Digital redesign of uncertain interval systems based on time-response resemblance via particle swarm optimization

In this paper, a particle swarm optimization (PSO) based approach is proposed to derive an optimal digital controller for redesigned digital systems having an interval plant based on time-response resemblance of the closed-loop systems. Because of difficulties in obtaining time-response envelopes for interval systems, the design problem is formulated as an optimization problem of a cost function in terms of aggregated deviation between the step responses corresponding to extremal energies of the redesigned digital system and those of their continuous counterpart. A proposed evolutionary framework incorporating three PSOs is subsequently presented to minimize the cost function to derive an optimal set of parameters for the digital controller, so that step response sequences corresponding to the extremal sequence energy of the redesigned digital system suitably approximate those of their continuous counterpart under the perturbation of the uncertain plant parameters. Computer simulations have shown that redesigned digital systems incorporating the PSO-derived digital controllers have better system performance than those using conventional open-loop discretization methods.