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1170 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005
Speed-Sensorless Control of Induction MotorUsing a Continuous Control Approach of
Sliding-Mode and Flux ObserverAdnan Derdiyok , Member, IEEE
Abstract—This paper presents a continuous approach of sliding-mode current and flux observers for an induction machine.The proposed observer structure both decouples machine equa-tions and makes them completely insensitive to rotor resistancevariation. An estimation algorithm based on these observers isproposed to calculate speed and rotor resistance independently.In the proposed algorithm, the speed and rotor resistance areconsidered to be unknown constants, because the speed and rotorresistance change slowly compared to the electrical variables suchas currents and fluxes. The simulation and experimental resultsdemonstrate the good performance of the proposed observerand estimation algorithm and of the overall indirect-field-ori-ented-controlled system.
Index Terms—Current and flux observer, induction machine(IM), speed and rotor resistance estimation.
I. INTRODUCTION
ESTIMATION of angular speed without measurement of
mechanical variables is a challenging problem due to high-
order and nonlinearity of the induction motor dynamics. In the
literature, voltage and current models of the induction machine
(IM) have generally been used together for flux estimation andthen speed has been estimated from those models [1], [2]. The
methods proposed imply the estimation of the time-derivative
with subsequent integration. However, implementation of an in-
tegrator for motor flux estimation is no easy task. A pure in-
tegrator has dc drift and initial value problems. To solve the
problems, the pure integrator has replaced by digital and/or pro-
grammable-cascaded low-pass filter (LPF) [3]–[6]. Another ap-
proach to the sensorless control problem is to consider the speed
as an unknown constant parameter and use this approach to es-
timate this parameter [7]–[9]. The idea here is that the speed
changes slowly compared to the electrical variables. This ap-
proach has been first formulated by Schauder [8] and with some
modification introduced in [9]–[11].The basic concepts and principles of the sliding-mode con-
trol of electrical drives have been demonstrated in [12] and
some aspects of the implementation have been illustrated in
[13]. Furthermore, sliding-mode observers have been proposed
for estimating the states of the control system. Benchaib et al.
[14] have introduced a control and observation of an induction
Manuscript receivedApril 11, 2003; revisedNovember 4, 2004. Abstract pub-lished on the Internet April 28, 2005.
The author is with the Department of Electrical and Electronics Engineering,Atatürk University, Erzurum 25240, Turkey (e-mail: [email protected]).
Digital Object Identifier 10.1109/TIE.2005.851594
motor using the sliding-mode technique. The observer model
is a copy of the original system, which has corrector gains
with switching terms. An adaptive sliding-mode observer for
sensorless field-oriented control of induction motors have been
presented by Parasiliti et al. [15], [16]. The observer detects
the rotor flux components in the stationary reference frame
by using motor mechanical equations. An additional relation
obtained by a Lyapunov function has identified the motor speed.
The observer proposed in this paper is similar to the one intro-duced in [17] in which flux integration problem was attempted
to solve by an integral scheme and a LPF is used to overcome
the discontinuous of the sliding-mode current observer. In this
study, a continuous type of sliding-mode current observer is de-
veloped and the presented idea has no flux integration problem.
The observer is designed by combining variable structure sys-
tems and Lyapunov approach. In the current and flux equations,
the similar parts are equated to sliding-mode functions (SMFs)
that are used to develop flux estimation and to determine speed
and rotor resistance of an induction motor by assuming that the
speed and rotor resistance are unknown constant parameters.
The algorithm introduced has no integration problem and onlyuses measurements of the stator currents and voltages to esti-
mate speed and rotor resistance. The method proposed is veri-
fied by the simulation and experiment.
II. IM MODEL AND OBSERVER DESIGN
A. Current Model of IM
A dynamic model for an induction motor in the rotor-flux-ori-
ented stationary reference frame, by choosing the stator currents
and rotor fluxes as state variables, is as follows
[13]:
(1)
(2)
The symbol and parameter definitions of these equations are
given in the Appendix.
