Switching between periodic orbits in impact oscillator by time-delayed feedback methods

Dimitri Costa; Vahid Vaziri; Ekaterina Pavlovskaia; Marcelo A. Savi; Marian Wiercigroch

doi:10.1016/j.physd.2022.133587

Switching between periodic orbits in impact oscillator by time-delayed feedback methods

Dimitri Costa^* (Corresponding Author), Vahid Vaziri, Ekaterina Pavlovskaia, Marcelo A. Savi, Marian Wiercigroch

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

An ability to exchange between different attractors can bring adaptability and new functionalities to an engineering system. While nonlinear controllers are widely used to stabilize on a preferred orbit, there is only a few which can exchange back and forth between two or more stable periodic responses.
This work proposes a new variation of the original Time-Delayed Feedback (TDF) control method capable to effectively switch back and forth between periodic orbits having only a limited knowledge of the system dynamics. The stable or unstable periodic responses of the system that are inside or outside a chaotic attractor can be targeted. The proposed control method named here as the
Fractional Time-Delayed Feedback Control (FTDF) is tested numerically and experimentally using a newly developed impact oscillator rig. Various responses including impacting and non-impacting orbits, high period attractors and chaos are considered. The main advantages of the FTDF over the TDF are presented by showcase scenarios where the TDF alone cannot safely perform the exchange
between orbits.

Original language	English
Article number	133587
Number of pages	14
Journal	Physica. D, Nonlinear Phenomena
Volume	443
Early online date	22 Nov 2022
DOIs	https://doi.org/10.1016/j.physd.2022.133587
Publication status	Published - 1 Jan 2023

Keywords

Nonsmooth dynamics
nonlinear control
multi-stability
dalayed systems

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10.1016/j.physd.2022.133587Licence: CC BY-NC-ND

Costa_etal_PDNP_Switching_Between_Periodic_VoR
© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Final published version, 5.54 MBLicence: CC BY-NC-ND

Cite this

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title = "Switching between periodic orbits in impact oscillator by time-delayed feedback methods",

abstract = "An ability to exchange between different attractors can bring adaptability and new functionalities to an engineering system. While nonlinear controllers are widely used to stabilize on a preferred orbit, there is only a few which can exchange back and forth between two or more stable periodic responses.This work proposes a new variation of the original Time-Delayed Feedback (TDF) control method capable to effectively switch back and forth between periodic orbits having only a limited knowledge of the system dynamics. The stable or unstable periodic responses of the system that are inside or outside a chaotic attractor can be targeted. The proposed control method named here as theFractional Time-Delayed Feedback Control (FTDF) is tested numerically and experimentally using a newly developed impact oscillator rig. Various responses including impacting and non-impacting orbits, high period attractors and chaos are considered. The main advantages of the FTDF over the TDF are presented by showcase scenarios where the TDF alone cannot safely perform the exchangebetween orbits.",

keywords = "Nonsmooth dynamics, nonlinear control, multi-stability, dalayed systems",

author = "Dimitri Costa and Vahid Vaziri and Ekaterina Pavlovskaia and Savi, {Marcelo A.} and Marian Wiercigroch",

note = "Acknowledgements The authors also acknowledge the financial support from Coordena{\c c}{\~a}o de Aperfei{\c c}oamento do Pessoal de Nivel Superior (CAPES), under the Grant Number 88881.189487/2018-01 and FAPERJ. ",

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AU - Costa, Dimitri

AU - Vaziri, Vahid

AU - Pavlovskaia, Ekaterina

AU - Savi, Marcelo A.

AU - Wiercigroch, Marian

N1 - Acknowledgements The authors also acknowledge the financial support from Coordenação de Aperfeiçoamento do Pessoal de Nivel Superior (CAPES), under the Grant Number 88881.189487/2018-01 and FAPERJ.

PY - 2023/1/1

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N2 - An ability to exchange between different attractors can bring adaptability and new functionalities to an engineering system. While nonlinear controllers are widely used to stabilize on a preferred orbit, there is only a few which can exchange back and forth between two or more stable periodic responses.This work proposes a new variation of the original Time-Delayed Feedback (TDF) control method capable to effectively switch back and forth between periodic orbits having only a limited knowledge of the system dynamics. The stable or unstable periodic responses of the system that are inside or outside a chaotic attractor can be targeted. The proposed control method named here as theFractional Time-Delayed Feedback Control (FTDF) is tested numerically and experimentally using a newly developed impact oscillator rig. Various responses including impacting and non-impacting orbits, high period attractors and chaos are considered. The main advantages of the FTDF over the TDF are presented by showcase scenarios where the TDF alone cannot safely perform the exchangebetween orbits.

AB - An ability to exchange between different attractors can bring adaptability and new functionalities to an engineering system. While nonlinear controllers are widely used to stabilize on a preferred orbit, there is only a few which can exchange back and forth between two or more stable periodic responses.This work proposes a new variation of the original Time-Delayed Feedback (TDF) control method capable to effectively switch back and forth between periodic orbits having only a limited knowledge of the system dynamics. The stable or unstable periodic responses of the system that are inside or outside a chaotic attractor can be targeted. The proposed control method named here as theFractional Time-Delayed Feedback Control (FTDF) is tested numerically and experimentally using a newly developed impact oscillator rig. Various responses including impacting and non-impacting orbits, high period attractors and chaos are considered. The main advantages of the FTDF over the TDF are presented by showcase scenarios where the TDF alone cannot safely perform the exchangebetween orbits.

KW - Nonsmooth dynamics

KW - nonlinear control

KW - multi-stability

KW - dalayed systems

U2 - 10.1016/j.physd.2022.133587

DO - 10.1016/j.physd.2022.133587

M3 - Article

VL - 443

JO - Physica. D, Nonlinear Phenomena

JF - Physica. D, Nonlinear Phenomena

SN - 0167-2789

M1 - 133587

ER -

Switching between periodic orbits in impact oscillator by time-delayed feedback methods

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