Convergence Properties of Direct Position and Speed Estimation in Synchronous Motor Drives

This paper analyzes direct position and speed estimation from a control theoretical and numerical standpoint. The paper develops the theory of local identifiability and defines the conditions such that position and speed can be identified uniquely based on a sufficiently accurate guess. Local identifiability typically holds at nonzero machine speeds and zero speeds with any perturbation, e.g. an injected high frequency signal in pwm control or a random switching ripple in direct control (except in isotropic machines). The position and speed is identifiable in more than 98.5% of feasible operation points “instantaneously”, and can be extrapolated from past estimates in the remaining cases. Finally, numerical solving strategies are studied and a combination of the Newton and conjugate gradient method is shown to provide suitable estimates within 1-5 solver iterations depending on the required accuracy.