Precision Trajectory Tracking on XY Motion Stage Using Robust Interval Type-2 Fuzzy PI Sliding Mode Control Method

Abstract

Precision contour tracking is one of the most important factors used to determine product quality in a machining tool. An interval type-2 fuzzy proportional–integral (PI) sliding mode control (IT2FPISMC) system is proposed herein to control the mover position of the two-axis motion stage with optical encoder sensors for trajectory feedback. A type-2 fuzzy method that can handle rule uncertainties is developed to approach the unknown nonlinear systems. The PI term is used to approximate the discontinuous control signal and mitigate the chattering phenomenon in the presence of unmodeled system dynamics and external disturbances. The adaptive control laws are derived based on the Lyapunov theorem, such that the closed-loop stability is guaranteed, and the output tracking errors of the system asymptotically converge to zero. A non-uniform rational B-spline interpolator with high accuracy is adopted in the biaxial linear stage. Moreover, typical circular, bowknot, heart, and star reference contours are tested. The results on the average tracking error and the tracking error standard deviation are experimented and compared to illustrate the performance of our proposed method. The tracking performance obtained from the IT2FPISMC method is better than that of the conventional method. Furthermore, the proposed method can achieve robustness for tracking different reference contours in industrial applications.