Research Unit on Systems Analysis and Control, National School of Engineering of Tunis, BP, 37, Le Belvédère, 1002 Tunis, Tunisia
Copyright © 2009 Rihem Farkh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The problem of stabilizing a second-order delay system using classical proportional-integral-derivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasipolynomials, is used to seek the set of complete stabilizing PID parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid or a triangle.