2000_yoon-seok han, ; jung-soo choi, ; young-seok kim, -- sensorless pmsm drive with a sliding mode...

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3588 IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 5, SEPTEMBER 2000

Sensorless PMSM Drive with a Sliding ModeControl Based Adaptive Speed and Stator Resistance

EstimatorYoon-Seok Han, Jung-Soo Choi , Member, IEEE , and Young-Seok Kim , Member, IEEE

Abstract This paper presents a new speed and position sen-sorless control method of permanent magnet synchronous motorsbased on the sliding mode observer. The sliding mode observerstructure and its design method are described. Also, Lyapunovfunctions are chosen for determining the adaptive law for thespeed and the stator resistance estimator. The effectiveness of theproposed observer is confirmed by the experimental results.

Index Terms PMSM (Permanent magnet synchronousmotor), sensorless control, sliding mode control, stator resistanceestimation.

I. INTRODUCTION

A PERMANENT magnetsynchronous motor (PMSM)is re-ceiving increased attention for drive applications becauseof its high torque to inertia ratio, superior power density, andhigh efficiency. However, the PMSM is generally constructedwith a fixed rotor field, supplied by rotor-mounted magnets.Therefore if the rotor position is known, then the position of the field can be determined. The rotor position can be obtainedby a shaft-mounted encoder or by a resolver. These compo-nents cause several disadvantages from the standpoint of drivecost, encumbrance, reliability, and noise immunity. Consideringthese disadvantages, sensorless control of the PMSM has re-ceived more attention.

In some studies, the rotor flux quantities are estimated bythe integration of machine terminal voltages and the rotor po-sition information was derived from these quantities [ 1]. How-ever, in this scheme, the poor precision and offset problem of the integral algorithm are major drawbacks. On the other hand,there was an attempt to detect the rotor angle directly from theterminal current error between the actual machine current andcalculated current on the hypothetical machine model [ 2]. But,the low accuracy differential operation may degrade the dy-namic performance due to system noise at the transient state.In [3] and [4], the implementation of an extended Kalman filter(EKF) is proposed for the rotor speed and position estimation.This approach makes use of a linearization of the system modelaround operating points. Though the EKF is well known, the

Manuscript received January 24, 2000. This work was supported by the De-velopment Program for the Examplary School in Information and Communica-tion from the Ministry of Information and Communication (MIC).

Y.-S. Han and Y.-S. Kim are with the School of Electrical and Computer En-gineering, Inha University (e-mail:[email protected]).

J.-S. Choi is with SENTEC Co. Ltd., 1129-49, Kuro-Dong, Kuro-Ku, Seoul,Korea.

Publisher Item Identifier S 0018-9464(00)07956-5.

convergence of the estimated speed and position are difficult toguarantee. In [ 5], a nonlinear full state observer is employedfor the rotor speed and position estimation using the machinemodel in which the dynamic equations as well as voltage equa-tions are included. However, since generally the parameter of the dynamic equation such as machine inertia or viscosity fric-tion coefficient are not well known and these values are easilychanged during normal operation, there are many restrictions inthe actual implementation.

This paper describes the new sensorless control of the PMSMusing a sliding mode observer. The proposed methodology in-corporates the Lyapunov algorithm to estimate the rotor speedand the stator resistance so that it can overcome the problemof sensitivity in the face of motor parameter variation. Also,without any mechanical information, the rotor speed is obtainedfrom adaptive scheme. Experimental results are carried out toverify the feasibility of the sensorless control for the PMSM.

II. SLIDING MODE OBSERVER

The model for the PMSM in the stationary referenceframe is characterized by (1)

(1)

where: stator - and -axes currents: stator - and -axes voltages

: induced voltage

: back emf constant,,

: ,: stator resistance

: stator inductance

Considering the PMSM, the rotor speed and the stator re-sistance are variable, which are to be estimated. From (1), thesliding observer is made as the following structure

(2)

where: observer input

: observer gain: Estimated values.

