IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i15p2331-d1443008.html
   My bibliography  Save this article

Dynamic Analysis and PD Control in a 12-Pole Active Magnetic Bearing System

Author

Listed:
  • Yigen Ren

    (Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China)

  • Wensai Ma

    (Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China)

Abstract

This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton’s second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system’s amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system’s spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor’s motion, but it also increases the system’s instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2331-:d:1443008
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/15/2331/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/15/2331/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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. 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.
    2. 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.

    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:gam:jmathe:v:12:y:2024:i:15:p:2331-:d:1443008. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.