New results on the robust stability of PID controllers with gain and phase margins for UFOPTD processes

This paper considers the problem of determining all the robust PID (proportional-integral-derivative) controllers in terms of the gain and phase margins (GPM) for open-loop unstable first order plus time delay (UFOPTD) processes. It is the first time that the feasible ranges of the GPM specifications provided by a PID controller are given for UFOPTD processes. A gain and phase margin tester is used to modify the original model, and the ranges of the margin specifications are derived such that the modified model can be stabilized by a stabilizing PID controller based on Hermite-Biehlers Theorem. Furthermore, we obtain all the controllers satisfying a given margin specification. Simulation studies show how to use the results to design a robust PID controller.