a continuous universe, the fuzzy set A is denoted by expression:

$$A = \int \frac{\mu\_A(\mathbf{x})}{\mathbf{x}} \tag{7}$$

Where *<sup>A</sup> xi* is known as membership function which may show how much x belongs to the set A, and U is known as the universe of discourse. In other words, the element x may belong to more than one fuzzy set, but with different membership values.

#### **2.1.2 Linguistic variables**

A linguistic variable has its value expressed qualitatively by a linguistic term and quantitatively by a membership function. A linguistic function is characterized by {n,T,X,m(n)} where n is the variable's name, T is the set of linguistic terms of n (Cold, Normal, Hot, Very Hot), X is the domain (Universe of Discourse) of n values which the linguistic term meaning is determined on (the temperature may be between 970º and 975ºC) and m(t) is a semantic function that assigns each linguistic term *t T* its meaning, what is a fuzzy set in X (that is, m: T→(X) where (X) is the fuzzy sets space).

## **2.1.3 Fuzzy sets operation**

258 Fuzzy Logic – Controls, Concepts, Theories and Applications

In the broad sense, a fuzzy controller is a rule-based fuzzy system, composed of a set of inference rules of the type If <Condition> Then <Action>, that define the control actions according to several ranges the controlled variables in the problem may assume. These ranges (usually poor defined) are modeled by fuzzy sets and named as linguistic terms. In this section, we present all the theoretic aspects for the development of the fuzzy controller.

Crisp sets have hard defined membership functions (either 0 or 1), while fuzzy set have soft defined membership functions. Given a set A in a universe U, the elements of this universe just belong or not to that set. That is, the element x is true *f x <sup>A</sup>* 1 , or false *f x <sup>A</sup>* 0 .

*<sup>A</sup> if x A f x if x A*

Zadeh(Zadeh, 1965) proposed a more general approach, so the characteristic function could yield float point values in the interval [0,1]. A fuzzy set A in a universe U is defined by a

sets can be defined in continuous or discrete universes. If the universe U is discrete and

*A*

*i A i*

*x <sup>x</sup> <sup>A</sup>* 

If U is a continuous universe, the fuzzy set A is denoted by expression:

belong to more than one fuzzy set, but with different membership values.

 *<sup>m</sup> <sup>A</sup> <sup>i</sup> i i*

 *<sup>A</sup> xi* is known as membership function which may show how much x belongs to the set A, and U is known as the universe of discourse. In other words, the element x may

*m A m*

*x x*

*x* <sup>1</sup> 

 

*<sup>A</sup> x <sup>A</sup> x* 

A linguistic variable has its value expressed qualitatively by a linguistic term and quantitatively by a membership function. A linguistic function is characterized by {n,T,X,m(n)} where n is the variable's name, T is the set of linguistic terms of n (Cold, Normal, Hot, Very Hot), X is the domain (Universe of Discourse) of n values which the linguistic term meaning is determined on (the temperature may be between 970º and 975ºC)

*x*

0 

1 ;

*<sup>A</sup> x* 0,1, that amounts the element x for the fuzzy set. Fuzzy

(5)

(7)

(6)

**2.1 Theoretic aspects** 

This can be expressed as

membership function

Where 

**2.1.2 Linguistic variables** 

finite, the fuzzy set A is usually denoted by expression:

**2.1.1 Fuzzy sets** 

Given fuzzy sets A and B contained in a universe of µA and µB, respectively, their operation are defined as sets theoretic operation (union, intersection and complement) as follows:

**Equality:** If for every *x U* , *A B x x* , then the set A is equal to set B.

**Subset:** If for every *x U* , *A B x x* , then the set B contains set A.

**Union:** This operation is similar to the union between two classic sets *A B* . The union between fuzzy sets may be written with membership functions of sets A and B, as follows:

$$
\mu\_{A \cup \mathcal{B}} \left( \mathbf{x} \right) = \max \left[ \mu\_A \left( \mathbf{x} \right), \mu\_{\mathcal{B}} \left( \mathbf{x} \right) \right] \tag{8}
$$

**Intersection:** This operation is similar to the intersection between two classic sets *A B* . The intersection between fuzzy sets may be written with membership functions of sets A and B, as follows:

$$\|\,\mu\|\_{A\cap B}(\mathbf{x}) = \min \|\mu\,\mu\_A(\mathbf{x}), \mu\_B(\mathbf{x})\|\tag{9}$$

**Complement:** The complement set of A, named as *A* , is defined by the membership function:

$$
\mu\_{\overline{A}}\left(\mathbf{x}\right) = 1 - \mu\_A\left(\mathbf{x}\right) \tag{10}
$$

**s-Norms:** These are combinations of membership functions of two fuzzy sets A and B, resulting in the union *A B* of set membership functions:

$$s\left[\mu\_A(\mathbf{x}), \mu\_B(\mathbf{x})\right] = \mu\_{A \cup B}(\mathbf{x})\tag{11}$$

The combination s should match these properties:


**t-Norms:** These are combinations of membership functions of two fuzzy sets A and B, resulting in the intersection *A B* of two set membership functions:

$$\mathbb{E}\left[\mu\_A(\mathbf{x}), \mu\_B(\mathbf{x})\right] = \mu\_{A \cap B}(\mathbf{x}) \tag{12}$$

The combination t should match these properties:


Fuzzy Control Applied to Aluminum Smelting 261

where conditions and consequences are fuzzy propositions built by linguistic expressions:

The rules 1 and 2 define "immediate" propositions, the rules 3 and 4 define combined propositions. These propositions use fuzzy operators NOT, OR and AND, respectively in 2,

Mamdani (Mamdani & Assilan, 1975) defined the use of fuzzy relations *RMM* and *RPM* in U x V as an interpretation for the rule IF <pert1> THEN <pert2>, where *RMM* and *RPM* are

*QMM x y pert pert x y* 1 2

*QPM x y pert pert x y* 1 2

Figure 3 shows the structure of a basic model of fuzzy system applied in industrial process. The fuzzy system structure consists of four subsystems: Input Fuzzification, Rule Database,

In this stage, the input variables (crisp variables) are converted into fuzzy values through a

real numbers mapping *<sup>n</sup> xUR* for a fuzzy set *<sup>n</sup> A R* '

1. acquire numeric values of input variables (crisp values); 2. map these variables in a universe of discourse U;

3. determine membership functions and linguistic variables.

