Observability analysis of PMSM

The current problems to successfully apply sensorless control techniques for Permanent Magnet Synchronous Motor (PMSM) are the existence of operating conditions for which the observer performance is remarkably deteriorated. This is due to difficulties in estimating correctly the rotor position at low speed. The failure of sensor-less schemes in some particular operating conditions has been always recognized in experimental settings. However, there are no sufficient theoretical observability analysis for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed specially to necessary observability condition analysis. Thus, we give here the necessary and sufficient states observability condition for the PMSM. An example is presented to illustrate the results.