Optimal sliding mode preview repetitive control for continuous-time nonlinear systems

In this paper, the problem of sliding mode preview repetitive control (SMPRC) for continuous-time nonlinear systems is proposed. First, an augmented delay system is constructed, in which the output of the modified repetitive controller is taken as a part of the augmented state vector. The augmented delay system is then transformed into the controllable canonical form by using state and linear transformations. To introduce preview compensation, a virtual optimal preview control (PC) law is designed for the uncontrollable subsystem. Next, a sliding mode control (SMC) law is cooperated with the virtual optimal PC law to ensure the robustness of the overall system in the presence of uncertainties and external disturbances. Stability of the proposed controller is also proved. Finally, the numerical simulation results demonstrate the effectiveness of the proposed method.Abbreviations: LQR: linear quadratic regulator; MRC: modified repetitive control; PC:preview control; PRC: preview repetitive control; RC: repetitive control; SFC: statefeedback control; SMC: sliding mode control; SMPRC: sliding mode preview repetitivecontrol.