1. x is Low 2. y is NOT Tall

3, and 4.

defined as

3. x is Low AND y is Tall 4. x is Low OR y is Tall

where *x U* and *y V* .

**2.2 Fuzzy system structure** 

Fig. 3. Fuzzy System Structure

**2.2.1 Input fuzzification** 

presented:

Inference Machine and Defuzzification.

*IF condition THEN conse quence* (17)

, min , (18)

, min , (19)

. The steps for fuzzification are

3. t[a,b] ≤ t[a',b'], if a < a' and b < b'

```
4. t[t[a,b],c]=t[a,t[b,c]]
```
#### **2.1.4 Fuzzy relations and compositions**

A fuzzy relation describes the presence or absence of an association (or interaction) between two or more sets. Likewise, given two universes U and V, the relation R defined in U x V is a subset of the Cartesian product of the two universes, so that R: U x V →{0,1}. That is, if any *x U* and *y V* are related, R(x,y)=1; otherwise R(x,y)=0. This relation (U,V) can be defined by the following characteristic function.

$$f\_A(\mathbf{x}) = \begin{cases} 1 \text{ if } \quad \text{and} \quad \text{only} \quad \text{if (x,y)} \in \mathbb{R}(\mathbf{U}, \mathbf{Y});\\ 0 \quad \text{otherwise} \end{cases} \tag{13}$$

Fuzzy relations represent the association degree between two or more fuzzy sets. The fuzzy operations (union, intersection and complement) are similarly defined. Given two fuzzy relations R(x,y) and S(x,y) defined in one space U x Y, the resulting membership functions are:

$$
\mu\_{\mathbb{R}\times\mathbb{S}}\left(\mathbf{x},\mathbf{y}\right) = \mu\_{\mathbb{R}}\left(\mathbf{x},\mathbf{y}\right) \* \mu\_{\mathbb{S}}\left(\mathbf{x},\mathbf{y}\right)
$$

$$
\mu\_{\mathbb{R}\times\mathbb{S}}\left(\mathbf{x},\mathbf{y}\right) = \mu\_{\mathbb{R}}\left(\mathbf{x},\mathbf{y}\right) \oplus \mu\_{\mathbb{S}}\left(\mathbf{x},\mathbf{y}\right)\tag{14}
$$

where \* is any t-norm and ⊕ is any t-co-norm.

Given U, V, and W as three universes of discourses, R as a relation on U x V, and S another relation on V x W, in order to obtain the composition R o S, that relates U and W, it is initially extended R and S to U x V x W. Since the relations R and S have now the same domain, then we can determine the relation support between the universes U x W by the following expression:

$$\mu\_{\rm R0S}(\mathbf{x}, z) = \sup \left[ \min \left\{ \mu\_{\rm R}^{\rm ext}(\mathbf{x}, y, z), \mu\_{\rm S}^{\rm ext}(\mathbf{x}, y, z) \right\} \right] \tag{15}$$

Where

$$
\mu\_{\mathbb{R}}^{ext} \left( \mathbf{x}, y, z \right) = \mu\_{\mathbb{R}} \left( \mathbf{x}, y \right)
$$

$$
\mu\_{\mathbb{S}}^{ext} \left( \mathbf{x}, y, z \right) = \mu\_{\mathbb{S}} \left( \mathbf{x}, y \right) \tag{16}
$$

The main difference between the fuzzy relation and the classic relation is that the latter *<sup>R</sup> x*,*y* assumes values 0 or 1, while fuzzy relation may assume infinite values between 0 and 1.

#### **2.1.5 Fuzzy implications**

Fuzzy rules are conditional structures that use heuristic methods through linguistic expressions in rule forms, composed by a condition (IF) and a consequence (THEN), forming the following structure

*IF condition THEN conse quence* (17)

where conditions and consequences are fuzzy propositions built by linguistic expressions:

1. x is Low

260 Fuzzy Logic – Controls, Concepts, Theories and Applications

A fuzzy relation describes the presence or absence of an association (or interaction) between two or more sets. Likewise, given two universes U and V, the relation R defined in U x V is a subset of the Cartesian product of the two universes, so that R: U x V →{0,1}. That is, if any *x U* and *y V* are related, R(x,y)=1; otherwise R(x,y)=0. This relation (U,V) can be

1 if and only if x, <sup>y</sup> R U,Y ;

Fuzzy relations represent the association degree between two or more fuzzy sets. The fuzzy operations (union, intersection and complement) are similarly defined. Given two fuzzy relations R(x,y) and S(x,y) defined in one space U x Y, the resulting membership functions

> *R S x*, ,, *y*

 *R S x*,,, *y* 

Given U, V, and W as three universes of discourses, R as a relation on U x V, and S another relation on V x W, in order to obtain the composition R o S, that relates U and W, it is initially extended R and S to U x V x W. Since the relations R and S have now the same domain, then we can determine the relation support between the universes U x W by the

> *ext ext R S <sup>R</sup> <sup>S</sup> x z x y z x y z* <sup>0</sup>

> > *ext R R*

The main difference between the fuzzy relation and the classic relation is that the latter

*<sup>R</sup> x*,*y* assumes values 0 or 1, while fuzzy relation may assume infinite values between 0

Fuzzy rules are conditional structures that use heuristic methods through linguistic expressions in rule forms, composed by a condition (IF) and a consequence (THEN),

 *x*,, , *y z x y*

> 

, sup min , , , , ,

*S S*

*ext*

 *R S x y x y*

> 

*<sup>R</sup> x y <sup>S</sup> x y* (14)

*x*,, , *y z x y* (16)

(13)

(15)

3. t[a,b] ≤ t[a',b'], if a < a' and b < b'

**2.1.4 Fuzzy relations and compositions** 

defined by the following characteristic function.

where \* is any t-norm and ⊕ is any t-co-norm.

<sup>0</sup> *Af x otherwise*

4. t[t[a,b],c]=t[a,t[b,c]]

are:

following expression:

**2.1.5 Fuzzy implications** 

forming the following structure

Where

and 1.


