Speed Control of Dc Motor Using Fuzzy Logic Controller

IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

Speed Control of Dc Motor Using Fuzzy Logic Controller Saurabh Dubey and S. K. Srivastava ABSTRACT: Conventional PID controllers were used to control the control the dc motor for various industrial processes from many years due to their simplicity in operation.PID controllers require mathematical models to control the plant for different process control applications. Fuzzy logic based control systems were introduced by Lotfi Zadeh to optimize linguistic variables the process control parameters in better way. This paper focuses on the use fuzzy logic to maintain the speed of DC motor close to the reference or desired speed. In fuzzy logic linguistic variables are used as input and output as opposed to numeric variables used in crisp logic. A fuzzy logic controller (FLC) is based on a set of control rules (fuzzy rules) among linguistic variables. In this paper dc motor is modelled and converted as a subsystem in Simulink. The fuzzy logic control strategy shows the improvement in various control parameters like maximum overshoot, settling time for the DC motor control. Hence this paper tries to demonstrate the capability of fuzzy logic to be used to control the speed of a dc motor.

KEYWORDS: DC motor, Fuzzy logic controller, Fuzzy logic.

INTRODUCTION DC machine is a highly versatile and flexible machine. It can satisfy the demands of load requiring high starting, accelerating and retarding torques. A dc machine is also easily adaptable for drives with range of speed control and fast reversal. They are widely used in industrial applications. The DC motors are used in rolling mills, in traction and in overhead cranes. They are also employed in many control applications as actuators and as speed or position sensors. In such applications, as that of position sensors and robotics, drives’ performance must precisely follow the desired performance. A number of control schemes such as proportional (P), proportional integral (PI), proportional derivative integral (PID), adaptive and fuzzy logic controller (FLCs) are used for control of speed of DC motors. The proposed controller system consists of multi-input fuzzy logic controller (FLC) for the speed control. The proposed system utilizes the fuzzy logic controller. Many industrial applications require that the drive precisely and quickly follow the changes in reference speed with minimum overshoot and minimum steady-state error. The fuzzy logic controller performs this required function of effective tracking of reference speed.

Fuzzy logic is a method of rule-based decision making used for expert systems and process control that emulates the ruleof-thumb thought process used by human beings. Due to these properties, fuzzy logic can be used to control a process that a human can control manually with expertise gained from experience. The linguistic control rules that a human expert can describe in an intuitive and general manner can be directly translated to a rule base for a fuzzy logic controller.

MATHEMATICAL MODEL OF DC MOTOR In armature voltage control scheme for separately excited dc motors, voltage applied to armature is varied without varying the voltage applied to the field. Equivalent model of dc motor is shown in following figure.

Saurabh Dubey and S . K. Srivastava Department of Electrical Engineering M.M.M. Engineering College Gorakhpur 273010 (UP) India Email: saurabh.dubey.6681@gmail.com and sudhirksri05@gmail.com

Fig. 1: DC motor model va = R a . ia t + La .

di a t dt

+ eb t (1)

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

eb t = K b . w(t) (2) Tm t = K t . ia t (3) Tm t = Jm .

dw t

+ Bm . w(t)(4)

dt

Where,

Va= armature voltage (V) Ra= armature resistance (Ω) La=armature inductance (H) Ia=armature current (A) Eb=back emf (V) W =angular speed (rad/s) Tm=motor torque (Nm ) θ=angular position of rotor shaft (rad) Jm =inertia of rotor (Kg-m2) Bm =viscous friction coefficient (Nms/rad) KT= torque constant (N-m/A) Kb=back emf constant (V/rad) Let us combine the upper equations together: va = R a . ia t + La .

K t . ia t = Jm .

dw t dt

di a t dt

+ K b . w(t) (5)

+ Bm . w(t) (6)

Laplace transforms of (5) and (6) are Va s = R a s . Ia s + La . Ia s . s + K b . W s (7) K t . Ia s = Jm . W s . s + Bm . W(s)(8)

Fig 2: Simulink model of dc motor

If current is obtained from (8) and substituted in (7) we have Va s = W s .

1 Kt

. La . Jm . s + R a . Jm + La Bm . s +

Ra.Bm+Kb.Kt (9) Then the transfer function which relates rotor speed and applied armature voltage is given as: W s Va s

=

Kt L a .J m .s 2 + R a .J m +L a .B m .s+ R a .B m +K b .K t

(10)

The relation between position and speed is: 1

θ s = . W(s)(11) s

Then the transfer function between shaft position and armature voltage at no-load is: θ s Va s

=

FUZZY LOGIC CONTROLLER

2

Kt L a .J m .s 3 + R a .J m +L a B m .s 2 + R a .B m +K b .K t .s

(12)

The model presented in this paper did not use the inbuilt MATLAB DC motor from Simulink, instead the dc motor has been designed from its characteristic differential equation and it is shown in Figure 2.

