Digital redesign of uncertain interval systems via a hybrid particle swarm optimiser

Abstract

In this paper, a hybrid optimiser incorporating particle swarm optimisation (PSO) and an enhanced NM simplex search method is proposed to derive an optimal digital controller for uncertain interval systems having an interval plant based on frequency-response resemblance. By combining the uncertain plant and controller, extremal systems for the redesigned digital system and its continuous counterpart can be obtained as the basis for comparison. The design problem is then formulated as an optimisation problem of an aggregated error function in terms of frequency-response deviation between the redesigned digital system and its continuous counterpart, and subsequently optimised by the proposed optimiser to obtain an optimal set of parameters for the digital controller. Thanks to the performance of the proposed hybrid optimiser, frequency envelope of the redesigned digital system using the digital controller evolutionarily derived by the proposed approach bare a better resemblance to its continuous-time counterpart in comparison to those obtained using existing open-loop discretisation methods.