Multi-loop PI/PID controllers design for disturbance rejection based on non-parametric effective model and non-convex optimisation

In this study, the authors address the design of the multi-loop controllers for multi-input and multi-output (MIMO) processes for disturbance rejection. Three types of disturbance rejection are analysed, and they demonstrate that those disturbance responses are directly related to the integral terms of the controllers. A concept of non-parametric effective model is introduced here to decompose a MIMO control system into several equivalent single-input and single-output control systems. Based on the effective model in each loop, a non-convex optimisation problem is established to obtain the optimal controller parameters with certain robustness indices. Considering the drawbacks of using random search algorithm, they develop a numerical algorithm to solve this non-convex optimisation problem. Simulation studies demonstrate that the proposed method improves the disturbance rejection compared with other decentralised controllers.