Backward Extended Kalman Filter to Estimate and Adaptively Control a PMSM in Saturation Conditions
Tanja Zwerger, Paolo Mercorelli
Abstract
This article describes the use of a combined extended Kalman filter, which is calculated using backward Euler discretization and a bivariate polynomial for the estimation of saturated nonlinear augmented states <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> . The benefit is the further processing of inductance in the control of a permanent magnetic synchronous machine. Backward Euler discretization is proposed in an extended Kalman filter 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 cross-coupling effects and spatial harmonics as well as under the influence of temperature variation in superposition. Measured results using HIL to validate the proposed algorithm and a discussion of the algorithm's advantages and disadvantages are included.