Controlling chaos of the forced pendulum with the OGY method

Author

Ogawa, Atsushi ; Yasuda, Masashi ; Ozawa, Yoshio ; Kawai, Tsuyoshi ; Suzuki, Ryuji ; Tsukamoto, Kazuyoshi

Author_Institution

Sanyo Electr. Co. Ltd., Osaka, Japan

Volume

3

fYear

1996

fDate

11-13 Dec 1996

Firstpage

2377

Abstract

A number of methods to control the phenomenon of chaos in nonlinear dynamical systems have been reported. Of these, the technique known as the OGY method, devised by Ott, Grebogi and Yorke (1990) has attracted attention as one which can confine the desired periodic motion with the application of a small external force. In our research, we have applied the OGY method to a forced pendulum with a cyclic external force applied in the horizontal direction, as a nonlinear dynamical system with a more complex structure than that of the Lorentz attractor. We first investigate in detail using bifurcation diagrams and Lyapunov exponents, the regions in which chaos occurs in a forced pendulum. We then present some issues related to the target focal point of the periodic orbit, which is needed in particular to execute control using the OGY method

Keywords

Lyapunov methods; bifurcation; chaos; nonlinear dynamical systems; pendulums; stability; Lyapunov exponents; OGY method; bifurcation diagrams; chaos control; cyclic external force; forced pendulum; nonlinear dynamical systems; periodic motion; Acceleration; Angular velocity; Chaos; Control systems; Damping; Force control; Gravity; Nonlinear control systems; Nonlinear equations; Numerical analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1996., Proceedings of the 35th IEEE Conference on

Conference_Location

Kobe

ISSN

0191-2216

Print_ISBN

0-7803-3590-2

Type

conf

DOI

10.1109/CDC.1996.573440

Filename

573440