1. Fuzzy Sliding Mode Controller for Induction
Motor Speed Control.
Kh. Belgacem M. Zerikat A. Hazzab
Abstract—In this paper, the design of a speed control scheme
based on fuzzy-sliding mode control for indirect field-orientated
induction motor (IM) is proposed. The proposed control design
uses the fuzzy logic techniques to dynamically control parameter
settings of the sliding mode control (SMC) equivalent control
action. The theoretical analyses for the proposed fuzzy sliding-
mode controller are described in detail. The numerical
simulation results of the proposed scheme have presented good
performances as compared to the classical sliding mode control
and fuzzy sliding mode, simulated results show that the proposed
controller provides high-performance dynamic characteristics
and is robust with regard to plant parameter variations and
external load disturbance.
Index Terms— high performance, induction motor, fuzzy
sliding mode control, robustness, IFOC
I. INTRODUCTION
he difficulty to control the induction machine is related to
the fact that the mathematical model in Park configuration
is nonlinear and highly coupled. Due to the development
of power electronics and microprocessors, the induction motor
control is possible by applying field oriented techniques [1-2].
These techniques provide the decoupling stator and rotor
machine frames that allow obtaining a dynamical model
similar to that of DC machine. Nevertheless, a discontinuous
behavior is imposed by the switching devices of the inverter
that supply the induction machine, and yields to a complex
mathematical model. Therefore, it is suitable to look for some
techniques, which are appropriate to discontinuous operation
of the switching devices. Among these techniques, one can
choose variable structure control method and its associated
sliding modes. This latter allows a high performance of the
control scheme and especially the robustness of the algorithm
with regard to changing parameters and external disturbances
[3-4]. The Sliding Mode Control (SMC) is a synthesis method
developed since1950s. With the development of the theory for
several decades it has been able to solve control problems of
multi-variable linear system, nonlinear system and random
system [4]. The sliding mode control concept consists of
moving the state trajectory of the system towards and to
maintain it around the sliding surface with the appropriate
logic commutation. This latter gives birth to a specific
behavior. In motors drive systems the chattering causes
harmful effects such as torque pulsation current harmonic and
acoustic noise, the alleviate the effects several researches have
been performed. The complete elimination of chattering can
be reached if the fuzzy sliding mode control component [6] is
implemented instead of the relay control. Moreover, the better
system accuracy in the steady state is also achieved.
Therefore, this paper is dedicated to design of new control
with fuzzy sliding mode.In the last decade; FLC has attracted
considerable attention as a tool for a novel control approach
because of the variety of advantages that it offers over the
classical control techniques. In recent years, FLC was
proposed for high-performance drives employing induction,
synchronous reluctance and conventional DC machines [5-6-
7]. Conventional control techniques require accurate
mathematical models describing the dynamics of the system
under study. These techniques result in tracking error when
the load varies fast and overshoot during transients [5]. In this
paper, a control system combing fuzzy logic and sliding mode
control techniques is proposed where fuzzy logic controllers
replace the inequalities which determine the parameters of the
sliding mode control. The fuzzy -sliding mode controller has
been achieved, fulfilling the robustness criteria specified in
the sliding mode control and yielding a high performance in
implementation to induction motor speed control. The
remainder of this paper is organized as follows Section 2
describes a mathematical of induction motor drive, Section 3
reviews the principle of the indirect field oriented control
(IFOC) of induction motor. Section 4 shows the development
of sliding mode controllers design for IM control. The
proposed fuzzy sliding mode control scheme is presented in
section 5 Section 6 gives some simulation results. Finally,
some conclusions are drawn in section 7
This work was supported in part by the laboratory LAAS Department of of
electrical engineering, ENSET-Oran, ALGERIA
Kh. Belgacem Author is with the ENSET-Oran, ALGERIA; e-mail:
kheira.belgacem@yahoo.
M.ZERIKAT with the ENSET-Oran, ALGERIA; e-mail: fr mokhtar.zerikat
@ enset-oran.dz
A.HAZZAB University center of Bechar B.P 417 Bechar, ALGERIA (e-
mail: a_hazzab@yahoo.fr).
