Self-Organizing Recurrent Fuzzy Wavelet Neural Network-Based Mixed $\rm{H}_{2}\rm{/ H}_{\rm{\infty }}$ Adaptive Tracking Control for Uncertain Two-Axis Motion Control System

Abstract

In this paper, an intelligent adaptive tracking control system (IATCS) based on the mixed $H_{2}/ H_{\rm{\infty }}$ approach for achieving high precision performance of a two-axis motion control system is proposed. The two-axis motion control system is an X-Y table driven by two permanent-magnet linear synchronous motors (PMLSMs) servo drives. The proposed control scheme incorporates a mixed $H_{2}/ H_{\rm{\infty }}$ controller, a self-organizing recurrent fuzzy-wavelet-neural-network controller (SORFWNNC), and a robust controller. The SORFWNNC is used as the main tracking controller to adaptively estimate an unknown nonlinear dynamic function (UNDF) that includes the lumped parameter uncertainties, external disturbances, cross-coupled interference, and frictional force. Furthermore, a robust controller is designed to deal with the approximation error, optimal parameter vectors, and higher order terms in Taylor series. Besides, the mixed $H_{2}/ H_{\rm{\infty }}$ controller is designed such that the quadratic cost function is minimized and the worst case effect of the UNDF on the tracking error must be attenuated below a desired attenuation level. The online adaptive control laws are derived based on Lyapunov theorem and the mixed $H_{2}/ H_{\rm{\infty }}$ tracking performance so that the stability of the IATCS can be guaranteed. The experimental results confirm that the proposed IATCS grants robust performance and precise dynamic response to the reference contours regardless of external disturbances and parameter uncertainties.