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

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

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Uittreksel

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.

Originele taal-2Engels
Pagina's (van-tot)3009-3023
Aantal pagina's15
TijdschriftNonlinear Dynamics
Volume98
Nummer van het tijdschrift4
Vroegere onlinedatum22 jun 2019
DOI's
StatusGepubliceerd - 1 dec 2019

Vingerafdruk

Feedforward Control
Feedforward control
Synchronization
Periodic Trajectories
Trajectories
Pendulum
Pendulums
Clocks
Numerical Study
Perturbation
Necessary Conditions
Motion
Sufficient Conditions

Citeer dit

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Enforcing synchronization in oscillators with Huygens’ coupling via feed-forward control. / Pena Ramirez, J. (Corresponding author); Nijmeijer, H.

In: Nonlinear Dynamics, Vol. 98, Nr. 4, 01.12.2019, blz. 3009-3023.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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N2 - 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.

AB - 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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