New results on the synthesis of PID controllers Academic Article uri icon


  • This paper considers the problem of stabilizing a first-order plant with dead-time using a proportional-integral-derivative (PID) controller. Using a version of the Hermite-Biehler Theorem applicable to quasipolynomials, the complete set of stabilizing PID parameters is determined for both open-loop stable and unstable plants. The range of admissible proportional gains is first determined in closed form. For each proportional gain in this range the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid, a triangle or a quadrilateral. For the case of an open-loop unstable plant, a necessary and sufficient condition on the time delay is determined for the existence of stabilizing PID controllers.

published proceedings


altmetric score

  • 3

author list (cited authors)

  • Silva, G. J., Datta, A., & Bhattacharyya, S. P.

citation count

  • 339

complete list of authors

  • Silva, GJ||Datta, A||Bhattacharyya, SP

publication date

  • February 2002