The rules 1 and 2 define "immediate" propositions, the rules 3 and 4 define combined propositions. These propositions use fuzzy operators NOT, OR and AND, respectively in 2, 3, and 4.

Mamdani (Mamdani & Assilan, 1975) defined the use of fuzzy relations *RMM* and *RPM* in U x V as an interpretation for the rule IF <pert1> THEN <pert2>, where *RMM* and *RPM* are defined as

$$
\mu\_{QMM}(\mathbf{x}, y) = \min \left[ \mu\_{pert1}(\mathbf{x}), \mu\_{pert2}(y) \right] \tag{18}
$$

$$
\mu\_{QPM}(\mathbf{x}, y) = \min \left[ \mu\_{pert1}(\mathbf{x}), \mu\_{pert2}(y) \right] \tag{19}
$$

where *x U* and *y V* .

#### **2.2 Fuzzy system structure**

Figure 3 shows the structure of a basic model of fuzzy system applied in industrial process. The fuzzy system structure consists of four subsystems: Input Fuzzification, Rule Database, Inference Machine and Defuzzification.

Fig. 3. Fuzzy System Structure

#### **2.2.1 Input fuzzification**

In this stage, the input variables (crisp variables) are converted into fuzzy values through a real numbers mapping *<sup>n</sup> xUR* for a fuzzy set *<sup>n</sup> A R* ' . The steps for fuzzification are presented:


Fuzzy Control Applied to Aluminum Smelting 263

1 1 1

exp exp

A fuzzy rule database is a collection of IF-THEN rules that can be expressed as:

written as rules. In essence, the rules model the fuzzy system behaviour.

*x x x x a a*

*<sup>l</sup> l ll R IF x is A AND AND x is A THEN x n* : 1 1 *<sup>y</sup> is B* (22)

Where *l l l M A and B* <sup>1</sup> 1,2, , , are fuzzy sets in *U R <sup>i</sup>* and *U R* respectively, *x col u u U U* 1 1 , , *n n* , and *y V* . *x* and *y* are linguistic variables. The knowledge of an expert is stored in this rule database, since all decisions taken by an expert can be

The fuzzy inference machine acts on a set of rules, denoted in (22), maps inputs (conditions) into outputs (consequences). In this stage, called inference, the fuzzy operations are performed on these variables. The conditions will trigger some rules then the variables of the triggered rules are combined, performing the implication and summing up the result of

for *B V* '

*<sup>l</sup> l l B A R x U*

*<sup>B</sup> B Bn* ' *yy y* <sup>1</sup>

c. Algebraic product for all t-norm operators and maximum for all s-norm operators. This

*<sup>B</sup> A AB <sup>l</sup> x u <sup>i</sup>*

*<sup>y</sup>* ' ' *x xy* <sup>1</sup> <sup>1</sup>

 

(25)

 

 *<sup>y</sup>* sup*txx* ' , ,*<sup>y</sup>*

The inference machine combines the m fired fuzzy sets, as expressed in:

There are two main types of inference machine: Product and Minimum.

*n n n*

(21)

, , for the fuzzy sets triggered for the

(23)

(24)

based on each rule that compose the

2 2

*<sup>A</sup> x*

'

**2.2.2 Fuzzy rule database** 

**2.2.3 Fuzzy inference machine** 

m rules.

all rules. The fuzzy rule database with m rules does:

Perform the fuzzy inference of *A U* '

where ⊕ denotes the t-norm operator.

b. Mamdani implication (19)

In the product Inference Machine, we use: a. inference of rule database individually

fuzzy rule database:

Determine the membership value *l l <sup>n</sup> A A <sup>n</sup> x x* <sup>1</sup> <sup>1</sup>

inference machine can be represented as follows:

'

*<sup>l</sup> <sup>m</sup> <sup>n</sup> <sup>l</sup>*

max sup

The variables mapping (crisp) is characterized by membership function µA(x)→[0,1]. Such functions may be classified in: Triangle-shaped, Trapezoidal, and Gaussian. These functions are shown in Figure 4.

Fig. 4c. Gaussian Function

The Triangle-shaped and Trapezoidal functions use the triangle fuzzificator:

$$\mu\_{A^\ast}(\mathbf{x}) = \begin{vmatrix} \left( 1 - \frac{\left| \mathbf{x}\_1 - \mathbf{x}\_1^\ast \right|}{b\_1} \right) \cdots \left( 1 - \frac{\left| \mathbf{x}\_n - \mathbf{x}\_n^\ast \right|}{b\_n} \right) & \text{if} & \mathbf{x} = \left| \mathbf{x}\_i - \mathbf{x}\_i^\ast \right| \le b\_i; \\\\ 0 & \text{if} & \mathbf{x} = \left| \mathbf{x}\_i - \mathbf{x}\_i^\ast \right| > b\_i \end{vmatrix} \tag{20}$$

The Gaussian function uses the Gaussian fuzzificator:

$$\mu\_{A^{\cdot}}(\mathbf{x}) = \exp^{\left(\frac{\left\|\mathbf{x}\_{1} - \mathbf{x}\_{1}^{\cdot}\right\|}{a\_{1}}\right)^{2}} \cdots \exp^{\left(\frac{\left\|\mathbf{x}\_{n} - \mathbf{x}\_{n}^{\cdot}\right\|}{a\_{n}}\right)^{2}}\tag{21}$$

#### **2.2.2 Fuzzy rule database**

262 Fuzzy Logic – Controls, Concepts, Theories and Applications

The variables mapping (crisp) is characterized by membership function µA(x)→[0,1]. Such functions may be classified in: Triangle-shaped, Trapezoidal, and Gaussian. These functions

Universe of discourse

*n n*

1 1 ;

*ii i*

(20)

*ii i*

*if x x x b*

*if x x x b*

The Triangle-shaped and Trapezoidal functions use the triangle fuzzificator:

*xx xx*

*<sup>n</sup> <sup>A</sup>*

*x b b*

1 1 1

are shown in Figure 4.

