International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
Comparative Study of Speed Control of Separately Excited DC
Motor Using PI Controller and Fuzzy Logic Controller
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
Department of Electrical Engineering, Delhi Technological University
(Formerly Delhi College of Engineering)
Abstract: This paper proposes the idea of using “Fuzzy Logic Technique” in estimating motor speed
and controlling it for DC motor. The rotor speed of the dc motor can be made to follow an arbitrarily
selected trajectory. The purpose is to achieve accurate trajectory control of the speed of DC Motor,
especially when the motor and load parameters are unknown. Such a control scheme gives very
accurate and precise result in very short time. The fuzzy logic controller employs if-else form
programming of the various conditions to control the motor speed and uses membership functions
for mapping input and output variables. This paper uses 49 rule base relating speed error and change
in speed error to control speed of motor. It also provides comparison of speed response of fuzzy
logic controller with the response achieved by PI controller for DC motor. The simulation results
prove that the control characteristic with fuzzy logic is better than that with the conventional PI
controller. The modeling of separately excited DC motor and its implementation is performed on
software MATLAB
Keywords: DC motor, Fuzzy logic controller, Membership functions, PI controller
I.
INTRODUCTION
DC motors are widely used in industries, robotics, electric vehicles, rolling mill motors and in wide
range of other applications because of their simplicity, ease of application, reliability and favorable
cost along with simple & continuous control characteristics. They are also easily adaptable for drives
as they provide a wide range of speed control and fast reversals. Many varieties of control schemes
such as traditional rheostatic control, proportional integral (PI), proportional derivation integral
(PID), fuzzy logic controller have been developed for speed control of dc motors. Specifically, the
paper describes the development of a fuzzy-logic controller to maintain constant speed in a separately
excited dc motor operating under loading conditions [7] [9].The non-linear characteristics of a DC
motor namely saturation and friction could degrade the performance of conventional controllers.
Several advance model-based control methods such as variable-structure control and model reference
adoptive control have been developed to reduce these effects. However, the performance of these
methods depends on the accuracy of system models and parameters. PID control though provides a
simple, stable and easy adjustment however the tuning of PID controller is difficult and requires exact
mathematical modelling [8][9].
In general an accurate non-linear model of an actual DC motor is difficult to find and parameter
values obtained from system identification may be only approximate values. Variable and
unpredictable outputs, noise propagation along series of unit processes and change in load dynamics
are some of the other motor control constraints.
II.
SEPARATELY EXCITED DC MOTOR
In a separately excited DC motor the field winding is used to excite the field flux. The armature
current is applied to the rotor via brush and commutator. Interaction of field flux and armature current
in the rotor produces torque. The effect of armature reaction has been neglected as the motor uses
interpoles or compensating winding. [9][10]
27
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
Fig 1: Circuit Diagram of a Separately Excited DC Motor
FIELD AND ARMATURE EQUATION
Field voltage is given by:
Vf = Rfif + Lf*(dif/dt)
(1)
where if , Rf and Lf are the field current, field resistance and field inductance respectively
Armature voltage is given by:
Va = Raia + La*(dia/dt) + Eg (2)
where ia, Ra and La are the armature current, armature resistance and armature inductance
respectively.
The motor back emf, is expressed as
Eg = Kvωif
(3)
where Kv is the motor voltage constant (in V/A-rad/sec) and ω is the motor speed (in rad/sec)[9]
TORQUE EQUATION AND ANALYSIS
For normal operation, the developed torque must be equal to the load torque plus the friction and
inertia, i.e. :
Td = J*(dω/dt) + Bω +Tl
(4)
Where,
B: Viscous friction constant (N.m/rad/sec)
Tl: Load Torque (N.m)
J: Inertia of the motor (Kg.m2) [9]
Developed Torque is also expressed as:
Td = Kt if ia
(5)
Where,
Kt: Torque constant
SPEED CONTROL TECHNIQUES IN DC MOTOR
1. Varying the armature voltage in the constant torque region
2. In the constant power region, field flux should be reduced to achieve speed above the rated speed.
III.
