Estimation of Rotor Position and Speed of Permanent Magnet Synchronous Motors With Guaranteed Stability

The control algorithms used in high performance ac drives require the knowledge of rotor position and, in the case of speed regulation, also of speed. Since in many applications rotational transducers cannot be installed, their reconstruction is needed. The use of observers is stymied by the fact that the dynamics of electrical machines are highly nonlinear and does not belong to the class studied by the nonlinear control community. In this paper solutions to both problems, which are particularly tailored for the widely popular permanent magnet synchronous motors, are provided. A key step for the design of both observers is the choice of a suitable set of coordinates. The position observer is a standard gradient search whose detailed analysis reveals outstanding (global asymptotic) stability properties. Furthermore, the analysis clearly exhibits the interplay between rotor speed and the gain of the gradient search—that (essentially) determines its convergence rate. The position observer is a simple two-dimensional nonlinear system, hence is easily implementable. The speed observer is designed following the immersion and invariance technique and is also shown to be globally convergent. Simulation and experimental results of the position observer, used together with a classical field-oriented control algorithm, are presented.