Hopf bifurcations in time-delayed nonlinear feedback control systems

Author

Moiola, Jorge L. ; Chen, Guanrong

Author_Institution

Dept. de Ingeniera Electrica, Univ. Nacional del Sur, Bahia Blanca, Argentina

Volume

1

fYear

1995

fDate

13-15 Dec 1995

Firstpage

942

Abstract

The Hopf bifurcation in a time-delayed nonlinear closed-loop control system is studied, where the nonlinear system has a linear dynamic plant represented by a feedforward transfer function and a nonlinear feedback controller represented by a Taylor series about an equilibrium operating point. The time delays occurred in the system are contained not only in the linear plant but also in the nonlinear feedback controller. The effective harmonic balance method is modified and applied to calculating the amplitude and frequency of the periodic solution emerging from the Hopf bifurcation of the dynamic system. Some new formulas containing up to an eighth-order harmonic balance approximation are derived, and two interesting examples are analyzed using the new results

Keywords

approximation theory; bifurcation; closed loop systems; delay systems; harmonic analysis; nonlinear control systems; nonlinear differential equations; series (mathematics); transfer functions; Hopf bifurcations; Taylor series; closed-loop control system; dynamic system; equilibrium operating point; feedforward transfer function; harmonic balance approximation; nonlinear differential equations; nonlinear feedback control systems; time-delayed systems; Adaptive control; Bifurcation; Control systems; Feedback control; Linear feedback control systems; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Taylor series; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.479106

Filename

479106