Fig. 4a. Triangle-shaped function

Fig. 4b. Trapezoidal Function

Fig. 4c. Gaussian Function

0

The Gaussian function uses the Gaussian fuzzificator:

'

A fuzzy rule database is a collection of IF-THEN rules that can be expressed as:

$$R^{(l)}: \text{IF} \quad \mathbf{x}\_1 \quad \text{is} \quad \quad A\_1^l \quad \text{AND} \dots \text{AND} \quad \mathbf{x}\_\mathbf{x} \quad \text{is} \quad A\_n^l \quad \text{THEN} \quad \mathbf{y} \quad \text{is} \quad B^l \tag{22}$$

Where *l l l M A and B* <sup>1</sup> 1,2, , , are fuzzy sets in *U R <sup>i</sup>* and *U R* respectively, *x col u u U U* 1 1 , , *n n* , and *y V* . *x* and *y* are linguistic variables. The knowledge of an expert is stored in this rule database, since all decisions taken by an expert can be written as rules. In essence, the rules model the fuzzy system behaviour.

#### **2.2.3 Fuzzy inference machine**

The fuzzy inference machine acts on a set of rules, denoted in (22), maps inputs (conditions) into outputs (consequences). In this stage, called inference, the fuzzy operations are performed on these variables. The conditions will trigger some rules then the variables of the triggered rules are combined, performing the implication and summing up the result of all rules. The fuzzy rule database with m rules does:


$$\mu\_{\mathcal{B}^l}^l(y) = \mathbf{Support}\left[\boldsymbol{\mu}\_{\boldsymbol{A}^\circ}(\boldsymbol{x}), \mu\_{\mathcal{R}}^l(\boldsymbol{x}, y)\right] \tag{23}$$

The inference machine combines the m fired fuzzy sets, as expressed in:

$$
\mu\_{\vec{B}}\left(y\right) = \mu\_{\mathbb{B}\_1}\left(y\right) \oplus \dots \otimes \mu\_{\mathbb{B}\_n}\left(y\right) \tag{24}
$$

where ⊕ denotes the t-norm operator.

There are two main types of inference machine: Product and Minimum.

In the product Inference Machine, we use:


$$\mu\_{\boldsymbol{\beta}^{\cdot}}(\boldsymbol{y}) = \max\_{l=1}^{m} \left[ \sup\_{\boldsymbol{x} \text{eu}} \left[ \mu\_{\boldsymbol{A}^{\cdot}}(\boldsymbol{x}) \prod\_{i=1}^{n} \mu\_{\boldsymbol{A}^{\cdot}}^{l}(\boldsymbol{x}) \mu\_{\boldsymbol{\beta}^{\cdot}}(\boldsymbol{y}) \right] \right] \tag{25}$$

Fuzzy Control Applied to Aluminum Smelting 265

where yi is the i-th element corresponding to the membership functions maximum and M is

During the Aluminum production process, several chemical additives are used in reduction industries to contro bath chemical and physical composition. These additives' aim to lower the liquidus temperature (Haupin&Kvande, 1993), i.e., to decline the melting point of cryolite (Na3AlF6), allowing the solubilisation of alumina (Al2O3) and therefore better energy use. There are two strategies for bath chemistry control: Heat Balance and Mass Balance. Any change in the cell's heat balancet results in changes in the bath chemical composition, as well as any change in the bath chemical composition causes changes in the heat balance. It is noted that there is a relationship between cell's heat balance and its current chemical composition, influencing the cells' productivity (Dias, 2002). The current model used for control strategy is based on correlation between bath temperature and fluoride excess (%AlF3) in the bath. Besides these correlations, there are other variables having some influence in the bath chemistry, which are also used in the

The electrolyte used in Aluminium reduction pots is basically composed of melted cryolite (Na3AlF6), Aluminum fluoride (AlF3), calcium fluoride (CaF2) and alumina (Al2O3), and its major concentration is formed by cryolite. The bath components' percentages are directly related to stability. The fluoride percentage has the property of lowering the cryolite melting point from about 1100ºC down to. Likewise, the bath is composed of a solid part (nonmelted cryolite) and liquid part (melted cryolite) which may vary according to the percentage of fluoride present in the bath. The greater the percentage of fluoride is, the lower the bath melting point is, therefore emphasizing the presence of liquid part in comparison with the solid part (mass balance), leading to a cooling of the cell (heat balance). Similarly, low quantities of fluoride emphasize the solid part regarding the liquid part,

There are many factors contributing to the Aluminum fluoride consumption, which is added in the pot during the Aluminum reduction process. In other to stabilize such situations during the process, a theoretical calculation is defined, considering the following

Addition due to the sodium and calcium oxide present in alumina (Al2O3), according to

3Na2O + 2AlF3 = 6NAF + Al2O (30)

Based on these information, the theoretical consumption is determined by the following

3CaO + 2AlF3 = 3CaF2 + Al2O3 (31)

AlF3[kg] = A\*%Na2O + B\*%CaO + C\*%AlF3 (32)

Addition due to the absorption by pot lining (Hyland et al, 2001).

**3. Bath chemistry control in aluminum reduction cells** 

the total of elements.

control strategy.

factors:

expression:

causing a heat of the cell (heat balance).

the equations 30 and 31:

In the Minimum Inference machine, we use:


$$\mu\_{\boldsymbol{\beta}^{\cdot}}(\boldsymbol{y}) = \max\_{l=1}^{m} \left[ \sup\_{\boldsymbol{x} \in \boldsymbol{u}} \min \left( \mu\_{\boldsymbol{A}^{\cdot}}(\boldsymbol{x}), \mu\_{\boldsymbol{A}^{\cdot}\_{1}}, \dots, \mu\_{\boldsymbol{A}^{\cdot}\_{n}}(\boldsymbol{x}\_{n}), \mu\_{\boldsymbol{\beta}^{\cdot}}(\boldsymbol{y}) \right) \right] \tag{26}$$

#### **2.2.4 Defuzzification**

In this stage, fuzzy output values are converted back in real values. This conversion is done through mapping, *B V* ' for a point *y V* . There are many methods for defuzzification, namely Centre of Gravity (or Centre of Area), Centre of Maxima, Average of Maxima, to name a few.

