A new method for designing analytical non-diagonal PID controller for two-by-two processes with time delays

A new analytical non-diagonal PID controller design method is proposed for industrial and chemical two-by-two 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 the controller is derived inversely from the proposed closed-loop transfer function. Pade approximation is then utilized to reproduce the decoupling controller in the form of a non-diagonal PID controller for implementation. Tuning rules for the proposed controller are developed based on system robust stability analysis. A simulation example is included to show the superiority of the proposed method