1. ISA
TRANSACTIONS®
ISA Transactions 44 ͑2005͒ 481–490
A novel sliding-mode control of induction motor using space
vector modulation technique
Tian-Jun Fu* Wen-Fang Xie†
Department of Mechanical & Industrial Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada
͑Received 20 September 2004; accepted 27 March 2005͒
Abstract
This paper presents a novel sliding-mode control method for torque control of induction motors. The control principle
is based on sliding-mode control combined with space vector modulation technique. The sliding-mode control
contributes to the robustness of induction motor drives, and the space vector modulation improves the torque, flux, and
current steady-state performance by reducing the ripple. The Lyapunov direct method is used to ensure the reaching and
sustaining of sliding mode and stability of the control system. The performance of the proposed system is compared
with those of conventional sliding-mode controller and classical PI controller. Finally, computer simulation results show
that the proposed control scheme provides robust dynamic characteristics with low torque ripple. © 2005 ISA—The
Instrumentation, Systems, and Automation Society.
Keywords: Sliding-mode control; Induction motor; Space vector modulation
1. Introduction Classical PI controller is a simple method used
in control of induction motor drives. However, the
The induction motor is widely used in industry, main drawbacks of PI controller are the sensitivity
mainly due to its rigidness, maintenance-free op- of performance to the system-parameter variations
eration, and relatively low cost. In contrast to the and inadequate rejection of external disturbances
commutation dc motor, it can be used in aggres- and load changes ͓2,3͔. Sliding-mode control
sive or volatile environments since there are no ͑SMC͒ is a robust control since the high gain feed-
risks of corrosion or sparks. However, induction back control input suppresses the influence of the
motors constitute a theoretically challenging con- disturbances and uncertainties ͓4͔. Due to its order
trol problem since the dynamical system is nonlin- reduction, good disturbance rejection, strong ro-
ear, the electric rotor variables are not measurable, bustness, and simple hardware/software imple-
and the physical parameters are most often impre- mentation by means of power inverter, SMC has
cisely known. The control of the induction motor attracted much attention in the electric drive in-
has attracted much attention in the past few de- dustry, and becomes one of the prospective control
cades; especially the speed sensorless control of methodologies for induction motor drives ͓5͔. The
induction motors has been a popular area due to its applications of SMC to electric motors have been
low cost and strong robustness ͓1͔. previously investigated by Utkin in Refs. ͓4,5͔,
where the author gives the basic concepts, math-
ematics, and design aspects of variable structure
*E-mail address: tianjun_fu@yahoo.com systems, as well as sliding mode as a principle
†
E-mail address: wfxie@me.concordia.ca operation mode.
0019-0578/2005/$ - see front matter © 2005 ISA—The Instrumentation, Systems, and Automation Society.

2. 482 Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490
Various SMC techniques for induction motors model of induction motor is given in Section 2 and
have been proposed in many literatures. The lin- SVM techniques in induction motor drives are dis-
earization SMC techniques were suggested in cussed in Section 3. Details of sliding-mode con-
Refs. ͓2,6,7͔. Linear reference models or input- troller design are given in Section 4, while the
output linearization techniques were used in the simulation results are presented in Section 5. Fi-
control of the nonlinear systems. A fuzzy SMC nally, some concluding remarks are given in Sec-
method was developed in Ref. ͓3͔. SMC acts in a tion 6.
