Enhancing The Performance Of DC Motor Speed Control Using Fuzzy Logic

Enhancing The Performance Of DC Motor Speed Control Using Fuzzy Logic

Ms. R. P. Suradkar Dr. A. G. Thosar

Student, M .E. EPS Principal

Government Engineering College MSSs College of Engineering and Technology Aurangabad, India. Jalna, India.

Abstract

This paper focuses on speed control of DC motor by conventional PI controller and Fuzzy Logic Controller (FLC). The DC motor is modelled using the state space equations, which are used to create the SIMULINK models of the above methods. The PI controller reduces the steady state error measured between motor speed (r) and reference speed (ref), while the Fuzzy Logic Controller (FLC) adjusts fuzzy membership functions to control the motor speed. The response of these methods is compared with each other.

1. Introduction

   In the industries, the speed of DC motor is controlled to perform different task and for load changes. The speed control can be achieved by using conventional method as PI controller or Fuzzy controller [1,2].

   In PI controller, the objective is to make the motor speed follow the reference speed. Thus PI controller is used to reduce or eliminate the steady state error measured between motor speed r reference speed ref [3].

   Fuzzy logic is used where the system is

   Fig.1:- DC motor speed control using PI Controller While modelling a DC motor, it can be

   described by state space equations.

   Where,

   = armature current

   = motor speed in rad/s

   = voltage applied to armature circuit

   nonlinear and difficult to calculate mathematical model. Intelligent techniques like Fuzzy logic developed to replace conventional control techniques. Thus, the effects of nonlinearity in conventional methods are reduced using Fuzzy logic. This fuzzy controller is similar to PI controller, when used with the defuzzification method [4,5].

   The fuzzy membership functions and rules are modified after applying to PI controller. The output of fuzzy controller is created by rules composed of two inputs and linguistic definitions. The output of FLC can be improved by varying fuzzy membership functions and rules [7].

   220

   200

   Motor Speed rad/sec

   180

   160

   140

   120

   DC Motor Speed Control using P-I Controller

2. DC motor speed control using PI controller

   The PI controller is used to control the speed of DC motor by reducing the steady state error measured between motor speed (r) and reference speed (ref). The PI controller with DC motor is as shown in block diagram.

   100

   				P-I Controlled Response Reference Input

   2.5 3 3.5 4 4.5 5

   Time in Sec

   Fig.2:- DC motor speed response with PI controller DC Motor Parameters used for the model

   are as shown in the Table1.

   Table 1:- DC Motor Parameters

   Parameters	Description	Value
   Ra	Armature resistance	4.67
   La	Armature inductance	170e-3 H

   J	Moment of inertia	42.6e-6 Kg-m
   f	Viscous friction coefficient	47.3e6Nm/rad/se
   K	Torque constant	14.7e-3N-m/A
   Kb	Back-EMF constant	14.7e-3Vsec/rad

3. DC motor speed control using Fuzzy Logic

   Instead of using system model, FLC operation based on heuristic knowledge and linguistic description is used. The lack of knowledge of developing membership functions and rules can give wrong results. Thus with sufficient knowledge of adjusting the rules and membership functions the performance of FLC can be improved .The design procedure of FLC contains three steps as

   1. Defining input and output

   2. Defining membership functions and rules

   3. Adjusting membership functions and rules.

      1. Defining Input and Output:

         In FLC error and change in error plays an important role to define controller input. For FLC the inputs are error (E) and change in error (CE).Where E is input is error between the reference speed r and actual speed a. The output for FLC is the change in armature voltage (CU). The equations of input & output are given by equations:

         E= e(k )= r (k )- a (k) ——-(3)

         CE= e(k )- e(k-1 )—————(4)

         CU= u(k )- u(k-1 )————-(5)

         Block diagram of Fuzzy logic controller including the input and output values is as shown in fig.3.

         Fig.3:- Block diagram of fuzzy logic controller

      2. Defining membership functions and rules:

         Table 2 shows the fuzzy linguistic terms used in this paper.

         Table 2:- Fuzzy Linguistic Terms

         Term	Definition
         PB	Positive Big
         PM	Positive Medium
         PS	Positive Small
         ZE	Zero
         NS	Negative Small
         NM	Negative Medium
         NB	Negative Big

         Input and output values are defined by seven fuzzy variables, where linguistic terms are used to represent the input and output from numerical and crisp value to linguistic forms. FLC output will be calculated after converting the input and output from crisp value in to linguistic forms. This conversion is done with the help of Fuzzy membership functions.

