Improved Equivalent-Input-Disturbance Method for Nonlinear Repetitive-Control Systems: Integration With High-Order Sliding-Mode Control

This study focuses on the problem of disturbance rejection in nonlinear repetitive-control systems. The conventional method for rejecting disturbance based on equivalent-input-disturbance (EID) produces phase lag and disturbance estimation errors, which limit disturbance-rejection performance. To mitigate this issue, conventional EID approaches typically use high-gain control. This study presents a new technique utilizing an improved EID estimator. The method consists of three aspects. First, the nonlinear plant is formulated using a Takagi–Sugeno fuzzy model. Second, the exogenous disturbance is treated as an EID. The phase lag caused by the EID filter is characterized based on the output error. An estimator incorporating a high-order sliding-mode observer is devised to compensate for the EID. The variable about phase lag is imposed on the observer input and the output error is reduced by fast convergence. Third, an adjustable factor is inserted into the low-pass filter to implement the tuning of the disturbance rejection bandwidth. The stability criteria and design procedures are given. In the end, the effectiveness and superiority of the developed method are demonstrated using a rotating system.