Fuzzy-set theory based optimal robust constraint-following control for permanent magnet synchronous motor with uncertainties

Abstract This paper proposes a novel optimal robust control design approach to address the high-performance trajectory tracking control problem for the permanent magnet synchronous motor (PMSM) system containing uncertainties by integrating the Udwadia–Kalaba theory and the fuzzy set theory. First, the uncertainties in the PMSM system are described as fuzzy uncertainties based on fuzzy set theory. Second, a deterministic robust control scheme is proposed based on the servo constraint control approach and the fuzzy estimated bound of uncertainties. The proposed control scheme’s objective is to guarantee the uncertain PMSM system to achieve deterministic performance: uniformly bounded and uniformly ultimately bounded. Third, based on the fuzzy description of uncertainties, a fuzzy performance index including steady-state controlled performance and control cost is constructed. An optimal parameters design problem of the proposed control is presented and solved by minimizing the fuzzy performance index with a unique analytic-form solution. The resulting control renders the uncertain PMSM system strictly to follow the servo constraint, and the fuzzy performance is optimized. Ultimately, simulations and experiments illustrate that the proposed control approach has excellent constraint tracking performance for PMSM systems with uncertainties.