Enforcing synchronization in oscillators with Huygens’ coupling via feed-forward control

J. Pena Ramirez (Corresponding author), H. Nijmeijer

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
36 Downloads (Pure)


This paper considers the problem of synchronizing a pair of oscillators with Huygens’ coupling to a desired periodic trajectory, by using feed-forward control. Two particular examples are considered: a modified version of the classical Huygens’ system of pendulum clocks coupled through a common bar and a pair of self-sustained mass–spring–damper oscillators mounted on a suspended bar. For both cases, it is demonstrated that if the coupling bar is excited by a suitably designed feed-forward control, then it is possible to indirectly force the oscillators to track a desired periodic trajectory. Additionally, sufficient and necessary conditions for the stability of the desired synchronous solution are derived by using the Poincaré method of perturbation and a numerical study is conducted in order to illustrate the theoretical findings. Ultimately, it is demonstrated that the proposed feed-forward control induces the desired synchronous motion provided that, besides the coupling bar, there exists a diffusive coupling between the oscillators and the intrinsic parameters of the system satisfy certain constraints.

Original languageEnglish
Pages (from-to)3009-3023
Number of pages15
JournalNonlinear Dynamics
Issue number4
Early online date22 Jun 2019
Publication statusPublished - 1 Dec 2019


  • Feed-forward control
  • Huygens’ coupling
  • Self-sustained oscillators
  • Synchronization


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