Repetitive control for a class of nonlinear systems

A repetitive control scheme which is applicable to a class of nonlinear systems with periodic reference signals is proposed. The nonlinear terms in the systems are assumed to be polynomially bounded. Sliding mode control is applied to an augmented system in which an integrator and a repetitive controller are combined in order to obtain a linear input-output relation. The stability condition for the repetitive control system realized by the proposed method is derived. It is shown that this system satisfies the internal model principle for a given frequency bandwidth. The frequency bandwidth is given by the stability condition. An illustrative example is given.