Methods to Obtain the Equivalent Controls of Sliding Mode Observers with Sinusoidal States

The paper presents a few methods to obtain the equivalent controls of sliding mode observers with sinusoidal states. Electric machines like the induction motor (IM) and permanent magnet synchronous motor (PMSM) have stationary frame models with sinusoidal states: currents, fluxes or EMFs. Sliding mode observers constructed based on these models use switching terms that sometimes need to be filtered in order to obtain the equivalent controls: they are needed for subsequent processes like calculations or estimation. These can be obtained based on simple low pass filtering; however, this method is not accurate and affects the performance of the downstream processes. The paper presents three methods that allow to obtain accurate equivalent controls. The methods can be used when the expected equivalent controls are a pair of sinusoids 90 degree out of phase. The methods presented require knowledge of the operating frequency - this is estimated using a phase locked loop.