**1.4 Semi active damping**

In semi active damping, the damper is adjustable and may be set to any value between the damper-allowable maximum and minimum values. Semi active control systems are a class of active control systems for which no external energy is needed like active control systems.

Fig. 3. Quarter-Car Model

In Fig 3, the model for one-quarter of a car is represented. The mass of this portion of the vehicle body (sprung mass) and one tire (unsprung mass) is defined respectively by *m*1 and *m*2 , with their corresponding displacements defined by *Y* and *X*. The suspension spring, <sup>1</sup> *k* , and damper, 1 *b* , are attached between the vehicle body and tire, and the stiffness of the tire is represented by 2 *k* . The relative velocity across the suspension damper of this model is defined by

$$
\sigma\_{rel} = \dot{\mathbf{y}} - \dot{\mathbf{x}} \tag{1}
$$

#### **1.5 Modeling of quarter car model**

114 Fuzzy Inference System – Theory and Applications

A passive suspension system is one in which the characteristics of the components (springs and dampers) are fixed. A passive control system does not require an external power source. Passive control devices impart forces that are developed in response to the motion of the wheel hop.

An active control system is one in which an external source of energy to control actuator(s) that apply forces to the suspension system and the schematic diagram of typical active suspension systems arrangement are shown in Fig 2. The force actuator is able to both add and dissipate energy from the system, unlike a passive damper, which can only dissipate

In semi active damping, the damper is adjustable and may be set to any value between the damper-allowable maximum and minimum values. Semi active control systems are a class of active control systems for which no external energy is needed like active control systems.

*k1*

Body mass (*m1*)

*k2*

Suspension mass (*m2*)

*b1*

Fig. 2. Active suspension system's oil/air connection diagram

**1.2 Passive damping** 

**1.3 Active damping** 

**1.4 Semi active damping** 

Fig. 3. Quarter-Car Model

*w* 

*x* 

*y* 

energy.

Before modeling an automatic suspension system, a quarter car model (i.e. model for one of the four wheels) is used to simplify the problem to a one-dimensional (only vertical displacement of the car is considered) spring-damper system. The reason for choosing the quarter car model is to analyze and control the suspension for each wheel separately and accurately. The schematic diagram of a quarter car system is shown in Figure 4

Fig. 4. Modeling of quarter-car suspension system

The parameters used for the system are shown in Table 1.


Table 1. Parameters of the active suspension system

Fuzzy Logic Controller for Mechatronics and Automation 117

b. Selecting the fuzzy inference rules. This generally depends on human experience and trial-and error. The interference rule is selected based on the open loop response of the suspension system.Typically; trial-and-error approach is done to obtain better result. c. Designing fuzzy membership functions for each variable. This involves determining the position, shape as well as overlap between the adjacent membership function, as these

d. Performing fuzzy inference based on the inference method. Smoothness of the final control surface is determined by the inference and defuzzification methods. The use of a universe of discourse requires a scale transformation, which maps the physical values of the process state variables into a universe of discourse. This is called normalization. Furthermore, output de-normalization maps the normalized value of the control output variables into their respective physical universe of discourse. In other words, scaling is the multiplication of the physical input value with a normalization factor so that it is mapped onto the normalized input domain. De-normalization is the multiplication of the normalized output value with a de-normalization factor so that it maps onto the physical output domain. Such scale transformation is required both for discrete and continuous universe of discourse. The scaling factors which describe a particular input normalization and output denormalization play a role similar to those of the gain coefficients in a conventional controller. In other words, they are of utmost importance with respect to controller performance and stability related issues, i.e., they are a source

produced and sent to the actuating valve for controlling the suspension.

are major factors in determining the performance of the fuzzy controller.

of possible instability, oscillation problems and deteriorated damping effects. e. Selecting a defuzzification method to derive the actual control action. The choice of the defuzzification method determines to a large extent the "quality" of control as well as the computational cost of the controller and hence must be chosen carefully. In this case

defuzzification is done by using gain block to minimize the disturbance.

Fig. 6. Block diagram representation of the control system

(car body) at any time, and the velocity of unsprung-mass. The manipulated variable is

In this system, 1 *k* represents the spring constant of the suspension system, *w* represents the road disturbances, and *x* represents the unsprung mass displacement. 1 *b* , 2 *k* and *y* represent damping constant of suspension, value of tyre stiffness and the sprung mass displacement respectively. Control force ( *MV* ) is the force from the controller which will be applied to the suspension system.

