Abstract. This paper investigates the performance of a fuzzy logic speed controller with a reduced rule base for an indirect vector controlled induction motor drive. Generally in the control of complex systems where high performance is required, traditional controllers does not meet the required performance. In this paper a fuzzy logic controller is developed in such a way that it can provide high performance while using lesser rule. The drive is simulated successfully using Simulink/MATLAB. The performance of the drive has been examined under various rigorous working conditions. The Simulation results show that the proposed fuzzy logic controller (FLC) works satisfactorily making the drive more suitable for high performance applications

Bhavnesh Kumar

Vivek Shrivastava

Y K Chauhan

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Performance Evaluation of reduced Rule Base Fuzzy Logic Controller 
for Indirect Vector Controlled Induction Motor Drive  
BHAVNESH KUMAR, Y. K. CHAUHAN,VIVEK SHRIVASTAVA 
School of Engineering, Gautam Buddha University, Gr. Noida, UP, India-201310 
 
 
Abstract. This paper investigates the performance of a fuzzy logic speed controller with a reduced rule 
base for an indirect vector controlled induction motor drive. Generally in the control of complex systems 
where high performance is required, traditional controllers does not meet the required performance. In this 
paper a fuzzy logic controller is developed in such a way that it can provide high performance while using 
lesser rule. The drive is simulated successfully using Simulink/MATLAB. The performance of the drive has 
been examined under various rigorous working conditions. The Simulation results show that the proposed 
fuzzy logic controller (FLC) works satisfactorily making the drive more suitable for high performance 
applications. 
 
Keywords :Induction motor, vector control, fuzzy logic controller  
1. Introduction 
Although induction motors are among the most widely used motors in the industrial as well as domestic 
applications as it provides many advantageous features such as low cost, reasonably small size, ruggedness, 
low maintenance, and operation with an easily available power supply. However, its speed control is quite 
complex due to the nonlinearity because of coupling and core saturation, which increase the challenge to use 
them in high performance applications [1]. In recent years vector control scheme (VCS) has made the task 
easy by separately providing the control over torque and flux by decoupling them. However, this decoupling 
feature can be adversely affected by the load disturbances, parameter variations and the nonlinearities, so 
controller design and selection plays a key role in drive performance [2].  
Fuzzy logic controller (FLC) is now a day is widely accepted as one of the best alternative to 
conventional proportional-integral-derivative (PID) controller used in the speed control applications where 
high performance is required. There are two main strengths of FLC: Firstly is that no mathematical model of 
the plant is needed, but knowledge of the expert is required to create a rule base. Secondly they have 
capability to handle various types of nonlinearities. FLC modeling incorporates certain amount of human 
knowledge into its component such as fuzzy rule bases, membership functions etc. These components must 
be selected with an utmost care as the selection of these components greatly influences the performance of 
FLC and decides the strength of FLC [3]-[4]. Lot of work has been reported witnessing the superior 
performance of drive with FLC in comparison to PI controller [5], [6], [7]. However most of these works are 
focused just on the speed performance evaluation while using a standard (7x7) rule base.  
The objective of this paper is to provide a detailed comparative study and to present a simplified FLC for 
an induction motor drive to produce a high standard of performance while employing a less complex 
structure, thus reducing computational burden and allowing for real-time operation at higher motor speeds 
with lower currents on computers having limited processor and memory resources. The drive is implemented 
with the help of Simulink/Matlab Software. 
2. Vector Control of Induction Motor  
2012 4th International Conference on Computer Modeling and Simulation (ICCMS 2012)
IPCSIT vol.22 (2012) © (2012) IACSIT Press, Singapore
81
 
 
 
Coupling effect between the flux and torque component of current in the induction motor makes its 
speed control sluggish and complex. Vector control force the AC drive to behave just like a DC drive, by 
transforming three phase quantities into two phase quantities and discarding the coupling effect. The 
schematic diagram of proposed indirect vector control induction motor drive is shown in Fig.1[2]. Indirect 
vector control is just like a direct vector control the only difference is that the unit vectors are computed by 
calculating the rotor flux angle using the measured speed position. From the d-q equivalent circuit of 
induction motor the following equations can be derived [7],[8]. 
The rotor equation of induction motor containing flux linkages as variables in synchronously rotating 
refernce frame indiacted by suffix ‘e’are given by 
 
0=++ edrsl
e
qr
e
qrr piR ψωψ                                                                               (1) 
0=++ eqrsl
e
dr
e
drr piR ψωψ                                                                               (2) 
 
Where rR ,
e
qri ,
e
dri ,
e
qrψ , edrψ , slω , p  are the rotor resistance, q- axes rotor current, d-axis rotor current, q-
axis rotor flux linkage, d-axis rotor flux linkage slip speed and differential operator respectively. 
The rotor q-axis and d-axis flux linkages are given by  
  
e
qrr
e
qsm
e
qr iLiL +=ψ                                                                               (3) 
e
drr
e
dsm
e
dr iLiL +=ψ                                                                                (4) 
Where, mL , rL ,
e
qsi and
e
dsi are mutual inductance, rotor inductance, q-axis stator current and d-axis stator 
current respectively. 
 
