Modified IMC-PID controllers and generalised PID controllers for first-order plus dead-time processes

In this paper, we provide a theoretical basis for a modified IMC-PID controller and its associated set-point response and disturbance rejection tradeoff as presented in a recent conference. We show that, while the modified IMC-PID controller can achieve set-point response and disturbance rejection tradeoff, the nominal stability property of the resulting closed-loop system can no longer be guaranteed. We then present a generalised PID controller which not only allows set-point response and disturbance rejection tradeoff to be achieved, but also possesses a guaranteed closed-loop nominal stability property. We illustrate by two simulation examples how generalised PID controllers and their associated tuning procedure can be applied to control first-order plus dead-time processes.