**3. Fuzzy lozic controller for point to point position control**

#### **3.1 Introduction**

Point-to-point position control is one of the motion control systems that concern much the precision and speed in its performance. Nevertheless, to develop such a high precision and speed controller is quite complicated because of the nonlinearity function in the system such as friction and saturation. Both conditions cannot be compensated or modeled simply by using the linear control theory. Thus, an alternative controller should be developed to overcome this nonlinearity system.

In the motion control system, two main sources are identified to be the parameters variations that cause the nonlinearity condition. There are frictions and inertia variations. The variations of the inertia occur because of numbers of different payload. The different payload at the same time would also cause the different Coulomb friction variations. Both variations are the main parts that need to be solved to improve the performance of the system.

P = Positive, Z = Zero, N = Negative, PB = Positive Big, PS = Positive Small, NB = Negative

For fuzzy inference, Mamdani's Min-Max method is used in both position and anti-swing control. As for defuzzification, centre of area or COA method is used to calculate the crisp value where the final outputs for both controllers are in Voltage. The results of the fuzzy controllers were obtained experimentally and the comparison between classical PID

Fuzzy Controllers show more satisfied result as compared to PID controller where the percentage overshoot and Settling Time were greatly improved. With lower settling time obtained by using the FLC, the performance of the rotary crane system is more stable than

Point-to-point position control is one of the motion control systems that concern much the precision and speed in its performance. Nevertheless, to develop such a high precision and speed controller is quite complicated because of the nonlinearity function in the system such as friction and saturation. Both conditions cannot be compensated or modeled simply by using the linear control theory. Thus, an alternative controller should be developed to

In the motion control system, two main sources are identified to be the parameters variations that cause the nonlinearity condition. There are frictions and inertia variations. The variations of the inertia occur because of numbers of different payload. The different payload at the same time would also cause the different Coulomb friction variations. Both variations are the main parts that need to be solved to improve the performance of the

**3. Fuzzy lozic controller for point to point position control** 

Where

Big, NS = Negative Small

Table 4. Positioning perfomances

Table 5. Anti-swing performances

overcome this nonlinearity system.

with the PID controller.

**3.1 Introduction** 

system.

controller and FLC is compared as in following table.

PID controller is one of the most used techniques in motion control system due to its simplicity and performances. However, PID controller could only be used effectively in linear system and does not work well with the nonlinearity system. Even if the model of the system is to be developed with PID controller, it would be complicated and this may affect the performance speed of the hardware.

Again, fuzzy approach is the most suitable technique in developing the control algorithm that relates with the nonlinearity function. With its capability in simplifying the model of the system, it can realize the high speed high precision of the system. M. M. Rashid et.al [5] in his article proposed a design of PID controller with added fuzzy logic controller (FLC) of fuzzy-tuned PID controller. With the addition of the FLC, the PID controller can adapt, learn or change its parameters based on the conditions and desired performance.

In this design, fuzzy logic is used to determine the PID controller gains, Kp, Ki, Kd as the function of error and error rate as illustrated in the following block diagram

Fig. 15. Structure of the Fuzzy-tuned PID controller

In developing the fuzzy-tuned PID controller, two design stages are used as follows:


Since there are three gains to be produced, there would be 3 fuzzy tuners to be designed. Each of them has two inputs (error and error rate) and one output (gain). Different membership functions and rules are constructed in each fuzzy tuner.

Fig. 16. Membership function of a) the error and b) error rate for Kp fuzzy tuner

Fuzzy Logic Controller for Mechatronics and Automation 127

To defuzzyfy the output Kd, COA is also used to produce the crisp value. Different membership functions are used for obtaining the gain Ki as shown in the following figures.

(a) (b)

Fig. 20. Membership function of a) the error and b) error rate for Ki fuzzy tuner

Finally, the gain Ki is defuzzified by using the COA as well to obtain the crisp value of integral gain Ki. The fuzzy-tuned PID controller is tested with rotary positioning system for

As listed in the table above, F-PID controller shows better performance with the improvement of the settling time and accuracy. Less error in F-PID controller indicates the high robustness of the controller and thus proving the capability of the fuzzy approach in

nominal object and increased inertia as visualized in the following figures.

Table 7. Rules constructed for Kd fuzzy tuner

Fig. 21. Membership function for output gain Ki

Table 8. Rules constructed for gain Ki.

this system.

