Using a Bivariate Polynomial in an EKF for State and Inductance Estimations in the Presence of Saturation Effects to Adaptively Control a PMSM

This paper takes into consideration a combined extended Kalman filter (CEKF) by using a bivariate polynomial for the estimation of
$L_{d}$
and
$L_{q}$
in saturation conditions. In the context of the Kalman filter (KF),
$L_{d}$
and
$L_{q}$
are modelled as nonlinear augmented states to control a permanent magnetic synchronous machine (PMSM). Once
$L_{d}$
and
$L_{q}$
are estimated, continuous monitoring of the machine saturation conditions is achieved to ensure the desired torque even under saturation conditions. The proposed adaptive control method based on maximum torque per ampere (MTPA) consists of an adaptive feedforward and PI controller. A discussion in light of the measured results using Hardware-in-the-loop is also included.