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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%)
II. EXTENDED MATHEMATICAL MODEL OF THE IM
III. DEVELOPMENT OF THE EKF ALGORITHM
IV. HARDWARE CONFIGURATIONV. V. EXPERIMENTAL RESULTS
INTRODUCTIONExtended-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.
INTRODUCTIONThe inclusion of the mechanical equation helps the estimation process by conveying the rotorstator 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 IMFor 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 IMThe 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 ALGORITHMFor 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 . This process requires the discretization of (3) and (4), or (5) and (6)
III. DEVELOPMENT OF THE EKF ALGORITHMAs mentioned before, EKF involves the linearized approximation of the nonlinear model [(7) and (8)] and uses the current estimation of states xe(k) and inputs ue(k) in linearization by using
III. DEVELOPMENT OF THE EKF ALGORITHMThe algorithm involves two main stages: prediction and filtering.
IV. HARDWARE CONFIGURATIONThe 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 RESULTSAccording to the KF theory, the Q, the D (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 D 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 RESULTSThe 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 IStep-Type Changes in (Fig. 4)
A. Scenario IStep-Type Changes in (Fig. 4)
V. EXPERIMENTAL RESULTSIn 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 IIVelocity and Load Torque Reversal (Fig. 5)
B. Scenario IIVelocity and Load Torque Reversal (Fig. 5)
V. EXPERIMENTAL RESULTSIn 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 IIIZero and Low Velocities (Fig. 6)
C. Scenario IIIZero and Low Velocities (Fig. 6)
VI. CONCLUSIONThe 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.