Online estimations for electrical and mechanical parameters of the induction motor by extended Kalman filter

Abstract

In this study, a novel extended Kalman filter (EKF)-based observer is designed to increase the number of estimated states and parameters of the induction motor (IM). To perform the online estimations of stationary axis components of stator currents and rotor fluxes ( $i_{s\alpha }$ , $i_{s\beta }$ , ${\phi }_{r\alpha }$ , and ${\phi }_{r\beta }$ ) as well as rotor mechanical speed ( ${\omega }_m$ ), which are required for direct vector control (DVC) systems along with the load torque ( $t_L$ ), rotor resistance ( $R_r$ ), magnetizing inductance ( $L_m$ ), and the reciprocal of the total inertia of the system ( ${\gamma }_T=1/J_T$ ), the proposed EKF uses the measured phase currents and voltages together with the measured rotor speed. To estimate all of the five states ( $i_{s\alpha }$ , $i_{s\beta }$ , ${\phi }_{s\alpha }$ , ${\phi }_{s\beta }$ , and ${\omega }_m$ ) plus four parameters ( $t_L$ , $R_r$ , $L_m$ , and ${\gamma }_T$ ), the proposed EKF-based observer does not include a switching operation nor a hybrid structure, which is a common approach in the literature for online state and parameter estimations of IMs and results in design complexity and computational load increase. In simulation studies, the estimation performance of the proposed EKF is tested and verified under the variations of $t_L$ , $R_r$ , $L_m$ , and ${\gamma }_T$ in DVC systems that perform the speed and position controls of IM. The obtained results confirm the satisfying tracking performances and thus better control achievements of the speed and position controlled IM drives in this paper. Moreover, the proposed EKF and the EKF without ${\gamma }_T$ -estimation are compared in the position control system to demonstrate the importance of the ${\gamma }_T$ estimation. In the comparison, nearly 10 times less mean square error (MSE) is obtained in the estimations of $t_L$ , $R_r$ , $L_m$ , and the magnitude of the rotor flux for the proposed EKF. Finally, the proposed EKF algorithm is tested and verified in real-time experiments with a challenging speed reversal scenario causing nonlinear variations in both $t_L$ and $R_r$ .