J. Intelligent Learning Systems & Applications, 2010, 2: 110-118
doi:10.4236/jilsa.2010.22014 Published Online May 2010 (http://www.SciRP.org/journal/jilsa)
Implementation of Adaptive Neuro Fuzzy
Inference System in Speed Control of Induction
Motor Drives
K. Naga Sujatha, K. Vaisakh
Department of Electrical Engineering, AU College of Engineering, Andhra University, Visakhapatnam, India.
Received December 18th, 2009; revised January 6th, 2010; accepted January 15th, 2010.
ABSTRACT
A new speed control approach based on the Adaptive Neuro-Fuzzy Inference System (ANFIS) to a closed-loop, variable
speed induction motor (IM) drive is proposed in this paper. ANFIS provides a nonlinear modeling of motor drive system
and the motor speed can accurately track the reference signal. ANFIS has the advantages of employing expert knowl-
edge from the fuzzy inference system and the learning capability of neural networks. The various functional blocks of
the system which govern the system behavior for small variations about the operating point are derived, and the tran-
sient responses are presented. The proposed (ANFIS) controller is compared with PI controller by computer simulation
through the MATLAB/SIMULINK software. The obtained results demonstrate the effectiveness of the proposed control
scheme.
Keywords: ANFIS Controller, PI Controller, Fuzzy Logic Controller, Artificial Neural Network Controller, Induction
Motor Drive
1. Introduction
Over the last three decades, variable speed drives are the
most complex of all power electronic systems. Drive
technology has been a confluence of many professionals
from other fields, such as electrical machines, control
systems and traditional power engineering. To a tradi-
tional power electronics engineer with expertise in the
design of, such as thyristor phase-controlled converters,
switching mode power supplies, or uninterruptible power
supply systems, the technology is incomprehensible be-
cause of its complexity and multidisciplinary characteris-
tics.
Modern variable speed drive applications require stee-
ples control and suitable dynamic response and accuracy.
These considerations have been met to a large extent in
the past decade by thyristor-controlled dc machines.
However, the dc machine remains expensive in relation
to the types of rotating machines. For the higher power
drives in industries, the lighter, less expensive, reliable
simple, more robust and commutator less induction mo-
tors are desirable and these motors are being applied to-
day to a wider range of applications requiring variable
speed. Unfortunately, accurate speed control of such
machines by a simple and economical means remains a
difficult task. With the development of the silicon-
controlled rectifier, triac and related members of the thy-
ristor family, it has become most feasible to design vari-
able-speed induction motor drives for a wide variety of
applications. Different techniques have been used, using
SCR controllers. A back-to back connected SCR’ are
used in series with the rotor phases to control their effec-
tive impedance [1-4]. A chopper-controlled external re-
sistance is used to control the speed by varying the duty
cycle of the chopper. A controlled rectifier is used in the
rotor circuit to feed the external resistance, and by vary-
ing the firing angle, the effective rotor impedance is con-
trolled.
Generally, variable speed drives for Induction Motor
(IM) require both wide operating range of speed and fast
torque response, regardless of load variations. This leads
to more advanced control methods to meet the real de-
mand. Very recently, the artificial intelligence tools, such
as expert system, fuzzy logic and neural network are
showing impact on variable frequency drives.

Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives111
They are applied to important fields such as variable
speed drives, control systems, signal processing, and sys-
tem modeling. Artificial Intelligent systems, means those
systems that are capable of imitating the human reasoning
process as well as handling quantitative and qualitative
knowledge. It is well known that the intelligent systems,
which can provide human like expertise such as domain
knowledge, uncertain reasoning, and adaptation to a noisy
and time-varying environment, are important in tackling
practical computing problems. ANFIS has gain a lot of
interest over the last few years as a powerful technique to
solve many real world problems. Compared to conven-
tional techniques, they own the capability of solving prob-
lems that do not have algorithmic solution. Neural net-
works and fuzzy logic technique are quite different, and
yet with unique capabilities useful in information process-
ing by specifying mathematical relationships among nu-
merous variables in a complex system, performing map-
pings with degree of imprecision, control of nonlinear
system to a degree not possible with conventional linear
systems [5-11]. To overcome the drawbacks of Neural
networks and fuzzy logic, Adaptive Neuro-Fuzzy Infer-
ence System (ANFIS) was proposed in this paper. The
ANFIS is, from the topology point of view, an implemen-
tation of a representative fuzzy inference system using a
Back Propagation neural network structure.
The purpose of this paper is to present a general
method for estimating both the nature of the dynamic
response and the values of the significant parameters and
operating constraints of typical induction machines con-
trolled by SCR controllers [12,13]. The dynamic behav-
ior of a closed-loop speed-control system with delta-
connected SCR’s in the rotor is discussed. The various
functional blocks of the feedback system which governs
the system behavior for small variations about the oper-
ating point are derived, and responses for speed perturba-
tions are obtained analytically and simulated.
2. State Space Approach
A Set of nonlinear differential equations can describe the
behavior of the induction motor [14-16]. If a complete
solution of the dynamic behavior of the induction ma-
chine is desired, these equations must be solved in detail.
By linerarizing these questions about a steady state oper-
ating condition, the resulting equations in state form can
describe the dynamics, and provide the future state and
output of the system.
Perturbations in reference voltage or firing angle and
load torque leads to changes in rotor speed. The analyti-
cal results used to investigate these speed changes are
obtained considering the various previous functional
blocks, where the different input and output variables are
denoted by X1, X2, X3 and X4. These variables are defined
as follows:
X1 =   , X2 = V, X3= Vc and X4 =  (1)
The differential equations, which govern the small
variations about the operating point, are written in terms
of the above variables and representing in matrix form in
Equation (2), where

1234
T
X
xx xx
, =
 
T
LR
uTV 12
T
uu
3. System Description
The system consists of a slip-ring induction motor with
three equal external resistances, each connected to the
rotor phase and three delta-connected phase-controlled
SCR's placed at the open star point of the rotor as shown
in Figure 1.
In variable speed ac induction motor drives, a con-
tinuous monitoring or control of slip speed or slip fre-
quency is required. A permanent magnet tachogenerator
is mounted on the rotor shaft to provide a dc signal pro-
portional to the rotor speed to the feedback control cir-
cuit.
The block diagram of the feedback control scheme of
the induction motor is shown in Figure 2.
The induction motor stator is supplied with constant
voltage, constant frequency supply. The rotor speed is
controlled and adjusted by advancing or retarding the
firing angle

of the SCRs. The tachogenerator output
voltage proportional to the rotor speed and is compared
54
1 1 1
11 2 2
33 2
122 2
2
4 4
121
3
33
100
0
100 00
0
00
00
1
00
GG
GGG G
G
L
R
KK KK
TTT K
T xx
K
TT
x
xT
x
x K
KKK K
T xx
TTT
K
TT



  
 



 
 
 

V



 




 
 






  
 

 
 











(2)

Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives 112
3 Phase
Supply
To Trigger Circuit
Rex
a
T1
Rex
Figure 1. Schematic diagram of phase controlled SCR’s in delta (Δ) configuration
Figure 2. Block diagram of feedback system
with a fixed dc level
R
V which represents the set speed.
The error voltage is forwarded to the controller. The set
peed is changed by varying
R
V automatically or manu-
ally. The controller may be a proportional, or propor-
tional integral or proportional integral derivation type.
The function of the controller is to give the required con-
trol voltage which will adjust the firing angle to the suit-
able value and can be used also as a stabilizing signal if
more than one controller is used.
The simulink block diagram of feedback control
scheme of the induction motor is shown in Figure 3.
Transfer functions for the functional blocks:
The transfer functions for the various functions blocks
of the feedback system are shown in Figure 4, and given
in details as follows:
1) Tachogenerator and filter: The transfer function of
this block is represented by:

1
1
1
1
K
Gs ST  (3)
where 1
K
is the combined gain of the tachogenerator
and the associated filter, and is the effective time
constant of the filter.
1
T
2) Controller: The change in the output voltage of the
tachogenerator is compared with the reference voltage
R
V and the resultant error voltage is fed to the controller.
The controller output voltage is corrected in accordance
with the input change in voltage. The change in the con-
troller output voltage is denoted as . The transfer
function of the proportional integral controller is:
c
V

2
1
2
(1 )
2
K
ST
Gs ST

 (4)
3) Firing Circuit: The firing circuit decides the change
in firing angle in accordance with the change in control
voltage . It consists of a ramp generator and a com-
parator. The ramp is synchronized with the signal avail-
able across the slip-rings of the machine. For a given
change in the control voltage , the change in firing
angle is given by:
c
V
c
V
1
c
V
m


 (5)
where m is the slope of the ramp. For the present study,
the firing circuit transfer function can be written as

