IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v189y2024ip1s0960077924012384.html
   My bibliography  Save this article

Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model

Author

Listed:
  • Bauomy, H.S.
  • EL-Sayed, A.T.
  • El-Bahrawy, F.T.

Abstract

One of the major problems in robotics research has been developing an actuator system for extremely dynamic-legged robots. High torque density and the capacity to control dynamic physical interactions are two design requirements for high-speed locomotion that are challenging for conventional actuators used in manufacturing applications to meet. To address this system and apply the desired control to reach the best stability position, the robot's foot was simulated with the Van der Pol equations, applied the required control, and studied that application. This work describes the actions of a new novel control mechanism known as the Integral Resonant Negative Derivative Feedback (IRNDF) controller, which reduces the vibration response of a double Van der Pol oscillator subjected to external excitations. This unique controller combines integral resonant control (IRC) and negative derivative feedback (NDF) controllers to provide a new controller effect for double Van der Pol oscillators. The multiple scale perturbation technique (MSPT) has been applied to solve the controlled system analytically. The MATLAB and MAPLE programs have been used to complete and clarify all of the numerical talks. The frequency response curves have been used to study the impact that altering the parameter values had on the amplitude. The controlled system vibration amplitude is governed by frequency-response equations (FREs), which have been constructed. In the vibration system, the IRC, NDF, and IRNDF controllers were compared to see which one was the best. Numerical results show that the unique IRNDF controller is the best at reducing oscillations and decreasing amplitude values. The effects of the effective parameters on the controlled system have been identified. The frequency-response equation that was derived has been used to plot the various response curves for the framework that show the stable and unstable zones when the controller is off and on. Lastly, excellent agreement between the derived numerical findings and the analytical ones was observed. Lastly, utilizing time histories and response curves to compare analytical and numerical solutions was fascinating and significant.

Suggested Citation

  • Bauomy, H.S. & EL-Sayed, A.T. & El-Bahrawy, F.T., 2024. "Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924012384
    DOI: 10.1016/j.chaos.2024.115686
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924012384
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115686?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. Song, Zigen & Ji, Fengchao & Xu, Jian, 2024. "Is there a user-friendly building unit to replicate rhythmic patterns of CPG systems? Synchrony transition and application of the delayed bursting-HCO model," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Chun-Hui He & Chao Liu, 2022. "A Modified Frequency–Amplitude Formulation For Fractal Vibration Systems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-8, May.
    3. Bauomy, H.S. & EL-Sayed, A.T., 2023. "Safety of a quarter-vehicle car through negative derivative feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Ghaleb, A.F. & Abou-Dina, M.S. & Moatimid, G.M. & Zekry, M.H., 2021. "Analytic approximate solutions of the cubic–quintic Duffing–van​ der Pol equation with two-external periodic forcing terms: Stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 129-151.
    5. Huang, Chengdai, 2018. "Multiple scales scheme for bifurcation in a delayed extended van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 643-652.
    6. Kimiaeifar, A. & Saidi, A.R. & Bagheri, G.H. & Rahimpour, M. & Domairry, D.G., 2009. "Analytical solution for Van der Pol–Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2660-2666.
    7. Cui, Yan & Liu, Suhua & Tang, Jiashi & Meng, Yimin, 2009. "Amplitude control of limit cycles in Langford system," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 335-340.
    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. Asma Alanazy & Yasser A. Amer & Ashraf Taha EL-Sayed & Fatma Sh. Mohammed & Taher A. Bahnasy, 2025. "Multi-Control Strategies on a Cubic–Quintic Nonlinear Hybrid Oscillator with External Excitation Under Resonance Conditions," Mathematics, MDPI, vol. 13(6), pages 1-24, March.

    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. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    2. repec:plo:pone00:0007427 is not listed on IDEAS
    3. 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).
    4. Alqudah, Mohammad & AlMheidat, Maalee & Alqarni, M.M. & Mahmoud, Emad E. & Ahmad, Shabir, 2024. "Strange attractors, nonlinear dynamics and abundant novel soliton solutions of the Akbota equation in Heisenberg ferromagnets," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    5. He, Chun-Hui & Liu, Chao, 2023. "Variational principle for singular waves," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    7. Liu, Zhenpu & Zhou, Shu & Zhu, Rui & Huang, Guodong & Chai, Yuan, 2025. "Research on synchronization in a Josephson junction-memristor system with dual capacitive membranes," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    8. Youhua Qian & Shuli Wang & Shuping Chen, 2023. "Multi-Frequency Homotopy Analysis Method for Coupled Van der Pol-Duffing System with Time Delay," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    9. Beregov, R.Y. & Melkikh, A.V., 2015. "De-synchronization and chaos in two inductively coupled Van der Pol auto-generators," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 17-28.
    10. 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).
    11. El-Dib, Yusry O. & Elgazery, Nasser S., 2022. "A novel pattern in a class of fractal models with the non-perturbative approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

    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:189:y:2024:i:p1:s0960077924012384. 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.