A design method for robust and quadratic optimal MIMO linear controllers

In this paper a design method was formulated to deal with robustness and performance specifications for any MIMO linear controller. The controller tuning procedure was expressed as an optimization problem in which novel time-domain integrals of the weighted squared error and weighted squared control signals, with initial state zero and inputs not necessarily defined over the Lebesgue normed space (L2+), were minimized. The control robustness is achieved by constraining the minimization such that the maximum complex/real ratio of the closed-loop control system eigenvalues was lower than one. The proposed tuning method was applied in the design of linear controllers with PID structure for a CSTR with disturbance noise and a nonlinear CSTR with control signal saturations, both reported in literature. The results show that the proposed control systems surpass the performance and robustness characteristics of the controllers designed with other reported methods.