Speed Control of DC Motor BY Fuzzy Logic

Abstract – In this paper, Fuzzy Logic

Controller (FLC) based speed control of

chopper-fed DC motor is proposed to

achieve swift response, less overshooting

3te

2ia

1omega

-K-

resistance

-K-km*phi

-K-kb*phi

-K-

damping

1/s

1/s-K-

1/La

-K-

1/J

2Tl

1Va

and precision speed control to have

wide torque-speed characteristics. The

proposed Fuzzy Logic Controller

applies the required control voltage

based on motor speed error ( ) and its

change ( ). The performance of the

driver system is evaluated under

different operating conditions using

Simulink toolbox of MATLAB. The

simulation results clearly depict the

superiority of proposed method over the

existing method such as PI control.

Index Terms-- DC motor, Fuzzy

Logic, Speed Control.

Introduction

THE speed of DC motors can be adjusted

with in wide boundaries so as to have easy

controllability and high performance. The

DC motors used in many applications such

as steel rolling mills, electric trains,

electric vehicles, electric cranes and

robotic manipulators require speed

controllers to perform their tasks. The

Speed control of DC motors was carried

out by means of voltage control in 1981

firstly by Ward Leonard. The regulated

voltage sources used for DC motor speed

control have gained more importance after

the introduction of thyristor as switching

devices in power electronics. Then

semiconductor components such as

MOSFET, IGBT and GTO have been used

as electric switching devices.

In general, the control of systems is

difficult and mathematically tedious due to

their high nonlinearity. To overcome this

difficulty, FLC can be developed. The best

applications of FLC are the time-variant

systems that are non-linear and ill-defined.

In this study, the speed response of a

DC motor exposed to fixed armature

voltage was investigated for under loaded

and unloaded operating conditions. The

chopper circuit is used as motor driver.

Firstly, the DC motor is operated for a

required reference speed under loaded and

unloaded operating conditions using PI

controller. Then, to make performance

comparison, the speed of the system is

controlled using FLC. From the simulation

results it is observed that the proposed

FLC outperforms the classical PI

controller in terms of overshoot and steady

state error.

The complete paper is organized as

follows: Section II explains mathematical

modeling of Dc motor. Section III gives

the description of Fuzzy Logic Controller

and its design. Section IV describes the

design and simulation of PWM chopper.

The simulation results, comparison and

discussion are presented in Section V.

Section VI concludes the work. The

parameters of DC motor are given in

Appendix.

Mathematical modeling of DC motor

The resistance and inductance of DC

motor field winding are represented by

and respectively. The resistance

and inductance of armature winding are

represented by and respectively in

the dynamic model. Armature reactions

effects are ignored in the description of the

motor. This negligence is justifiable

because the motor used has either inter-

poles or compensating winding. The fixed

voltage is applied to the field winding

and therefore the field current settles down

to a constant value.

A linear model of simple DC motor can

be constructed using the mechanical and

electrical equation as shown below:

(1)

(2)

Fig. 1. MATLAB/ Simulink model of

DC motor

The dynamic model of DC motor

can be designed these differential

equations and MATLAB Simulink blocks

as shown in Fig. 1.

III.Description and Design of Fuzzy Logic

Controller

The fuzzy logic foundation is based on

the simulation of people’s opinion and

perceptions to control any system. One of

the methods to simplify complex system is

to tolerate to imprecision, vagueness and

uncertainty up to some extent. An expert

operator develops flexible control

mechanism using words like “suitable”,

“not very suitable”, “high”, “little high”

that are frequently used words in people’s

life. Fuzzy logic control is constructed on

these logical relationships. Fuzzy sets are

used to show linguistic variables.

Defining inputs, outputs and universe of

discourse

The goal of designed fuzzy logic

controller in this study is to minimize

speed error. If the speed error is bigger,

then the controller input is expected as

bigger. In addition, the change of error

plays an important role to define controller

input. Consequently fuzzy logic controller

uses error ( ) and change of error ( ) for

linguistic variables which are generated

from the control rules. Equation (3)

determines required system equations.

The output variable is the change in

control variable ( ) of motor driver.

The value is integrated to achieve

desired Alfa value. Here is an angular

value determining duty cycle of PWM dc-

dc converter designed in this paper.

Where , and are gain

coefficients and is time index. The

block diagram of a dc motor control is

shown in fig (2).

