Performance Analysis of Fuzzy Logic And PID Controller for PM DC Motor Drive Khalid Al-Mutib 1, N. M. Adamali Shah 2, Ebrahim Mattar 3

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1 Performance Analysis of Fuzzy Logic And PID Controller for PM DC Motor Drive Khalid Al-Mutib 1, N. M. Adamali Shah 2, Ebrahim Mattar 3 1 King Saud University, Riyadh, Saudi Arabia, muteb@ksu.edu.sa 2 King Saud University, Riyadh, Saudi Arabia, anoormuhamed@ksu.edu.sa 3 University of Bahrain, College of Engineering. Kingdom of Bahrain, ebmattar@uob.edu.bh Abstract - This paper proposes to control the speed of the permanent magnet (PM) DC motor drive using fuzzy logic control (FLC) based on Matlab simulation environment. The proposed speed controller is developed based on fuzzy logic, to minimize maximum overshoot and steady state error. A comparison study and analysis of proposed fuzzy logic control to classical PID control system applied to PM DC motor is presented. The entire system is modeled and simulated using the matlab simulink tool box. The detailed simulation results confirm the better reduction in maximum overshoot and steady state error by the proposed FLC than the classical PID controller. controllers show high performance only for one unique act point and also it has high starting overshoot, sensitivity to controller gains and sluggish response due to sudden change in load. The FLC provides a systematic way to incorporate the human intelligence in the controller without knowing the mathematical model of the system. The stability of the system and wide range of operating speed are achieved through fuzzy logic controller. When the optimum membership functions are chosen for input and output of the FLC then it works with selfturing capability and its stability depends upon rule base. Keywords: DC drive, fuzzy logic controller, speed control, PID. 1. Introduction DC motor provides easy controllability and high performance, due to its speed can be varied within wide boundaries. DC drive has vast applications such as electric traction, electric cranes and robotic where manipulation of speed controller is required to perform their tasks [4]. In general, the control of systems is difficult and mathematically tedious due to their high nonlinearity properties. This leads to the need of more efforts to obtain more exact mathematical model of the plan to be controller and not simple mathematical operations. Fuzzy logic controller has proven effective for complex, non-linear and imprecisely defined processes for which standard model based control techniques are impractical or impossible [10-12]. The FLC is indeed capable of providing the accuracy required by high performance drive system without need of mathematical model. FLC offers simple, quicker and more reliable solution because they are viewed in form of set theory [2]. It also accommodates nonlinearity without utilization of mathematical model. The most important features of FLC is, its simplicity and less intensive mathematical design requirements. The speed of the DC motor is normally controlled by varying armature voltage or flux. In armature controlled dc motor the desired speed is obtained by varying armature voltage. However, the conventional proportional integral derivative(pid) controller has difficulty in dealing with dynamic speed tracking due to parameter variations, and load disturbances. Hence these Fig. 1. Matlab/simulink model of DC motor In this paper, the speed response of DC motor exposed to variable armature voltage is designed based on fuzzy logic controller. The DC motor is operated for a required reference speed under loaded operating condition. Then, to make performance comparison of proposed model, the speed of the system is compared with classical PID system. The proposed system provides low maximum overshot and steady state error. Numerical simulations confirm the accuracy of the propose model. 2. DC motor models A linear model of permanent magnet (PM) DC motor can be represented by their mechanical equation and electrical equation as follows [1]. dia Va La RaIa eb (1)

2 d m KmIa Jm Bm m TL (2) where Va is the applied armature input voltage, e b = K b ω m is the back electro-motive-force (EMF) voltage, Ia is the armature current TL is the load torque and ω m is the rotor angular speed. The dynamic model of the system is formed using these differential equations and Matlab simulink blocks as shown in figure 1. The armature reactions effects are neglected since the motor used has either inter-poles or compensating winding. variable value is to be decided from the encoded in the rules as shown in figure 3. Fuzzy inference consist of two processing methods namely, Mamdani s method and Sugeno or Takagi- Sugeno-Kang method to calculate fuzzy output [9]. Out of it Mamdani is more suitable for DC machine and induction machine control. The fuzzy output from the fuzzy inference is process through defuzzification to get the crisp value. Fig. 2. Fuzzy Logic Controller 3. Fuzzy Logic Controller 3.1. Description Fuzzy logic controller contains four main parts, out of which two perform transformations. They are fuzzifier (transformation 1), knowledge base, Inference engine and defuzzifier (transformation 2). Fuzzification measure the values of input variable and converts them into suitable linguistic values. Knowledge base consist a database and provides necessary definitions, which are used to define linguistic control rules. This rule base characterized the control goals and control policy of the domain experts by means of a set of linguistic control rules. Decisionmaking logic or inference mechanism is main part of fuzzy controller. It has the capability of simulating human decision making based on fuzzy concepts and of inferring fuzzy control actions employing fuzzy implication and the rules of inference in fuzzy logic. Defuzzification is a scale mapping, which converts the range of values of output variables into corresponding universe of discourse and also yields a nonfuzzy control action from an inferred fuzzy control action. This transformation is performed by membership function (MF). There are number of MF and their shapes are initially defined by the user Input and Output Membership Functions of FLC The triangular MFs are selected for both input and output variable. There are five MFs for input variable e and two MFs for input variable ce, whereas there are five MFs for output variable. Depending upon the input variable values, the output Fig. 3. Fuzzy rules for speed control The final output torque is then calculated as the average of the individual centroid, weighted by their height (degree of membership). The FLC output torque is applied to the PWM. The PWM controls the DC motor to the desired speed. Fig. 4. Surface of the rule

