Controlled synchronization: A Huygens' inspired approach

J. Pena Ramirez; A. Denasi; A. Rodriguez-Angeles; J. Alvarez Gallegos; H. Nijmeijer; K. Aihara

doi:10.3182/20140824-6-ZA-1003.01807

Controlled synchronization: A Huygens' inspired approach

J. Pena Ramirez, A. Denasi, A. Rodriguez-Angeles, J. Alvarez Gallegos, H. Nijmeijer, K. Aihara

Research output: Contribution to journal › Conference article › peer-review

3 Citations (Scopus)

Abstract

This paper considers synchronization as a control problem. In particular, a (robust) controller for achieving synchronization in pairs of second order nonlinear systems is designed. The design is inspired by the classical experiment on synchronization of pendulum clocks, as described by Christiaan Huygens. In the proposed control scheme, the systems do not interact directly but through an exogenous system. Ultimately, it is demonstrated that Huygens' controller, can be used to perform in-phase and anti-phase synchronized tasks, with the advantage that 'small' control gains are required. The stability of the closed-loop system is analyzed using perturbation theory and the proposed controller is experimentally validated on a pair of Cartesian robots.

Original language	English
Pages (from-to)	3098-3103
Number of pages	6
Journal	IFAC Proceedings Volumes
Volume	47
Issue number	3
DOIs	https://doi.org/10.3182/20140824-6-ZA-1003.01807
Publication status	Published - 2014
Event	19th World Congress of the International Federation of Automatic Control (IFAC 2014 World Congress) - Cape Town International Convention Centre, Cape Town, South Africa Duration: 24 Aug 2014 → 29 Aug 2014 Conference number: 19 http://www.ifac2014.org

Bibliographical note

Funding Information:
∗Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan (email: [email protected]) ∗∗Eindhoven University of Technology, P.O. Box 513 5600 MB Eindhoven, The Netherlands (email: [email protected]) ∗∗∗Research Center for Advanced Studies (Cinvestav-IPN), Mechatronics Group, Mexico, D.F. (email: [email protected]) ∗∗∗∗Center for Scientific Research and Higher Education at Ensenada, Mexico (CICESE), Carretera Ensenada-Tijuana No. 3918, Zona Playitas, C.P. 22860, Ensenada, B.C. Mexico. (e-mail: [email protected]) †(email: [email protected]) ‡(email: [email protected])

Keywords

Control applications
Controlled synchronization
Huygens' controller
Perturbation theory
Robust control
Second order systems

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10.3182/20140824-6-ZA-1003.01807

Cite this

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abstract = "This paper considers synchronization as a control problem. In particular, a (robust) controller for achieving synchronization in pairs of second order nonlinear systems is designed. The design is inspired by the classical experiment on synchronization of pendulum clocks, as described by Christiaan Huygens. In the proposed control scheme, the systems do not interact directly but through an exogenous system. Ultimately, it is demonstrated that Huygens' controller, can be used to perform in-phase and anti-phase synchronized tasks, with the advantage that 'small' control gains are required. The stability of the closed-loop system is analyzed using perturbation theory and the proposed controller is experimentally validated on a pair of Cartesian robots.",

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note = "Funding Information: ∗Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan (email: [email protected]) ∗∗Eindhoven University of Technology, P.O. Box 513 5600 MB Eindhoven, The Netherlands (email: [email protected]) ∗∗∗Research Center for Advanced Studies (Cinvestav-IPN), Mechatronics Group, Mexico, D.F. (email: [email protected]) ∗∗∗∗Center for Scientific Research and Higher Education at Ensenada, Mexico (CICESE), Carretera Ensenada-Tijuana No. 3918, Zona Playitas, C.P. 22860, Ensenada, B.C. Mexico. (e-mail: [email protected]) †(email: [email protected]) ‡(email: [email protected]) ; 19th World Congress of the International Federation of Automatic Control (IFAC 2014 World Congress), IFAC 2014 ; Conference date: 24-08-2014 Through 29-08-2014",

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AU - Pena Ramirez, J.

AU - Denasi, A.

AU - Rodriguez-Angeles, A.

AU - Alvarez Gallegos, J.

AU - Nijmeijer, H.

AU - Aihara, K.

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AB - This paper considers synchronization as a control problem. In particular, a (robust) controller for achieving synchronization in pairs of second order nonlinear systems is designed. The design is inspired by the classical experiment on synchronization of pendulum clocks, as described by Christiaan Huygens. In the proposed control scheme, the systems do not interact directly but through an exogenous system. Ultimately, it is demonstrated that Huygens' controller, can be used to perform in-phase and anti-phase synchronized tasks, with the advantage that 'small' control gains are required. The stability of the closed-loop system is analyzed using perturbation theory and the proposed controller is experimentally validated on a pair of Cartesian robots.

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KW - Controlled synchronization

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KW - Perturbation theory

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Controlled synchronization: A Huygens' inspired approach

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