B. A Continuous Sliding-Mode Current Observer
A current observer, in which SMFs, stator currents, and volt-
ages are taken as inputs, is designed as follows [17]:
(3)
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1172 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005
Fig. 1. Block diagram of the plant model and observer structure.
where is the sampling period of the current measurement, and
and are the present and previous values of
, respectively.
C. Flux Observer
When the trajectories of the system reach the sliding surfaces,
i.e., , the observed currents match the actual ones. Since
the SMFs in (3) converge to the related term in the current (1)
and the same terms are seen in the flux (2), the following equa-tions can be written for the flux observer:
(31)
(32)
III. ESTIMATION OF SPEED AND ROTOR RESISTANCE
It is reasonable to assume that and if their vari-
ations are very slow when compared with the electrical variables
such as stator currents and rotor fluxes. Time derivatives of (10)
and (11) are
(33)
(34)
Equations (33) and (34) can be written in matrix form as
(35)
To get the speed and rotor resistance, (35) is arranged as follows:
(36)
To calculate the speed and rotor resistance from (36), we need
the information of the derivatives of the fluxes. We obtain very
simple equations for the derivative of fluxes in (31) and (32) that
can be calculated easily.
If actual states are replaced with the o bserved
ones in (36), the speed and rotor resistance can
be calculated since , , and are available. Then, (36)
can be written for speed and rotor resistance as
(37)
and can be written by their first-order approximation in
a discrete-time version as
(38)
(39)
From (29) and (30), and can be calculated easily as
(40)
(41)
In (37), if the currents and SMFs are
replaced with their equalities given by (3), (29), (30), (38), and(39), the estimation equations of the speed and rotor resistance
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DER DIYO K: S PEE D-SEN SOR LES S C ONT ROL OF IND UCT ION MOTOR U SING A CO NTINUO US C ONTRO L AP PROACH 1 17 3
Fig. 2. Simulation results under 5-N1
m load. (a) Actual and estimated speeds( ! ; ̂! )
. (b) Estimation of rotor resistance ( ̂
R
). (c) Calculated current (i
).
(d) Observed current ( ̂
i
). (e) Current estimation error (s
).
become totally the functions ofthe currenterrors , stator
voltages and constant motor parameters .
The block diagram of the developed observer structure is
illustrated in Fig. 1. As seen from the figure, the speed and
rotor resistance estimations are the functions of the estimated
currents, SMFs and estimated fluxes that are available in (3),
(29)–(32), (38), and (39).
IV. RESULTS AND DISCUSSION
The motor used in both the experiment and simulation is a
4-hp, 380-V Y-connected four-pole IM. Machine parameters
are given in the Appendix. The simulation result shown in Fig. 2
has been obtained under a 5-N m load.
The first step for the speed estimation is the current observa-
tion. The calculated and observed -axis currents are illustrated
in Fig. 2(c) and (d), respectively, and the current estimation error
is shown in Fig. 2(e). It is obvious from these results that the cur-
rent convergence is satisfied, and the SMFs match the related
terms in the plant model.
Since the SMFs converge to the related terms in the current
model and the same terms are also seen in the flux model, it
is expected to have the flux convergence as well. Based on the
current and flux observers, the speed and rotor resistance are es-
timated. The estimated and actual speeds are plotted in Fig. 2(a),and the estimation of the rotor resistance is shown in Fig. 2(b).
The results obtained demonstrate that the convergence of the
current, speed, and rotor resistance is achieved.
The real-time control and observer program are imple-
mented by using the software of digital signal processor (DSP)
TMS320C31. A dcmachine is coupled to the shaft of the IM
as a load. A feedback control system is applied to the indi-
rect-field-oriented (IFO) IM drive system. In the inner loop of
the control system, a standard proportional plus integral (PI)
controller is used for current control and another PI controller
is used in the outer loop for speed control. The parameters of
the PI controller are tuned to obtain suf ficient performance
of the control system. The sampling period is set to 1 msfor the speed and 100 s for currents measurements. In the
implementation, a 6–Hz LPF is utilized at the output of the
speed estimator to prevent noise and oscillations produced by
the speed estimator. A PC is used for data logging, data com-
munication, and downloading. The stator currents are detected
through Hall-effect sensors. The performance of the observer
is tested in the implementation for trapezoidal references. The
trapezoidal references are chosen to show the performance of
the proposed method in both directions at variable and constant
speeds.
