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

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Abstract

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.

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Authors and Affiliations

  1. Center for Scientific Research and Higher Education at Ensenada, CONACYT-CICESE, Carretera Ensenada-Tijuana 3918, Zona Playitas, C.P. 22860, Ensenada, B.C., Mexico

    J. Pena Ramirez

  2. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    H. Nijmeijer

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  1. J. Pena Ramirez
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  2. H. Nijmeijer
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Pena Ramirez, J., Nijmeijer, H. Enforcing synchronization in oscillators with Huygens’ coupling via feed-forward control. Nonlinear Dyn 98, 3009–3023 (2019). https://doi.org/10.1007/s11071-019-05062-x

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