Control of a Chaotic Parametrically Driven Pendulum

Abstract

We have controlled chaos in a pendulum with vertically driven pivot over a range of drive frequencies and damping levels. Using two variations on the OGY method [Ott, Grebogi, and Yorke, Phys. Rev. Lett. 64, 1196 (1990)], and with eddy-current damping as a control parameter, we have stabilized the motion of the pendulum about several of its unstable period-1, -2, and -4 limit cycles. Sampling the angular position at a correct choice of phase within the drive cycle simplified the OGY control rule. A time-proportioning rule was also found to provide robust control.