The method Centre of Gravity evaluates the center of area corresponding to the union of fuzzy sets that contributed to the result. It is mathematically represented by the formula:

$$\overline{y} = \frac{\sum\_{i=1}^{N} y\_i \mu\_{\mathcal{B}}(y\_i)}{\sum\_{i=1}^{N} \mu\_{\mathcal{B}}(y\_i)} \quad (27)$$

where *y* is the resulting center of gravity, *<sup>i</sup> y* is the center of the individual membership function and *B i y* is the area of a membership function modified by the fuzzy inference result (not null values).

The Centre of Maxima method uses the higher values of membership functions. The not null values are considered weights and the result is obtained as a support point among them. It is evaluated by the following equation:

$$\overline{\hat{y}} = \frac{\sum\_{i=1}^{N} y\_i \sum\_{i=1}^{N} \mu\_M(y\_i)}{\sum\_{i=1}^{N} \sum\_{i=1}^{N} \mu\_M(y\_i)} \tag{28}$$

where *<sup>M</sup> <sup>i</sup> y* are the membership functions maximum (height) points.

The Average of Maxima method uses the maximum point of each membership function and takes the mean value as the defuzzified value. It is represented by the following formula:

$$\overline{y\_i} = \sum\_{i=1}^{M} \frac{y\_i}{M} \tag{29}$$

c. Algebric product for all t-norm operators and minimum for all s-norm operators. This

*ll L <sup>n</sup>*

In this stage, fuzzy output values are converted back in real values. This conversion is done

namely Centre of Gravity (or Centre of Area), Centre of Maxima, Average of Maxima, to

The method Centre of Gravity evaluates the center of area corresponding to the union of fuzzy sets that contributed to the result. It is mathematically represented by the formula:

*N*

*i N*

 

1

*y*

*i*

where *y* is the resulting center of gravity, *<sup>i</sup> y* is the center of the individual membership

The Centre of Maxima method uses the higher values of membership functions. The not null values are considered weights and the result is obtained as a support point among them. It

*N N*

*i i N N*

1 1

1 1

The Average of Maxima method uses the maximum point of each membership function and takes the mean value as the defuzzified value. It is represented by the following formula:

> *M i*

*i <sup>y</sup> <sup>y</sup>*

*y*

*y* are the membership functions maximum (height) points.

*i i*

1

 

(26)

for a point *y V* . There are many methods for defuzzification,

(27)

*iB i*

*y y*

*B i y* is the area of a membership function modified by the fuzzy inference

(28)

<sup>1</sup> *<sup>M</sup>* (29)

*i Mi*

*y y*

*y*

*M i*

*y*

*B i*

*<sup>B</sup> AAA B <sup>n</sup> <sup>l</sup> x u* ' ' *<sup>y</sup> x x <sup>y</sup>* <sup>1</sup> <sup>1</sup>

max supmin , , , ,

In the Minimum Inference machine, we use: a. inference of rule database individually

inference machine can be represented as follows:

*m*

b. Mamdani implication (19)

**2.2.4 Defuzzification** 

name a few.

function and

where *<sup>M</sup> <sup>i</sup>* 

is evaluated by the following equation:

result (not null values).

through mapping, *B V* '

where yi is the i-th element corresponding to the membership functions maximum and M is the total of elements.

## **3. Bath chemistry control in aluminum reduction cells**

During the Aluminum production process, several chemical additives are used in reduction industries to contro bath chemical and physical composition. These additives' aim to lower the liquidus temperature (Haupin&Kvande, 1993), i.e., to decline the melting point of cryolite (Na3AlF6), allowing the solubilisation of alumina (Al2O3) and therefore better energy use. There are two strategies for bath chemistry control: Heat Balance and Mass Balance. Any change in the cell's heat balancet results in changes in the bath chemical composition, as well as any change in the bath chemical composition causes changes in the heat balance. It is noted that there is a relationship between cell's heat balance and its current chemical composition, influencing the cells' productivity (Dias, 2002). The current model used for control strategy is based on correlation between bath temperature and fluoride excess (%AlF3) in the bath. Besides these correlations, there are other variables having some influence in the bath chemistry, which are also used in the control strategy.

The electrolyte used in Aluminium reduction pots is basically composed of melted cryolite (Na3AlF6), Aluminum fluoride (AlF3), calcium fluoride (CaF2) and alumina (Al2O3), and its major concentration is formed by cryolite. The bath components' percentages are directly related to stability. The fluoride percentage has the property of lowering the cryolite melting point from about 1100ºC down to. Likewise, the bath is composed of a solid part (nonmelted cryolite) and liquid part (melted cryolite) which may vary according to the percentage of fluoride present in the bath. The greater the percentage of fluoride is, the lower the bath melting point is, therefore emphasizing the presence of liquid part in comparison with the solid part (mass balance), leading to a cooling of the cell (heat balance). Similarly, low quantities of fluoride emphasize the solid part regarding the liquid part, causing a heat of the cell (heat balance).

There are many factors contributing to the Aluminum fluoride consumption, which is added in the pot during the Aluminum reduction process. In other to stabilize such situations during the process, a theoretical calculation is defined, considering the following factors:


$$\text{\textbullet Na}\_2\text{O} + \text{2AlF}\_3 = \text{6NAF} + \text{Al}\_2\text{O} \tag{30}$$

$$\text{\textbullet\text{CaO}} + \text{2AlF}\_3 = \text{\textbullet\text{CaF}\_2} + \text{Al}\_2\text{O}\_3 \tag{31}$$

Based on these information, the theoretical consumption is determined by the following expression:

$$\text{AlF3[kg]} = \text{A\*@Na2O} + \text{B\*@CaO} + \text{C\*@AlF3} \tag{32}$$

Fuzzy Control Applied to Aluminum Smelting 267

*<sup>I</sup> Kg* <sup>86400</sup> 0,009 <sup>96485</sup>

where I is the current in Amperes. A hypothetically Current Efficiency of 100% means that production is equal to the theoretical maximum. However, part of the Aluminum formed in