The error (e) approaches to its smallest

value when the motor speed is attained to

nominal value. If we reverse this value,

the error interval can be defined between

-200 to 200.

Fig. 2. The Block diagram of a dc motor

control

When the simulation of system was

performed at unloaded condition, the

change of error is shown in Fig 3. In this

fig, the change of error can be seen

between -1.6 and 0.1 intervals. Then this

change is optimized between –1 and 1 in

the membership functions.

Fig. 3. Change of Error.

In order to optimize the speed control,

the intervals of membership functions are

found after some manual changes as

follows

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10

ew + - - + + - - + + -

ce - - + + - - + + - -

The gain values are determined for these

intervals in simulation model as

=1/150, =1 and = 150 x 103.

Defining membership functions and

control rules

The system speed comes to reference

value by means of the defined rules. For

example, the first rule on Table 1 can be

described as if ( ) is NL and ( ) is NL

then ( ) is PL. According to this rule, if

error value is negative large and change of

error value is negative large than output,

change of Alfa will be positive large.

Fig.4. Dynamic Signal Analysis

TABLE I

Where, A1, A2. . . Represents reference

intervals.

In this condition, corresponding A2

interval in Fig 4, motor speed is larger

than reference speed and still wants to

increase strongly. This is one of the worst

conditions in control process. Because of

the fact that Alfa is smaller than the

required value, its value can be increased

by giving output PL value. This state

corresponds to motor voltage decreasing.

All conditions in control process are

shown in Fig.4.

TABLE I

To calculate FLC output value, the

inputs and outputs must be converted from

‘crisp’ value into linguistic form. Fuzzy

membership functions are used to perform

this conversion. In this paper, all

membership functions are defined

between –1 and 1 interval by means of

input scaling factors , and output

scaling factor . The linguistic terms

N

L

NM NS Z PS PM PL

NL PL PL PL PL NM Z Z

NM PL PL PL PM PS Z Z

NS PL PM PS PS PS Z Z

Z PL PM PS Z NS NM NL

PS Z Z NM NS NS NM NL

PM Z Z NS NM NL NL NL

PL Z Z NM NL NL NL NL

1Va

Saturation

RepeatingSequence

if { }In Out

If Action Subsystem1

elseif { }In Out

If Action Subsystemu1

u2

if(u1<=u2)

elseif(u1>u2)

If

-K-

Gain1

0

Constant3

2Vdc

1alfa

Output Reset

for input and output values are represented

by seven membership functions as show in

Fig.5.

(a)

(b)

(c)

Fig. 5. Membership Functions for (a)

Speed error (b) change of speed error

and (c) Change of Alfa.

Design and Simulation of PWM

chopper

The PWM DC chopper used as a driver

in this work can change the average value

of armature voltage applied from a fixed

DC source by switching a power switch

such as thyristor, BJT. Because of wide

spread use of separately excited DC motor

in industrial application, the speed control

of this motor is mentioned here.

The average output voltage can be

calculated as,

Vdo=δV

-------(4)

Where, is the DC source voltage. The

can be controlled using two methods:

Hold fixed and change

(frequency modulation)

Hold period ( ) fixed and

change rate (pulse width

modulation)

In this paper, one-quadrant DC chopper is

designed as a driver. In one-quadrant

driver, load voltage and load current can

take only positive values. DC chopper

model used in simulation model is shown

in Fig. 6. To control average output

voltage, , pulse width modulation

(PWM) technique is used.

Va

Tl

omega

ia

te

dc motor model

1/z

Unit Delay

Step

Scope3

Scope2

Scope1

Scope

1/s

Integrator1

-K-

Gain3

-K-

Gain2

1

GainFuzzy Logic Controller

alfa

VdcVa

DC_ChopperModel

200

Constant1

200

Constant

Fig 6. Simulink Model of PWM dc

Chopper

Fundamentally, the operating

principle of driver model is based on the

comparison of two signals. The first signal

is a triangular waveform with 2KHZ

chopping frequency and other one is fixed

linear signal which represents time

equivalent of alpha trigging angle (t).

Fig. 7. Input and output signals of

driver model

Since chopping frequency is 2 KHZ,

the amplitude of triangular waveform

starts from zero and reaches =

0.0005 value. On the other hand, the Alfa

signal from controller is multiplied by

0.0005/360 value to calculate the time

corresponding to this angle. Alpha time

signal and triangular signals are U1 and U2

respectively in the ‘IF’ block used in

simulation model, as shown in Fig. 6.

