Design and performance evaluation of a novel fractional order filtered PI controller for fractional order time delay systems

This study introduces an innovative algorithm for designing a PI controller filtered with fractional-order derivatives or integrals. The algorithm is applied to two distinct models of fractional-order time delay systems. A new reference model is proposed, utilising a unity feedback structure and incorporating a fractional-order time-delayed Bode transfer function in the forward path. The parameters of this proposed reference model are determined based on the specified phase margin and gain margin requirements. Before solving the design problem, the stability analysis of the proposed reference model is analysed through a theorem. Next, the four nonlinear equations with four unknown parameters are formulated and a solution method is provided in this study. By employing the recently introduced reference model, a robust fractional-order controller is formulated. The effectiveness of this robust controller is validated through simulations that employ various phase and gain margin specifications and through the existing controllers in the literature.