Two-Dimensional Repetitive Control of Uncertain Takagi-Sugeno Systems Based on a New Equivalent-Input-Disturbance Estimator

This study presents a two-dimensional (2-D) repetitive control method to address the issues of periodic tracking and disturbance suppression in uncertain Takagi-Sugeno systems. The disturbance and uncertainty are treated as an equivalent-input-disturbance (EID). However, the conventional EID estimators typically suppress the EID through high gain. Meanwhile, the low-pass filter associated with EID causes a certain degree of phase lag. A proportional-integral (PI) filter is integrated with an EID estimator to develop a PI-EID structure to improve the estimation accuracy. Based on the self-learning mechanism of repetitive control, the 2-D repetitive controller is used to achieve a high level of tracking. Unlike the conventional nonlinear repetitive control methods, the state observer and the PI-EID estimator are membership function dependent. The gains of both controllers switch in line with the signs of the time derivative of the normalized premise variables, and this framework takes full account of the information of the nonlinear membership functions. The controller design procedures and the stability conditions are detailedly presented. Finally, a rotation speed control experiment is conducted to validate the developed PI-EID method.