关键词: OGY方法, 齿轮系统, 非线性动力学, 混沌控制

Abstract: In view of the chaotic motion happening in some parameter space of system of a gear pair with clearance nonlinearity, the OGY(Ott-Grebogi-Yorke) chaos control method is used to stabilize the unstable periodic orbits which embedded in the chaotic attractor in two ways. Aiming at the limitation of classical OGY method which can only apply to discrete dynamical system, one is to make use of the motion equation and its variational form to apply the OGY method directly in periodically excited time-continuous system according to the theory of system dynamics. For the situation that the motion equation is not available, another method is to construct time series of system’s stroboscopic section data, from which the unstable periodic orbits and necessary information for estimating the parameter perturbation can be determined. The control effects of the two methods are compared through numerical simulation.

Key words: Nonlinear dynamics, Ott-Grebogi-Yorke method, Chaos control, Gear system