Implementation of Skogestad’s Internal Model Control Rule in Tuning Proportional-Integral Controllers for Two-Input and Two-Output Systems Considering Individual Controller Performance Trade-off

Abstract In industrial plants, tuning of decentralized Proportional-Integral-Derivative feedback (PID) controllers in Multiple-Input and Multiple-Output (MIMO) systems is a complex problem, due to input and output interactions, that must be done to ensure individual control objectives are met, while system being sufficiently robust. In this study, a two-input and two-output (TITO) PI controller tuning algorithm was developed considering controller performance prioritization given performance trade-offs, expressed as the novel Individual Controller Performance Trade-off Coefficient (ICPTC), and system robustness, expressed as sensitivity peaks from the generalized Nyquist stability plot. Simplified effective open-loop transfer functions (EOTFs) of the two input-output channels were derived and used along with Skogestad’s Internal Model Control (SIMC) to calculate PI controller gains. Extensive simulations using Wood-Berry (WB) and Vinante-Luyben (VL) distillation column models were made to observe how the sensitivity peaks behave across the simulations, which was then used as the basis of the developed tuning algorithm. A simplified tuning algorithm, which requires less information compared to the main algorithm, was also derived. A mapping algorithm was also created, allowing specific controller gains from other studies to be mapped to an equivalent set of controller gains in the algorithm’s search field. The effectiveness of the three algorithms were tested using Wardle-Wood distillation column (WW) and Xiong and Cai (XC) process models. It was demonstrated using the main algorithm that there is a trade-off between controller performances when ICPTC is varied, at different values of design sensitivity peaks between 1.96 to 4. The usefulness of the simplified tuning and mapping algorithms were also illustrated in the study. This study is potentially useful in tuning TITO PI controllers in industrial plants, where meeting individual control objectives while maintaining robustness is more important than optimizing overall control performance.