IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v193y2025ics0960077925001511.html
   My bibliography  Save this article

Negative derivative feedback control and bifurcation in a two-degree-of-freedom coupled dynamical system

Author

Listed:
  • Bauomy, H.S.
  • EL-Sayed, A.T.
  • Amer, T.S.
  • Abohamer, M.K.

Abstract

A popular benchmark problem in the field of control is the cart-pendulum system. The system has only one control input for two degrees of freedom (2DOF), making it utterly underactuated. Its highly nonlinear structure makes it suitable for validating a variety of linear and nonlinear controllers. There are numerous applications, such as rocket propellers, tank missile launchers, self-balancing robots, ship stabilisation, earthquake-resistant building design, etc. This work describes a control and bifurcation method for the response vibrations of the 2DOF auto-parametric pendulum (Cart-pendulum) model with harmonic excitation. To reduce the detrimental vibrations created by the system's operation, it is managed via negative derivative feedback (NDF). Bifurcation analysis is conducted on the studied model at two different gain values of the controller to identify various bifurcations occurring within the system. The main aim of this study is to explore the effectiveness of the control method and bifurcation analysis in stabilising pendulum vibrations. By using the averaging technique to solve the nonlinear differential equations and modelling the system using an NDF controller, an analytical solution is produced. The Runge–Kutta technique fourth-order (RK4) is used to compare the approximate answers to the numerical simulations and find a good match. The stability and steady-state amplitude of nonlinear systems were examined and compared before and after control. After implementing the NDF control mechanism, it was discovered that a number of system factors had an impact. To verify their comparability, MATLAB software was used to compare the numerical and analytical solutions at time-history and FRCs. Frequency response curves (FRCs) and ideal system operating conditions were investigated at different controller and system parameter values. Finally, the chaos motion and vibration amplitude of the system are suppressed by the control systems.

Suggested Citation

  • Bauomy, H.S. & EL-Sayed, A.T. & Amer, T.S. & Abohamer, M.K., 2025. "Negative derivative feedback control and bifurcation in a two-degree-of-freedom coupled dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001511
    DOI: 10.1016/j.chaos.2025.116138
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925001511
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116138?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.

    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:193:y:2025:i:c:s0960077925001511. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.