Using a Bivariate Polynomial in an EKF for State and Inductance Estimations in the Presence of Saturation Effects to Adaptively Control a PMSM
Tanja Zwerger, Paolo Mercorelli
Abstract
This paper takes into consideration a combined extended Kalman filter (CEKF) by using a bivariate polynomial for the estimation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{d}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{q}$ </tex-math></inline-formula> in saturation conditions. In the context of the Kalman filter (KF), <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{d}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{q}$ </tex-math></inline-formula> are modelled as nonlinear augmented states to control a permanent magnetic synchronous machine (PMSM). Once <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{d}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{q}$ </tex-math></inline-formula> 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.