The optimum point is reached when the variables are stabilized around a setpoint. Each variable is assigned a setpoint, but the cells are subjected to many disturbances that have effect on every controlled variable. This makes the process even harder to control and more complex to model (Prasad, 2000; McFadden et al., 2001; Welch, 2002). Process experts take actions, sometimes predefined, to control the process based on their experience in the process. This means their decisions are usually taken without any model of the system. For that reason, an AI technique approach is useful since it does not need to model analytically the whole process but it can represent it with some accuracy and yield good results. To address the fluoride addition problem, we can build a fuzzy system in which all the process knowledge can be included as rules, and provided that process operators usually refer to variables using linguistic terms, Fuzzy sets can be used to

**4. Fuzzy control applied for fluoride addition in aluminum reduction cells** 

Fuzzy Controllers have been applied in industrial plants, since many solutions are sold with this technology as part of it(Cao et al, 2010). In Aluminum industry, the Aluminum fluoride addition control is usually performed by parameterized equations, confidentially protected. These are made by data collection and numeric approximation. This model has a poor performance since the plant is very nonlinear and complex and its modeling is very difficult. Very often the process operators must take manual actions to control the process. This decision making process for fluoride addition in reduction cells is a routine for adjusting the

In order to maintain performance and stability of electrolytic cells, some action on thermal balance and mass balance is required (Welch, 2000), acting on process variables. These variables are used to determine how much Aluminum fluoride should be added into the bath. Bath chemistry control stands as a great challenge for Aluminum smelters, since it is

Since human intervention in this process is often required, a fuzzy controller must follow the actions operators usually take when analyzing recent data from the cells. In this sense, a linguistic processing is needed to represent the process data under a fuzzy view. Also, a survey with process engineers responsible for the bath chemistry control is performed in order to find out which data the process operators usually look at before performing a fluoride addition. TThese data can also represent the process dynamic behaviour. In this

(33)

*Al CO Al O CO* 2 23 23 3 (34)

*Al*

the bath is recombined again with carbon gas, as showed in the equation (34).

represent these linguistic terms.

bath composition and hence its performance.

intrinsic to the thermal balance of electrolytic cells.

**4.1 Design procedure** 

where A, B and C are constants and %Na2O, %CaO and %AlF3 represent respectively the percentages of sodium oxide, calcium oxide and Aluminum fluoride. The electrolyte composition control represents a challenge in Aluminum reduction industries, due to the intrinsic relation between heat and mass balance.

Usually the bath chemistry control is performed daily or weekly, collecting all the information about thermal and mass balance (Bath Temperature, Liquidus Temperature, Super Heat, Fluoride, Bath Composition and so on). With this information, the process team should take decisions on how much should be added into the bath in order to keep temperature and fluoride under control near a setpoint. Figure 5 shows a scheme of this process.

Fig. 5. Bath Chemistry Process Schematic Diagram


Table 1. Variables used in the Bath Chemistry Control Process

### **3.1 Challenges on this control**

The strongest impact of this process in Aluminum smelting is the direct influence on Current Efficiency and on ledge. Because of that, a careful control is required in order to keep both bath temperature and Aluminum fluoride stable. The Current Efficiency means literally how much is produced from the maximum allowed, according to equation 32.

where A, B and C are constants and %Na2O, %CaO and %AlF3 represent respectively the percentages of sodium oxide, calcium oxide and Aluminum fluoride. The electrolyte composition control represents a challenge in Aluminum reduction industries, due to the

Usually the bath chemistry control is performed daily or weekly, collecting all the information about thermal and mass balance (Bath Temperature, Liquidus Temperature, Super Heat, Fluoride, Bath Composition and so on). With this information, the process team should take decisions on how much should be added into the bath in order to keep temperature and fluoride under control near a setpoint. Figure 5 shows a scheme of this

%ALF3 Percentage of AluminumFluoride in the bath %CaF2 Percentage of Calcium Fluoride in the bath AlF3A Amount of Aluminum Fluoride to be added CaF2A Amount of Calcium Fluoride to be added Na2CO3A Amount of Sodium Carbonate to be added LIFE Time elasped (in days) since cell startup

The strongest impact of this process in Aluminum smelting is the direct influence on Current Efficiency and on ledge. Because of that, a careful control is required in order to keep both bath temperature and Aluminum fluoride stable. The Current Efficiency means literally how much is produced from the maximum allowed, according to equation 32.

intrinsic relation between heat and mass balance.

Fig. 5. Bath Chemistry Process Schematic Diagram

**Variable Description**  TMP BathTemperature

Table 1. Variables used in the Bath Chemistry Control Process

**3.1 Challenges on this control** 

process.

$$K g\_{Al} = \left(\frac{I\*86400}{96485}\right)\*0,009\tag{33}$$

where I is the current in Amperes. A hypothetically Current Efficiency of 100% means that production is equal to the theoretical maximum. However, part of the Aluminum formed in the bath is recombined again with carbon gas, as showed in the equation (34).

$$\text{Ca}^{\cdot} + \text{3CO}\_{2} \rightarrow \text{Al}\_{2}\text{O}\_{3} + \text{3CO} \tag{34}$$

The optimum point is reached when the variables are stabilized around a setpoint. Each variable is assigned a setpoint, but the cells are subjected to many disturbances that have effect on every controlled variable. This makes the process even harder to control and more complex to model (Prasad, 2000; McFadden et al., 2001; Welch, 2002). Process experts take actions, sometimes predefined, to control the process based on their experience in the process. This means their decisions are usually taken without any model of the system. For that reason, an AI technique approach is useful since it does not need to model analytically the whole process but it can represent it with some accuracy and yield good results. To address the fluoride addition problem, we can build a fuzzy system in which all the process knowledge can be included as rules, and provided that process operators usually refer to variables using linguistic terms, Fuzzy sets can be used to represent these linguistic terms.

## **4. Fuzzy control applied for fluoride addition in aluminum reduction cells**

Fuzzy Controllers have been applied in industrial plants, since many solutions are sold with this technology as part of it(Cao et al, 2010). In Aluminum industry, the Aluminum fluoride addition control is usually performed by parameterized equations, confidentially protected. These are made by data collection and numeric approximation. This model has a poor performance since the plant is very nonlinear and complex and its modeling is very difficult. Very often the process operators must take manual actions to control the process. This decision making process for fluoride addition in reduction cells is a routine for adjusting the bath composition and hence its performance.

