Homotopy continuation based observer for position sensorless PM synchronous machine drives

Abstract

A novel unified position sensorless observer is proposed using homotopy continuation. A single observer is used to estimate the rotor position and speed at high speed, low speed, and standstill. The position and speed are treated as independent variables such that the PMSM dynamic equation is a parametrized algebraic function f where the zeros identify the position and speed estimate. A homotopy is identified that maps the zeros of f at sampling time instant k − 1 into the zeros of f at sampling time instant k. As the algebraic equation has multiple zeros, the homotopy is designed to identify the closest zero that, assuming reasonable sampling, identifies the correct position and speed. Benefits of the proposed method are instantaneous estimation and lack of convergence transients once a rough estimate is available through initial position estimation with polarity detection. The concept is validated at low and high speed using high-fidelity simulations.