Multi-loop PI controller design based on the direct synthesis for interacting multi-time delay processes

In this article, a new analytical method based on the direct synthesis approach is proposed for the design of a multi-loop proportional-integral (PI) controller. The proposed design method is aimed at achieving the desired closed-loop response for multiple-input, multiple-output (MIMO) processes with multiple time delays. The ideal multi-loop controller is firstly designed in terms of the relative gain and desired closed-loop transfer function. Then, the standard multi-loop PI controller is obtained by approximating the ideal multi-loop controller using the Maclaurin series expansion. The simulation study demonstrates the effectiveness of the proposed method for the design of multi-loop PI controllers. The multi-loop PI controller designed by the proposed method shows a fast, well-balanced, and robust response with the minimum integral absolute error (IAE).