Discrete-time repetitive control with ideal error dynamics

This paper deals with the problem of repetitive control for discrete-time systems on the basis of ideal error dynamics together with periodic disturbance compensation. By replacing the sign function in an attracting law with the saturation function, a repetitive controller is designed, where the chattering problem is avoided and the periodic disturbances can be rejected completely. The steady-state error band, absolute attractive layer and the monotone decreasing region of the error dynamics are defined, and the bounds are derived in details, for characterizing the closed-loop tracking performance with respect to control parameters. The proposed approach is of the equally important feature of the reaching law method, i.e., the ease and efficiency of obtaining the control law. With a CVCF PWM inverter as an illustrative example, both numerical and experimental results are presented to verify effectiveness of the proposed control scheme.