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Speed-Sensorless Estimation for Induction
motors using Extended Kalman Filters
Murat Barut; Seta Bogosyan; Metin Gokasan;
Industrial Electronics, IEEE Transactions on
Volume: 54 , Issue: 1
Digital Object Identifier: 10.1109/TIE.2006.885123
Publication Year: 2007 , Page(s): 272 - 280
IEEE JOURNALS
PPT(100%)
教 授： 龔應時
學 生： 楊政達
outline

I. INTRODUCTION

II. EXTENDED MATHEMATICAL MODEL OF THE IM

III. DEVELOPMENT OF THE EKF ALGORITHM

IV. HARDWARE CONFIGURATIONV.

V. EXPERIMENTAL RESULTS
INTRODUCTION

Extended-kalman-filter-based estimation algorithms that could be used in
combination with the speed-sensorless field-oriented control and direct-torque
control of induction motors are developed and implemented experimentally

The algorithms are designed aiming minimum estimation error in both
transient and steady state over a wide velocity range, including very low and
persistent zero-speed operation

Although good results have been obtained in those studies in the relatively low
and high-speed operation region, the performance at zero stator frequency or
at very low speed is not satisfactory or not addressed at all.
INTRODUCTION

The inclusion of the mechanical equation helps the estimation process by
conveying the rotor–stator relationship when the stator currents cease to carry
information on rotor variables at zero speed

In the proposed EKF algorithms, the stator and rotor flux amplitudes and
positions are also estimated in addition to the stator currents (referred to the
stator stationary frame), which are also measured as output.
II. EXTENDED MATHEMATICAL MODEL OF
THE IM

For speed sensorless control,the model consists of differential equations based
on the stator and/or rotor electrical circuits considering the measurement of
stator current and/or voltages

Being different from previous EKF-based estimators, which estimate the rotor
velocity using the aforementioned equations, the extended IM model derived in
this paper also includes the equation of motion to be utilized for the estimation
of the rotor velocity
II. EXTENDED MATHEMATICAL MODEL OF
THE IM

The EKF-based estimators designed for FOC and DTC are based on the
extended IM models in the following general form:
III. DEVELOPMENT OF THE EKF
ALGORITHM

For nonlinear problems, the KF is not strictly applicable since linearity plays
an important role in its derivation and performance as an optimal filter

The EKF attempts to overcome this difficulty by using a linearized
approximation where the linearization is performed about the current state
estimate [21]. This process requires the discretization of (3) and (4), or (5) and
(6)
III. DEVELOPMENT OF THE EKF
ALGORITHM

As mentioned before, EKF involves the linearized approximation of the
nonlinear model [(7) and (8)] and uses the current estimation of states ˆxe(k)
and inputs ˆue(k) in linearization by using
III. DEVELOPMENT OF THE EKF
ALGORITHM

The algorithm involves two main stages: prediction and filtering.
IV. HARDWARE CONFIGURATION

The experimental test-bed for the EKF-based estimators is given in Fig. 2. The IM
in consideration is a three-phase fourpole 4-kW motor; the detailed specifications of
which will be given in the experimental results section
IV. HARDWARE CONFIGURATION
V. EXPERIMENTAL RESULTS

According to the KF theory, the Q, the Dξ (measurement error covariance
matrix), and the Du (input error covariance matrix) have to be obtained by
considering the stochastic properties of the corresponding noises .

However, since these are usually not known, in most cases, the covariance
matrix elements are used as weighting factor or tuning parameters.

The Dξ and Du are determined taking into account the measurement errors of
the current and voltage sensors and the quantization errors of the ADCs, as
given below.
V. EXPERIMENTAL RESULTS
V. EXPERIMENTAL RESULTS
A. Scenario I—Step-Type Changes in (Fig. 4)

The EKF schemes for both models are tested under step-type variations of the
load torque, as can be seen in Fig. 4. These step variations are created by
switching the load resistors ON and OFF.

The small value of this estimation error is an important indicator for the good
performance of the EKF in the high-velocity range under load and no load.
A. Scenario I—Step-Type Changes in (Fig. 4)
V. EXPERIMENTAL RESULTS
B. Scenario II—Velocity and Load Torque Reversal (Fig. 5)

In this scenario tested for both models, the velocity/load torque (varying
linearly with velocity) is reversed by changing the input frequency, while the
motor is running under a load torque of 19 N · m.

The estimated load torque/velocity tracks the linear variation of the measured
torque/velocity through 1450 to −1450 r/min.
B. Scenario II—Velocity and Load Torque Reversal (Fig. 5)
V. EXPERIMENTAL RESULTS
C. Scenario III—Zero and Low Velocities (Fig. 6)

In this scenario, while the motor is running at 10 r/min, at t = 20 s, nm is
stepped down to 0 r/min and is kept at zero for 64 s; at the end of this interval,
nm is stepped up to 10 r/min .

As a result, the stator-based estimator yields a velocity error of −4 r/min, while
for the rotor-based estimator, this error remains within −2 r/min.
C. Scenario III—Zero and Low Velocities (Fig. 6)
VI. CONCLUSION

The developed EKF scheme offers a more generalized and yet effective
solution for the sensorless estimation of IMs over a wide speed range and at
zero speed, motivating the use of the estimation method with sensorless FOC
and DTC of IMs.

The results can be further improved with the estimation of
temperature and frequency dependent uncertainties of stator and rotor
resistances and other system parameters based on the application.