A Comparative Analysis of FLC and ANFIS
Controller for Vector Controlled Induction
Motor Drive
Erdal Kılıç
Hasan Rıza Özçalık
Department of Electrical and Electronics Engineering
Kahramanmaras Sutcu Imam University
Kahramanmaras, Turkey
ekilic@ksu.edu.tr
Department of Electrical and Electronics Engineering
Kahramanmaras Sutcu Imam University
Kahramanmaras, Turkey
ozcalik@yahoo.com
Şaban Yılmaz
Sami Şit
Department of Electrical and Electronics Engineering
Kahramanmaras Sutcu Imam University
Kahramanmaras, Turkey
sabanyilmaz1@hotmail.com
Department of Electrical and Electronics Engineering
Kahramanmaras Sutcu Imam University
Kahramanmaras, Turkey
samisit@hotmail.com
Abstract— This paper presents an adaptive neuro-fuzzy
inference system (ANFIS) based speed control for indirect field
oriented controlled induction motor drive. The obtaining of
maximum torque and efficiency in the motor necessitates a
successful nonlinear speed control method due to the non-linear
structure of the system. In this work, a fuzzy logic controller
(FLC) and ANFIS controller has been developed for speed
control of induction motors. Parameters of ANFIS are tuned
with on-line direct self-tuning method. The performance of
proposed controllers has been examined in different working
conditions. Simulation studies shows robustness and suitability
of drive for high performance drive applications.
by the vector control system [8-10]. The vector control
method uses the dynamic mathematical model of induction
motor and allows independent control of flux and torque.
With this method induction motor can be controlled like a
separately excited dc machine [11-13]. The field oriented
control which is the first vector control method of induction
motor drive is widely used in high performance drive system
[14-16]. The controller used in high performance control
structure is required to be resistant to parameter changes and
disturbance input. It is very difficult to resolve these
problems with the conventional fixed-parameter controllers.
Therefore, studies in recent years have shifted to the robust
and non-linear controller design [5-7, 17].
Artificial neural networks (ANN) have gained a wide
attention in control applications. It is the ability of the
artificial neural networks to model nonlinear systems that can
be the most readily exploited in the synthesis of non-linear
controllers. The learning and adapting capability of neural
networks makes them ideal for control purposes. An ANN
can be successfully applied even if the motor which is to be
controlled and the load parameters are unknown [18-20].
Fuzzy logic has been successfully used in numerous fields
such as control systems engineering, power engineering,
industrial automation and optimization. FLC has proven
effective for complex, non-linear and imprecisely defined
processes for which standard model based control techniques
are impractical or impossible [21-23].
Fuzzy systems and neural networks are both very popular
techniques that have seen increasing interest in recent years.
ANFIS, developed in the early 90s by Jang, combines the
concepts of fuzzy logic and neural networks to form a hybrid
intelligent system that enhances the ability to automatically
learn and adapt [24-26].
Keywords— adaptive neuro-fuzzy control; fuzzy logic control;
vector control; induction motor, self-tuning.
I.
INTRODUCTION
Induction motors have been used as the workhorse of
industrial and residential motor applications because of the
low maintenance, high robustness, simple construction and
high efficiency. For general purpose applications, induction
motors have mainly been deployed in constant-speed motor
drives. However, in recent years the induction motor drives
have been able to be used in variable speed applications with
the rapid development of electronic devices and converter
technology. Many researchers have focused on developing
algorithms for effective control of high performance
induction motor drives. In recent studies, the benefits of
using intelligence-based methods have been clearly
demonstrated to increase the performance of induction motor
drives [1-7].
For electrical drives high dynamic performance is
mandatory so as to respond to the changes in command speed
and torques. These requirements of ac drives can be fulfilled
978-1-4763-7239-8/15/$31.00 ' 2015 IEEE
102
Rotor flux position is given by:
In this study, the efficient control algorithm has been
developed in order to induction motor speed control using
FLC and ANFIS. The control algorithm for induction motor
drive has been implemented by using MATLAB software.
The indirect field oriented control technique which is the
widespread used in high performance induction motor drives
has been preferred. The performance of the induction motor
drive has been analyzed for variable speed and sudden load.
θ s = ∫ ωs .dt
Because of the multiplication terms of state variables, the
induction motor model is the nonlinear state equations. The
state variables are isd, isq, ψrd, ψrq and ωr.
II. DYNAMIC MODEL OF INDUCTION MOTOR
III. CONTROLLER DESIGN
A dynamic model of the induction motor to be controlled
must be known in order to understand, analyze and design
vector controlled drives. It has been found that the dynamic
model equations developed on a rotating reference frame is
easier to describe the characteristics of induction motors.
