P⋅SPR⋅D and P⋅SPR⋅D⋅I control for linear multi-variable systems —Stabilization based on high gain output feedback—

This paper is concerned with a set-point servo problem for MIMO systems with PldrSPRldrD control. The PldrSPRldrD control is constructed by introducing a SPR (strict positive real) element instead of the I element in PID control. The purpose is to design a PldrSPRldrD controller for asymptotic stabilization and to adjust P, SPR, D parameter matrices for improving convergence speed of responses under guaranteeing the stability. In our method, we consider a certain hypothetical system derived from the closed-loop system with PldrSPRldrD control in order to apply high gain output feedback. Then the P, SPR, D parameter matrices are adjusted by making zero dynamics of the hypothetical system asymptotically stable and performing the high gain output feedback. The proposed method is fundamentally based on the high gain output feedback theorem. The PldrSPRldrD control is extended to PldrSPRldrDldrI control for improving steady state performance. The effectiveness of the method is confirmed by simulation results for unstable MIMO systems.