From Figure 5, applying Newton's law, the following differential equations are obtained

$$m\_1 \ddot{y} = -b\_1(\dot{y} - \dot{x}) - k\_1(y - x) + MV \tag{2}$$

$$m\_2\ddot{\mathbf{x}} = b\_1(\dot{y} - \dot{\mathbf{x}}) + k\_1(y - \mathbf{x}) - k\_2(\mathbf{x} - \mathbf{w}) - MV\tag{3}$$

#### **1.6 Fuzzy logic controller for the suspension system**

Typically a fuzzy logic controller is composed of three basic parts; (i) input signal fuzzyfication, (ii) a fuzzy engine that handles rule inference and (iii) defuzzification that generates a continuous signal for actuators such as control valves. The schematic diagram is shown in Figure 6.

Fig. 5. Schematic diagrams for a typical fuzzy logic controller

The fuzzification block transforms the continuous input signal into linguistic fuzzy variables such as small, medium, and large. The fuzzy engine carries out rule inference where human experience can easily be injected through linguistic rules. The defuzzification block converts the inferred control action back to a continuous signal that interpolates between simultaneously fired rules.

#### **1.7 Design of fuzzy controller for the suspension system**

The basic process of designing a fuzzy logic controller for the suspension systems involves 5 steps:

a. Formulating the problem and selecting the input and output variables state. For this suspension system, the inputs to the fuzzy controller are the velocity of sprung mass

In this system, 1 *k* represents the spring constant of the suspension system, *w* represents the road disturbances, and *x* represents the unsprung mass displacement. 1 *b* , 2 *k* and *y* represent damping constant of suspension, value of tyre stiffness and the sprung mass displacement respectively. Control force ( *MV* ) is the force from the controller which will be

From Figure 5, applying Newton's law, the following differential equations are obtained

Typically a fuzzy logic controller is composed of three basic parts; (i) input signal fuzzyfication, (ii) a fuzzy engine that handles rule inference and (iii) defuzzification that generates a continuous signal for actuators such as control valves. The schematic diagram is shown in

The fuzzification block transforms the continuous input signal into linguistic fuzzy variables such as small, medium, and large. The fuzzy engine carries out rule inference where human experience can easily be injected through linguistic rules. The defuzzification block converts the inferred control action back to a continuous signal that interpolates between

The basic process of designing a fuzzy logic controller for the suspension systems involves 5

a. Formulating the problem and selecting the input and output variables state. For this suspension system, the inputs to the fuzzy controller are the velocity of sprung mass

11 1 *m y b y x k y x MV* ( )( ) (2)

21 1 2 *mx b* ( )( )( ) *<sup>y</sup> x k <sup>y</sup> x k x w MV* (3)

applied to the suspension system.

Figure 6.

**1.6 Fuzzy logic controller for the suspension system** 

Fig. 5. Schematic diagrams for a typical fuzzy logic controller

**1.7 Design of fuzzy controller for the suspension system** 

simultaneously fired rules.

steps:

(car body) at any time, and the velocity of unsprung-mass. The manipulated variable is produced and sent to the actuating valve for controlling the suspension.


Fig. 6. Block diagram representation of the control system

Fuzzy Logic Controller for Mechatronics and Automation 119

are changes in different modes. However to be more realistic, various types input disturbances are applied into the system, such as sinusoidal, square wave, saw-tooth input disturbances in order to observe the performances of the Fuzzy controller. Since road disturbances do not have a particular pattern, different types input disturbances such as sinusoidal and random signals are used so that the controller can control all type road

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

squarewave road input to suspension system

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

tsec

tsec

tsec

1 output response of suspension system with fuzzy controller

20 Fuzzy controller actions to suspension system

tsec

tsec

0.5 output response of suspension system with fuzzy controller

tsec

<sup>5</sup> Fuzzy controller actions to suspension system

Sinusoidal road input to suspension system

Fig. 9. Suspension controller responses with sinusoidal input

Fig. 10. Suspension controller responses with square-wave input

disturbances.




