Intelligent mixed H2/H∞ adaptive tracking control system design using self-organizing recurrent fuzzy-wavelet-neural-network for uncertain two-axis motion control system

Abstract In this paper, an intelligent adaptive tracking control system (IATCS) based on the mixed H2/H∞ approach under uncertain plant parameters and external disturbances 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 H2/H∞ controller, a self-organizing recurrent fuzzy-wavelet-neural-network controller (SORFWNNC) and a robust controller. The combinations of these control methods would insure the stability, robustness, optimality, overcome the uncertainties, and performance properties of the two-axis motion control system. The SORFWNNC is used as the main tracking controller to adaptively estimate an unknown nonlinear dynamic function that includes the lumped parameter uncertainties, external disturbances, cross-coupled interference and frictional force. Moreover, the structure and the parameter learning phases of the SORFWNNC are performed concurrently and online. Furthermore, a robust controller is designed to deal with the uncertainties, including the approximation error, optimal parameter vectors and higher order terms in Taylor series. Besides, the mixed H2/H∞ controller is designed such that the quadratic cost function is minimized and the worst case effect of the unknown nonlinear dynamic function on the tracking error must be attenuated below a desired attenuation level. The mixed H2/H∞ control design has the advantage of both H2 optimal control performance and H∞ robust control performance. The sufficient conditions are developed for the adaptive mixed H2/H∞ tracking problem in terms of a pair of coupled algebraic equations instead of coupled nonlinear differential equations. The coupled algebraic equations can be solved analytically . The online adaptive control laws are derived based on Lyapunov theorem and the mixed H2/H∞ tracking performance so that the stability of the proposed IATCS can be guaranteed. Furthermore, the control algorithms are implemented in a DSP-based control computer. From the experimental results, the motions at X-axis and Y-axis are controlled separately, and the dynamic behaviors of the proposed IATCS can achieve favorable tracking performance and are robust to parameter uncertainties.