IDEAS home Printed from https://ideas.repec.org/a/hin/complx/1641953.html
   My bibliography  Save this article

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Author

Listed:
  • Jing Wang
  • Shaojuan Ma
  • Peng Hao
  • Hehui Yuan

Abstract

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

Suggested Citation

  • Jing Wang & Shaojuan Ma & Peng Hao & Hehui Yuan, 2019. "Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter," Complexity, Hindawi, vol. 2019, pages 1-12, December.
  • Handle: RePEc:hin:complx:1641953
    DOI: 10.1155/2019/1641953
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/1641953.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/8503/2019/1641953.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2019/1641953?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
    ---><---

    References listed on IDEAS

    as
    1. Zhang, W. & Yao, M.H. & Zhan, X.P., 2006. "Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 175-186.
    2. Inayat-Hussain, Jawaid I., 2009. "Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2664-2671.
    Full references (including those not matched with items on IDEAS)

    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. Li, Tzuu-Hseng S. & Kuo, Chao-Lin & Guo, Nai Ren, 2007. "Design of an EP-based fuzzy sliding-mode control for a magnetic ball suspension system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1523-1531.
    2. Yigen Ren & Wensai Ma, 2024. "Dynamic Analysis and PD Control in a 12-Pole Active Magnetic Bearing System," Mathematics, MDPI, vol. 12(15), pages 1-23, July.
    3. Inayat-Hussain, Jawaid I., 2009. "Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2664-2671.
    4. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.
    5. Farrukh Hafiz Nagi & Jawaid Iqbal Inayat-Hussain & Syed Khaleel Ahmed, 2022. "Fuzzy Bang-Bang Relay Control of a Rigid Rotor Supported by Active Magnetic Bearings," Energies, MDPI, vol. 15(11), pages 1-20, May.
    6. Zhang, Wei & Zu, Jean W., 2008. "Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1152-1167.
    7. Li, J. & Tian, Y. & Zhang, W., 2009. "Investigation of relation between singular points and number of limit cycles for a rotor–AMBs system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1627-1640.

    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:hin:complx:1641953. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.