A fuzzy cross-coupled linear quadratic regulator for improving the contour accuracy of bi-axis machine tools

This paper presents a control strategy consisting of a fuzzy cross-coupled linear quadratic regulator (FCCLQR) and a feedforward (FF) compensator to improve the contour accuracy of bi-axis machine tools. The linear quadratic penalty function applied in the proposed controller includes the contour error, the tracking error and the control effort over a finite future time window. The time-varying feedback gains are dependent on the trajectory commands and are obtained by the FCCLQR. The stability of the closed-loop system is verified using the Linear Matrix Inequality (LMI) technique. The feasibility and superiority of the proposed approach are demonstrated by tracking a heart-shaped trajectory using a biaxial machine tool.