Design of extended simplified decoupling for multivariable processes with multiple time delays

In this paper, a simplified decoupling method is proposed for multivariable processes by introducing coefficient matching to obtain a stable, proper, and causal simplified decoupler. Accordingly, transfer functions of decoupled apparent processes can be expressed as a set of n equivalent independent processes and then derived as a ratio of the original open-loop transfer function to the diagonal element of the dynamic relative gain array. The proportional-integral/ proportional-integral derivative (PI/PID) controller is then directly employed to enhance the overall performance of the decoupling control system while avoiding difficulties arising from properties inherent to simplified decoupling. Some simulation studies are considered to demonstrate the simplicity and effectiveness of the proposed method.