transient state to enhance the stability, while fuzzy
technique functions in the steady state to reduce
chattering. In Refs. ͓8–10͔, the Lyapunov direct 2. Dynamic model of induction motor
method is used to ensure the reaching and sustain-
ing of the sliding mode. These SMC methods re- A three-phase induction motor with squirrel-
sult in a good transient performance, sound distur- cage rotor is considered in the paper. Assuming
bance rejection, and strong robustness in a control that three-phase ac voltages are balanced and sta-
system. However, the chattering is a problem in tor windings are uniformly distributed and based
SMC and causes the torque, flux, and current on the well-known two-phase equivalent motor
ripple in the systems. In Ref. ͓9͔, sliding-mode representation, the nonsaturated symmetrical in-
concepts were used to implement pulse width duction motor can be described in the fixed coor-
modulation ͑PWM͒. This implementation method dinate system ͑␣ , ␤͒ by a set of fifth-order nonlin-
is simple and efficient by means of power inverter ear differential equations with respect to rotor
since both implementation of SMC and PWM im- velocity ␻, the components of rotor magnetic flux
ply high-frequency switching. However, this ␺␣ , ␺␤, and of stator current i␣ , i␤ ͓4͔:
method causes severe ripple in the torque signal
due to the irregular logic control signals for in- d␺␣ Rr Lm
= − ␺␣ − ␻␺␤ + Rr i␣ ,
verter. To overcome this problem, an rms torque- dt Lr Lr
ripple equation was developed in Ref. ͓11͔ to
minimize torque ripple. In Ref. ͓12͔, a direct d␺␤ Rr Lm
torque control ͑DTC͒ is combined with space vec- = − ␺␤ + ␻␺␣ + Rr i␤ ,
dt Lr Lr
tor modulation ͑SVM͒ techniques to improve the
torque, flux, and current steady-state wave forms
through ripple reduction.
With the development of microprocessors, the
di␣
=
Lr
2 −
dt LsLr − Lm
ͩ
Lm d␺␣
Lr dt
− R si ␣ + u ␣ , ͪ
ͩ ͪ
SVM technique has become one of the most im-
portant PWM methods for voltage source inverter di␤ Lr Lm d␺␤
= 2 − − R si ␤ + u ␤ ,
͑VSI͒. It uses the space vector concept to compute dt LsLr − Lm Lr dt
the duty cycle of the switches. It simplifies the
digital implementation of PWM modulations. An d␻ P
aptitude for easy digital implementation and wide = ͑ T − T L͒ ,
dt J
linear modulation range for output line-to-line
voltages are the notable features of SVM ͓13,14͔. 3P Lm
Thus SVM becomes a potential technique to re- T= ͑i ␺ − i ␺ ͒ , ͑1͒
2 Lr ␤ ␣ ␣ ␤
duce the ripple in the torque signal.
This paper presents a new sliding-mode control- where ␻ is the electrical rotor angle velocity; ␺
ler for torque regulation of induction motors. This = ͓␺␣␺␤͔T, i = ͓i␣i␤͔T, and u = ͓u␣u␤͔T are rotor
novel control method integrates the speed sensor- flux, stator current, and stator voltage in ͑␣ , ␤͒
less SMC with the SVM technique. It replaces the coordinate, respectively; T and TL are the torque
PWM component in the conventional SMC with of motor and load torque; J is the inertia of the
the SVM so that the torque ripple of induction rotor; P is the number of pole pairs. Rr and Rs are
motors is effectively reduced while the robustness rotor and stator resistances, Lr and Ls are rotor and
is ensured at the same time. stator inductances, and Lm is the mutual induc-
The paper is organized as follows. The dynamic tance.

3. Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490 483
Fig. 1. Three-phase two-level PWM inverter.
3. SVM techniques in induction motor drives
Fig. 2. Space vectors.
The SVM technique is the more preferable
scheme to the PWM voltage source inverter since sponding to the rotation frequency of the vector
it gives a large linear control range, less harmonic ͓14͔. In order to reduce the number of switching
distortion, and fast transient response ͓13,14͔. A actions and make full use of active turn-on time
scheme of a three-phase two-level PWM inverter for space vectors, the vector us is commonly split
with a star-connection load is shown in Fig. 1. into two nearest adjacent voltage vectors and zero
In Fig. 1, uLi, i = 1,2,3, are pole voltages; ua , ub, vectors U0 and U7 in an arbitrary sector. For ex-
and uc are phase voltages; uo is neutral point volt- ample, during one sampling interval, vector us in
age; Vdc is the dc link voltage of PWM. Their sector I can be expressed as
relationships are
T0 T1 T2 T7
1 u s͑ t ͒ = U0 + U1 + U2 + U7 , ͑3͒
uLi = ± Vdc, i = 1,2,3, TS TS TS TS
2
where TS is the sampling time, and TS − T1 − T2
1 = T0 + T7 ജ 0, T0 ജ 0, and T7 ജ 0.
