Attracting-law-based discrete-time repetitive control

This paper presents a digital repetitive control design on the basis of attracting law (AL). A control law, together with the disturbance compensation, can be derived by applying the AL which includes a measure of disturbance-rejection. Chattering is alleviated by a sign-function continuous approximation technique. To characterize the closed-loop performance, the steady-state error band, absolute attractive layer and the monotone decreasing region of the error dynamics are derived. The proposed method has the similar feature to the reaching-law approach, i.e., the ease for the control design. Numerical simulation and experiment results are presented to verify the validity of the proposed method.