Signal injection and averaging for position estimation of   Permanent-Magnet Synchronous Motors
  Sensorless control of Permanent-Magnet Synchronous Motors at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation induced. This paper proposes a clear and original analysis based on second-order averaging of how to recover the position information from signal injection; this analysis blends well with a general model of magnetic saturation. It also experimentally demonstrates the relevance for position estimation of a simple parametric saturation model recently introduced by the authors. 
Al Kassem Jebai, Fran\c{c}ois Malrait, Philippe Martin and Pierre   Rouchon
math.OC