This paper studies the tracking control of periodic discrete-time system. A free-chatting attracking law and the methods of compensating disturbance are presented for designing the repetitive controller. The attracking law implanted in the controller drives the tracking error to origin monotonously in the finite time. The disturbance not eliminated by the repetitive controller is restricted in the upper bound of compensate errors. The steady state error band illustrates that the system is robust steady for the convergence of attracking law. Both simulation and experiments on the servo motor demonstrate the effectiveness of the repetitive controller design work.