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Analytical and Experimental Analyses of Nonlinear Vibrations in a Rotary Inverted Pendulum

Rahimi Dolatabad, Mohammad Javad | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 53675 (58)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Khayyat, Amir Ali Akbar; Pasharavesh, Abdolreza
  7. Abstract:
  8. Investigation of possible vibratory responses of dynamical systems around their stable equilibria is an essential step which must be taken before their both design and application. The attained results of such a study can largely help to prevent instability in closed-loop stabilized systems by avoiding excitation of the system in the neighborhood of its resonance. In this paper, nonlinear oscillations of a Rotary Inverted Pendulum (RIP) enjoying a full-state feedback controller is investigated. Lagrange’s equations are employed to derive an accurate 2-DoF mathematical model whose parameters are extracted by both measurement and 3D modeling of the real system components. The perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined using the results of this solution. Findings reveal the existence of hardening and softening-type resonances respectively at the first and the second vibrational modes leading to a wide frequency range with moderately large-amplitude vibrations which must be avoided when adjusting a time-varying set-point for the system. The analytical results are verified by experimental measurements and a very good agreement is observed
  9. Keywords:
  10. Inverted Pendulum ; Analytical Modeling ; Dynamic Stability ; Nonlinear Vibration ; Nonlinear Dynamical System

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