Differential equations in synchronously rotating d-q
reference frame model can be arranged as follows in order to
induction motor [27-30].
disd
1
=
dt σ Ls
⎡
⎤
Lm Rr
Lm
⎢ − RE isd + σ Lsωsisq + 2 ψ rd + ωr ψ rq + Vsd ⎥
L
L
r
r
⎣
⎦
⎤
Lm
Lm Rr
1 ⎡
ψ rq + Vsq ⎥
⎢ − RE isq − σ Lsωsisd − ωr ψ rd +
dt σ Ls ⎣
Lr
L 2r
⎦
dψ rd Rr Lm
Rr
=
isd − ψ rd + (ωs − ωr )ψ rq
dt
Lr
Lr
disq
=
dψ rq
(2)
Fig. 1. Structure of fuzzy logic controller
(3)
(4)
dωr 3 pLm
B
T
=
(isqψ rd − ψ rq isd ) − ωr − L
dt
2 JLr
J
J
(5)
Rr Lm 2
L2r
and
σ =1−
Lm 2
Ls Lr 2
A. Fuzzy Logic Controller
Fuzzy systems are very useful in situations involving
highly complex systems. A fuzzy logic controller has four
main components as shown in Fig. 1, fuzzification, inference
engine, rule base and defuzzification [31-32].
(1)
RL
R
= r m isq − r ψ rq − (ωs − ωr )ψ rd
dt
Lr
Lr
RE = Rs +
(10)
Input and output variables are constituted by using 7
membership functions. They are NB (Negative Big), NM
(Negative Medium), NS (Negative Small), Z (Zero), PS
(Positive Small), PM (Positive Medium) and PB (Positive
Big). Membership functions are selected as Gaussian shape
as shown in Fig. 2.
(6)
where ωs and ωr are respectively, electrical synchronous
stator and rotor speed, Vsd , Vsq, isd , isq , ψrd and ψrq are stator
voltages, stator currents and rotor fluxes d-q components
reference frame; Rs and Rr are stator and rotor resistances, Ls
and Lr are stator and rotor main inductances, Lm is mutual
inductance between stator and rotor, p is number of motor
poles, J is system inertia, B is viscous friction coefficient, TL
is load torque, RE is equivalent resistance, σ is leakage
coefficient. The electromagnetic torque and electrical rotor
speed that linked to shaft motor speed as given by:
Fig. 2. Membership function for inputs and outputs variables.
3 pLm
Te =
(isqψ rd − ψ rqisd )
2 Lr
(7)
ωr = p.Ω
(8)
The inputs of the FLC are the error signal (e) and the
change of error (∆e). Input (e) is the error between the
desired current id* (or iq* ) value and the actual plant current id
(or iq).
The motor slip frequency can be calculated from the
reference values of the stator current components as follow:
ωsl = ωs − ωr =
*
Lr isq
Rr isd*
(9)
103
e = id* , q − id , q
(11)
Δe = e(k ) − e(k − 1)
(12)
In FLC, a rule base is constructed to control the output
variable. The fuzzy rules are given in Table 1.
TABLE I.
Output
e
Oi1 = μ Ai ( x) =
FUZZY RULES
1
⎡ x − ci ⎤
1+ ⎢
⎥
⎣ ai ⎦
bi
i=1,2,3
(15)
i=1,2,3
(16)
∆e
NB
NB
NB
NM
NB
NS
NB
Z
NB
PS
NM
PM
NS
PB
Z
NM
NB
NB
NB
NM
NS
Z
PS
NS
NB
NB
NM
NS
Z
PS
PM
Z
NB
NM
NS
Z
PS
PM
PB
PS
NM
NS
Z
PS
PM
PB
PB
PM
NS
Z
PS
PM
PB
PB
PB
PB
Z
PS
PM
PB
PB
PB
PB
Oi1+ 2 = μ Bi ( y ) =
1
⎡ y − ci + 2 ⎤
1+ ⎢
⎥
⎣ ai + 2 ⎦
bi + 2
where, {ai, bi, ci} is the parameter set and A is the linguistic
term. Bell-shaped membership function is selected for each
node.
Layer 2: This layer is rule inference layer. Every node in
this layer is a fixed node labeled as ∏ which multiplies the
incoming signals and sends the product out. Each node
output corresponds to the firing strength of a fuzzy rule.
B. Anfis Controller
ANFIS, proposed by J.S.R. Jang [26, 33], is an intelligent
technique and is proved to be efficient in problems like
classification, modeling, and control of complex systems.
ANFIS are realized by an appropriate combination of neural
and fuzzy systems. The premise parameters and consequent
parameters are tuned using back-propagation algorithm. The
proposed neuro-fuzzy controller incorporates fuzzy logic
algorithm with a five layer artificial neural network (ANN)
structure as shown in Fig. 3. ANFIS architecture that has two
inputs e and Δe and one output Vd (or Vq).
Oi2 = wi = μ Ai ( x) μ Bi ( y )
i=1,2,3
(17)
Layer 3: This layer is normalization layer. Every node in
this layer is a circle node labeled N. The i-th node calculates
the ratio of the rule’s firing strength to the sum of all rules’
firing strength.
Oi3 = wi =
wi
∑ wi
i=1,2,3
(18)
i
Layer 4: This layer is consequent layer. All nodes are an
adaptive mode with node function:
Oi4 = wi f i = wi ( pi x + qi y + ri )
i=1,2,3
(19)
where anfis is a normalized firing strength from layer 3, and
{pi, qi, ri } is the parameter set of this node.
