Repetitive Control System with Variable Structure Controller

This paper presents a new design method for repetitive control that employs discrete-time variable structure (VS) control algorithm. First, an extended system containing an internal model of repetitive control is derived. Based on that, a sliding mode is designed, and a sliding sector is denned around it. A variable structure control law is then designed so that the state converges inside the sliding sector in a finite numbers of steps and then stays in the sector forever. It ensures that there exists a Lyapunov function that decreases monotonically in the state space. Thus the system is asymptotically stable. Simulation results show that the proposed control system provides good performance.