Since rotor flux linkage is aligned with d-axis 
e
drr ψψ =                                                                                       (5) 
0=eqrψ                                                                                        (6) 
0=eqrpψ                                                                                (7) 
 
From the above equations 
0=+ rsl
e
qrriR ψω                                                                                  (8) 
0=+ r
e
drr piR ψ                                                                              (9) 
 
Therefore  
e
qs
r
me
qr iL
Li −=                                                                              (10) 
e
qs
r
m
r
re
dr iL
L
L
i −=ψ                                                                             (11) 
 
And the electromagnetic torque obtained from machine flux linkages and currents is given by: 
)(
22
3 e
qs
e
dr
r
m
e iL
LPT ψ=                                                                                 (12) 
 
 
 
 
 
82
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.1 Schematic model of  Indirect vector control induction motor drive 
3.  Fuzzy Logic Controller Designing 
In order to design a fuzzy speed controller, speed error rke ωω −=
*)(   and change in speed error 
)1()()( −−= kekekce   are the two inputs for the controller, while after the decision making 
electromagnetic torque is produced. Basically it is made up of four components: fuzzification, rule base, 
inference engine, and defuzzification. Before giving to the fuzzy controller Input variables (speed error and 
change in speed error) are scaled using a scaling factor. Utmost care must be taken in choosing the scaling 
factor as it affects the stability, oscillations and damping of the system [8]. The values of scaling factors Ke, 
Kce and Kcu calculated using the motor data are 0.006, 20 and 1 respectively. 
3.1.   Fuzzification 
This is a process in which the crisp input variables to the fuzzy controller are transformed into a 
normalized fuzzy set. A fuzzy set is a set containing the range of input values and an associate membership 
function describing the degree of confidence of the input belonging to this range. All the linguistic variables 
of the fuzzy-control system (speed error, speed-error variation) were scaled into a common discourse 
universe with values between [−1, 1]. As a consequence, it was possible to map all the variables 
simultaneously with a unique set of membership functions.  
3.2.Rule Base 
The rule base was designed with (3x3) 9 rules in comparison to 49 rule of standard rule base. The 
linguistic terms used for input and output variables  are described as: “ZE” is “Zero”; “NE” is “Negative”; 
and “PE” is “Positive”. The universe of discourse for the linguistic variables “speed-error” and “change in 
speed error” was was therefore normalized to [−1, 1] by scaling them before the fuzzification process.  The 
Rules used for this particular problem are given in Tab.1[2]. 
 
Tab.1 Rulebase for FLC 
e→ 
ce↓ 
NE ZE PE
NE NE NE ZE
ZE NE ZE PE
PE ZE PE PE
 
The rules are in general format of “if anticedent1 and antecedent2 then consiquent”. 
3.3.Fuzzy Inference Engine 
The Fuzzy inference engine has two basic tasks to perform: (i) determining the degree to which each rule 
is relevant to the current situation as characterized by the inputs , and (ii) drawing conclusions using the 
Fuzzy
Speed
Controller
2 / 3
conversion
Hysterisis
Band
Current
Controller
3-phase
Inverter
Vdc
I M
1 r
m
sT
L
+
1
z
P/2
∫
m r
dr
L T
λ
slω
rω
eθ
+
+
+
−
+
−
*ω e
q si
e
d si
cba iii ,,
*
rψ
eK
ceK
cuK
83
 
 
 
current inputs (speed error and change in speed error) and the information in the rule-base.Mamdani type 
fuzzy inference engine is used for theis particular work. 
3.4.Defuzzification 
Converse to the fuzzification process is a defuzzification process in which the combined output fuzzy set 
produced from the inference engine is translated into a crisp output value of real-world meaning. Among the 
various defuzzification techniques centre of gravity (COG) is chosen for this work because of its known 
merits [11]. COG method is based upon the general formulae given as: 
∑
∑
=
== l
i
i
l
i
ii
x
xx
u
1
1
)(
)(
μ
μ                                                                              (13) 
Where ix is a running point in a discrete universe, and )( ixμ  is its membership value in the membership function. 
4. Results & Discussion  
For the performance evaluation of the proposed fuzzy logic controller based vector control induction 
motor drive detailed study has been carried out for which drive was simulated several times under different 
operating conditions such as sudden change in command speed, step change in load. The parameters of the 
4KW, 3phase, 415 V squirrel cage induction motor used for this work are given below in Tab.2.  
 
