Fractional‐order active disturbance rejection repetitive control for fractional‐order systems

Abstract This paper investigates the problem of fractional‐order active disturbance rejection repetitive control (FADRRC) for a class of fractional‐order systems with unknown external disturbances. The proposed controller enhances the robustness and tracking performance of the classical active disturbance rejection control, especially for the periodic reference signals. A fractional‐order extended state observer (FESO) is first incorporated into the repetitive controller to estimate both the fractional‐order system state and the unknown external disturbances. Next, the linear bandwidth‐parameterization method is used to tune the parameters of both the controller gain and the gain of the observer. Then, the design problem of the FADRRC law is transformed into the stability problem of the fractional‐order system. Sufficient stability conditions are derived in terms of the small gain theorem. Finally, numerical simulation results demonstrate the effectiveness of the proposed method.