An Adaptive Sliding-Mode Observer for Induction Motor Sensorless Speed Control

Dec, 2008

授課老師： 王明賢 教授

學 生 ： 楊智淵

南台科技大學電機系

高等伺服控制報告

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005Jingchuan Li, Longya Xu, Fellow, IEEE, and Zheng Zhang, Senior Member, IEEE

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Outline

Abstract I. INTRODUCTION II. SLIDING-MODE CURRENT AND FLUX OBSERVER DESIGN A. Current Observer I B. Current Observer II C. Rotor Flux Observer Design III. ADAPTIVE SPEED ESTIMATION IV. STABLITY ANALYSIS V. SIMULATION RESULTS A. Simulation Results by MATLAB B. HIL Evaluation Results by TI 2812 DSP VI. EXPERIMETAL RESULTS VII. CONCLUSION REFERENCES

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Abstract

An adaptive sliding-mode flux observer is proposed for sensorless speed control of induction motors in this paper.

Two sliding-mode current observers are used in the method to make flux and speed estimation robust to parameter variations.

The adaptive speed estimation is derived from the stability theory based on the current and flux observers

The system is first simulated by MATLAB and tested by hardware-in-the-loop

Simulation and experimental results are presented to verify the principles and demonstrate the practicality of the approach.

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INTRODUCTION

To make flux and speed estimation robust to parameter variations, a novel adaptive sliding-mode flux and speed observer is proposed in the paper

Two sliding-mode current observers are used in the proposed method

The effects of parameter deviations on the rotor flux observer can be alleviated by the interaction of these two current sliding-mode observers

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The stability of the method is proven by Lyapunov theory.

An adaptive speed estimation is also derived from the stability theory.

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SLIDING-MODE CURRENT AND FLUX OBSERVER DESIGN

Defining stator currents and rotor fluxes as the state variables,we can express the induction motor model in the stationary frame as

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The adaptive sliding-mode observer

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A. Current Observer I

The first sliding-mode current observer is defined as

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According to the above formulas, the current error equation is

From the equivalent control concept [8], if the current trajectories reach the sliding manifold, we have

By selecting large enough, the sliding mode will occur

, and then it follows that

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B. Current Observer II

The second sliding-mode current observer is designed differently from (3) as

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By subtracting (1) from (6), the error equation becomes

From an equivalent control point of view, we have

where

.

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C. Rotor Flux Observer Design

Combining the results from (5) and (8), the rotor flux observer can be constructed as

where L is the observer gain matrix to be decided such that theobserver is asymptotically stable.

From (5) and (8), the error equation for the rotor flux is

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III. ADAPTIVE SPEED ESTIMATION

In order to derive the adaptive scheme, Lyapunov’s stability theorem is utilized. If we consider the rotor speed as a variable parameter, the error equation of flux observer is described by the following equation:

where

is the estimated rotor speed

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The candidate Lyapunov function is defined as

Where is a positive constant. We know that V is positive definite.The time derivative of V becomes

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Let be an arbitrary positive constant. With this assumption, the above equation becomes

Letting the second term be equal to the third term in (14), we can find the following adaptive scheme for rotor speed identification:

where

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In practice, the speed can be found by the following proportional and integral adaptive scheme

Where and are the positive gains.

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IV. STABLITY ANALYSIS

Since the second term is equal to the third term in (14), the time derivative of becomes

It is apparent that (17) is negative definite. From Lyapunov stability theory, the flux observer is asymptotically stable, guaranteeing the observed flux to converge to the real rotor flux.

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V. SIMULATION RESULTS

To evaluate the proposed algorithm for the rotor flux and speed estimation, computer simulations have been conducted using MATLAB.

To further investigate the implemental feasibility, the estimation and control algorithm are evaluated by hardware-in-the-loop (HIL) testing

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A. Simulation Results by MATLAB

Fig. 3 shows the speed command, real speed, estimated speed, and the speed estimation error

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Fig. 4 shows the real and estimated rotor flux and the flux estimation error

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B. HIL Evaluation Results by TI 2812 DSP

1. The control software is implemented and evaluated in real time and can be debugged very easily in the absence of motor.

3. The control software can be easily transferred to the real drive system with only minor changes.

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Fig. 7shows the motor step response to a speed command at 0.5 pu( 900 r/min).

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Fig. 8 shows the real and estimated rotor flux and the estimated flux angle

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Fig. 9 shows the motor response to a trapezoidal speed command

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VI. EXPERIMETAL RESULTS

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VII. CONCLUSION

A novel adaptive sliding-mode observer for sensorless speed control of an induction motor has been presented in this paper

The proposed algorithm consists of two current observers and one rotor flux observer.

The two sliding-mode current observersare utilized to compensate for the effects of parameter variations on the rotor flux estimation

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REFERENCES

[1] C. Schauder, “Adaptive speed identification for vector control of induction motors without rotational transducers,” IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1054–1061, Sep./Oct. 1992. [2] F. Z. Peng and T. Fukao, “Robust speed identification for speed-sensorless vector control of induction motors,” IIEEE Trans. Ind. Appl., vol. 30, no. 5, pp. 1234–1240, Sep./Oct. 1994. [3] Y. R. Kim, S. K. Sul, and M.-H. Park, “Speed sensorless vector control of an induction motor using an extended Kalman filter,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, Oct. 4–9, 1992, pp. 594–599. [4] H. Kubota, K. Matsuse, and T. Nakano, “DSP-based speed adaptive flux observer of induction motor,” IEEE Trans. Ind. Appl., vol. 29, no. 2, pp. 344–348, Mar./Apr. 1993.

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REFERENCES

[5] G. Yang and T. H. Chin, “Adaptive-speed identification scheme for a vector-controlled speed sensorless inverter-induction motor drive,” IEEE Trans. Ind. Appl., vol. 29, no. 4, pp. 820–825, Jul./Aug. 1993. [6] A. Derdiyok, M. K. Guven, H. Rehman, N. Inanc, and L. Xu, “Design and implementation of a new sliding-mode observer for speed-sensorless control of induction machine,” IEEE Trans. Ind. Electron., vol. 49, no. 5, pp. 1177–1182, Oct. 2002. [7] H. Rehman, A. Derdiyok, M. K. Guven, and L. Xu, “A new current model flux observer for wide speed reange sensorless control of an induction machine,” IEEE Trans. Ind. Electron., vol. 49, no. 6, pp. 1041–1048, Dec. 2002.

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