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

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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