Experimental bifurcation control of a parametric pendulum

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

doi:10.1177/1077546315613237

Experimental bifurcation control of a parametric pendulum

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

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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 language	English
Pages (from-to)	2256-2268
Number of pages	14
Journal	Journal of Vibration and Control
Volume	23
Issue number	14
Early online date	1 Nov 2015
DOIs	https://doi.org/10.1177/1077546315613237
Publication status	Published - 1 Aug 2017

Keywords

parametric pendulum
time-delayed feedback method
bifurcation control
experimental dynamics

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Accepted Manuscript
Aline S De Paula, Marcelo A Savi, Vahid Vaziri, Ekaterina Pavlovskaia, Marian Wiercigroch, Experimental bifurcation control of a parametric pendulum, Journal of Vibration and Control 23(14) pp. 2256-2268. Copyright © The Author(s) 2015. Reprinted by permission of SAGE Publications.
Accepted author manuscript, 2.75 MBLicence: Unspecified

Ekaterina Pavlovskaia
- Engineering, Engineering - Head of School of Engineering, Personal Chair
- Centre for Applied Dynamics Research (CADR)
Person: Academic

Cite this

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title = "Experimental bifurcation control of a parametric pendulum",

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.",

keywords = "parametric pendulum, time-delayed feedback method, bifurcation control, experimental dynamics",

author = "{de Paula}, {Aline S.} and Savi, {Marcelo A.} and Vahid Vaziri and Ekaterina Pavlovskaia and Marian Wiercigroch",

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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doi = "10.1177/1077546315613237",

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T1 - Experimental bifurcation control of a parametric pendulum

AU - de Paula, Aline S.

AU - Savi, Marcelo A.

AU - Vaziri, Vahid

AU - Pavlovskaia, Ekaterina

AU - Wiercigroch, Marian

N1 - 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.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

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.

KW - parametric pendulum

KW - time-delayed feedback method

KW - bifurcation control

KW - experimental dynamics

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DO - 10.1177/1077546315613237

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JO - Journal of Vibration and Control

JF - Journal of Vibration and Control

SN - 1077-5463

IS - 14

ER -

Experimental bifurcation control of a parametric pendulum

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Ekaterina Pavlovskaia

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