In order to maintain performance and stability of electrolytic cells, some action on thermal balance and mass balance is required (Welch, 2000), acting on process variables. These variables are used to determine how much Aluminum fluoride should be added into the bath. Bath chemistry control stands as a great challenge for Aluminum smelters, since it is intrinsic to the thermal balance of electrolytic cells.

#### **4.1 Design procedure**

Since human intervention in this process is often required, a fuzzy controller must follow the actions operators usually take when analyzing recent data from the cells. In this sense, a linguistic processing is needed to represent the process data under a fuzzy view. Also, a survey with process engineers responsible for the bath chemistry control is performed in order to find out which data the process operators usually look at before performing a fluoride addition. TThese data can also represent the process dynamic behaviour. In this

Fuzzy Control Applied to Aluminum Smelting 269

Fig. 6a. Fuzzy sets for the bath temperature

Fig. 6c. Fuzzy sets for Life

Fig. 6b. Fuzzy sets for Percentage of Aluminum fluoride in the bath

work they are: Bath Temperature (TMP), Percentage of aluminum fluoride in the bath(ALF), Cell operation time (also known as Pot life) (LIFE). Moreover, the Temperature and Fluoride trend information (TTMP and TALF, respectively)are also viewed by process operators and should be taken into account for fuzzy processing, provided that Bath temperature and Aluminum Fluoride are negatively correlated, which means as one is rising the other is falling. The past fluoride additions are also considered in a separate variable called Accumulated Aluminum Fluoride (ALF3AC), so the information of how much fluoride has been added into the bath in the last three cycles is considered for fuzzy processing. And finally, the output variable for the fuzzy system is Fluoride addition (ALF3A), which is the control variable. It is important to note that the variables TMP, ALF and LIFE are measured, but TTMP, TALF and ALF3AC are calculated from TMP and ALF, as shown in equations.

$$TTPMP\left(t\right) = TMP\left(t\right) - TMP\left(t - 1\right) \tag{35}$$

$$TALF(t) = ALF(t) - ALF(t-1) \tag{36}$$

$$ALF3AC\left(t\right) = \sum\_{i}^{3} ALF3A\left(t - i\right) \tag{37}$$

After these variables have been chosen, each one is assigned linguistic terms like process operators usually call, as shown in table 2.


Table 2. Fuzzy Variables used in this system and their linguistic terms

#### **4.1.1 Fuzzy sets**

The linguistic terms for each process variable are used to form the fuzzy sets, which are characterized by membership functions, as described in 2.1. The membership functions related to each fuzzy set were determined by the dynamic behaviour of each variable as the process evolves. All sets are represented by trapezoidal functions whose limits are based on a qualitative knowledge on the plant. Figures 6a-6g show the fuzzy sets plots for each input variable and for the output variable.

work they are: Bath Temperature (TMP), Percentage of aluminum fluoride in the bath(ALF), Cell operation time (also known as Pot life) (LIFE). Moreover, the Temperature and Fluoride trend information (TTMP and TALF, respectively)are also viewed by process operators and should be taken into account for fuzzy processing, provided that Bath temperature and Aluminum Fluoride are negatively correlated, which means as one is rising the other is falling. The past fluoride additions are also considered in a separate variable called Accumulated Aluminum Fluoride (ALF3AC), so the information of how much fluoride has been added into the bath in the last three cycles is considered for fuzzy processing. And finally, the output variable for the fuzzy system is Fluoride addition (ALF3A), which is the control variable. It is important to note that the variables TMP, ALF and LIFE are measured, but TTMP, TALF and ALF3AC are calculated from TMP and

**Input Variables Linguistic terms** 

TTMP Bath Temperature Trend Rise, Fall TALF Aluminum Fluoride Trend Rise, Fall Output Variable Linguistic terms

LIFE Cell Life Young, Average, Old

Table 2. Fuzzy Variables used in this system and their linguistic terms

*i ALF AC t ALF A t i* 3

After these variables have been chosen, each one is assigned linguistic terms like process

TMP Bath Temperature Very Cold, Cold, Normal, Hot, Very Hot ALF Aluminum Fluoride Very Low, Low, Normal, High, Very High

ALF3A Aluminum Fluoride to be added No Add, Very Low, Low, Mid-Low,

The linguistic terms for each process variable are used to form the fuzzy sets, which are characterized by membership functions, as described in 2.1. The membership functions related to each fuzzy set were determined by the dynamic behaviour of each variable as the process evolves. All sets are represented by trapezoidal functions whose limits are based on a qualitative knowledge on the plant. Figures 6a-6g show the fuzzy sets plots for each input

*TTMP t TMP t TMP t* 1 (35)

*TALF t ALF t ALF t* 1 (36)

<sup>3</sup> 3( ) (37)

Very Low, Low, Normal, High, Very

Normal, Mid-High, High, Very High,

High, Ultra High

Super High, Ultra High

ALF, as shown in equations.

operators usually call, as shown in table 2.

ALF3AC Accumulated Aluminum Fluoride

variable and for the output variable.

**4.1.1 Fuzzy sets** 

Fig. 6a. Fuzzy sets for the bath temperature

Fig. 6b. Fuzzy sets for Percentage of Aluminum fluoride in the bath

Fig. 6c. Fuzzy sets for Life

Fuzzy Control Applied to Aluminum Smelting 271

In order to define the fuzzy rules, a database T was built by taking the process variables records from the chosen inputs and outputs. This database encompasses three years of operation and has over 800,000 records. This huge number of records allows querying each combination of variables' fuzzy sets against the database in order to find which output value was chosen in the most of times. This means that the rules definition cannot be performed by interviews as fuzzy system designers usually do, however some adjusts on the rules may be made by process experts. Table 3 shows the number of fuzzy sets for each

**Variable (VAR) Number of Fuzzy Sets (NVAR)** 

1800

Through these combinations, one can perform a statistical research in the process database and find which output fuzzy set has more occurrences for every single combination. Table 4 shows how the fuzzy rule database look like, taking into account these combinations. It is assumed for interpretation the connector AND for all rules. Table 5 shows a case for

Fig. 6g. Fuzzy sets for Amount of Aluminum fluoride to be added

**4.1.2 Fuzzy rules definition** 

variable and the number of combinations:

x NTTMP x NTALF x NALF3AC)

Table 3. Combinations of Fuzzy Sets

defining an output for a given rule.