         The fuzzy membership function can be of different shapes such as triangular and trapezoidal.

         The FLC uses Fuzzy rules. These rules are in the form of IF_THEN statements If error E is negative big (NB) and change in error (CE) equal to positive big (PB) then change in armature Voltage (CU) is zero (ZE). Table III shows the initial rules.

         E CE	NB	NM	NS	ZE	PS	PM	PB
         PB	ZE	PS	PM	PB	PB	PB	PB
         PM	NS	ZE	PS	PM	PB	PB	PB
         PS	NM	NS	ZE	PS	PM	PB	PB
         ZE	NB	NM	NS	ZE	PS	PM	PB
         NS	NB	NB	NM	NS	ZE	PS	PM
         NM	NB	NB	NB	NM	NS	ZE	PS
         NB	NB	NB	NB	NB	NM	NS	ZE

         Table 3:- Initial Rules

         With the basic reference of PI control the initial rules are constructed.

         The process of defuzzification is required to send out armature voltage. The output in the form of fuzzy sets is converted to crisp value for getting the armature voltage. The center of gravity method is used as defuzzification method.

      3. Adjusting fuzzy range of membership functions and rules:

      By adjusting the membership functions the performance of FLC can be improved. When the

      the membership function duration is changed , finer control is achieved . The final membership functions are obtained by adjusting membership f unction and rules.

      Table 4:- Final Rules

      220

      				Fuzzy Logic Controlled Response Reference Input

      200

      DC Motor Speed Control using Fuzzy Logic Controller

      E CE	NB	NM	NS	ZE	PS	PM	PB
      PB	NM	NS	NS	NB	PB	PB	PB
      PM	NM	NM	NS	NB	PB	PB	PB
      PS	NB	NM	NM	ZE	PB	PB	PB
      ZE	NB	NB	NM	ZE	PM	PB	PB
      NS	NB	NB	NB	ZE	PM	PM	PB
      NM	NB	NB	NB	NB	PS	PM	PM
      NB	NB	NB	NB	NB	PS	PS	PM

      180

      Motor Speed rad/sec

      160

      140

      120

4. Simulation Results

   Speed control system of dc motor using FLC is developed by using basic PI controller. The DC motor speed response for PI controller is as shown in Fig.2.When fuzzy logic controller is developed it gives results as shown in Fig.4.The results can be developed by modifying the membership functions ,The modified results are as shown in Fig.5.

   DC Motor Speed Control Using Fuzzy Logic Controller

   				Fuzzy Logic Controlled Response Reference Input

   240

   220

   200

   Motor Speed rad/sec

   180

   160

   140

   120

   100

   80

   2.5 3 3.5 4 4.5 5

   Time in Sec

   100

   80

   2.5 3 3.5 4 4.5 5

   Time in Sec

   Fig.5:- DC motor speed response with modified FLC

5. Conclusion:

From the results obtained by simulating the Mat lab/Simulink models of PI controller and fuzzy logic controller, It is observed that the fuzzy logic controller with modified membership function outperforms the conventional controller. This gives the scope for research to improve performance by incorporating knowledge and modifying membership functions.

The comparison can be understood with the help of following table.

Table 5:- Comparison of Different Controllers

FLC

Fig.4:- Dc motor speed response with

7. References

1. M. Chow and A. Menozzi, "On the comparison of emerging and conventional techniques for DC motor control," Proc. IECON, pp. 1008-1013, 1992.

2. H. Butler, G. Honderd, and J. V. Amerongen, "Model reference adaptive control of a direct-drive DC motor," IF.RF. Mag. Cont. Sys., vol. 9, no. 1, pp. 80-84, 1989.

3. H. Ying, W.Siler, and J.JBckley,Fuzzy control theory: nonlinear case,Automatics, vol.26, no3, pp.513- 52 0, 1990

4. J. Klir, George, Yuan, Bo.Fuzzy sets and Fuzzy logic Theory Applications

5. B. Kosko, Neural networks and fuzzy systems, Prentice hall, 1991.

6. M. H. Nehrir, F. Fatehi, and V. Gerez,, Computer modeling for enhancing instruction of electric machinery ,IEEE Trans Educ 38 (1995), 166~170.

7. S. Li and R. Challoo, Restructuring an electric machinery course with an integrative approach and computer-assisted teaching methodology, IEEE Trans Educ 49 (2006), 16~28.