Fig. 17. Membership function of output, Kp


Table 6. Rules base for Kp

In defuzzification, the output of crisp value is then obtained by using the Centre of Area (COA) method for gain Kp.

The following figures show the membership function of error, error rate, output and rule base for deriving the gain Kd

Fig. 18. Membership function of a) the error and b) error rate for Kd fuzzy tuner

Fig. 19. Membership function for output gain Kd

In defuzzification, the output of crisp value is then obtained by using the Centre of Area

The following figures show the membership function of error, error rate, output and rule

(a) (b)

Fig. 19. Membership function for output gain Kd

Fig. 18. Membership function of a) the error and b) error rate for Kd fuzzy tuner

Fig. 17. Membership function of output, Kp

Table 6. Rules base for Kp

(COA) method for gain Kp.

base for deriving the gain Kd


Table 7. Rules constructed for Kd fuzzy tuner

To defuzzyfy the output Kd, COA is also used to produce the crisp value. Different membership functions are used for obtaining the gain Ki as shown in the following figures.

Fig. 20. Membership function of a) the error and b) error rate for Ki fuzzy tuner

Fig. 21. Membership function for output gain Ki


Table 8. Rules constructed for gain Ki.

Finally, the gain Ki is defuzzified by using the COA as well to obtain the crisp value of integral gain Ki. The fuzzy-tuned PID controller is tested with rotary positioning system for nominal object and increased inertia as visualized in the following figures.

As listed in the table above, F-PID controller shows better performance with the improvement of the settling time and accuracy. Less error in F-PID controller indicates the high robustness of the controller and thus proving the capability of the fuzzy approach in this system.

Fuzzy Logic Controller for Mechatronics and Automation 129

Mobile robots are generally those robots which can move from place to place across the ground. Mobility give a robot a much greater flexibility to perform new, complex, exciting tasks. The world does not have to be modified to bring all needed items within reach of the robot. The robots can move where needed. Fewer robots can be used. Robots with mobility can perform more natural tasks in which the environment is not designed specially for them. These robots can work in a human centred space and cooperate with men by sharing

A mobile robot needs locomotion mechanisms that enable it to move unbounded throughout its environment. There is a large variety of possible ways to move which makes the selection of a robot's approach to locomotion an important aspect of mobile robot design. Most of these locomotion mechanisms have been inspired by their biological counterparts which are adapted to different environments and purposes.[9],[10] Many

In mobile robotics the terms omnidirectional, holonomic and non holonomic are often used,

The terms holonomic and omnidirectional are sometimes used redundantly, often to the confusion of both. Omnidirectional is a poorly defined term which simply means the ability to move in any direction. Because of the planar nature of mobile robots, the operational space they occupy contains only three dimensions which are most commonly thought of as the x, y global position of a point on the robot and the global orientation, θ, of the robot. Whether a robot is omnidirectional is not generally agreed upon whether this is a twodimensional direction, x, y or a three-dimensional direction, x, y, θ. In this context a non

 The robot configuration is described by more than three coordinates. Three values are needed to describe the location and orientation of the robot, while others are needed to

The robot has two DOF, or three DOF with singularities. (One DOF is kinematically

 The robot configuration is described by three coordinates. The internal geometry does not appear in the kinematic equations of the abstract mobile robot, so it can be ignored.

The robot can instantly develop a wrench in an arbitrary combination of directions

 Non holonomic robots are most prevalent because of their simple design and ease of control. By their nature, non holonomic mobile robots have fewer degrees of freedom than holonomic mobile robots. These few actuated degrees of freedom in non holonomic mobile robots are often either independently controllable or mechanically decoupled, further simplifying the low-level control of the robot. Since they have fewer

In this context a holonomic mobile robot has the following properties:

**4. Mobile autonomous robot system** 

biologically inspired robots walk, crawl, slither, and hop.

holonomic mobile robot has the following properties:

The robot has three DOF without singularities.

a discussion of their use will be helpful.[9]

describe the internal geometry.

possible but is it a robot then?)

x, y, θ.

**4.1 Introduction** 

a workspace together [9].

**4.2 Mechanism** 

Fig. 22. System responses of a) nominal object and b) increased inertia


Table 9. Comparison of the performances of PID and F-PID controllers.
