Nonlinear Dynamics

, Volume 9, Issue 4, pp 391–417 | Cite as

A simple feedback control system: Bifurcations of periodic orbits and chaos

  • K. Yagasaki


We consider a pendulum subjected to linear feedback control with periodic desired motions. The pendulum is assumed to be driven by a servo-motor with small time constant, so that the feedback control system can be approximated by a periodically forced oscillator. It was previously shown by Melnikov's method that transverse homoclinic and heteroclinic orbits exist and chaos may occur in certain parameter regions. Here we study local bifurcations of harmonics and subharmonics using the second-order averaging method and Melnikov's method. The Melnikov analysis was performed by numerically computing the Melnikov functions. Numerical simulations and experimental measurements are also given and are compared with the previous and present theoretical predictions. Sustained chaotic motions which result from homoclinic and heteroclinic tangles for not only single but also multiple hyperbolic periodic orbits are observed. Fairly good agreement is found between numerical simulation and experimental results.

Key words

Bifurcation chaos pendulum feedback control second-order averaging Melnikov method experiment 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • K. Yagasaki
    • 1
  1. 1.Department of Mechanical EngineeringTamagawa UniversityMachida, TokyoJapan

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