PI CONTROLLER
The PI controller computes the controlled output by calculating the proportional and integral errors
and summing these two components to compute the output. In PI controller due to presence of the
integral term, steady state error of speed is zero, making the system quite accurate. It does not require
high gain as required in proportional gain controller. However it has certain drawbacks like if very
fast response is desired, the penalty paid is a higher overshoot which is undesirable. [10]
28
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
Fig
2: PI Controller block diagram
FUZZY LOGIC CONTROLLER
Fuzzy logic control is a control algorithm based on a linguistic control strategy, which is derived from
expert knowledge into an automatic control strategy. While the other control systems use difficult
mathematical calculation to provide a model of the controlled plant, it only uses simple mathematical
calculation to simulate the expert knowledge. Although it doesn't need any difficult mathematical
calculation however it gives good performance in a control system. Thus, it can be one of the best
available answers today for a broad class of challenging control problems. [1][2][3][10]
Fig 3:
Block diagram of a Fuzzy Logic Controller
The fuzzifier scales and maps input variables to fuzzy sets. Inference engine with the help of rule base
does the approximate reasoning and deduce the control action. Defuzzifier converts fuzzy output
values to control actions.
ADVANTAGE OF USING FUZZY TECHNIQUE
Fuzzy technique have gained in wide acceptance in expert systems, control units, automatic
transmission bullet train between Tokyo and Osaka and in wide range of applications because of fast
adaptation, high degree of tolerance, smooth operation, reduction in the effect of non-linearity, easy
if-else logics and inherent approximation adaptability.
A fuzzy logic controller (FLC) has already been proved analytically to be equivalent to a non-linear
PI controller when a non-linear defuzzification method is used. Also, the result from the comparisons
of conventional and fuzzy logic control techniques in the form of a FLC and fuzzy compensator
showed fuzzy logic can reduce the effects of non-linearity in a DC motor and improve the
29
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
performance of a controller. [1][2][3][10]
IV.
RULE BASE FOR SPEED CONTROL OF DC MOTOR
In this paper, the speed controller make use of 49 rules mentioned in the matrix below, based on
which Fuzzy Logic controller operates to give the desired result
Fig 4: Rule Matrix for Fuzzy speed control
Where,
e
ce
du
NB
NM
Speed error
Change in speed error
Control output
Negative big
Negative medium
NS
Z
PB
PM
PS
Negative small
Zero
Positive big
Positive medium
Positive small
Fig 5: FIS Editor
Fig 6: Membership Function for change in speed
The general considerations in the design of the controller are:
30 Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
1. If both error and change in speed error are zero maintain the present control setting i.e. output=0.
2. If the error is not zero but is approaching this value at a satisfactory rate, then maintain the present
control setting.
3. If the error is growing then change the control signal output depending on the magnitude and sign
of error and change in speed error to force the error towards zero.
The typical rules of the table are read as (shaded portion in matrix):
IF e=Z AND ce= Z THEN du = Z
IF e=Z AND ce= PS THEN du = PS
IF e=PS AND ce= Z THEN du= PS
IF e=PS AND ce= PS THEN du= PM
Fig 7: Membership Function for change in speed error
Fig 8: Membership function for output
31
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
Fig 9: Rules
Fig 10: Rule Viewer
32
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
Fig11: Surface Viewer
Fig12: Matlab/Simulink Model of PI Controller
The MATLAB model with the P-I controller has one outer speed loop, one inner current loop and one
feedback loop where speed is multiplied by gain Kb to give back emf .The speed error between the
reference speed and the actual speed of the motor is fed to the P-I controller, and the Kp and Ki are
the proportional and integral gains of the P-I controller. A step response as load torque is applied to
the motor. The DC motor is designed with the help of making use of Laplace transform for equations
33
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
discussed in section II for separately excited DC motor.
