Observer-based modified repetitive control for fractional-order non-linear systems with unknown disturbances

This study investigates the problem of observer-based modified repetitive control for a class of fractional-order non-linear systems in the presence of unknown external disturbances. An equivalent-input-disturbance estimator is incorporated into the controller block to compensate the unknown external disturbances. The main objective of this study is to design a modified repetitive controller for the addressed system such that the system output can exactly trace the given periodic reference signal by attenuating both periodic and aperiodic disturbances. To be precise, by employing the Lyapunov stability theory together with the linear matrix inequality approach, sufficient conditions that ensure the existence of such a controller are obtained. It is to be noted that the advantage of using equivalent-input-disturbance estimator in the controller design is that it can reject both periodic and aperiodic disturbance signals effectively without requiring any prior knowledge of them. Finally, two numerical simulation examples are provided to illustrate the effectiveness and applicability of the proposed control technique.