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

In this paper, a nonlinear robust optimal control (NROC) for uncertain two-axis motion control system via adaptive dynamic programming (ADP) and neural networks (NNs) is proposed to improve the robustness against parameter variations and compounded disturbances. The two-axis motion control system is an X-Y table driven by two permanent-magnet linear synchronous motors (PMLSMs) servo drives. The tracking control problem of the nonlinear X-Y table with uncertainties is transformed to a regulation problem. Then, it is solved by an infinite horizon optimal control scheme using a critic NN. Consequently, the NN is developed via ADP learning algorithm to facilitate the online solution of the modified Hamilton-Jacobi-Bellman (HJB) equation corresponding to the nominal system for approximating the optimal control law. The uniform ultimate boundedness of the closed-loop system is proved using the Lyapunov approach and the tracking error asymptotically converges to a residual set. The validity and robustness of the proposed control system are verified by experimental analysis. The control algorithms have been developed in a control computer based on a dSPACE DS1104 DSP control computer. From the experimental results, the dynamic behaviors of the two-axis motion control system using the proposed NROC can achieve robust optimal tracking control performance against parameter uncertainties and compounded disturbances.