A SIMPLE FEEDBACK-CONTROL SYSTEM - BIFURCATIONS OF PERIODIC-ORBITS AND CHAOS

We consider a pendulum subjected to linear feedback control with perio dic desired motions. The pendulum is assumed to be driven by a servo-m otor with small time constant, so that the feedback control system can be approximated by a periodically forced oscillator. It was previousl y shown by Melnikov's method that transverse homoclinic and heteroclin ic orbits exist and chaos may occur in certain parameter regions. Here we study local bifurcations of harmonics and subharmonics using the s econd-order averaging method and Melnikov's method. The Melnikov analy sis was performed by numerically computing the Melnikov functions. Num erical simulations and experimental measurements are also given and ar e compared with the previous and present theoretical predictions. Sust ained chaotic motions which result from homoclinic and heteroclinic ta ngles for not only single but also multiple hyperbolic periodic orbits are observed. Fairly good agreement is found between numerical simula tion and experimental results.