1.1 Mathematical Model

The effective mathematical model of PMSM is critical for controller and observer design for PMSM-based Variable Frequency Drives (VFDs). Even though PMSMs are inherently non-linear systems, for most practical purposes, they can be approximated and modeled as a linear time-invariant dynamic system. The following section briefly introduces simple linear dynamic models of the PMSM in the stationary and rotational reference frame.