Integration of Active Disturbance Rejection and Repetitive Control for Fractional-Order Time-Delay Systems

In this paper, a fractional-order active disturbance rejection repetitive control (FADRRC) scheme is proposed for fractional-order time-delay systems. The unified control framework integrates a bandwidth-parameterized fractional extended state observer (FESO), modified repetitive control and a filtered Smith predictor. The FESO online estimates system states and lumped disturbances, the filtered Smith predictor compensates time-delay deviation to weaken sensitivity to model mismatch, and repetitive control eliminates steady-state error for periodic reference signals. By fractional frequency-domain stability theory and the small-gain theorem, two BIBO stability criteria for nominal and mismatched cases are derived, reformulating the controller design as a pole placement problem of fractional-order transfer functions. Numerical simulations on a fractional-order time-delay PMSM servo system verify that the proposed FADRRC possesses superior periodic tracking accuracy and disturbance rejection capability compared with existing ESO-RC and DOB-RC methods, which confirms the validity of the presented control strategy.