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This paper presents an optimal two-stage extended Kalman filter (OTSEKF) for closed-loop flux, torque, and speed estimation of a permanent magnet synchronous motor (PMSM) to achieve sensorless DTC-SVPWM operation of drive system. The novel observer is obtained by using the same transformation as in a linear Kalman observer, which is proposed by C.-S. Hsieh and F.-C. Chen in 1999. The OTSEKF is an effective implementation of the extended Kalman filter (EKF) and provides a recursive optimum state estimation for PMSMs using terminal signals that may be polluted by noise. Compared to a conventional EKF, the OTSEKF reduces the number of arithmetic operations. Simulation and experimental results verify the effectiveness of the proposed OTSEKF observer for DTC of PMSMs

A Two-stage Kalman Filter for Sensorless Direct Torque Controlled PM Synchronous Motor Drive