Discrete sliding mode repetitive control based on parabola approach law

According to the characteristics of parabola function, a new discrete-time sliding mode repetitive control method based on parabola approach law is proposed for the periodic trajectory tracking of uncertain discrete-time systems in modern industrial production. The discrete sliding mode controller based on parabola approach law can effectively suppress chattering, and the discrete sliding mode repetitive controller based on ideal switching dynamics can solve the problem of periodic disturbance. The convergence characteristics of parabola approach law are analyzed, including absolute convergence layer, monotone convergence layer and steady-state error band, which are used to describe the dynamic performance of system error under different parameters. The simulation results verify the effectiveness of the proposed control method.