On the Stabilizing PID Controllers for Integral Processes

In this note, we show how to determine the set of stabilizing parameters of a proportional-integral-derivative controller for an integrator plus dead time process. In particular, by exploiting a version of the Hermite-Biehler theorem applicable to quasipolynomals, the admissible range of the proportional gain is computed first. Then, for each value of the proportional gain in that range, the set of stabilizing values of the integral and derivative gain are found. It is shown that the procedure is greatly simplified with respect to the case of a second-order integral process with dead time.