Towards sensorless observers for sinusoidal electric machines with variable speed and no mechanical model: A promising approach for PMSMs

One of the major issues in developing sensorless observers for AC Sinusoidal Machines, and for all kinds of Electric Machines, is to deal with variable speed relying only on the electromagnetic model, without using any mechanical information. In this paper, the case of Permanent Magnet Synchronous Machines is considered as first benchmark. A novel and promising design strategy is presented to develop a simple sixth-order observer for estimating rotor speed/position and magnetic flux amplitude, in the context of non-zero variable speed, with unknown constant sign and bounded derivative. This framework does not cover yet any arbitrarily-varying mechanical speed, but it goes far beyond the typical simplifying assumption of “slowly-varying speed”, which is actually meant as “constant speed” in the common theoretical analysis. In the proposed method, the rotation dynamics of the machine back-electromotive force is represented by means of the Lie Groups formalism, and no open-loop integration of stator voltages and currents is adopted. Lyapunov-like and Singular Perturbations techniques are then exploited to achieve regional practical asymptotic stability, with a very wide region of attraction. The mild limitations on such stability domain are carefully analyzed and discussed. Numerical simulations are provided to show the effectiveness of the proposed observer, under heavily variable mechanical speed. Finally, taking cue from the features of the presented approach, future steps are outlined in order to further weaken the restrictions on the speed variations and to extend the results to other electric machines.