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An Adaptive Sliding-Mode Observer for
Induction Motor Sensorless Speed Control
Jingchuan Li, Longya Xu, Fellow, IEEE, and Zheng Zhang
Industry Applications, IEEE Transactions on
Volume: 41 , Issue: 4
Digital Object Identifier: 10.1109/TIA.2005.851585
Publication Year: 2005 , Page(s): 1039 - 1046
IEEE JOURNALS
教 授： 龔應時
學 生： 林哲偉
Outline
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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
Abstract
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An adaptive sliding-mode flux observer is proposed for sensorless speed
control of induction motors in this paper.
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Two sliding-mode current observers are used in the method to make flux and
speed estimation robust to parameter variations.
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The adaptive speed estimation is derived from the stability theory based on the
current and flux observers.
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Simulation and experimental results are presented to verify the principles and
demonstrate the practicality of the approach.
INTRODUCTION
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To make flux and speed estimation robust to parameter variations, a novel adaptive
sliding-mode flux and speed observer is proposed in the paper.
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Two sliding-mode current observers are used in the proposed method.
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The effects of parameter deviations on the rotor flux observer can be alleviated by
the interaction of these two current sliding mode observers.
The stability of the method is proven by Lyapunov theory.
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An adaptive speed estimation is also derived from the stability theory.
SLIDING-MODE CURRENT AND FLUX
OBSERVER DESIGN
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Defining stator currents and rotor fluxes as the state variables ,we can
express the induction motor model in the stationary frame as
The adaptive sliding-mode observer
A. Current Observer I
The first sliding-mode current observer is defined as
According to the above formulas, the current error equation is
B. Current Observer II
The second sliding-mode current observer is designed differently from
By subtracting before equation, the error equation becomes
C. Rotor Flux Observer Design
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Combining the results from Observer II equation, the rotor flux observer
can be constructed as
Where L is the observer gain matrix to be decided such that the observer is
asymptotically stable.
From Observer II equation, the error equation for the rotor flux is
III. ADAPTIVE SPEED ESTIMATION
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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:
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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 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 before equation, we
can find the following adaptive scheme for rotor speed identification:
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In practice, the speed can be found by the following proportional and
integral adaptive scheme:
IV. STABLITY ANALYSIS
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Since the second term is equal to the third term in (14), the time derivative
of becomes
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It is apparent this equation is negative definite. From
Lyapunov stability theory, the flux observer is asymptotically
stable, guaranteeing the observed flux to converge to the real
rotor flux.
V. SIMULATION RESULTS
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To evaluate the proposed algorithm for the rotor flux and speed estimation,
computer simulations have been conducted using MATLAB.
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To further investigate the implemental feasibility, the estimation and
control algorithm are evaluated by hardware-in-the-loop (HIL) testing.
A. Simulation Results by MATLAB
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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.
B. HIL Evaluation Results by TI 2812 DSP
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Fig. 7 shows 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
VI. EXPERIMETAL RESULTS
VII. CONCLUSION
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A novel adaptive sliding-mode observer for sensorless speed control of an
induction motor has been presented in this paper.
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The proposed algorithm consists of two current observers and one rotor
flux observer.
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The two sliding-mode current observers are utilized to compensate for the
effects of parameter variations on the rotor flux estimation.