II. INDUCTION MOTOR MODEL
The induction motor model expressed in terms of the state
variables is given by equation (1):
T

2. rem
drgqr
r
r
qs
r
rm
qr
qrgdr
r
r
ds
r
rm
dr
qsqr
r
rm
dr
r
m
qssrdsss
s
qs
dsqr
r
m
dr
r
rm
qsssdssr
s
ds
C
J
P
J
f
C
J
P
dt
d
L
R
I
L
RL
dt
d
L
R
I
L
RL
dt
d
V
L
RL
L
L
IRIL
L
I
dt
d
V
L
L
L
RL
ILIR
L
I
dt
d
−−=
−−=
+−=
⎥
⎦
⎤
⎢
⎣
⎡
++−−−=
⎥
⎦
⎤
⎢
⎣
⎡
++++−=
ωω
φωφφ
φωφφ
φωφσω
σ
ωφφσω
σ
2
2
1
1
(1)
Where Is, Vs, Φs, Rs, Ls the stator current and voltage vector
components, the rotor flux linkage, resistance and inductance
respectively. The subscripts s and r stand for stator and rotor,
d and q are the components of a vector with respect to a
synchrounsly rotating frame. ω, ωg are the angular speed of
coordinate system and the angular speed of rotor shaft
respectively. P denotes the number of pole pairs, J is the total
rotor inertia and Cem is the electromagnetic torque.
III. INDIRECT FIELD ORIENTED CONTROL
The main objective of the vector control of induction motors
is, as in DC machines, to independently control the torque and
the flux; this is done by using a (d-q) rotating reference frame
synchronously with the rotor flux space vector [11] as shown
in fig. 1, the d axis is aligned with the rotor flux space vector.
Under this condition we have: Φdr = Φr and Φqr = 0.
For the ideal state decoupling the torque equation become
analogous to the DC machine as follows:
qsdr Iφ
r
m
em
L
L
PC = (2)
Fig. 2. Shows the implemented of an induction motor indirect
filed –oriented control (IFOC) [8]
÷
*
*
rφ *
dsi
sω
*
emC
glω
*
ω ÷
*
*
qsi
*
dsv
sθˆ
Electric power
network
M
3 ~
ω
dsI
*
asv
*
bsv
PI
m
r
p.L
L
PI
Speed
regulator
P(θ)-1
dq → ABC
P(θ)
ABC→ dq
Voltage
source
inverter
Rectifier
+filter
mL
1
r
rm
L
.RL
s
1
Defluxage
*
qsv
*
csv
qsI
∑
Fig.2. Field oriented control
IV. SLIDING MODE CONTROL
The variable structure and its associated sliding regimes
are characterized by a discontinuous nature of the control
action with which a desired dynamic of the system is obtained
by choosing appropriate sliding surfaces. The control actions
provide the switching between subsystems which give a
desired behavior of the closed loop system [9-10]. Fig.3
illustrates a sliding mode phenomenon, which consists of an
infinite switching of the control action within the
neighborhood of the sliding surface.
Assuming that the system is controllable and observable, the
sliding mode control objectives consist of the following steps:
-Design of the switching surface S(x) so that the state
trajectories of the plant restricted to the equilibrium surface
have a desired behavior such as tracking, regulation and
stability.
Determine a switching control strategy, U to drive the state
trajectory into the equilibrium surface and maintain it on the
surface. This strategy has the form:
eqUskU +−= )sgn( (3)
Where Ueq is called equivalent control which is used when the
system state is in the sliding mode [11]. k is a constant and it
Fig.1: Orientation of the rotor flux
Stator axis
O
Rotor axis
d axisq axis
Is
φr = φdr
θr
θθs
Iqs
Ids
Fig.3 State trajectory in sliding mode regime

3. is the maximal value of the controller output .s is called
switching function because the control action switches its sign
on the two sides of the switching surface s = 0 . s is defined as
[11],[12]:
ees .λ+= & (4)
Where and x* is the desired state. λ is a
constant. sgn(s) is a sign function, which is defined as:
xxe −= *
(5)
⎪⎩
⎪
⎨
⎧
>
<−
=
01
01
)sgn(
sif
sif
s
The control strategy adopted here will guarantee the system
trajectories move toward and stay on the sliding surface s = 0
from any initial condition if the following condition meets:
sss .. η−≤& (6)
Where η is a positive constant that guarantees the system
trajectories hit the sliding surface in finite time [11],[13].
Using
a sign function often causes chattering in practice. One
solution is to introduce a boundary layer around the switch
surface:
(7)eqs UUU +=
Where: Us =-k.sat(s/φ) and constant factor φ defines the
thickness of the boundary layer. sat(s/φ ) is a saturation
function that is defined as:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
>⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
≤
=⎟
⎠
⎞⎜
⎝
⎛
1sgn
1
ϕϕ
ϕϕ
ϕ s
if
s
s
if
s
ssat (8)
The function between Us and s /φ is shown in the fig. 4.
This controller is actually a continuous approximation of the
ideal relay control [11-14]. The consequence of this control
scheme is that invariance of sliding mode control is lost. The
system robustness is a function of the width of the boundary
layer.
