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 journalArticlepeer-review

3 Citations (Scopus)
5 Downloads (Pure)


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 languageEnglish
Article number133587
Number of pages14
JournalPhysica. D, Nonlinear Phenomena
Early online date22 Nov 2022
Publication statusPublished - 1 Jan 2023

Bibliographical note

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.


  • Nonsmooth dynamics
  • nonlinear control
  • multi-stability
  • dalayed systems


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