Advanced IMC-PID controller design for the disturbance rejection of first order plus time delay processes

A new analytical method for a proportional-integral-derivative (PID) controller cascaded with a lead/lag filter based on the basis of the renowned internal model control (IMC) theory is proposed for the first-order plus dead time (FOPDT), the integrator plus dead time (IPDT), and the unstable FOPDT processes. Analytical tuning rules for the PID filter controller are derived in the transparent way for enhancing the disturbance rejection. A two degree of freedom (2DOF) control scheme is utilized to cope with both the regulatory and servo problems in a simple manner. Several illustrative examples are conducted for a broad class of time-delay processes and the simulation results demonstrate that the proposed method affords better performances for both the disturbance rejection and set-point tracking in compared with those of recently well-known design methods, since the controllers in the simulation study are all tuned to have the same degree of robustne ss in terms of the maximum sensitivity. To demonstrate the robustness of the controllers, the worst-case model mismatch is introduced by inserting perturbation uncertainty in all process parameters simultaneously. The resulting PID characteristics confirm that the proposed controllers hold greater robustness against perturbation uncertainty.