Optimal model-following control of non-minimum-phase singular perturbation systems

In order to overcome part of the poor properties in nonminimum-phase (NMP) singularly perturbed systems, an optimal control mechanism based on model-following control scheme is proposed. The major results of this paper are: (1) the zeros of both original system and subsystems are proved to be in the same side of complex plane if singular parameter ε is sufficiently small and in consequence some NMP properties of the original system are retained in subsystems; (2) the optimal control which is analyzed based on the slow subsystem can easily be computed by a modified Runge-Kutta method; (3) sufficient conditions for the existence of optimal model-following control (MFC) is proposed and is proved mathematically; (4) some poor properties of NMP systems are upgraded by proper choice of the optimal criterion. Simulation results show that both slow subsystem and original system behave very close to the prespecified model under the proposed control mechanism