uo = ± Vdc ,
6 The required time T1 to spend in active state U1
is given by the fraction of U1 mapped by the de-
ua = uL1 − uo ;ub = uL2 − uo ;uc = uL3 − uo . ͑2͒ composition of the required space vector uS onto
the U1 axis, shown in Fig. 2 as U1X. Therefore
The SVM principle is based on the switching
between two adjacent active vectors and two zero ͉U1X͉
vectors during one switching period ͓13͔. From T1 = T ͑4͒
Fig. 1, the output voltages of the inverter can be ͉ U 1͉ S
composed by eight switch states U0 , U1 , … , U7,
and similarly
corresponding to the switch states
S0͑000͒ , S1͑100͒ , … , S7͑111͒, respectively. These ͉U2X͉
vectors can be plotted on the complex plane ͑␣ , ␤͒ T2 = T . ͑5͒
as shown in Fig. 2. ͉ U 2͉ S
The rotating voltage vector within the six sec- From Fig. 2, the amplitude of vector U1X and
tors can be approximated by sampling the vector U2X are obtained in terms of ͉us͉ and ␪,
and switching between different inverter states
during the sampling period. This will produce an ͉ u S͉ ͉U2X͉ ͉U1X͉
= = . ͑6͒
sin͑2␲ 3͒ ր sin ␪ sin͑␲ 3 − ␪͒ր
approximation of the sampled rotating space vec-
tor. By continuously sampling the rotating vector
and high-frequency switching, the output of the Based on the above equations, the required time
inverter will be a series of pulses that have a domi- period spending in each of the active and zero
nant fundamental sine-wave component, corre- states are given by

4. 484 Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490
t5
Ά ·
3Tz Tm
4 + 2 + Tm+1 , sector = I,III,V;
m = 1,3,5, respectively
3Tz Tn
= + + Tm , sector = II,IV,VI; ,
4 2
m = 2,4,6 and
n = 3,5,1, respectively
Fig. 3. Pulse command signal pattern. 3Tz
t6 = + Tm + Tn . ͑8͒
4
͉uS͉sin͑␲ 3 − ␪͒
ր
T1 = TS ,
͉U1͉sin͑2␲ 3͒ ր
4. Sliding-mode controller design
͉uS͉sin ␪
T2 = TS ,
͉U2͉sin͑2␲ 3͒ ր The objective of SMC design is to make the
modulus of the rotor flux vector ␺r, and torque T
T z = T 0 + T 7 = T s − ͑ T 1 + T 2͒ . ͑7͒ track to their reference value ␺r and T*, respec-
*
tively.
The pulse command signals pattern for the in-
verter for Sector I can be constructed in Fig. 3. 4.1. Selection of the sliding surfaces
Similarly, according to the vector sequence and
timing during a sampling interval given in Table 1, The transient dynamic response of the system is
other five pulse command signal patterns, associ- dependent on the selection of the sliding surfaces.
ated with sector II, sector III, …, sector VI can be The selection of the sliding surfaces is not unique.
obtained. Hence the required time periods in a According to Ref. ͓15͔, the higher-order sliding
sampling interval can be given as modes can be selected; however, it demands more
information in implementation. Considering the
Tz
t1 = , SMC design for an induction motor supplied
4 through an inverter ͑Fig. 1͒, two sliding surfaces
Ά ·
Tz Tm
are defined as
4 + 2 ,
sector = I,III,V;
ˆ
S1 = T* − T , ͑9͒
m = 1,3,5, respectively
t2 = Tz Tn ,
4 + 2 ,
sector = II,IV,VI; d * ˆ
* ˆ
S 2 = C ͑ ␺ r − ␺ r͒ + ͑ ␺ r − ␺ r͒ . ͑10͒
n = 3,5,1, respectively dt
Tz Tm + Tn The positive constant C determines the convergent
t3 = + , speed of rotor flux. T* and ␺r are the reference
*
4 2
ˆ
torque and reference rotor flux, respectively. T and
3Tz Tm + Tn ˆ
␺r are the estimated torque and rotor flux, and
t4 = + ,
4 2 ˆ ͱ
ˆ2 ˆ2 ˆ ˆ
␺r = ␺␣ + ␺␤, where ␺␣ and ␺␤ are the estimated
rotor flux in ͑␣ , ␤͒ coordinate. Once the system is
Table 1 driven into sliding surfaces, the system behavior
Time duration for selected vectors.
will be determined by S1 = 0 and S2 = 0 in Eqs. ͑9͒
U0 U ma U na U7 Un Um U0 and ͑10͒. The objective of control design is to
force the system into sliding surfaces so that the
Tz / 4 Tm / 2 Tn / 2 Tz / 2 Tn / 2 Tm / 2 Tz / 4
torque and rotor flux signals will follow the re-
a
Um and Un are two adjacent voltage vectors. spective reference signals.

5. Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490 485
4.2. Invariant transformation of sliding surfaces transformation of a discontinuity surface has no
effect upon the equivalent control value on the
In order to simplify the design process, the time
manifolds S = 0 or q = 0.
derivative of sliding surfaces’ function S can be
decoupled with respect to two phase stator voltage
4.3. Selection of the control law
vectors u = ͓u␣u␤͔T. Projection of the systems mo-
tion in the subspaces S1 and S2 can be written as The direct method of Lyapunov is used for the
stability analysis. Considering the Lyapunov func-
dS tion candidate ␯ = 0.5STS ജ 0, its time derivative is
= F + Au, ͑11͒
dt ␯ = ST͑F + Au͒ .
˙ ͑16͒
where F = ͓f 1 f 2͔T, u = ͓u␣u␤͔T, and S = ͓S1S2͔T. Select the control law as
Functions f 1 , f 2, and matrix A can be obtained u␣ = − k1 sgn͑q1͒ − k2q1 , ͑17a͒
as follows by differentiating structure switching
function ͑9͒ and ͑10͒ and substituting correspond- u␤ = − k1 sgn͑q2͒ − k2q2 , ͑17b͒
ing relations from the mathematical model,
where
˙
f 1 = T* + ͩ
3P 1 ˙ ˆ˙
ˆ
2 Rr r r
ˆ2 ˆ ͪˆ
␺ · ␺ + ␴ L s␺ r · ␻ + ␴ ␥ T , sgn͑q͒ = ͭ + 1,q Ͼ 0
− 1,q Ͻ 0
, ͮ
͑12͒ and
k1,k2
2 ˆ
T are positive constants.
˙* ¨* ˆ
f 2 = C ␺ r + ␺ r + ␴ R rR s␺ r − Rr ␻ˆ
3P ␺ ˆ Theorem: Consider the induction motor ͑1͒, with
r
the developed sliding mode controller ͑17a͒ and
− ͩ ͪ
2
3P
2
2
Rr
ˆ
T2
ˆ3
␺r
+ ͩ
2Rr
Lr
˙
ˆ
− C ␺, ͪ ͑13͒
͑17b͒ and stable sliding surfaces ͑9͒ and ͑10͒. If
k1 , k2 are chosen so that ͑k1 + k2͉qi͉͒ Ͼ max͑f *͒,
where i = 1, 2, the reaching condition of sliding
i
˙
surface ␯ = STS Ͻ 0 is satisfied, and control system
ͫ ͬ
˙
ˆ ˆ
a 1␺ ␤ − a 1␺ ␣ will be stabilized.
A= , ͑14͒ Proof: From the time derivative of Lyapunov
ˆ ˆ
a 2␺ ␣ a 2␺ ␤ function ͑16͒, the following equation can be de-
rived:
where ␴ = 1 / ͑LsLr − Lm͒, ␥ = LrRs + LsRr, a1
2
␯ = ST͑F + Au͒ = ͑q1 f * − k1͉q1͉ − k2q2͒
˙ 1 1
ˆ
= ͑3P / 2͒␴Lm and a2 = −͑1 / ␺r͒␴RrLm; ␻ is the es-
ˆ
timated rotor angle velocity. + ͑ q 2 f * − k 1͉ q 2͉ − k 2q 2͒ ,
2 2
From Eqs. ͑12͒ and ͑13͒, it is noted that func-
͑18͒
tions f 1 and f 2 do not depend on either u␣ or u␤.
Therefore the transformed sliding surfaces, q where ͓f * f *͔ = ͑A−1F͒T.
