Experimental bifurcation control of a parametric pendulum

Aline S. de Paula, Marcelo A. Savi, Vahid Vaziri, Ekaterina Pavlovskaia, Marian Wiercigroch

Research output: Contribution to journalArticle

5 Citations (Scopus)
3 Downloads (Pure)

Abstract

The aim of the study is to maintain the desired period-1 rotation of the parametric pendulum over a wide range of the excitation parameters. Here the Time-Delayed Feedback control method is employed to suppress those bifurcations, which lead to loss of stability of the desired rotational motion. First, the nonlinear dynamic analysis is carried out numerically for the system without control. Specifically, bifurcation diagrams and basins of attractions are computed showing co-existence of oscillatory and rotary attractors. Then numerical bifurcation diagrams are experimentally validated for a typical set of the system parameters giving undesired bifurcations. Finally, the control has been implemented and investigated both numerically and experimentally showing a good qualitative agreement.
Original languageEnglish
Pages (from-to)2256-2268
Number of pages14
JournalJournal of Vibration and Control
Volume23
Issue number14
Early online date1 Nov 2015
DOIs
Publication statusPublished - 1 Aug 2017

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Pendulums
Dynamic analysis
Feedback control
Control systems

Keywords

  • parametric pendulum
  • time-delayed feedback method
  • bifurcation control
  • experimental dynamics

Cite this

Experimental bifurcation control of a parametric pendulum. / de Paula, Aline S.; Savi, Marcelo A.; Vaziri, Vahid; Pavlovskaia, Ekaterina; Wiercigroch, Marian.

In: Journal of Vibration and Control, Vol. 23, No. 14, 01.08.2017, p. 2256-2268.

Research output: Contribution to journalArticle

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note = "Acknowledgments The authors would like to thank the Brazilian Research Agencies CNPq, CAPES and FAPERJ and through the INCT-EIE (National Institute of Science and Technology - Smart Structures in Engineering) the CNPq and FAPEMIG for their support. The Air Force Office of Scientific Research (AFOSR) is also acknowledged. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the support of ANP, FINEP and MCT through PRH-PB/MCT, and also the support of Petrobras. The authors also would like to thank the Brazilian Research Agencies CNPq, CAPES and FAPERJ and through the INCT-EIE (National Institute of Science and Technology - Smart Structures in Engineering) the CNPq and FAPEMIG for their support. The Air Force Office of Scientific Research (AFOSR) is also acknowledged.",
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AB - The aim of the study is to maintain the desired period-1 rotation of the parametric pendulum over a wide range of the excitation parameters. Here the Time-Delayed Feedback control method is employed to suppress those bifurcations, which lead to loss of stability of the desired rotational motion. First, the nonlinear dynamic analysis is carried out numerically for the system without control. Specifically, bifurcation diagrams and basins of attractions are computed showing co-existence of oscillatory and rotary attractors. Then numerical bifurcation diagrams are experimentally validated for a typical set of the system parameters giving undesired bifurcations. Finally, the control has been implemented and investigated both numerically and experimentally showing a good qualitative agreement.

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