Stackelberg-Theoretic Optimal Robust Control for Constrained Permanent Magnet Linear Motor With Inequality Constraints

The management of uncertainty and inequality constraint is essential for the high-speed and high-precision motion control of a permanent magnet linear motor (PMLM). This article develops a robust control with a dual-parameters optimization for the constrained PMLM system. The uncertainties considered in this article, including parameter uncertainties and external disturbances, are bounded within prescribed fuzzy sets. The tracking error is desired to maintain within a specified range (i.e., the inequality constraint) due to the limited travel range and the demand for bounded tracking performance of the PMLM system. By employing a state transformation, the bounded state is converted into an unbounded one. Therefore, the inequality constraint is creatively integrated into the trajectory tracking control problem. Based on the transformed system, an optimal robust control is established which can be divided into two steps. First, a deterministic robust control is proposed which guarantees the practical stability: uniform boundedness and uniform ultimate boundedness. Second, a two-player Stackelberg game is formulated to seek the optimal control parameters. The cost function of each player in the game reflects both the control performance and the control cost such that the tradeoff problem between the two conflicting criteria is further clarified. Finally, experimental results demonstrate the superior performance of the proposed optimal robust control over two existing control schemes.