Optimal high‐order constraint following control of permanent magnet synchronous motor based on uncertainty boundary

ABSTRACT The permanent magnet synchronous motor (PMSM) has uncertainties such as nonlinear friction dynamics, unknown interference, and mismatched model parameters. This triggers a forced reduction in motion accuracy. Therefore, an optimal high‐order constraint following control method is developed to improve robustness. First, nonlinear friction is incorporated into the PMSM system to build a more accurate dynamic model. Udwadia‐Kalaba (U‐K) approach is applied to establish the constraint force of analytic form to satisfy nominal desired constraints. Then, in order to compensate for the influence of uncertainty, a flexible high‐order constraint following control method based on constraint force is proposed. The method is founded on the boundary information of uncertainty. According to the stability proof of Lyapunov, it is indicated that the proposed control method has the uniform boundedness and uniform ultimate boundedness. Further, an optimization strategy based on performance boundaries and control costs is designed. According to the engineering requirements, the control parameters are reasonably optimized. Finally, MATLAB simulation and rapid control prototype experiments jointly verify the effectiveness of the proposed optimal control method.