Backward Extended Kalman Filter to Estimate and Adaptively Control a PMSM in Saturation Conditions

The following paper describes the use of a combined extended Kalman filter (CEKF) which is calculated using a backward Euler discretisation and a bivariate polynomial for the estimation of the saturated nonlinear augmented states Ld and Lq. The benefit is the further processing of the inductance in the control of a permanent magnetic synchronous machine (PMSM). A backward Euler discretisation is proposed in an extended Kalman filter (EKF) structure to obtain stability for long sampling times, which are due to the complexity of software to be implemented in the microcontroller. Hardware-in-the-loop (HIL), as an emulator, is used for validation of the functionality of the presented estimation method in the saturation region under the influence of both of cross-coupling effects and spatial harmonics as well as under the influence of temperature variation in superposition. Measured results using HIL to validate the pro-posed algorithm and a discussion of the algorithm's advantages and disadvantages are included.