Analytical Design of Optimal Robust Two-degree-of-freedom Controller for Unstable Processes with Time Delays

In this study, we analytically design a two-degrees-of-freedom (2-DoF) controller for unstable processes with time delays based on the internal model control (IMC) principle. We also propose an enhanced IMC filter to improve the robustness and output performance of the controller. Based on our analysis of the system's stability, robustness, and output performance, we propose a rule for selecting the optimal sensitivity function to achieve the best performance/robustness tradeoff. Finally, we formulate a method for controller tuning as a constraint optimization problem and propose an analytical tuning method. Simulation study results show the effectiveness of the proposed method.