Fractional order active disturbance rejection control design for non-integer order plus time delay models

This paper proposes a time-delayed fractional order active disturbance rejection control (TD-FADRC) strategy to address a class of time-delayed fractional order systems represented by non-integer order plus time delay (NIOPTD) models. To accurately estimate the fractional order states, the fractional order extended state observer (FESO) is utilized with introducing an artificial delay block to synchronize inputs. The studied model and its corresponding observer are treated as a holistic plant, based on which several types of fractional order proportional-integral-derivative (FPID) with constrained order are employed as feedback controllers. By unfolding the resulting open-loop plant in the frequency domain, the controller gains can be derived explicitly from the typical robustness metrics, that is, the phase margin and gain crossover frequency. The performance, robustness, and delay issue are consequently all concerned. To guarantee the closed-loop stability, the controller gains under a given observer bandwidth are limited within a bounded region mapped by the D-decomposition method. Through representative simulations, the merits of the proposed strategy for such models are revealed.