Maximum sensitivity based analytical tuning rules for PID controllers for unstable dead time processes

In this paper, maximum sensitivity and internal model control (IMC) based proportional-integral-derivative (PID) controllers are designed for unstable first-order plus-dead-time (UFOPDT) processes. The designed controller parameters are functions of the UFOPDT model parameters and the IMC closed loop tuning parameter. The tuning parameter plays a vital role and determines the closed loop performance and robustness of the designed controller. Systematic guidelines are provided for selection of this tuning parameter based on maximum sensitivity. Analytical tuning rules are developed for the controller parameters for different time delay to time constant ratios with desired level of robustness. These controller settings allow the operator to deal with the closed-loop control system performance-robustness trade-off by specifying the robustness level (maximum sensitivity). Simulation studies have been carried out on various UFOPDT processes to explain the advantages of the proposed analysis.