Hopf bifurcation control for some nonlinear torsional vibration system with delayed feedbacks

Torsional vibration generally causes serious instability and great damage in many rotating machinery. Hopf bifurcation control for some nonlinear torsional vibration system with delayed feedbacks is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equa...

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Bibliographic Details
Published inProceedings of the 31st Chinese Control Conference pp. 402 - 407
Main Authors Zhang Wenming, Wang Bohua, Li Haibin, He Minjia, Liu Shuang
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2012
Subjects
Bifurcation
Delay
Hopf bifurcation
limit cycle
Limit-cycles
Mathematical model
Stability analysis
time delays feedback
torsional vibration
Vibrations
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Summary:Torsional vibration generally causes serious instability and great damage in many rotating machinery. Hopf bifurcation control for some nonlinear torsional vibration system with delayed feedbacks is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is established, and a nonlinear time-delayed feedback controller is proposed. Under the condition of primary resonance, perturbation analysis of the controlled system is carried out with the method of multiple scales. The influence of time delays on Hopf bifurcation and limit cycle in torsional vibration system is studied. The stability conditions and amplitude formula of limit cycle are given. Finally, numerical simulations are performed to verify the analytical results. The conclusion can provide theoretical reference for further research on more complexed mechanical drive system.
ISBN:1467325813
9781467325813
ISSN:1934-1768