The fuzzy logic control is based on the simulation of how people work and anticipate to any problem in real world. A complex problem or system may be simplified by allowing some degree of imprecision, vagueness and uncertainty up to some extent. An expert operator develops A flexible control mechanism can be developed by using one’s expertise with the words like "suitable, not very suitable, high, little high, much and far too much" that are frequent and obvious words in people's life. In the classical control paradigm, much stress is laid on the precision of the input, the intermediate steps that process them, and the modelling of the system in question.

Whereas a fuzzy logiuc solution is tolerant to the imprecision in the inputs and the model of the system and still produces an output that is desired out of the system. This was put in a more effective way by Lofti A. Zadeh, the father of fuzzy set theory, “when he said most applications of fuzzy logic exploit its tolerance for imprecision.”

Fuzzy Logic Controller (FLC) The principal design parameters for a fuzzy logic controller are as given below. Figure 3 shows the controller between the pre-processing block and post processing block.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020 Defuzzification Defuzzification module performs following functions:  Performs the defuzzification which converts the set of modified control output values into a single pointwise value.  Performs an output de-normalization which maps the point wise values of the control output onto its physical domain.

A defuzzification strategy aims at producing a non-fuzzy control action that best represents the possibility of an inferred fuzzy control action.

Post processing The block after defuzzification is a post processing block which consists of often an output gain that can be tuned and also become as an integrator.

SIMULATION AND RESULTS

Fig.3: process blocks of fuzzy logic Preprocessing This block represents the measurement stage where the crisp values of the input variables are measured using some measurement system. So in fuzzy control applications, observed data are usually crisp.

Fuzzification Fuzzification is related to the vagueness and imprecision in a natural language. It is subjective valuation which transforms a measurement into a valuation of a objective value, hence it could be defined as a mapping from an observed input space to fuzzy sets in certain input universes of discourse. Hence fuzzification module performs a scale transformation which maps the current values of input process state variables into a normalised universe of discourse.

Rule Base The basic function of rule base is to represent in a structured the control policy of an experienced process operator and/or control engineer in the form of a set of production rules such asIf (Process state) then (control output) The if part of such rule is called rule antecedent and is a description of a process state in terms of a logic combination of atomic fuzzy prepositions. The then part of the rule is called rule consequent and is a description of a control output in terms of a logic combination of atomic fuzzy prepositions.

Hence a fuzzy control rule is a fuzzy conditional statement in which the antecedent is a condition in its application domain and the consequent is a control action for the system under control.

The aim of the FLC designed in this study is to limit the speed error to a minimum value. The input to the controller increases with increase in the error. Hence, the controller produces a larger control signal to reduce the error. In addition, the change of error is also important, and used as another controller input. Consequently, three linguistic variables are used for FLC: 1. Error (e) 2. Change of errors 3. Control output Here, error (ek) = reference speed-actual speed And, change of (error) = ek – ek-1

Fig. 4: Mamdani fuzzy inference system developed for fuzzy controller Membership functions of linguistic variables: The linguistics variables are defined as fuzzy set. A membership function is a curve define, shows a valve of a fuzzy variables in a certain region are mapped to a membership valve μ (degree of membership) between 0 and 1.

The following figure shows the membership function used to define linguistic variables of the present FLC.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

Fig. 8: IF-THEN rule base for fuzzy logic control

Fig.5: Membership Function for input (error).

Above control rules combined with the membership functions are used to control the speed of the dc motor. When the step input is given to the system the system’s output which is the speed of the motor is compared with that of reference speed input and hence following result was obtained.

Fig 6: Membership Function for input (cherror)

Fig.9: Comparison between reference speed input and actual motor speed

Fig.7: Membership Function for output (control) Rule-base

CONCLUSIONS

System speed comes to reference value by means of the defined rules. For example, third rule on rule base determines, 'if error is Z and change of error (cherror) is N then control output is NS. According to this rule, if error value is zero and change of error value is negative then control output is negative small.

In this paper a DC motor is controlled using fuzzy logic controller. A mathematical model to control the DC motor is developed and the motor is controlled using fuzzy controller.

The simulation results so obtained show that the fuzzy controller is able to follow closely the variations in reference

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013 speed. From the output speed wave form, we can see that the proposed fuzzy logic controller is able to give a smooth speed control with less overshoot and no oscillations. Hence, fuzzy logic controller design was proposed and implemented using the principles of artificial intelligence.

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