CONTROLLING CHAOS EXPERIMENTALLY IN SYSTEMS EXHIBITING LARGE EFFECTIVE LYAPUNOV EXPONENTS

We investigate experimentally the performance of the Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 116 (1989)] feedback concept to control c haotic motion. The experimental systems are a driven pendulum and a dr iven bronze ribbon. Both setups have unstable periodic orbits characte rized by large effective Lyapunov exponents. All control vectors for t he feedback control are extracted from the experimental data. To do th is for the pendulum a global model obtained by the flow field analysis of Cremers and Hubler [Z. Naturforsch. Teil A 42, 797 (1987)] is used , and for the bronze ribbon linear approximations in embedding space a re exploited. We analyze the problems that arise due to the amplificat ion of noise by large effective Lyapunov exponents in the determinatio n of the control values as well as in the performance of the experimen tal control. Successful control can be achieved in our experiments by applying the ''local control method'' which allows a quasicontinuous a djustment of the control parameter in contrast to adjusting the contro l parameter only once per return time of the Poincare map.