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

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).