Fractional order active disturbance rejection control with the idea of cascaded fractional order integrator equivalence

This paper presents a fractional order (FO)-active disturbance rejection control (ADRC) with a FO extended state observer (FOESO) design. Applying this FOESO, a typical second order motion plant can be converted into a cascadedfractionalorderintegrator(1∕s2r;0<r<1) with considering all other dynamics and internal/external disturbances as totaldisturbances. Therefore, a single proportional controller which is not sensitive to system noise can realize a stable control system. According to the frequency characteristics of equivalent FO system model, the FO-ADRC control system is robust to systematic uncertain dynamics and disturbances. Furthermore, without differential action which is needed for the typical double integrator plant control, the proposed control system achieves good robustness to high-frequency noise. Simulation and experiments on PMSM speed servo system are performed, showing that the proposed FO-ADRC behaves better than integer order ADRC (IO-ADRC) and FOPI controller. This FO-ADRC methodology can be simply extended to general control plants.