1 2
= ͓q1q2͔T, are introduced to simplify the design From Eq. ͑18͒, it is noted that if one chooses
process and to construct the candidate Lyapunov ͑k1 + k2͉qi͉͒ Ͼ max͑f *͒, where i = 1 , 2, the time de-
i
function in the next subsection. Sliding surfaces q rivative of Lyapunov function ␯ Ͻ 0. Thus the ori-
˙
and S are related by an invariant transformation: gin in the space q ͑and in the space S as well͒ is
asymptotically stable, and the reaching condition
q = ATS. ͑15͒ of sliding surface is guaranteed. The torque T andˆ
Remark 1: According to Ref. ͓4͔, the purpose of ˆ
rotor flux ␺r will approach to the reference torque
invariant transformation is to choose the easiest and reference rotor flux, respectively.
implementation of the SMC technique from the Remark 2: From Eqs. ͑17a͒ and ͑17b͒, it is ob-
entire set of feasible techniques. A linear invariant served that the control command u␣ is used to

6. 486 Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490
Fig. 4. The block diagram of SMC with SVM. Fig. 5. The block diagram of PI with SVM.
force sliding mode occurring on the manifold q1 ing mode control method ͑SMC with SVM͒.
= 0, while u␤ is used to force sliding mode occur- Meanwhile, the proposed control method has been
ring on the manifold q2 = 0. The sliding mode oc- compared with the conventional SMC ͓9͔ and
curring on the manifold q = 0 is equivalent to its classical PI control method ͓16͔. The sliding-mode
occurrence on the manifold S = 0 ͓4͔. After the observer discussed in Ref. ͓5͔ is adopted to esti-
sliding mode arises on the intersection of both sur- mate the rotor flux and the torque of an induction
ˆ * ˆ motor without using speed sensors. This observer
faces S1 = T* − T = 0 and S2 = C͑␺r − ␺r͒ + ͑d / dt͒ has been proved to have good convergence and
* ˆ ˆ ˆ
ϫ͑␺r − ␺r͒ = 0, then T = T* and ␺r = ␺*. Therefore a
r asymptotic stability ͓9͔. The block diagrams of
complete decoupled control of torque and flux is torque control of the induction motor are shown in
achieved. Fig. 4 ͑SMC with SVM͒, Fig. 5 ͑PI with SVM͒,
Remark 3: It is well known that sliding-mode and Fig. 6 ͑conventional SMC͒.
techniques generate undesirable chattering and * *
In Fig. 4, u␣ and u␤ are control signals, derived
cause the torque, flux, and current ripple in the from the control law ͑17a͒ and ͑17b͒, and
system. However, in the new control system, due ͱ͑u␣͒2 + ͑u␤͒2 = ͉us͉, ␪ = a tan͉͑u␤͉ / ͉u␣͉͒ ͑see Fig.
* * * *
to the SVM technique giving a large linear control 2͒. In Fig. 5, the parameters of the PI controller
range and the regular logic control signals for in- are tuned by trial and error to achieve the “best”
verter ͓13͔, which means less harmonic distortion, control performance. In Fig. 6, the inverter logic
the chattering can be effectively reduced. control signals are obtained through the SMC
method while they are calculated by using SVM
5. Simulations techniques in the proposed method ͑Fig. 4͒. This
turns out to be the major difference between the
In this section, simulation results are presented conventional SMC and the proposed SMC method
to show the performance of the proposed new slid- with SVM.
Fig. 6. The block diagram of conventional SMC.

7. Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490 487
Table 2
Induction motor nominal parameters.
Ls= 590 ␮H P=1
Lr= 590 ␮H J = 4.33e − 4 N m s2
Lm= 555 ␮H B = 0.04 N m s / rad
Rs= 0.0106 ⍀ rated voltage= 24 V
Rr= 0.0118 ⍀
The simulations are implemented by using
A Matlab S function is developed to
Matlab/Simulink.
implement the SVM block. A 10-kHz fixed
switching frequency for the inverter is used. For
SMC with SVM, parameters k1 and k2 are selected
as k1 = 0.1 and k2 = 0.3.
The nominal parameters of the test induction
motor are listed in Table 2.