0


0

0.5

displacement(cm)

0.5

displacement(cm)

magnitude(cm)

1

displacement(cm)

magnitude(cm)

displacement(cm)

In this case, velocity of sprung mass (car body) and difference between sprung mass velocity and unsprung mass velocity are used as fuzzy controller inputs and the output is the actuator force. The universe of discourse of the input and output variables are selected based on the results of simulation under different conditions. Triangle membership for the input and output variables with seven values is used for each variable. The triangular membership function are Negative Big [NB], Negative medium [NM], Negative small [NS], Zero [ZE], Positive Small [PS], Positive Medium [PM], Positive Big [PB] respectively. The block diagram of the suspension system control by fuzzy-logic is shown in Figure 8 and 9

#### **1.8 Quantization levels of a universe of discourse (range of membership function)**

Fuzzy quantization level basically determines the number of primary fuzzy sets. The number of primary fuzzy sets determines the smoothness of the control action and thus, can vary depending on the resolution required for the variable. The choice of quantization level has an essential influence on how fine a control can be obtained (Lee, 1990a). A coarse quantization for large errors and finer quantization for small errors are the usual choice in the case of quantized continuous domains.

Fig. 7. Fuzzy input membership function

Fig. 8. Fuzzy output membership function

According to different input conditions, the actuating valve will open from –100% to +100% for smooth control of suspension. In this work, scaling for both two inputs is set from -8 to +8 with an increment of 2 from the lowest value and that for output is set from -100 to 100% with increment of 25% is the from lowest value.

#### **1.9 Fuzzy controller performance for suspension control**

The performance of the controller is investigated through various studies involving nominal operating condition and also when the set point is fixed to zero and the input disturbance

In this case, velocity of sprung mass (car body) and difference between sprung mass velocity and unsprung mass velocity are used as fuzzy controller inputs and the output is the actuator force. The universe of discourse of the input and output variables are selected based on the results of simulation under different conditions. Triangle membership for the input and output variables with seven values is used for each variable. The triangular membership function are Negative Big [NB], Negative medium [NM], Negative small [NS], Zero [ZE], Positive Small [PS], Positive Medium [PM], Positive Big [PB] respectively. The block diagram of the suspension system control by fuzzy-logic is shown in Figure 8 and 9

**1.8 Quantization levels of a universe of discourse (range of membership function)** 

the case of quantized continuous domains.

Fig. 7. Fuzzy input membership function

Fig. 8. Fuzzy output membership function

with increment of 25% is the from lowest value.

**1.9 Fuzzy controller performance for suspension control** 

Fuzzy quantization level basically determines the number of primary fuzzy sets. The number of primary fuzzy sets determines the smoothness of the control action and thus, can vary depending on the resolution required for the variable. The choice of quantization level has an essential influence on how fine a control can be obtained (Lee, 1990a). A coarse quantization for large errors and finer quantization for small errors are the usual choice in

According to different input conditions, the actuating valve will open from –100% to +100% for smooth control of suspension. In this work, scaling for both two inputs is set from -8 to +8 with an increment of 2 from the lowest value and that for output is set from -100 to 100%

The performance of the controller is investigated through various studies involving nominal operating condition and also when the set point is fixed to zero and the input disturbance are changes in different modes. However to be more realistic, various types input disturbances are applied into the system, such as sinusoidal, square wave, saw-tooth input disturbances in order to observe the performances of the Fuzzy controller. Since road disturbances do not have a particular pattern, different types input disturbances such as sinusoidal and random signals are used so that the controller can control all type road disturbances.

Fig. 9. Suspension controller responses with sinusoidal input

Fig. 10. Suspension controller responses with square-wave input

Fuzzy Logic Controller for Mechatronics and Automation 121

and output response are also shown. In Figure 12, sawtooth input disturbance with output values [0 2] (disturbance changing from 0 to 1) and frequency of 0.5 Hz is used, the controller action and output response are also shown. In Figure 13, random number input disturbance with variance of 1, mean value of 0, initial speed of 0 and sampling time 0 is

Fig. 13. Block diagram of FLC rotary crane system with position control and anti swing

seemed to be satisfactory, since more than 85% disturbances are rejected in all cases.

disturbances, fuzzy controller is able to eliminate the disturbances entirely.

