【摘要】 针对单级间隙非线性齿轮系统在部分参数区域发生的混沌运动,运用OGY(Ott-Grebogi-Yorke)控制原理以两种途径实现了混沌吸引子内部不稳定周期轨道的稳定化。考虑到经典OGY方法只适用于离散动力系统的局限性,根据系统运动方程及其变分形式,指出了将OGY控制算法直接应用于周期性连续时间系统的方法和步骤;对于系统方程未知的情形,根据系统轨线频闪数据时间序列,从中提取不稳定周期轨道及计算参数扰动所需的信息,实现了混沌控制。通过数值模拟比较了采用这两种途径的控制效果。更多还原

【Abstract】 In view of the chaotic motion happening in some parameter space of system of a gear pair with clearance nonlineariry, 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.更多还原