5.1. Simulation results of stator current, rotor
torque and rotor flux
Figs. 7–9 show the stator current i␣, torque re-
Fig. 8. Rotor flux responses. ͑a͒ PI with SVM, ͑b͒ SMC, ͑c͒
SMC with SVM.
sponses, and rotor flux responses when the refer-
ence torque signal is a rectangular wave with fre-
quency 2.5 Hz.
Based on the simulation results shown in Fig. 9,
the output torque comparison of three control
methods is shown in Table 3.
From Fig. 7, it is noted that the resulting current
has the largest harmonic distortion for PI with
SVM, and the smallest harmonic distortion for
SMC with SVM. Fig. 8 shows that the estimated
rotor flux tracks the reference input well in all
three control methods, but PI with the SVM con-
trol scheme has the most oscillation and biggest
overshoot, while SMC with SVM has the least os-
cillation and no overshoot. Due to the sudden
change of stator current, two disturbances appear
at 0.2 and 0.4 s in Figs. 8͑a͒ and 8͑c͒. However, no
Fig. 7. Stator current i␣. ͑a͒ PI with SVM, ͑b͒ SMC, ͑c͒ disturbances are found in Fig. 8͑b͒. This demon-
SMC with SVM. strates the fact of the strong robustness of the con-

8. 488 Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490
Fig. 9. Torque responses. ͑a͒ PI with SVM, ͑b͒ SMC, ͑c͒ Fig. 10. Torque responses with a sine-wave reference sig-
SMC with SVM. nal. ͑a͒ PI with SVM, ͑b͒ SMC, ͑c͒ SMC with SVM.
ventional SMC since it is used in the observer, the 5.2. Torque tracking
controller, and even the PWM. Fig. 9 and Table 3
In order to test the torque tracking convergence
show that, among three control methods, SMC
to various reference torque signals, different kinds
with SVM has the best torque tracking perfor-
of waves are selected as the reference torque sig-
mance with significant reduced torque ripple. The
nals. Figs. 10 and 11 show torque responses of the
simulation results demonstrate that the new con-
three control methods when the reference torque
trol approach can achieve the exact decoupling of
signals are sine wave and piecewise wave, respec-
the motor torque and rotor flux, and shows satis-
tively.
factory dynamic performance.
From Figs. 10 and 11, it is noted that the pro-
posed new control method exhibits high accuracy
Table 3 in torque tracking when the reference torque sig-
Comparison of the three control methods.
nal is changed to different signals.
Mean-square error
Controllers of output torque Torque ripple
5.3. Load disturbances
PI with SVM 0.637% ±12%
SMC 0.284% ±8%
To test the robustness of the developed control
SMC with SVM 0.004% ±0.85% method, the external load disturbance has been in-
troduced to the proposed control system. Fig. 12

9. Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490 489
Fig. 11. Torque responses with a piecewise wave reference
signal. ͑a͒ PI with SVM, ͑b͒ SMC, ͑c͒ SMC with SVM.
shows torque and speed responses of three control
methods when external load disturbance is a band-
limited white noise with 6.25e − 5 noise power.
From Fig. 12, it is demonstrated that the torque
response of the proposed new control system is
insensitive to external load perturbation. Although
the speed has small oscillation because of the dis-
turbance, the new control system is stable, and
strong robust.
Fig. 12. Torque and speed responses with disturbance. ͑a͒
6. Conclusions PI with SVM, ͑b͒ SMC, ͑c͒ SMC with SVM.
In this paper, a novel SMC approach integrating ventional SMC method, this new scheme has low
with the SVM technique for an induction motor torque ripple, low current distortion, and high-
has been presented. Complete decoupled control performance dynamic characteristics. Moreover,
of torque and flux is obtained and significant this new control scheme can achieve high accu-
torque ripple reduction is achieved. Comparing racy in torque tracking to various reference torque
with the classical PI control method and the con- signals and shows very strong robustness to exter-

10. 490 Tian-Jun Fu, Wen-Fang Xie / ISA Transactions 44, (2005) 481–490
nal load disturbances. Therefore the proposed space-vector modulation in a high-performance sen-
novel control method is simple, accurate, and ro- sorless AC drive. IEEE Trans. Ind. Appl. 40, 170–176
bust. ͑2004͒.