3 3.3. Design of FLC The controller observes the speed error signal e( and corresponding updates the controller output so that the actual motor speed y( matches the reference set speed r(. There are two input signals to the fuzzy controller, one is the error e( that is the difference of set speed r( and actual speed y(, and the other is the derivative of error ce(. listed in the table 1. A comparative study is carried out to investigate the accuracy of the proposed FLC controller to the classical PID controller by introducing the disturbance in the reference set speed. The disturbance Fig. 7. Comparison of system responses for no load using FLC and PID Controllers is apply of few seconds at each stage and the result were studied. In a discrete system, de(/ = Δe(/Δt = ce(/ts, where ce( = Δe( in the sampling time Ts. With constant Ts, ce( is proportional to de(/. Fig. 5. FLC simulink model 4. PID controller Convention PID controller system in paper [5] is used to compute the control signal to the PM DC motor for tracking the reference speed as shown in the figure 6. The Proportional- Integral-Derivative (PID) controller used is de( C( Kpe( KI e( KD where K P is the proportional gain, K I is the integral gain, and K D is the derivative gain. Fig. 7. Comparison of system responses for no load using FLC and PID controllers From the figure we can observe that the system with FLC controller correctly follows the reference signal. TABLE I DC MOTOR PARAMETER Parameter Values Armature resistance (Ra) 2 Ω Armature inductance (La) 0.05 mh Moment of inertia (Jm) 1.98 Kg m2 Damping co-efficient (Bm) 0.01 Nm-s/rad Torque constant (Kt=Km φ) 14.7 Nm/Amp Back EMF constant (K=Kb φ) 14.7 V-sec /rad Fig. 6. PID simulink model 5. Simulation Results To validate the control strategies as explain above, digital simulation were carried out on the PM DC motor model by their governing equations and simulated using Matlab/Simulink. The parameters in the DC motor used are

4 Fig. 8. Comparison of system responses for load impact using FLC and PID controllers Fig. 9. Comparison of system responses for load impact using FLC and PID controllers zoomed Fig. 11. Comparison of system responses for the continuous disturbance in the control signal using FLC and PID controllers 6. Conclusion PM DC motor speed control has been performed in Matlab simulink environment. DC motor speed has been controlled with classical PID controller and Fuzzy logic controller (FLC). From the simulation result, it is observed that FLC has clearly better performance for providing Tr (rise time), ess (steady state error) and percentage maximum overshoot (Mp) criteria in comparison with PID controller. FLC also has more sensitive responses against load disturbances in according to classical PID controller. Acknowledgments This work is supported by NPST program by King Saud University (Project No. : 08-ELE ). 7. References [1] K. Ogata, Modern Control Engineering, Englewood Cliffs, NJ: Prentice Hall, [2] J. Yan, M. Ryan and J. Power, Using Fuzzy Logic Toward Intelligent System, NJ: Prentice Hall, [3] Y. Tipsuwan, Yodyium, Fuzzy Logic Microcontroller Implementation for DC motor Speed Control, IECON 99 Proceedings, pp , [4] S.Aydemir, S. Sezen, H. M. Ertunc, Fuzzy Logic Speed Control of DC Motor, Power Electronics and Motion Control Conference, pp , [5] K. Ang, G. Chong, and Y. Li, PID Control System Analysis, Design and Technology, IEEE Trans.Control System Technology, vol. 13, pp , July Fig. 10.Comparison of system responses for disturbance in the control signal using FLC and PID controllers [6] G. Abbas, N. Abouchi, A. Sani, C. Condemine, Design and Analysis of Fuzzy Logic Based Robust PID controller for PWM-Based Switching Converter, IEEE International Symposium on Circuits and Systems ISCAS, pp , 2011.

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