PID controller design with optimal robust performance for unstable first-order plus delay time processes

An optimal proportional-integral-derivative (PID) controller for unstable process was introduced in this work. Internal model control (IMC) could achieve robustness and dynamic performance for stable process, while determination the filter time λ was a problem as before, especially for unstable process. This work proposed a modified internal model control (MIMC) for unstable first-order plus delay time (UFOPDT) process, and the MIMC was realized by an equivalent PID controller. Analyzing the integral of absolute error (IAE) and the maximum sensitivity (Ms) of these control systems, here find that the traditional IMC could not have the optimal robustness or the optimal performance. A robust performance index using the IAE weighted by Ms was presented. With an empirical weighted factor of this index, the PID parameters were optimized and its fitting formula was obtained for UFOPDT processes. Simulation results show that the proposed PID control system has good dynamic performance and proper robustness.