Download - 6.Speed Control of DC Motor by Fuzzy Logic1
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