Sensor Less SMC Observer

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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)

0278-0046/$20.00 © 2005 IEEE






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



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)




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



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.

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Sensor Less SMC Observer