188 Pankaj Kumari Meena, Dr. Bharat Bhushan

International Journal of Electronics, Electrical and Computational SystemIJEECS

ISSN 2348-117XVolume 6, Issue 6

June 2017

Simulation for Position Control of DC Motor using FuzzyLogic

Pankaj Kumari MeenaPG Scholar

Department of Electrical Engg., DelhiTechnological University

New Delhi, India

Dr. Bharat BhushanProfessor

Department of Electrical Engg.Delhi Technological University

New Delhi,India

Abstract-The purpose of this project is to control theposition of DC Motor by using Fuzzy Logic Controller(FLC) with MATLAB application. The scope includes thesimulation and modeling of DC motor, fuzzy controllerand conventional PID controller as benchmark to theperformance of fuzzy system. The position control is anadaptation of Closed Circuit Television (CCTV)system.[1] Fuzzy Logic control can play important rolebecause knowledge based design rules can be easilyimplemented in the system with unknown structure and itis going to be popular since the control design strategy issimple and practical. This make FLC an alternativemethod to the conventional PID control method used innonlinear industrial system. The results obtained fromFLC are compared with PID control for the dynamicresponse of the closed loop system. Overall performanceshow that FLC perform better than PID controller.

Keywords: Fuzzy Logic Controller, Position Control,Fuzzy Logic Toolbox, DC Servo Motor, MATLAB

Ι. INTRODUCTIONIn recent years DC motors are used in highperformance drive system because of itsadvantages. A DC servo motor which is usually aDC motor of low power rating is used as an actuatorto drive a load[2]. It is having high ratio of startingtorque to inertia and faster dynamic response.Because of their high reliability, flexibility and lowcost, DC servo motors are widely used in industrialapplications, robot manipulators and homeappliances where speed and position control ofmotor are required. It is a common actuator incontrol system, it is directly provides the rotary andtransitional motion and the field excitation isprovided by permanent magnet and remainsconstant under all operating conditions. DC servo

drive systems normally use the full four quadrantoperations which allow bidirectional speed controlwith regenerative braking capabilities. Theconventional methods have the followingdifficulties, it depends on the accuracy of themathematical model of the system and the expectedperformance is not met due to the load disturbances.The classical linear control shows goodperformance only at one operating speeds. Fuzzylogic is a technique to embody human like thinkinginto a control system[4]. Fuzzy control has beenprimarily applied to the control of processesthrough fuzzy linguistic performances. The fuzzycontroller gives the better dynamic performance aswell as error reduction[5][12].

II. MATHEMATICAL MODEL OF THE DCSERVOMOTOR

Fig.1. Schematic Representation of the DCservomotor

Fig.1. represented the servo motor model[1][2][3][6].

Let’s consider:-E

a(t) =Input voltage

189 Pankaj Kumari Meena, Dr. Bharat Bhushan

International Journal of Electronics, Electrical and Computational SystemIJEECS

ISSN 2348-117XVolume 6, Issue 6

June 2017

ia(t) =Armature current

Ra= Armature resistance

La= Armature inductance

Eb(t) =Back e.m.f

Tm= Developed Torque

ωm

=Motor angular velocity

J=Motor moment of inertia B=Viscous frictioncoefficient K

b=Back e.m.f constant

KT=Torque constant

Here, the differential equation of armature circuit is-

Ea(t) =R

a.i

a(t)+L

a.di

a(t)/dt+E

b(t) (1)

The Torque equation is-

Tm

(t) = J.dωm

(t)/dt + B.ωm

(t) (2)

The torque developed by motor is proportional tothe product of the armature current and field currenti.e. T

m(t) = K

f.i

f.i

a(3)

Where, Kfis constant. In armature – controlled D.C.

motor the field current (if) is kept constant

i.e. Tm

= KT.i

a(4)

Where, KT

= Kf.i

fis torque constant. The back e.m.f.

of motor is proportional to the speed

i.e. Eb(t) = K

b. ω

m(5)

Where, Kbis back e.m.f. constant. In order to create

the block diagram of system initial conditions arezero and Laplace transform is implemented to theequations. i.e.

Ea(s) = R

a.I

a(s) + sL

a.I

a(s) + E

b(s)

Ia(s) = Ea (s)-E

b(s)/sL

a+ R

a(6)

Tm

(s) = sJ.ωm(s) + B.ω

m(s)

ωm

(s) = Tm(s)/ sJ + B (7)

Tm(s) = K

T.I

a(s) (8)

Eb(s) = K

b. ω

m(s) (9)

Fig.2.Block Diagram of DC motor

III. Fuzzy Logic Controller

The Fuzzy Logic Controller is designed to have twofuzzy state Variables and one control variable forachieving position control of the DC ServoMotor[5][10][12]. These two input variable are the errorand change in error. The fuzzy logic controllerinitially converts the crisp error and change in errorvariables into fuzzy variables and then are mappedinto linguistic labels. Membership functions ofinput ‘velocity’, ‘error’ and output ‘control’ areshown in fig. which consists of two inputs and oneoutput. Different membership functions are used forthe fuzzy set of the input and output vectors. Thereare seven linguistic variables for the input velocity,error, and output control. All the MFs aresymmetrical for positive and negative values of thevariables. The linguistic labels are divided intoseven groups.

The seven linguistic variables are NB- negative big,NM - negative medium, NS - negative small, Z-zero, PS- positive small, PM – positive medium, PB- positive big.

Fig.3. Basic structure of FLC

190 Pankaj Kumari Meena, Dr. Bharat Bhushan

International Journal of Electronics, Electrical and Computational SystemIJEECS

ISSN 2348-117XVolume 6, Issue 6

June 2017

The fuzzy controller block for a DC motor is shownin figure 5. The three principal elements to a fuzzylogic controller are 1. Fuzzification module(Fuzzifier) 2. Rule base and Inference engine 3.Defuzzification module (Defuzzifier).

