Multi-loop PI/PID Controller Design Based on Direct Synthesis for Multivariable Systems

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