An adaptive smooth second-order sliding mode repetitive control method with application to a fast periodic stamping system

Abstract

This paper proposes an adaptive smooth second-order sliding mode repetitive control method for a class of non-linear systems with unknown disturbances and uncertainties. The key point is that the control law combines the advantages of adaptive second-order sliding mode control with the benefits of repetitive control. When both periodic and aperiodic disturbances exist in the system, the proposed method forces the sliding mode into a smaller pre-specified region in finite time, and when only periodic disturbance exists, the proposed method forces the sliding mode to converge to zero. Compared with pure sliding mode control, the proposed method is especially suitable for systems with sudden periodic load disturbances, for example from periodic impacts. Pure sliding mode control needs to adjust at each impact. Repetitive control knows each impact is coming and learns how to handle it, while sliding mode control can be dedicated to addressing aperiodic disturbances. This can result in smaller error levels. The stability of the proposed method is proved based on a Lyapunov approach. The performance is evaluated on a hydraulic press system via simulations.