Discrete-Time Implementation Issues in Back-EMF Observer for Sensorless Control of PMSM and SynRM

Extended back-electromotive force (back-EMF) based sensorless control of permanent magnet and synchronous reluctance machines is considered in this paper. The analytical models of two possible discrete-time implementation alternatives for the observer are investigated and the dynamics of the back-EMF estimates is characterized analytically. It can be seen that, even in the case of perfect parameter matching, a small detail of the discrete-time implementation structure can heavily affect the estimation error. This could lead to detrimental effects on control capability, efficiency and stability under heavy load torque conditions or in the flux-weakening region (i.e. at high-speed). In fact, the proposed analysis proves that a relatively large error can arise, depending on the structure of the discrete-time observer and motor inductance. Optimal accuracy can be guaranteed adopting a proper implementation. Simulation and experimental results based on a commercial drive system are presented to validate the analytical developments and to prove the effectiveness of the proposal.