3
3
3
1
K
Gs ST  (6)
where 3
K
is equal to l/m, and the time constant is equal
to one half of the maximum expected delay. If the slip of
the rotor at the operating point is s, then the time constant
is given by:
3
T
3
1
23
Tsf 

 (7)
c T2
b
Rex
T3
_
TACHO
GENERATOR
REF.VOLTAGE
SLIP RING
ROTOR
+
ERROR SIGNAL
CONTROL
VOLTAGE
c
V
SLIP RING
I.M
DELTA
CONNECTED
SCR’s
FIRING
CIRCUIT
P/PI/PID
CONTROLLER
“

”
FIRING
ANGLE
R
V
3-PHASE SUPPLY


Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives
JILSA
113
Figure 3. The simulink block diagram of feedback control scheme of the induction motor drive
Figure 4. Functional blocks of closed-loop system
4) Induction Motor: The torque developed by the ma-
chine at a given operating point is a function of speed of
the machine and the firing angle of the thyristors. The
difference between the developed torque and the load
torque is applied to the rotating elements. The torque
developed by the machine is presented by
(,)
d
TF

  (8)
where

is the rotor speed in rad/sec, and

is the
firing angle.
For the dynamic behavior of the induction machine
about any operating point for a given perturbation, the
small change in the developed torque can be represented
in terms of the small changes in rotor speed and firing
angle as:
tan
tan
d
d
d
T
T
Tcons t
cons t
 




 

(9)
or
45d
TK K



 (10)
The constants 4
K
and 5
K
depend upon the operat-
ing point and are to be obtained from the steady-state
characteristics of the system.
The resultant change in the developed torque is repre-
sented as the summation of the outputs of the two blocks
(4) and (5). The change in the developed torque is com-
pared with the change in load torque and the resultant
value is forwarded to the mechanical system, whose
transfer function can be expressed as:

1
G
m
G
K
Gs ST  (11)
where G
K
= 1
F
and =
G
T
J
F
(6)
(5)
(4) (2) (3)
d
T
_
+
R
V
SPEED

CHARACT.
I.M.TECH
T

_
ELECTRICAL
TORQUE
“

” FIRING
ANGLE
c
V
ERROR
SIGNAL
22
2
(1 )
K
ST
ST
3
3
1
K
ST 4
d
c
T
K




5
d
c
T
K




1
G
G
K
ST
1
1
1
K
ST
+
L
T
+
(1)
-K
-K
Switch
S1
Sco
p
e
-
Gain
Gain
-
+
PI Controller
ANFIS Con-
troller
Without any controller
Transfer
Function
+
Transfer
Function
Transfer
Function
Step
Ste
p
+

Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives 114
F is the frictional constant in N.m/rad/s, and J is the
moment of inertia of the rotating system in 2
m
G
K

.
4. ANFIS Based Speed Controller
Artificial Intelligent tools such as Fuzzy Logic and Arti-
ficial Neural Networks have shown great potential on
variable frequency drives. Artificial Neural Networks are
concerned with adaptive learning, nonlinear function
approximation, and universal generalization; fuzzy logic
with imprecision and approximate reasoning [17,18]. But
they share some common shortcomings that hinder them
from being used more widely. For example, neural net-
works, often suffer from a slow learning rate. This draw-
back renders neural networks less than suitable for time
critical applications. Therefore, new and enhanced meth-
ods can be put forward.
The fuzzy neural network is constructed to merge
fuzzy inference mechanism and neural networks into an
integrated system so that their individual weaknesses are
overcome. The ANFIS system determines a control ac-
tion by using a neural network which implements a fuzzy
inference. In this way, the prior expert’s knowledge can
be incorporated easily. The controller has two states, a
learning state and a controlling state. In the learning state,
the performance evaluation is carried out according to
the feedback which represents the process state. If in-
put-output training data is available, the performance can
be assessed easily, and supervised learning can be em-
ployed.
5. Adaptive Neuro-Fuzzy Principle
The fuzzy inference commonly used in ANFIS is first
order Sugeno fuzzy model because of its simplicity,
high interpretability, and computational efficiency, built-
in optimal and adaptive techniques. A typical architec-
ture of an ANFIS is as shown in Figure 5. Among
many FIS models, the Sugeno fuzzy model is the most
widely applied one for its high interpretability and
computational efficiency, and built-in optimal and adap-
tive techniques. For a first order Sugeno fuzzy model, a
common rule set with two fuzzy if-then rules can be
expressed as:
Rule 1: if x is A1 and y is B1, then z1 = p1x + q1y + r1
Rule 2: if x is A2 and y is B2, then z2 = p2x + q2y + r2
where Ai and Bi are the fuzzy sets in the antecedent, and
pi, qi and ri are the design parameters that are determined
during the training process.
Layer 1: Every node in this layer contains member-
ship functions.