**2. Fuzzy logic controller for rotary crane system automation** 

Four types of input disturbances are used to observe the controller action with respect to input and the responses of the suspension output. Both controller action and output response

The designed fuzzy logic controller and hybrid controller were applied to a car Active suspension system. Since the road model is almost irregular therefore different type disturbances are applied to the system. Fuzzy logic controller was applied to car suspension system with different type disturbances. While the sinusoidal input is applied to the suspension system, fuzzy controller eliminates 75% of the disturbances during first 4 sec. and about 90% for the rest period. In the case of square wave disturbances, average 50% disturbances were rejected from the system during whole period. For the saw-tooth wave disturbances, 15-20% disturbances are present during all over the period. For random

The main purpose of controlling a Rotary crane is transporting the load as fast as possible without causing any excessive sway at the final position. Active sway angle control of Rotary crane consists of artificially generating sources that absorb the energy caused by the unwanted

In Rotary Crane System, two main objectives are to be achieved that is the positioning and at the same time avoiding the swinging of the hooked object. These two functions are depending on the speed of the crane motion. Usually the crane is handled manually by human operator and the balancing control is also done by him/her. The balancing control is depending on the skills/experiences of the human operator to move the payload safely and

sway angle of the rope in order to cancel or reduce their effect on the overall system.

used, the controller action and output response are also shown.

control.

**1.10 Summary** 

**2.1 Introduction** 

The responses of suspension system using fuzzy controller for square wave, sinusoidal, and saw-tooth input disturbances are shown in Figure 10 to 13 respectively. In Figure 10, sine wave input disturbance with amplitude of 1(cm) and frequency of 1 Hz is used, the controller action and output response are also shown. In Figure 11, square wave input disturbance with amplitude of 1 (cm) and frequency of 1 Hz is used, the controller action

saw-tooth road input to suspension system

Fig. 11. Suspension controller responses with saw tooth wave input

Fig. 12. Suspension controller response with random number input

and output response are also shown. In Figure 12, sawtooth input disturbance with output values [0 2] (disturbance changing from 0 to 1) and frequency of 0.5 Hz is used, the controller action and output response are also shown. In Figure 13, random number input disturbance with variance of 1, mean value of 0, initial speed of 0 and sampling time 0 is used, the controller action and output response are also shown.

Fig. 13. Block diagram of FLC rotary crane system with position control and anti swing control.

Four types of input disturbances are used to observe the controller action with respect to input and the responses of the suspension output. Both controller action and output response seemed to be satisfactory, since more than 85% disturbances are rejected in all cases.

### **1.10 Summary**

120 Fuzzy Inference System – Theory and Applications

The responses of suspension system using fuzzy controller for square wave, sinusoidal, and saw-tooth input disturbances are shown in Figure 10 to 13 respectively. In Figure 10, sine wave input disturbance with amplitude of 1(cm) and frequency of 1 Hz is used, the controller action and output response are also shown. In Figure 11, square wave input disturbance with amplitude of 1 (cm) and frequency of 1 Hz is used, the controller action

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> -1

10 fuzzy controller actions to suspension system

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> -10

0.4 output response of suspension system with fuzzy controller

<sup>5</sup> Random-number road input to suspension system

40 Fuzzy controller actions to suspension system

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> -0.4

tsec

0 2 4 6 8 10

0 2 4 6 8 10

0 2 4 6 8 10

tsec

tsec

0.5 output response of suspension system with fuzzy controller

tsec

tsec

tsec

saw-tooth road input to suspension system

Fig. 11. Suspension controller responses with saw tooth wave input


> -5 0 5





0

0

displacement(cm)

magnitude(cm)

displacement(cm)

displacement(cm)

magnitude(cm)

displacement(cm)

Fig. 12. Suspension controller response with random number input

The designed fuzzy logic controller and hybrid controller were applied to a car Active suspension system. Since the road model is almost irregular therefore different type disturbances are applied to the system. Fuzzy logic controller was applied to car suspension system with different type disturbances. While the sinusoidal input is applied to the suspension system, fuzzy controller eliminates 75% of the disturbances during first 4 sec. and about 90% for the rest period. In the case of square wave disturbances, average 50% disturbances were rejected from the system during whole period. For the saw-tooth wave disturbances, 15-20% disturbances are present during all over the period. For random disturbances, fuzzy controller is able to eliminate the disturbances entirely.