Equation for back emf of motor can be written as:
Eg = Kvω(s)if
(6)
From motor’s basic armature equation, and taking Laplace Transform on both sides of the equation,
we will get:
Ia(s) = (Va(s) – Eg(s))/(Ra + Las) (7)
And from the Torque equation, we have
ω(s) = (Td(s) - TL(s) )/(Js+B) (8)[10]
Motor
Speed
in
rpm
Time in seconds
Fig 13: Speed V/S Time Response of PI controlled DC Motor
Fig14: Matlab/Simulink Model of Fuzzy Logic Controller
34
Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
The MATLAB model with Fuzzy logic controller has one outer speed loop, one inner current loop
and one feedback loop where speed is multiplied by gain Kb to give back emf . The speed error
between the reference speed and the actual speed of the motor is fed to the fuzzy logic controller(e)
and (ce) are speed error and change in speed error. Unit delay function has been introduced to
calculate change in speed error i.e e(k)-e(k-1).DC Motor models has been built in same line as
discussed in PI controller. [8]
Motor
Speed
in
rpm
Time in seconds
Fig 15:Speed V/S Time Response using Fuzzy logic controller
Motor
Speed
in
rpm
Time in seconds
Fig 16: Speed V/S Time Response using PI & Fuzzy logic controller
VI CONCLUSION
The background of separately DC Motors is studied and a study of the characteristics of separately
excited DC motor is done. We have studied basic definition and terminology of PI controller and
fuzzy logic controller and successfully implemented fuzzy logic by creating rule base for the speed
control of separately excited DC motor. Graph for the speed response of separately excited DC Motor
35 Maulik Kandpal , J. N. Rai, Anmol Aggarwal
International Journal of Electronics, Electrical and Computational System
IJEECS
ISSN 2348-117X
Volume 4, Special Issue
March 2015
using fuzzy logic controller is successfully simulated in MATLAB and compared with graph for the
speed response of separately excited DC Motor with PI controller. It is established that fuzzy logic
controller has better performance in comparison to PI controller as there is no overshoot and also
fuzzy logic has a finer control response with respect to load control.
V.
Appendix-A
SPECIFICATIONS OF THE SEPARATELY EXCITED DC MOTOR
Motor Rating
= 5 HP
Manufacturer
=Kiltoskar Electric
Insulation Class
=A
Rated Voltage
=220V
Rated Current
=21A
Armature resistance (Ra)
= 0.5 Ω
Armature inductance (La)
= 0.002 H
Mechanical inertia (J)
= 0.0167 Kg.m2
Friction coefficient (B)
= 0.0167 N.m/rad/sec
Back emf constant (k)
= 0.8 V/rad/sec
REFERENCES
[1] Fuzzy And Soft Computing- Jyh-shing, Roger Jang, Chuen-Tsai Sun
[2] K. B. Mohanty,“Fuzzy remote controller for converter DC motor drives” , Parintantra, Vol. 9, No.
1, June 2004
[3] Zimmermann, H. (2001). Fuzzy Set Theory and Its Applications. Boston: Kluwer Academic
Publishers. ISBN 0-7923-7435-5
[4] Yager, Ronald R, Filev, Dimitar P. (1994). Essentials of Fuzzy Modelling and Control. New York:
Wiley. ISBN 0-471-01761-2
[5] Santos, Eugene S. (1970). “Fuzzy Algorithms”. Information and Control 17 (4)
[6] B.C Kuo–Digital Control Systems-2nd Edition
[7]. J.N. Rai, Mayank Singhal and Mayank Nandwani, “Speed Control of DC Motor using Fuzzy
Logic Technique”, IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE), Volume 3,
Issue 6, page 41-48, Nov.-Dec. 2012.
[8]. Deepshikha, Dr. Ramesh Kumar, “Fuzzy Logic Speed Controller for Separately Excited Dc
Motor and Its Comparison with PID Speed Controller” IOSR Journal of Electrical and Electronics
Engineering (IOSR-JEEE) e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 9, Issue 4 Ver. I (Jul –
Aug. 2014), PP 46-52
[9].Control System Engineering, I.J. Nagrath, D.P. Kothari
[10] L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning,”
Inf Sci, Vol. 8, 1975.
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Maulik Kandpal , J. N. Rai, Anmol Aggarwal