Analytical two-degrees-of-freedom (2-DOF) decoupling control scheme for multiple-input-multiple-output (MIMO) processes with time delays

A two-degrees-of-freedom (2-DOF) decoupling control scheme is proposed for multiple-input-multiple-output (MIMO) processes with time delays. The set-point response and load-disturbance response of each process output can be separately regulated and optimized online. The two respective controller matrices for set-point tracking and load-disturbance rejection are analytically derived based on the H-2 optimal performance specification and rational transfer function approximation. A simplified stability condition is given to check the resulting control system stability, together with a graphical approach, in terms of the multivariable spectral radius stability criterion, to evaluate the robust stability of the control system in the presence of the process additive and multiplicative uncertainties. Correspondingly, an on-line tuning rule for the adjustable parameters of the two controller matrices is given to accommodate the unmodeled process dynamics. Finally, illustrative examples are given to demonstrate the merits of the proposed 2-DOF decoupling control scheme