Tab.2 Induction motor parameters 
Parameter Value
Stator Resistance ( ) 1.405           Ω
Rotor Resistance ( ) 1.395           Ω
Stator Inductance ( ) 0.005839     H
Rotor Inductance ( ) 0.005839     H
Mutual Inductance ( ) 0.1722         H
Inertia ( ) 0.0131 Kg.m2
Pole Pair ( ) 2
Friction Factor ( ) 0.002985 N.m.s
 
For comparison, beside the implementation of fuzzy logic controller for vector controlled induction 
motor drive one other controller i.e. PI controller is implemented  in the Simulink environment.   
4.1.Reference Speed Tracking 
The drive is started up from stand still to trace the speed command of 120 rad/sec. without any load. 
Fig.2 gives the speed responses of the drive with fuzzy logic controller and PI controller. In Fig.2 it can be 
easily observed that the speed response of the drive with FLC shows no sign of overshoot as observed with 
PI controller thus reducing the settling time. Steady state error with both the controllers is almost zero.  
 For the checking of robustness, the drive was tested by applying step changes in command speed at 
regular interval of 0.5 sec. The drive is initially started from standstill to trace the speed of 120 rad/sec., 60 
rad/sec, 120 rad/sec, -120 rad/sec and 60 rad/sec respectively at a regular interval of 0.5 sec. It can be evident 
from the reponse graph shown in Fig.3 that FLC gives better performance in comaparison to PI controller.  
 
Fig.2 Comparison of speed response during start-up to reference speed tracking 
84
 
 
 
 
 
Fig.3.speed response of the drive under step change in command speed 
4.2. Load Disturbance Rejection  
The drive is started under noload condition to track the command speed of 120 rad/sec. After attaining 
steady state condition the drive was brought under loaded condition by applying rated load of 26 Nm at time 
sec1=t  . The drive was then brought to the no-load condition by suddenly removing the applied load at time 
sec2=t . From the response shown in Fig.4 it is evident that both controllers rejected the load disturbance 
but the FLC based drive recovered very quickly under both conditions. 
  
 
Fig.4 Speed response of drive during application of rated load at sec1=t  and removal of load at sec2=t . 
5. Conclusion  
This work investigates and analyzed the performance of indirect vector controlled induction motor drive 
with a fuzzy logic controller having minimum sized rulebase with nine rules. The drive has been simulated 
for different loading conditions such as sudden change in reference speed, step change in load torque, etc. 
using Simulink/MATLAB. The results have shown that the proposed FLC has worked satisfactorily making 
the drive more robust for high performance in the industrial applications. 
6. References 
[1] BIMAL K Bose, Modern Power Electronics and AC Drives, prentice hall, Eaglewood Cliffs, New Jersey, 1986. 
[2] M N Uddin; T.S.  Radwan; M.A. Rahman, Performances of Fuzzy-Logic-Based Indirect Vector Control for 
Induction Motor Drive, IEEE Transactions on Industry Applications, vol. 38, No. 5, 2002, PP1219-1225. 
[3] T S Radwan; M N Uddin; M A Rahman, A new and simple Structure of fuzzy logic based Indirect Field Oriented 
Control of Induction Motor Drive, IEEE Power Electronics Specialists Conference, 2004, PP 3290-3294. 
[4] Z Ibrahim; E Levi, A Comparative Analysis of Fuzzy Logic and PI Speed Control in High-Performance AC Drives 
Using Experimental Approach, IEEE Transactions on Industry applications, vol. 38, No. 5,  2002, PP 1210-1218. 
[5] CHENG Shanmei; WAN Shuyun; DUM Zhengcheng, A Fuzzy Speed Controller of Induction Motors, International 
Conference on Intelligent Mechatronics and Automation, 2004, PP 747-750. 
[6] BENUDHAR Sahu; K.B.Mohanty ;SWAGAT Pati, A Comparative Study on Fuzzy and PI Speed Controllers for 
Field-Oriented Induction Motor Drive, International Conference on Industrial Electronics, Control and Robotics, 
2010, PP 191-196.  
[7] M N Marwali, Implementation of Indirect Vector Control on an Integrated Digital Signal Processor - Based System, 
IEEE Transactions on Energy Conversion, vol. 14, No. 2, 1999, PP 139-146.  
85
 
 
 
[8] N Mariun; S B Mohd Noor; J Jasni; Omar S. Bennanes, A fuzzy logic based controller for an indirect vector 
controlled three phase induction motor, IEEE Region 10 conference, vol. 4, 2004, PP 1-4. 
[9] M. Masiala; B. Vafakhah; A. Knight; J. Salmon, Performances of PI and Fuzzy–Logic Speed Control of Field–
Oriented Induction Machine Drives, Canadian Conference on Electrical and Computer Engineering, 2007, PP 397-
400. 
[10]CHUNHUA Zang, Vector controlled PMSM drive based on fuzzy speed controller, International Conference on 
Industrial mechatronis and Automation, 2010, PP 199-202. 
[11]B N Kar; K B Mohanty; M Singh, Indirect vector control of induction motor using fuzzy logic controller, 
International conference on Environment and Electrical Engineering, 2011, PP 1-4. 
  
 
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Performance Evaluation of Reduced Rule Base Fuzzy Logic Controller for Indirect Vector Controlled Induction Motor Drive

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Performance Evaluation of Reduced Rule Base Fuzzy Logic Controller for Indirect Vector Controlled Induction Motor Drive

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