Nonlinear Robust Optimal Control via Adaptive Dynamic Programming of Permanent-Magnet Linear Synchronous Motor Drive for Uncertain Two-Axis Motion Control System

In this article, a nonlinear robust optimal control (NROC) scheme for uncertain two-axis motion control system via adaptive dynamic programming (ADP) and neural networks (NNs) is proposed. The two-axis motion control system is an X-Y table actuated by permanent-magnet linear synchronous motor servo drives. First, the motions of the tracking contour in X-axis and Y-axis of the X-Y table are stabilized through feedback linearization control (FLC) laws. However, the control performance may be destroyed due to parameter uncertainties and compounded disturbances. Therefore, to improve the robustness of the control system, an NROC is designed to achieve this purpose. The tracking control problem of the X-Y table with uncertainties is transformed to a regulation problem. Then, it is solved by an infinite horizon optimal control using a critic NN. Consequently, the NN is developed via ADP learning algorithm to facilitate the online solution of the Hamilton-Jacobi-Bellman equation corresponding to the nominal system for approximating the optimal control law. The uniform ultimate boundedness of the closed-loop system is proved utilizing the Lyapunov approach and the tracking error asymptotically converges to a residual set. The validation of the proposed control schemes are carried out through experimental analysis. The control algorithms have been implemented using a DSP control board. A comparison of control performances using FLC, adaptive FLC, and FLC-based NROC is investigated. From the experimental results, the dynamic behaviors of the two-axis control system using the proposed FLC-based NROC can achieve robust optimal control performance against parameter uncertainties and compounded disturbances.