The statistical research may fall into three cases:

TMP 5 ALF 5 LIFE 3 TTMP 2 TALF 2 ALF3AC 6 Total of combinations (NTMP x NALF x NLIFE

Fig. 6d. Fuzzy sets for Temperature Trend

Fig. 6e. Fuzzy sets for Fluoride Trend

Fig. 6f. Fuzzy sets for Accumulated Aluminum fluoride

Fig. 6d. Fuzzy sets for Temperature Trend

Fig. 6e. Fuzzy sets for Fluoride Trend

Fig. 6f. Fuzzy sets for Accumulated Aluminum fluoride

Fig. 6g. Fuzzy sets for Amount of Aluminum fluoride to be added

### **4.1.2 Fuzzy rules definition**

In order to define the fuzzy rules, a database T was built by taking the process variables records from the chosen inputs and outputs. This database encompasses three years of operation and has over 800,000 records. This huge number of records allows querying each combination of variables' fuzzy sets against the database in order to find which output value was chosen in the most of times. This means that the rules definition cannot be performed by interviews as fuzzy system designers usually do, however some adjusts on the rules may be made by process experts. Table 3 shows the number of fuzzy sets for each variable and the number of combinations:


Table 3. Combinations of Fuzzy Sets

Through these combinations, one can perform a statistical research in the process database and find which output fuzzy set has more occurrences for every single combination. Table 4 shows how the fuzzy rule database look like, taking into account these combinations. It is assumed for interpretation the connector AND for all rules. Table 5 shows a case for defining an output for a given rule.

The statistical research may fall into three cases:

Fuzzy Control Applied to Aluminum Smelting 273

**Rule Rule output (Least membership index)** 

The implication operation chosen in this work is the product method, meaning that every output set is multiplied by the rule's least membership value. And for the aggregation operation, the output sets build the geometric shape by the maximum. The defuzzification method is the centre of area. Figure 7 shows the geometric shape made by the output sets

The fuzzy algorithm was directly implemented in an industrial plant of aluminum reduction. Initially 10 pots were chosen from one potline, to which the operators were instructed to intervene only when there is an extreme need. However, it is worth

Mid-High (0.6)

Very Low (0.4)

Mid-High (0.32)

High (0.32)

"if **TMP** is *Cold(0.6)* and **ALF** is *Low(1)* and **LIFE** is *Young(0.68)* and **ALF3AC** is *Normal(1)* and **TTMP** is *Fall(1)* and **TALF** is *Fall(1)*"

"if **TMP** is *Normal(0.4)* and **ALF** is *Low(1)* and **LIFE** is *Young(0.68)* and **ALF3AC** is *Normal(1)* and **TTMP** is *Fall(1)* and **TALF** is *Fall(1)*"

"if **TMP** is *Cold(0.6)* and **ALF** is *Low(1)* and **LIFE** is *Normal(0.32)* and **ALF3AC** is *Normal(1)* and **TTMP** is *Fall(1)* and **TALF** is

"if TMP is *Normal(0.4)* and ALF is *Low(1)* and

with their least membership index in table 7.

**4.3 Result and validation** 

Table 7. Rules triggered for the fuzzy values in the case of table 6

Fig. 7. Implication, Aggregation and Defuzzification operations

LIFE is *Normal(0.32)* and ALF3AC is *Normal(1)* and TTMP is *Fall(1)* and TALF is

*Fall(1)*"

*Fall(1)*"



Table 4. Fuzzy Rule Database Structure


Table 5. Fuzzy rule definition upon database research

#### **4.2 Fuzzy operations**

Real world (crisp) values are fuzzified by the membership functions defined in figures 6a-6f, which may yield fuzzy values in one or two sets. We used the minimum operator to apply the fuzzy values. Table 6 shows an example of fuzzification and table 7 show an example of the fuzzy minimum operator:


Table 6. Fuzzy Values for a case

 **Case 3** – there are no records matching the condition of a given rule, which means the rule output should be chosen later by a process expert, however it is likely that this

**Fluoride** 

1 Very Cold Very Low Young Very Low Fall Fall Det. by queries 2 Very Cold Very Low Young Very Low Fall Rise Det. by queries 3 Very Cold Very Low Young Very Low Rise Fall Det. by queries 4 Very Cold Very Low Young Very Low Rise Rise Det. by queries 5 Very Cold Very Low Young Low Fall Fall Det. by queries

1800 Very Hot Very High Old Ultra High Rise Rise Det. by queries

"if **TMP** is *Normal* and **ALF** is *Very Low* and **LIFE** is *Normal* and **ALF3AC** is *Normal* and **TTMP** is *Fall* and **TALF** is *Rise*"

Thus, as for this rule, the output is chosen as *Very High*, since it is the decision more often.

Real world (crisp) values are fuzzified by the membership functions defined in figures 6a-6f, which may yield fuzzy values in one or two sets. We used the minimum operator to apply the fuzzy values. Table 6 shows an example of fuzzification and table 7 show an example of

 **Variable Crisp Value Fuzzy Values (with membership indexes)** 

70 Kg Normal (1)

Bath Temperature (TMP) 962ºC Cold (0.6) and Normal (0.4)

Cell Life (LIFE) 596 days Young (0.68) and Normal (0.32)

**Conditional Variables Consequence** 

**Fluoride Trend** 

**Temp. Trend** 

, which is

, whose

**Fluoride to be** 

**added** 

**Case 1** - there is only one most frequent set for a condition of a given rule Rl

**Case 2** – there are two or more frequent set for a condition of a given rule Rl

**Cell Life Accum.** 

… … … … … … … …

A query against a database is performed, and the following result is found:

**ALF3A** is *Normal* Twice **ALF3A** is *High* 3 Times **ALF3A** is *Very High* 6 Times

Table 5. Fuzzy rule definition upon database research

Aluminum Fluoride (ALF) 9.82 % Low (1)

Temperature Trend (TTMP) -13ºC Fall (1) Fluoride Trend (TALF) - 3% Fall (1)

going to be the rule's output.
