Hopf bifurcations in time-delayed nonlinear feedback control systems

Jorge L. Moiola; Guanrong Chen

doi:10.1109/CDC.1995.479106

Hopf bifurcations in time-delayed nonlinear feedback control systems

Jorge L. Moiola
, Guanrong Chen

Research output: Journal Publications and Reviews › RGC 22 - Publication in policy or professional journal

7 Citations (Scopus)

Abstract

The Hopf bifurcation in a time-delayed nonlinear closed-loop control systems is studied, where the nonlinear system has a linear dynamic plant represented by a feed-forward 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.

Original language	English
Pages (from-to)	946-948
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	1
DOIs	https://doi.org/10.1109/CDC.1995.479106
Publication status	Published - 1995
Externally published	Yes
Event	Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA Duration: 13 Dec 1995 → 15 Dec 1995

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title = "Hopf bifurcations in time-delayed nonlinear feedback control systems",

abstract = "The Hopf bifurcation in a time-delayed nonlinear closed-loop control systems is studied, where the nonlinear system has a linear dynamic plant represented by a feed-forward 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.",

author = "Moiola, \{Jorge L.\} and Guanrong Chen",

year = "1995",

doi = "10.1109/CDC.1995.479106",

language = "English",

volume = "1",

pages = "946--948",

journal = "Proceedings of the IEEE Conference on Decision and Control",

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note = "Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) ; Conference date: 13-12-1995 Through 15-12-1995",

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TY - JOUR

T1 - Hopf bifurcations in time-delayed nonlinear feedback control systems

AU - Moiola, Jorge L.

AU - Chen, Guanrong

PY - 1995

Y1 - 1995

N2 - The Hopf bifurcation in a time-delayed nonlinear closed-loop control systems is studied, where the nonlinear system has a linear dynamic plant represented by a feed-forward 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.

AB - The Hopf bifurcation in a time-delayed nonlinear closed-loop control systems is studied, where the nonlinear system has a linear dynamic plant represented by a feed-forward 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.

UR - https://www.scopus.com/pages/publications/0029546791

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0029546791&origin=recordpage

U2 - 10.1109/CDC.1995.479106

DO - 10.1109/CDC.1995.479106

M3 - RGC 22 - Publication in policy or professional journal

SN - 0191-2216

VL - 1

SP - 946

EP - 948

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4)

Y2 - 13 December 1995 through 15 December 1995

ER -

Hopf bifurcations in time-delayed nonlinear feedback control systems

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