Active disturbance rejection repetitive control for fractional-order time-delay systems with unknown disturbance†

In this paper, the problem of fractional-order active disturbance rejection repetitive control (FADRRC) for a class of fractional-order time-delay systems is investigated. First, a fractional-order extended state observer (FESO) is used to estimate the internal dynamics and the unknown external disturbances. Next, the linear bandwidth-parameterization method is applied to tune the gains of both the the observer and controlle. To reduce the impact of time-delay, a low-pass filter is added to the FESO. Then, the design problem of the FADRRC law is converted to the stability problem of the fractional-order system. Sufficient stability conditions are obtained by using the small gain theorem. Finally, numerical simulation results demonstrate the effectiveness of the proposed control method.