Chattering Reduction in Sliding Mode Observers with Sinusoidal States using Continuous Equivalent Control Feedback

The paper presents a chattering reduction method for a certain class of estimators: sliding mode observers with sinusoidal states. Estimation problems for common AC machines like the Induction Motor (IM) and Permanent Magnet Synchronous Motor (PMSM) involve working with dynamic systems with sinusoidal states (currents, fluxes, EMFs). In Direct Field orientation control, the fluxes or EMFs can be estimated using a sliding mode observer, this uses discontinuous feedback terms of the type $M\cdot sign(s)$. These high frequency switching terms produce chattering, especially when operating with noisy measurements. The paper presents a method to reduce chattering: this is done by partially replacing the switching terms with their continuous equivalents. First, a subset of the observer equations is implemented, the sliding mode terms are generated and filtered to obtain the equivalent controls (which are continuous signals). Then, the equivalent controls are used to partially replace the switching terms in the remainder of the observer equations. The paper presents an observer for the induction machine as a design example. The paper also shows the complex coefficient filter used to process the switching terms to obtain the equivalent controls.