1,1,2
i
iA
oxi   (12)


2
1,3,4
i
iB
oyi 

 (13)
where i
A

and i
B

can adopt any fuzzy membership
function (MF).
Figure 5. Adaptive neuro fuzzy structure
z
Controlled
output
y
Input2
x
input1

Fuzzification Inference entgne Defuzzification
Layer 1
Input layer
i
w
i
i
w
i
A
B
Layer 2
Fuzzfier layer
Input layer
Layer 3
Inference layer
Input layer
Layer 4
Defuzzifler layer
Interence layer
Input layer

Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives115
Layer 2: This layer chooses the minimum value of
two input weights.
 
2,1,2
ii
iiA B
owx yi   (14)
Layer 3: Every node of these layers calculates the
weight, which is normalized.
3
12
,1,2
i
ii
w
ow i
ww
 
 (15)
where i w is referred to as the normalized firing
strengths.
Layer 4: This layer includes linear functions, which
are functions of the input signals.
4(),
iiiiiii
owzwpxqyri 1,2 (16)
where i
w is the output of layer 3, and {pi, qi, ri} is the
parameter set. The parameters in this layer are referred to
as the consequent parameters.
Layer 5: This layer sums all the incoming signals.
2
51122
112
iii
i
wz wz
owz
ww




 (17)
The output z in Figure 5 can be rewritten as:
  
  
11 11 11
22 22 2
zwxp wyqwr
wxp wyq wr


2
(18)
In this paper the normalized membership functions of
input variables and output variable are shown in Figures
6 and 7. The Three-dimensional plot of Fuzzy Control
surface is shown in Figure 8.
6. Simulation Results
In this paper, performance of the proposed ANFIS speed
controller is evaluated and is compared with PI controller
and without any controller. The controller parameters are
chosen to optimize the performance criterion of the dy-
namic operation, and then the tuning was empirically
improved. The simulation is carried out to observe the
performance of the system at different load perturbations.
Figure 6. Triangular membership functions for input
variables e and e
Figure 7. Triangular membership functions for output
variable
Figure 8. Three-dimensional plot of control surface
The software environment used for this simulation is
Matlab ver. 7.1, with simulink package.
The change in rotor speed is due to the perturbations in
reference voltage or firing angle and load torque. The
analytical results used to investigate these speed changes
are obtained considering the various previous functional
blocks, where the different input and output variables are
denoted by X1, X2, X3 & X4. The differential equations
which govern the small variations about the operating
point in terms of above variables are given in Equation
(2).
The perturbation studies were carried out at different
operating points with different system parameters (gains
and time constants) which are given in Appendix. Studies
are carried out at operating points with various system
parameters (gains and time constants). The simulation
results give the present perturbation study for step
change in the load torque and reference voltage. From
the Figures 9 to 11 the starting transients are realized for
ANFIS controller at different operating conditions. It can
be observed from the figures that the performance of the
ANFIS gives better response compared with PI controller
and without any controller.
7. Conclusions
A framework for tuning and self organizing ANFIS con-
troller has been presented. This approach has been con-

Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives 116
trasted without any controller and with PI controller. The
dynamic behavior of a closed-loop, variable speed induc-
tion motor drive which uses three silicon controlled rec-
tifiers has been studied in this paper. Transfer function
blocks of the system for small variations about an oper-
ating point are derived, and the transient responses with
the analytical studies have been carried out. Comparison
of ANFIS controller, without any controller and with PI
controller under normal operation for a given load torque
and reference speed perturbations has been presented. It
Figure 9. Variation of speed deviation at 5% load change
Figure 10. Variation of speed deviation at 10% load change

Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives117
Figure 11. Variation of speed deviation at 15% load change
has been demonstrated that the proposed method gives a
good response, regardless of parameter variations or ex-
ternal force. Simulation results have shown the capabili-
ties of the proposed controller in tracking predetermined
desired speed trajectory.
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Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives 118
Appendix
Various Gains and Time Constants used for Perturbation Study (Motor Speed 'N = 1050 rpm)
K1 = 0.032
K2 = 0.25
K3 = –60
K4 = –0.0363
K5 = 40.0
T1 = 0.009
T2 = 0.22
T3 = 0.01111
K5 = –0.095
TG = 15.6