1. Speed-Sensorless Estimation for Induction motors using Extended Kalman Filters 教 授： 龔應時 學 生： 楊政達 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%)

2. outline I. INTRODUCTION II. EXTENDED MATHEMATICAL MODEL OF THE IM III. DEVELOPMENT OF THE EKF ALGORITHM IV. HARDWARE CONFIGURATIONV. V. EXPERIMENTAL RESULTS

3. 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.

4. 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.

5. 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

7. 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:

8. 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)

9. 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

10. III. DEVELOPMENT OF THE EKF ALGORITHM The algorithm involves two main stages: prediction and filtering.

12. 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

13. IV. HARDWARE CONFIGURATION

14. V. EXPERIMENTAL RESULTS According to the KF theory, the Q, the D ξ (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.

15. V. EXPERIMENTAL RESULTS

16. 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)

18. V. EXPERIMENTAL RESULTS 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)

20. V. EXPERIMENTAL RESULTS 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)

22. 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.