Layer 5: This layer is output layer. The single node in this
layer is a fixed node labeled ∑ that computes the overall
output as the summation of all incoming signals:
Oi5 = ∑ wi f i
i=1,2,3
i
(20)
The parameters of ANFIS are updated using the back
propagation error term as follow:
Fig. 3. Structure of ANFIS controller for induction motor
∂E
= k1.e + k2 .Δe
∂O 5
Layer 1: This layer is fuzzification layer. Degrees of
membership functions are calculated in this layer for each
input variable. The input variables of ANFIS are chosen as
the error (e) and the change of error (∆e) that given by
Equation (11), (12). Every node i in this layer is an adaptive
node with node function:
x = e (t )
(13)
y = Δe(t )
(14)
(21)
The input signals error (e) and the change of error (∆e)
multiplied by the coefficients k1 and k2.
α k +1 = α k − η
∂E
∂α k
(22)
where α is any of the parameters of ANFIS and η is learning
rate. The error will be reduced next training iteration.
104
IV. SIMULATION
The reference value of high speed is changed from 1000
rpm to 1400 rpm at time, t=0.5 sec and again from 1400 rpm
to 800 rpm at time, t=1.5 sec. The motor has been started
under no load and with sudden load (TL=19 Nm) at t=1.0 sec.
Simulation results of speed reference at 1000 rpm in Fig.5,
it is observed that the speed response has no overshot and
rise time 0.1 sec with all controllers. The performance of
controllers that is obtained by setting reference speed from
1000 rpm to 1400 rpm is shown in Table II.
The system for vector control induction motor is simulated
in MATLAB software. The performance of the proposed
ANFIS based induction motor drive is investigated at
different operating conditions. The block diagram of
simulation system is shown in Fig. 4.
TABLE II.
PERFORMANCE OF CONTROLLERS FOR HIGH SPEED
Performance Term
Rise Time (sec)
Overshoot (%)
Settling Time (sec)
Steady State Error (%)
PI
0.050
0.0
0.075
0.0
FLC
0.045
0.0
0.067
0.0
ANFIS
0.035
0.0
0.055
0.0
The load torque of 19 Nm is applied at t=1.0 sec. The
performance of controllers is shown in Table III for load.
TABLE III.
Performance Term
Transient Deviation (rpm)
Transient Response Time (sec)
Fig. 4. Vector control of induction motor block diagram
The controller outputs Vsd and Vsq are stator voltages d-q
components reference frame. Rotor flux position (θ) is used
for coordinate transformations. In this study the inverter DC
link voltage Vdc set at 530 VDC and switching frequency set
at 5 kHz.
The parameters of induction motor are as follows:
P=3 kW
U=380 V
I=6,7 A
n=1430 rpm
Rs=1,45Ω
Rr =1,93 Ω
p=2
Ls = 0,2 H
M=19 Nm
PERFORMANCE OF CONTROLLERS FOR SUDDEN LOAD
PI
33
0.10
FLC
15
0.07
ANFIS
8
0.03
The reference value of low speed is changed from 100 rpm
to -100 rpm at t=0.5 sec and again from -100 rpm to 100 rpm
at time, t=1.0 sec. The motor has been run without load.
Fig.6 is shown the low speed response of controllers. The
performance of controllers is shown in Table IV.
Lm=0,1878 H
J=0,03 kg.m2
B=0,03Nm.s/rad
In order to prove the superiority of the proposed ANFIS, a
comparison is made with the response of FLC and PI speed
controller based induction motor drive. PI, FLC and ANFIS
methods are tested in order to variable high speed and low
speed targets, under no load and with sudden load. Fig.5 is
shown the high speed response of controllers.
Fig. 6. Low speed response of PI, FLC and ANFIS
TABLE IV.
PERFORMANCE OF CONTROLLERS FOR LOW SPEED
Performance Term
Rise Time (sec)
Overshoot (%)
Settling Time (sec)
Steady State Error (%)
PI
0.038
1.2
0.05
0.15
FLC
0.035
0.5
0.04
0.1
ANFIS
0.035
0.6
0.04
0
It can be concluded that the ANFIS shows good dynamic
performance during rise time, overshoot, variable speed
references and sudden load. Considering the all operating
conditions, ANFIS yielded better performance than PI
controller and FLC due to its good learning and
generalization capabilities.
Fig. 5. High speed response of PI, FLC and ANFIS
105
V. CONCLUSIONS
Prevalence of induction motors applications in industrial
areas requires efficient control of these motors. In this study,
high efficient control algorithms have been developed for
vector control of induction motor. This paper presents a
comparative performance study of induction motor drive
with PI, FLC and ANFIS controller for speed control. These
methods have been tested via MATLAB software.
Simulation results show that the ANFIS method has shown
better performance response of variable speed and sudden
load when compared with the results obtained using PI and
FLC method. It also shows good adaptability to variation of
parameters and very good dynamic performance and
robustness during the transient period and during the sudden
loads. It is concluded that the proposed ANFIS controller has
shown superior performance than conventional PI controller
and FLC controller. The proposed method can be used in the
vector controlled induction motor drives for high dynamic
performance applications.
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