The results of the estimation algorithm at high and low speeds
are shown in Figs. 3 and 4 in which the actual and observed
speeds [Figs. 3(a) and 4(a)], the actual and observed currents[Figs. 3(b) and (c) and 4(b) and (c)] and the SMFs [Figs. 3(d)
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1174 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005
Fig. 3. Experimental results of the speed estimation at a 1000-rpm trapezoidal reference trajectory (a) Measured and estimated speeds( ! ; ̂! )
; (b) Measured
current (i
) (c) Observed current ( ̂
i
); (d) SMF (
).
Fig. 4. Experimental results of the speed estimation at a 50-r/min trapezoidal reference trajectory. (a) Measured and estimated speeds ( ! ; ̂! ) . (b) Measured
current (i ). (c) Observed current ( ̂
i ). (d) SMF ( ).
and 4(d)] are plotted. The SMFs drive the estimated currents to
the measured ones and the derivative of the fluxes is obtained
by these functions. The accuracy of the derivatives of the flux
observations is reflected in the speed plots. In Figs. 3(a) and
4(a), the actual and estimated speeds are shown on top of eachother. As clearly seen in these figures, the observer performance
is satisfactory at constant, and linear increasing and decreasing
region of the reference speeds. It is observed in all figures that
the SMFs are successfully modulated to match currents, and en-
able us to get the speed and rotor resistance information. The es-
timation of the rotor resistance will overcome the problem of re-sistance variation that is normally needed for the slip frequency
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DER DIYO K: S PEE D-SEN SOR LES S C ONT ROL OF IND UCT ION MOTOR U SING A CO NTINUO US C ONTRO L AP PROACH 1 17 5
Fig. 5. Experimental results of rotor resistance estimation.
calculation in an IFO vector control of an IM. The experimental
result of rotor resistance estimation is shown in Fig. 5.
V. CONCLUSION
A continuous control algorithm of sliding-mode current and
flux observers has been developed for the speed-sensorless IFO
control of an IM. The equations to estimate speed and rotor re-
sistance have been obtained from the flux observer that is based
on the current model of the induction motor. The proposed al-
gorithm achieves the following features:
• removes the discontinuity of sliding-mode current and
flux observers;
• decouples the machine equations;
• removes the effect of rotor resistance on the current and
flux equations;
• removes the flux terms from the equations of the speed
and rotor resistance.
The performance of the estimation algorithm has been tested
at high- and low-amplitude trapezoidal speed references. The re-
sults demonstrate that the speed converges on its real values suc-
cessfully in both cases. The simulation and experimental results
also show that the SMFs are successfully modulated to match
currents, and enable us to get the speed and rotor resistance in-formation.
APPENDIX
A. Symbols
rotor time constant;
reciprocal of rotor time constant
electrical rotor speed;
and axes;
rotor fluxes in coordinates;
stator currents in coordinates;
stator voltages in coordinates;mutual inductance;
rotor and stator inductances;
rotor and stator resistances.
B. Motor Parameters
mH
mH
mH
C. Definitions of the Constants
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Adnan Derdiyok (M’98) was born in Horasan,Turkey, in 1964. He received the B.S. degree in elec-trical engineering from the Technical University of Istanbul, Istanbul, Turkey, in 1988, the M.S. degreefrom Middle East Technical University, Ankara,Turkey, in 1993, and the Ph.D. degree from YıldızTechnical University, Istanbul, Turkey, in 1997.
In 2000, he was with The Ohio State University,
where he was engaged in post-doctoral research anddevelopment of sensorless control techniques for in-duction motors. Since 1997, he hasbeen with Atatürk
University, Erzurum, Turkey, where he is currently an Associate Professor. Hisresearch interests include control of electrical machines, sensorless control of
IMs, modeling andcontrol of switched reluctance motors,and fuzzy andsliding-mode control techniques.