The fuzzification module assigns suitable linguisticvalues for the input data, this may be viewed aslabels of fuzzy sets. The knowledge-base, consistingof input and output membership functions, alongwith the rule-base provides information for theappropriate fuzzification operations. In order toobtain the desired fuzzy control action,defuzzification is performed on the fuzzy inputvariables with the help of rulebase and inferencemechanism. The rules commonly used are the IF,THEN rules. The inference mechanism is the kernelof fuzzy logic controller. The control rules areevaluated by an inference mechanism. Individualrule based inference (firing) is used here. TheMamdani algorithm is used for the implementationof the inference mechanism. Defuzzification is atechnique of converting the final combined fuzzyconclusion into a crisp one. The defuzzified outputis in turn applied to the plant.

Fig.4(a) Fig.4(b)

Fig.4(c) Fig.4(d)

Fig.4.Triangular Membership Functions of ‘e’, ‘ce’and ‘u’ and output trajectory

Fig.5(a) Fig.5(b)

Fig.5(c) Fig.5(d)

Fig.5.Gaussian Membership Functions of ‘e’, ‘ce’and ‘u and output trajectory

Fig.6(a) Fig.6(b)

Fig.6(c) Fig.6(d)

Fig.6.Trapezoidal Membership Functions of ‘e’,‘ce’ and ‘u’ and output trajectory

The fuzzy-rule-based matrix used for the proposedDC servo motor specific FLC algorithm is shown intable I [9]. The top row and left column of the matrixindicate the fuzzy set of the variables ‘velocity’ and‘error’ respectively, and the MFs of the outputvariable ‘control’ are shown in the body of the

191 Pankaj Kumari Meena, Dr. Bharat Bhushan

International Journal of Electronics, Electrical and Computational SystemIJEECS

ISSN 2348-117XVolume 6, Issue 6

June 2017

matrix. There are 7*7=49 possible rules in thematrix.

Table I: The control rules of Fuzzy Logic Controller

After designing the rule, we can get the surfaceviewer in Fig. that represent the rule of FLC.Where as the x-axis is error ‘e’ and y-axis change iserror ‘ce’ and z-axis is output ‘u’.

Fig.7. Surface Viewer of FLC

IV. CONCLUSION

A fuzzy logic based controller for a DC servomotorhas been studied. The results have been comparedto the conventional controller. The design of thefuzzy logic controller has been explained and theperformance was evaluated by simulation. Thesimulation results indicate that FLC provides thebest performance in comparison with PI controller,and the shape of the FLC surface is smoother thanthat of PI controller[7][8][13][14] . In Fuzzy logiccontrol it is not necessary to change the controlparameters at any conditions. It does not happen inconventional PI. It is clear that the fuzzy PIcontroller is more advantageous than conventionalPI because the settling time is very low compared to

the conventional PI Controller. It gives betterdynamic response. This proposed scheme is verysuitable for applications of industrial positioncontrol drives.

REFERENCES[1] M. GOPAL, “Digital Control and State Variable

Methods.” Fourth edition[2] I.J. Nagrath & M. Gopal, “Control Systems

Engineering,” New Age publication, Fifth edition.[3] Math Works, Fuzzy Logic Toolbox User’s Guide[4] S.F. Abd-Alkarim “Application of Fuzzy Logic in

Servo Motor”,Al-Khwarizmi Engineering Journal2007, Vol.3, No.2, pp. 8 -16

[5] H. Aloui, A. Ben Jridi, N. Chaker and R. Neji,“Fuzzy Control for Speed Tracking of an ElectricalVehicle enclosing an Axial-Flux SynchronousMotor”, IEEE 14th International Conference onSciences and Techniques of Automatic Control &Computer Engineering, 2013, pp. 36-42.

[6] K.Premkumar, B.V. Manikandan “Adaptive FuzzyLogic Speed Controller for Brushless DC motor”,IEEE International Conference on Power, Energyand Control, 2013, pp. 290.

[7] Modern control engineering 5th edition, K.Ogataprentice hall, 2012

[8] Zakharov Alexei, Halasz Sandor,“Robust SpeedFuzzy Logic Controller for DC Drive”, 0-7803-3627-5/97/$5.00 IEEE, pp. 385-389, 1997

[9] Lee C. "Fuzzy Logic in Control Systems", Fuzzylogic controller, part II .IEEE Trans. On Systems,Man. And cybernetics 1990.

[10] Nasser T. and others "Design and Applications ofFuzzy Logic for The Speed Control of a Direct-Drive DC Motor", 4th International Conference,Cattaee, Amman-Jordan 2002.

[11] Zhao ZY, Tomizuka M.Isaka S."Fuzzy GainScheduling of PID Controllers" Proceedings of theIEEE.Conference on Control Applications.Dayton,Ohio 1992.

[12] Dr. Shereen F. Abd-Alkarim, “Application of FuzzyLogic in Servo Motor”, Al-Khwarizmi EngineeringJournal,Vol.3, No.2, pp8 -16 (2007).

[13] G.-R. Yu, R.-C. Hwang, and C.-P. Lin, "OptimalFuzzy Control of the Spindle Motor in a CD-ROMDrive Using Genetic Algorithms," presented atAsian Control Conference, 2004.

[14] "Control Tutorial for Matlab: DC Motor SpeedModeling,"

[15] I. K. Bousserhanel, A. Hazzabl, M. Rahli, M. Kamli,and B. Mazari, "Adaptive PI Controller using FuzzySystem Optimized by Genetic Algorithm forInduction Motor Control," presented at CIEP-IEEE,Puebla, Mexico, 2006.