P·SPR·D control design via LMI for linear MIMO systems and its extension to adaptive control

Abstract

This paper concerns with P·SPR·D control for set-point servo problem of linear MIMO systems and its extension to adaptive control. The P·SPR·D control is a structured controller introducing a SPR (strict positive real) element instead of I element for PID control. The purpose is to design a P·SPR·D controller for aysmptotical stabilization and to adjust P, SPR, D gain matrices for the improvement of control performances. We make stability analysis of the P·SPR·D control via LMI, based on Lyapunov's direct method. We extend the P·SPR·D control to adaptive P·SPR·D control in the case where plant parameters change. Namely, we make an effort to stabilize the closed-loop system and to improve convergence speed to the desired equilibrium by adding an adaptive control mode with a time-varying gain matrix to the usual P·SPR·D controller. Consequently the closed-loop system keeps asymptotical stability against unknown plant-parameter changes. For the adaptive P·SPR·D control we propose, it is not necessary to assume the minimum phase property of the plant. The P·SPR·D control can be modified to P·SPR·D+I control for improving the steady state performance (an off-set).