Applying averaging theory to the permanent magnet synchronous motor drive

Many permanent magnet synchronous motor drive systems can be regarded as two time scale systems. In this paper, a singular perturbation technique is employed to decompose the system into two linear time invariant subsystems. These linear subsystems have been exploited with a conventional linear observer technique to develop observers for the rotor position and velocity using measurements of currents. This paper demonstrates that it is possible to use an average value of the velocity in the rotor position observer. Under fairly mild assumptions, bounds are derived for the error in position estimates