一类非线性相对转动系统的混沌运动及多时滞反馈控制

建立一类含非线性粘滑摩擦力的两质量非线性相对转动系统的动力学方程. 研究此非线性相对转动系统在外激励作用下的混沌运动及多时滞反馈控制. 当系统在外激励作用下处于混沌状态时, 考虑引入多时滞反馈对系统的混沌运动进行控制. 应用Melnikov理论给出系统在Smale意义下的混沌临界条件, 研究了多时滞反馈对系统运动及混沌临界值的影响规律. 并结合系统相图、Poincare截面图和功率谱分析多时滞反馈参数对系统混沌运动的控制作用. 关键词： 多时滞 相对转动 控制 数值仿真

Chaos and the control of multi-time delay feedback for some nonlinear relative rotation system

The dynamic equation of some nonlinear relative rotation system with two masses has been established, which contains a kind of nonlinear sick-slip friction. Chaotic motion and the control effect of multi-delay feedbacks of the nonlinear relative rotation system under external excitation are investigated. When the system is in chaos under external excitation, the multi-time delay is applied to control the chaotic motion. The chaotic critical conditions of parameters about Smale commutation are given in terms of Melnikov theory, while the influence of multi-delay feedbacks on the system movement state and chaotic critical conditions is studied. The control impacts of multi-time delay parameters on chaotic motion are studied by phase diagram, Poincare map and power spectrum, separately.
Keywords： multi-time delay relative rotation system control numerical simulation