Predictor-based fractional disturbance rejection control for LTI fractional-order systems with input delay

In this paper, a predictor-based fractional disturbance rejection control (PFDRC) scheme is proposed for processes subject to input delay. The proposed scheme can be generally applied to open-loop stable, integrative, and unstable integer-order processes, but it can be particularly utilized for open-loop stable fractional-order systems. A closed-loop reference model is formulated based on Bode’s ideal transfer function. The primary control design objective is to enable the output of input-delay process to follow the closed-loop reference model. Towards this end, the closed-loop transfer function of the PFDRC must take the same structure as that of the reference model. Meanwhile, the adverse effects of the input delay must be mitigated. To meet the latter, a filtered Smith predictor (FSP) is employed to provide a prediction of delay-less output response. To address the former, process dynamics are treated as a common disturbance; then, a fractional-order extended state observer (FESO) is introduced to estimate the delay-less output response and also the total disturbance (i.e. external disturbance and system uncertainties). The PFDRC feedback controller is easily derived by the gain crossover frequency of Bode’s ideal transfer function which facilitates the tuning process. The convergence analysis of the FESO is carried out in terms of BIBO stability. The effectiveness of the proposed control scheme is verified through three illustrative examples from the literature.