Determination of stabilizing feedback gains for second-order systems with time delay

Author

Silva, Guillermo J. ; Datta, Aniruddha ; Bhattacharyya, S.P.

Author_Institution

Dept. of Electr. Eng., Texas A&M Univ., College Station, TX, USA

Volume

6

fYear

2001

fDate

2001

Firstpage

4658

Abstract

In this paper we consider the problem of stabilizing a second-order plant with dead-time using a constant gain controller. Due to the presence of the time delay, the number of roots of the characteristic equation of the closed-loop system is infinite, making the problem posed in this paper a difficult one. A complete analytical characterization of all stabilizing feedback gains is provided using a version of the Hermite-Biehler Theorem applicable to quasipolynomials. Both open-loop stable and unstable plants are considered. The results reported in this paper will serve as a stepping stone for tackling the more complicated cases of stabilization using a PI or a PID controller

Keywords

closed loop systems; control system analysis; delays; feedback; gain control; polynomials; stability; Hermite-Biehler theorem; PI controller; closed-loop system; constant gain controller; dead-time; open-loop stable plants; open-loop unstable plants; quasipolynomials; second order plant stabilisation; stabilizing feedback gains; stepping stone PID controller; Delay effects; Delay systems; Equations; Feedback; Mathematical model; Open loop systems; Parametric statistics; Process control; Stability analysis; Three-term control;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2001. Proceedings of the 2001

Conference_Location

Arlington, VA

ISSN

0743-1619

Print_ISBN

0-7803-6495-3

Type

conf

DOI

10.1109/ACC.2001.945715

Filename

945715