Digital redesign of uncertain interval systems based on extremal gain/phase margins via a hybrid particle swarm optimizer

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