Independent design of multi-loop PI/PID controllers for interacting multivariable processes

The interactions between input/output variables are a common phenomenon and the main obstacle encountered in the design of multi-loop controllers for interacting multivariable processes. In this study, a novel method for the independent design of multi-loop PI/PID controllers is proposed. The idea of an effective open-loop transfer function (EOTF) is first introduced to decompose a multi-loop control system into a set of equivalent independent single loops. Using a model reduction technique, the EOTF is further approximated to the reduced-order form. Based on the corresponding EOTF model, the individual controller of each single loop is then independently designed by applying the internal model control (IMC)-based PID tuning approach for single-input/single-output (SISO) systems, while the main effects of the dynamic interactions are properly taken into account. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.