Diffeomorphism-Based Robust Bounded Control for Permanent Magnet Linear Synchronous Motor With Bounded Input and Position Constraints

This article develops a diffeomorphism-based robust bounded control (DRBC) for the permanent magnet linear synchronous motor system subject to inequality constraints (i.e., bounded input and position constraints) and uncertainties. The uncertainties, including parameter uncertainties and external disturbances, are potentially nonlinear and fast time varying. The bound of the uncertainty is described by a fuzzy set. To overcome the bounded input constraint, a robust bounded control is proposed based on a novel input diffeomorphism scheme, which is in a deterministic form and not if-then rule based. Furthermore, to overcome the bounded position constraint, a transformed system is formulated by a state diffeomorphism scheme, which transforms the bounded state-constrained system to an unconstrained one. Thus, the output of the controlled system can be restricted to a prescribed range. The DRBC guarantees both the uniform boundedness and the uniform ultimate boundedness of the transformed system. A fuzzy performance index, which combines the steady-state performance (the average fuzzy performance) and control effort, is then established based on the fuzzy description of uncertainty. As a result, the design parameter optimization can be solved by minimizing the performance index. Experimental results demonstrate that the DRBC is of superior tracking performance and robustness without violating the prescribed inequality constraints.