V. FUZZY SLIDING MODE CONTROLLER
In this section, a fuzzy sliding surface is introduced to
develop a sliding mode controller. Which the parameter k will
be adapted by an inference fuzzy system for eliminate the
chattering phenomenon.
The IF-THAN rules of fuzzy sliding mode controller can be
described as [11]:
Rule 1: IF s is BN THEN k is Bigger
Rule 2: IF s is MN THEN k is Big
Rule 3: IF s is ZE THEN k is Medium
Rule 4: IF s is MP THEN k is Small
Rule 5: IF s is BP THEN k is Smaller
Where BN, MN, JZ, MP and BP are linguistic terms of
antecedent fuzzy set, they mean Big Negative, Medium
Negative, Just Zero, Medium Positive, and Big Positive,
respectively. We can use a general form to describe these
fuzzy rules:
Ri : if s is Ai then k is Bi , i = 1,…,5 (9)
Where Ai and Bi are a triangle-shaped fuzzy number, see fig.
4 and fig. 5. Let X and Y be the input and output space, and A
be an arbitrary fuzzy set in X. Then a fuzzy set, i A R o in Y,
can be determined by each Ri of (9). We use the sup-min
compositional rule of inference [11]
VI. SIMULATION RESULTS
To demonstrate the proposed fuzzy sliding control Scheme
success, it has been tested by simulation, in Order to evaluate
the performances under a variety of Operating conditions. The
numerical values for the Tested induction motor is
summarized in Table I
TABLE I
RATING OF TESTED INDUCTION MOTOR
Rated values Power 1.5 kW
Frequency 50 Hz
-1.5ϕ -ϕ -0.5ϕ 0 0.5ϕ ϕ
k
-k/2
0
-k/2
-k
Fig. 4. The first part (Us) of the Sliding Mode
Control
Us
BN JZ BP
µ
0
MN MP
s
2
ϕ
−
2
ϕ ϕϕ−
Fig. 5. The input membership function of the FSMC
µ
0
mediumbig biggersmaller small
k
Fig. 6. The output membership function of Fuzzy
Sliding Mode Control

4. Voltage Δ/Y 220/
380
V
Current Δ/Υ 6.4/
3.7
A
Motor Speed 1420 Tr/min
pole pair (p) 02
Rated parameters Rs 4.85 Ω
Rr 3.805 Ω
Ls 0.274 H
Lr 0.274 H
M 0.258 H
Constant J 0.031 Kg.m2
The configuration of the overall control system is shown in
Fig. 7. It mainly consists of an induction motor, a ramp
comparison current-controlled pulse width modulated (PWM)
inverter, a slip angular speed estimator, direct and inverse
Park transformations, indirect field oriented control bloc based
on fuzzy sliding mode current controller, and an outer speed
feedback control loop, which contains a fuzzy sliding mode
controller.
The controller algorithm is housed inside the personal
Computer with Pentium-4 microprocessor and all numerical
values of the simulation model are obtained either by
measurements. The software environment used of these
simulation experiments is Matlab-software with Simulink
Toolboxes. Fig.8, shows the disturbance rejection response of
the fuzzy sliding mode controller when the machine is
operated at 100 [rad/s] under no load and a nominal load
disturbance torque (10 N·m) is suddenly applied at 0.5 sec and
eliminated at 1 sec, followed by a speed reversal (-100 rad/s)
at 2 sec. The fuzzy sliding mode controller rejects the load
disturbance very rapidly with a negligible steady state error.
Moreover, the torque and flux responses are highly decoupled.
The simulation of the control with the Sliding Mode Control is
shows in the fig. 7. A comparison between the speed control
of the IM by a SMC and a FSMC shows clearly that the
FSMC gives good performances
CONCLUSION
In this work, we have presented a fuzzy sliding mode
controller for speed control of induction motors. This study
has successfully demonstrated the design of the fuzzy sliding
mode for the speed and the indirect field orientation control of
induction motor. The proposed scheme has presented
satisfactory performances (no overshoot, minimal rise time,
est disturbance rejection) for time-varying external force
disturbances. The simulation results obtained have confirmed
the excellent decoupling and the efficiency of the proposed
scheme. Finally, some of the states like torque and stator
current components have chattering with sliding mode
controller, whereas these are free of chattering with fuzzy
sliding mode controller. In other words, for chattering free,
robust control of decoupled induction motor drive, fuzzy
sliding mode controller is a better choice than sliding mode
controller.
REFERENCES
[1] P. Vas, “Vector control of AC machines” (Clarendon
Press-Oxford edition, 1990).
