Optimal H2 IMC based PID tuning rules for unstable time delay processes

Many PID tuning rules are available for unstable first order plus time delay process. However, most of them are complex. In this work, optimal H
₂
principles are used along with internal model control (IMC) to develop simple tuning rules for a PID controller. The tuning rules are developed for different time delay to time constant ratios. Maximum sensitivity (M
_s
) is used for the selection of the IMC tuning parameter. Different examples are considered to compare the closed loop performances for set point tracking and disturbance rejection. Robustness of the proposed design is also carried out under perturbations in the process parameters. It is observed that the present tuning rules provide improved performances when compared to recently reported methods in the literature.