Improved Nonlinear Extended Observer Based Adaptive Fuzzy Output Feedback Control for a Class of Uncertain Nonlinear Systems With Unknown Input Hysteresis

Abstract

This study focuses on the problem of adaptive fuzzy dynamic surface output feedback control for a class of uncertain nonlinear systems subjected to unknown input hysteresis. A Prandtl–Ishlinskii (PI) model is applied to the uncertain nonlinear system for describing the unknown input hysteresis, making the controller design feasible. In addition, a nonlinear extended state observer (NESO) is designed for simultaneously estimating the unmeasurable states and generalized disturbances, including the nonlinear hysteresis term of the PI model and external disturbances. In addition, a novel nonlinear function is designed to replace the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fal(\cdot)$</tex-math></inline-formula> function of the general NESO to address a modification that increases the convergence speed. Considering the incorporation of the improved nonlinear extended state observer (INESO), an adaptive output feedback control scheme is proposed based on fuzzy logic system and dynamic surface techniques. A command filter is employed to avoid the “explosion of complexity” problem inherent in the backstepping technique, while compensating the filtering error caused by adopting the filter. The Lyapunov approach is used to demonstrate the stability of the entire closed-loop system. Experiments regarding a piezoelectric micro–positioning stage are conducted, the results of which illustrate that the proposed adaptive fuzzy output feedback control method can guarantee a satisfactory tracking performance.