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HAN et al. : SENSORLESS PMSM DRIVE WITH A SLIDING MODE AND STATOR RESISTANCE ESTIMATOR 3589

The sliding hyperplane is defined upon the stator currenterrors.

(3)

The estimation error dynamic is given by the followingequation

(4)

III. ESTIMATOR OF SPEED AND STATOR RESISTANCE

In order to estimate rotor speed and stator resistance, a Lya-punov function is used. The Lyapunov function is chosen as

(5)

Under the assumption that the rotor speed is constant withinone estimation period, derivative of the Lyapunov functionbecomes

(6)

Substituting (4) into (6), then following equation is obtained

(7)

where, , . According tothe Lyapuvovs stability theory, must be obeyed to guaranteethat the observer is stable. In order to drive the system to beconvergent, that is ., let

(8a)

(8b)

From (8a), estimation algorithms of the rotor speed and thestator resistance may be derived. Also, the observer input mustbe chosen to satisfy the inequality (8b). Rearranging (8a) appro-priately, then two novel equations are obtained as

(9a)(9b)

From (9a), the stator resistance estimator may be derived as

(10)

Also, from (9b), the speed estimator may be derived as

(11)

Fig. 1. Block diagram of the proposed algorithm.

The estimated rotor position is obtained by integrating therotor speed.

The block diagram of sliding mode observer and adaptive es-timators for PMSM are shown in Fig. 1.

IV. DESEIG OF OBSERVER GAIN

In order to guarantee the derivative of the Lyapunov function, the observer gains and for observer input must

be chosen the satisfy inequality (8b)

(12)

The sufficient conditions for satisfying the inequality (12) are

(13)(14)

The condition for satisfying inequality (13) and (14) can berespectively derived as

(15)

if if (16)

where, , : positive constant.

V. EXPERIMENTAL RESULTS

Fig. 2 shows the overall system, which consists of a 400 W8 pole PMSM and DC generator. All of the proposed algo-rithms including the speed and the rotor resistance estimatorare implemented using a TMS320C31. A three-phase PWMinverter is constructed by using the IGBT, and the gate-firinglogic to implement SVPWM is developed by using the motioncoprocessor.


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HAN et al. : SENSORLESS PMSM DRIVE WITH A SLIDING MODE AND STATOR RESISTANCE ESTIMATOR 3591

Fig. 7. Performance of observer with speed and stator resistance estimator.

4) The experiments showed that this method was veryeffective.

REFERENCES

[1] R. Wu et al. , Permanent magnet motor drive without a shaft sensor, IEEE Trans. Ind. Appl. , vol. 27, no. 5, pp. 10051011, 1991.

[2] N. Matsui et al. , Brushless dc motor control without position and speedsensor, IEEE Trans. Ind. Appl. , vol. 28, no. 1, pp. 120127, 1992.

[3] A. Bado et al. , Effective estimation of speed and rotor position of aPM synchronous motor drive by a Kalman filtering technique, in Proc. IEEE PESC92 , 1992, pp. 951957.

[4] R. Dhaouadi et al. , Design and implementation of an extended Kalmanfilter for the state estimation of a permanent magnet synchronousmotor, IEEE Trans. Power Electron. , vol. 6, pp. 491497, 1991.

[5] R. B. Sepe et al. , Real-time observer-based (adaptive) control of a per-manent-magnet synchronous motor without mechanical sensor, IEEE Trans. Ind. Appl. , vol. 28, no. 6, pp. 13451352, 1992.

[6] T. Furuhashi et al. , Position-and-velocity sensorless control for brush-less DC motors using an adaptive sliding mode observer, IEEE Trans. Industrial Electronics , vol. 39, no. 2, pp. 8995, 1992.

2000_yoon-seok han, ; jung-soo choi, ; young-seok kim, -- sensorless pmsm drive with a sliding mode...

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