Results, Comparison and Discussion

Fig.8. Simulink Model of Fuzzy Logic

Speed control of chopper-fed dc motor

Fig 9 and Fig 10 illustrate the

comparison of simulation results between

fuzzy controller and PI controller for the

50 N-m load conditions. The validity of

simulation time is set to 1 sec. The load

torque is varied from 0 to 50 N-m at 0.6

sec. It shows the performance of a dc

motor drive for step change in load torque

condition. The drive tracing the speed,

armature current and torque variation for

this occurrence can be observed form the

Figs.

The controller designed has been

simulated for 10, 30 and 50 Nm load

values; then percent overshoot (%Mp) and

steady state error (ess) have been

measured. The response for PI controller

with different Kp and Ki coefficients and

fuzzy logic controller responses are

compared on Table 2. As seen from the

table fuzzy logic controller outperforms PI

controller in terms of overshoot and steady

state error.

Fig.9. Simulation results with fuzzy

logic controller

Fig.10. Simulation results with PI

controller

TABLE II

The controller designed has been

simulated for no load condition; then

percent overshoot (%Mp), rise time (tr)

and steady state error (ess) have been

measured. PI controller responses for

different Kp Ki coefficients and fuzzy

logic controller responses are compared on

Table 3 As seen from the table FLC

outperforms PI controller in terms of

overshoot, rise time and steady state error

criteria.

TABLE III

C1 : KP = 100, KI = 15

C2: KP = 200, KI = 25

C3: KP = 300, KI = 28

C4: KP = 400, KI = 30

Conclusion

Separately excited DC motor speed

control using fuzzy logic controller has

been proposed and proved at MATLAB

Simulink environment. The simulation

results show that FLC has better

performance for providing Tr (rise time),

ess (steady state error) and %Mp (percent

overshoot) criteria in comparison with PI

controller. The FLC has more sensitive

PI

PI

Load 10 N-

m

30 N-

m

50 N-m

C1 % Mp 5.955 5.045 5.627

ess 0.393 -0.288 -0.191

C2 %Mp 5.635 5.6315 5.632

ess -0.25 -0.195 -0.15

C3 %Mp 5.7315 5.7315 5.7315

ess -0.18 -0.15 -0.12

C4 %Mp 5.895 5.895 5.895

ess -.1175 -0.09 -0.075

FLC %Mp 0.81 2.04 4.93

ess 0.0062 -.0045 -.018

Criteria

PI FLC

C1 C2 C3 C4

tr 0.141 0.141 0.141 0.141 0.036

ess -.093

3

-

0.579

-

0.415

-

0.262

-0.01

%Mp 5.527 5.631 5.731 5.894 0.68

response against load disturbances

compared to PI controller.

References

[1]. Y. Tipusuwan and Y. Chow, “Fuzzy

logic microcontroller implementation for

dc motor speed control”, IEEE

proceedings, 1999.

[2]. Y.S. Ettomi, S.B.M. Noor and S.M.

Bashi, “Micro Controller Based

adjustable closed loop dc motor

speed controller”, IEEE

proceedings, 2003, Vol. 2, P. 59 –

63.

[3]. A. Dumitrescu, D.Fodor, T.Jokinen,

M.Rosu, S.Bucurencio “Modeling

and simulation of electric drive

system using MATLAB/Simulink

environments”, International

Conference on Electric Machines

and Drives (EMD), 1999, pp.451-

453.

[4]. B.K.Bose, “Expert system, Fuzzy

Logic and neural network

applications in power

electronics and motion control”, proc

.IEEE, vol.82, PP.1303-1323, Aug.

1994.

[5]. http://www.mathworks.com (The

official site for MATLAB &

SIMULINK as Fuzzy Logic

Toolbox).

[6]. Gopal K. Dubey, “Fundamentals of

Electrical Drives”, Narosa Publishers

2nd Edition.

[7]. R. Krishnan, “Electric motor drives

modeling, Analasis and control”,

Prentice –Hall of India Private

Limited, New Delhi.

APPENDIX

DC MOTOR PARAMETERS

Parameters Description Value

Ra Armature

Resistance

0.5

La Armature

Inductance

0.003

J Moment of

Inertia

0.0167

K=Ke(Kb x

)

=K1 (K x

)

Motor

Constant

0.8

B1 Damping

Ratio of

mechanical

system

0.0167