͓13͔ Holtz, J., Pulsewidth modulation for electronic power
conversion. Proc. IEEE 82, 1194–1213 ͑1994͒.
Acknowledgment
͓14͔ Zhou, K. and Wang, D., Relationship between space-
vector modulation and three-phase carrier-based
The project was supported by the Faculty Re-
PWM: A comprehensive analysis. IEEE Trans. Ind.
search Development Program from Concordia Electron. 49, 186–196 ͑2002͒.
University. The authors would like to thank the ͓15͔ Perruquetti, W., et al., Sliding Mode Control in Engi-
reviewers for comments and suggestions. neering. Marcel Dekker, Inc., New York, 2002.
͓16͔ Tursini, M., Petrella, R., and Parasiliti, F., Adaptive
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͓2͔ Chen, F. and Dunnigan, M. W., Sliding-mode torque degree in electrical engineering
and flux control of an induction machine. IEE Proc.: from Shenyang University of
Electr. Power Appl. 150, 227–236 ͑2003͒. Technology, China, in 1988. He
͓3͔ Barrero, F., Gonzalez, A., Torralba, A., Galvan, E., had been working as a senior en-
and Franquelo, L. G., Speed control of induction mo- gineer and project manager in
tors using a novel fuzzy sliding-mode structure. IEEE several electric motor companies
in China from 1988 to 2002. He is
Trans. Fuzzy Syst. 10, 375–383 ͑2002͒. currently working toward the
͓4͔ Utkin, Vadim I., Sliding Modes in Control and Opti- M.A.Sc. degree in mechanical
mization. Springer-Verlag, Berlin, 1992. and industrial engineering at Con-
͓5͔ Utkin, Vadim I., Sliding mode control design prin- cordia University, Canada. His re-
ciples and applications to electric drives. IEEE Trans. search interests include control
Ind. Electron. 40, 23–36 ͑1993͒. theory applications, electrical ma-
͓6͔ Shieh, Hsin-Jang and Shyu, Kuo-Kai, Nonlinear chine drives, power electronics, and hybrid electric vehicle control.
sliding-mode torque control with adaptive backstep-
ping approach for induction motor drive. IEEE Trans.
Ind. Electron. 46, 380–389 ͑1999͒. Wen-Fang Xie is an assistant
͓7͔ Benchaib, A., Rachid, A., and Audrezet, E., Sliding professor with the Department of
mode input-output linearization and field orientation Mechanical and Industrial Engi-
for real-time control of induction motors. IEEE Trans. neering at Concordia University,
Canada. She was an Industrial
Power Electron. 14, 3–13 ͑1999͒. Research Fellowship holder from
͓8͔ Soto, Rogelio and Yeung, Kai S., Sliding-mode con- Natural Sciences and Engineering
trol of induction motor without flux measurement. Research Council of Canada and
IEEE Trans. Ind. Appl. 31, 744–750 ͑1995͒. served as a senior research engi-
͓9͔ Yan, Zhang, Jin, Changxi, and Utkin, V. I., Sensorless neer in InCoreTec, Inc. Canada
sliding-mode control of induction motors. IEEE Trans. before she joined Concordia Uni-
Ind. Electron. 47, 1286–1297 ͑2000͒. versity. She had worked as a re-
͓10͔ Benchaib, A., Rachid, A., and Audrezet, E., Real-time search fellow in Nanyang Techno-
sliding-mode observer and control of an induction mo- logical University, Singapore
from 1999 to 2001. She received her Ph.D. from The Hong Kong
tor. IEEE Trans. Ind. Electron. 46, 128–137 ͑1999͒. Polytechnic University in 1999 and her Masters degree from
͓11͔ Kang, Jun-Koo and Sul, Seung-Ki, New direct torque Beijing University of Aeronautics and Astronautics in 1991. Her
control of induction motor for minimum torque ripple research interests include nonlinear control in mechatronics, artifi-
and constant switching frequency. IEEE Trans. Ind. cial intelligent control, induction motor control, advanced process
Appl. 35, 1076–1082 ͑1999͒. control, image processing, and pattern recognition.
͓12͔ Lascu, C. and Trzynadlowski, A. M., Combining the
principles of sliding mode, direct torque control, and