PID controller design for first-order-plus-dead-time model via Hermite-Biehler theorem

This paper discusses PID stabilization of a first-order-plus-dead-time (FOPDT) process model using the stability framework of the Hermite-Biehler theorem. The FOPDT model approximates many processes in the chemical and petroleum industries. Using a PID controller and first-order Pade approximation for the transport delay, the Hermite-Biehler theorem allows one to analytically study the stability of the closed-loop system. We derive necessary and sufficient conditions for stability and develop an algorithm for selection of stabilizing feedback gains. The results show an infinite gain margin in the case of small delays, and an upper bound that is a function of plant parameters and can be easily computed, for large delays. Finally, the results of this paper can be extended to higher order plants.