IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i5p2981-2988.html
   My bibliography  Save this article

Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method

Author

Listed:
  • de Paula, Aline Souza
  • Savi, Marcelo Amorim

Abstract

Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge–Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.

Suggested Citation

  • de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2981-2988.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2981-2988
    DOI: 10.1016/j.chaos.2009.04.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909003798
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.04.039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "A multiparameter chaos control method based on OGY approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1376-1390.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zheng, Y.G. & Yu, J.L., 2022. "Stabilization of multi-rotation unstable periodic orbits through dynamic extended delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Nana, B. & Yamgoué, S.B. & Tchitnga, R. & Woafo, P., 2018. "On the modeling of the dynamics of electrical hair clippers," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 14-23.
    3. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    4. Costa, Dimitri & Pavlovskaia, Ekaterina & Wiercigroch, Marian, 2024. "Feedback control of chaos in impact oscillator with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    6. Nana, B. & Yamgoué, S.B. & Tchitnga, R. & Woafo, P., 2017. "Dynamics of a pendulum driven by a DC motor and magnetically controlled," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 18-27.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    2. García, P., 2022. "A machine learning based control of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Gritli, Hassène, 2019. "Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 127-145.
    4. Boukabou, Abdelkrim & Mekircha, Naim, 2012. "Generalized chaos control and synchronization by nonlinear high-order approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2268-2281.
    5. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2981-2988. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.