Analytical decoupling PI/PID controller design for two-by-two processes with time delays

An analytical non-diagonal PI/PID controller design method is proposed for two-by-two (TITO) processes with time delays. By extending the concept of coupling matrix for uncertain multivariable delay-free processes to TITO processes with time delays, the relation between the non-diagonal and the diagonal elements of decoupling controller is determined, and thus, the realisable optimal closed-loop transfer function can be intuitively identified. The decoupling controller is derived inversely from the proposed closed-loop transfer function. Pade approximation is then utilised to reproduce the decoupling controller in the form of a non-diagonal PI/PID controller for implementation. Tuning rules for the proposed controller are developed based on system robust stability analysis. Simulation examples are included to show the superiority of the proposed method.