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Third-Order Superharmonic Resonance Analysis and Control in a Nonlinear Dynamical System

Author

Listed:
  • Ali Kandil

    (Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab City 21934, Egypt
    Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt)

  • Yasser S. Hamed

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mohamed S. Mohamed

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Jan Awrejcewicz

    (Department of Automation, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, 90-924 Lodz, Poland)

  • Maksymilian Bednarek

    (Department of Automation, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, 90-924 Lodz, Poland)

Abstract

The present work discusses the dynamical analysis of the superharmonic resonance in a mass-damper-spring model controlled by a cubic-position negative-velocity feedback (CPNV) controller. Thanks to the harmonic balance technique, the approximate solution of the studied model can be extracted and then checked for stability using Floquet exponents. The cubic-position control gain is adjusted in order to suppress the model’s steady oscillations. In addition, the negative-velocity control gain is adjusted in order to shrink the period of the transient oscillations. Several plots are included to relate the car’s oscillatory amplitude with the model’s different parameters pre- and post-control so that we can determine the optimum conditions for running the model safely.

Suggested Citation

  • Ali Kandil & Yasser S. Hamed & Mohamed S. Mohamed & Jan Awrejcewicz & Maksymilian Bednarek, 2022. "Third-Order Superharmonic Resonance Analysis and Control in a Nonlinear Dynamical System," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1282-:d:792196
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