[2] M. A. Ouhrouche, C. Volet : Simulation of a Indirect
Field-Oriented Controller for an Induction Motor Using
Matlab/Simulink Software Package, Proc. Of IASTED Int.
Conf. Modeling and Simulation (MS’2000), USA.
[3]. C.Min Lin ,C.Fei Hsu “Adaptive fuzzy sliding-mode
control for induction servomotor systems”, IEEE Transactions
on Energy Conversion, vol. 19, n°2, June 2004, pp. 362-368
[4] D.Mitić, M. Milojković, D.Antić” Tracking System Design
Based on Digital Minimum Variance Control with Fuzzy
Sliding Mode” IEEE Trans. Automat Vol. 1-4244-1468-7/07
pp 495-496 2007
[5] A. Rubaai , M. D. Kankam,” Experimental Verification of
hybrid fuzzy control strategy for High performance brushless
DC drive system”, IEEE Trans. On industry applications
Vol.17, N°2, march-April 2001, pp.503-512
[6] H.Yu Q. Hu and X.Ding” Fuzzy Sliding Mode Variable
Structure Control of Three-phase Rectifier” Fourth
International Conference on Fuzzy Systems and Knowledge
Discovery (FSKD 2007)
[7] R.Jong Wai, C.M. Lin and Ch.Fei Hsu, “Adaptive fuzzy
slidingmode control for electrical servo drive”, Fuzzy Sets
and Systems 143 (2004) 295–310
[8] L. Baghli, “Contribution to Induction Machine Control:
Using Fuzzy Logic, Neural Networks and Genetic
Algorithms”, Doctoral Thesis Henri Poincaré University,
January 1999. (Text in French.).
[9].R. Abdessemed, A. L. Nemmour, V F.Tomachevitch
“Cascade Sliding Mode Control of a Stator Field Oriented
Double Fed Asynchronous Motor Drive(DFAM)”. In:
Archives of electrical engineering, Vol. LI, N°03, pp. 371-
387, 2002, Poland.
[10] M. Zhiwen, T. Zheng, F. Lin and X. You, “A New
Sliding-Mode Current Controller for Field Oriented
Controlled Induction Motor Drives”, IEEE Int. Conf. IAS
(2005), pp. 1341- 1346, 2005.
[11] A.Hazzab, I K Bousserhane, M Kamli “Design of a
Fuzzy Sliding Mode Controller by Genetic Algorithms for
Induction Machine Speed Control ”international Journal of
Emerging Electric Power Systems Volume 1, Issue 2( 2004)
[12] K.C. Ng, Y. Li, D.J. Murray-Smith and K.C. Sharman,
“Genetic Algorithms Applied to Fuzzy Sliding Mode
Controller Design” , Proc. 1st IEE/IEEE Int. Conf. on GA in
Eng. Syst., Innovation, Appl. Scheffield 1995.
[13] A. Derdiyok, M. K. Guven, Habib-Ur Rahman and N.
Inane, “ Design and Implementation of New Sliding-Mode
Observer for Speed- Sensorless Control of Induction
Machine” , IEEE Trans. on Industrial Electronics, Vol. 1.
N°3, 2002.
[14] JI-CHANG LE and YA-HU KUO, “Decoupled fuzzy
sliding-mode control”, IEEE Trans. on Fuzzy Systems, Vol. 6
N°3, 1998.

5. Defluxage
÷
*
*
rφ *
dsi
sωglω
*
ω ÷
*
*
qsi
*
dsv
sθˆ
Rectifier
+
Filter
Electric power
network
(U, f)
-
M
3 ~
ω
mds_I
*
v
*
bsv
as
PI
m
r
p.L
L
PI
1
P(θ)-1
dq →
ABC
mL
Voltage
source
inverter
P(θ)
ABC →
dq
r
rm
L
.RL
s
1
*
qsv *
csv
mqs_I
∑
( )wS
dt
de
KeKdteK 321 −⋅−⋅− ∫ asI
bsI
-
Gs
Gk
( )ξ/sat Sk ⋅−
-
csI
Fig. 6: Block diagram of proposed fuzzy sliding mode speed and
currents control of induction motor

6. Speed(rad/s)
Speed(rad/s)
Time (sec) Time (sec)
Torque(N.m)
Torque(N.m)
Time (sec) Time (sec)
Rotorflux(Wb)
Rotorflux(Wb)
Time (sec) Time (sec)
Statorcurrent(A)
Statorcurrent(A)
Time (sec) Time (sec)
Fig.7 Simulated results of sliding mode speed control of
induction motor
Fig. 8 Simulated results of fuzzy sliding mode speed
control of induction motor

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