一类非自治机械系统的混沌同步控制研究  

STUDYING ON THE SYNCHRONIZATION CONTROL OF A CLASS OF NON-AUTONOMOUS MECHANICAL SYSTEM

作　　者：彭建奎[1] 俞建宁[2] 张建刚[2] 张莉[3] 张旭东[2] 

机构地区：[1]甘肃联合大学数学与信息学院,兰州730000 [2]兰州交通大学数理与软件工程学院,兰州730070 [3]兰州工业高等专科学校基础学科部,兰州730050

出　　处：《机械强度》2009年第5期719-726,共8页Journal of Mechanical Strength

基　　金：甘肃省自然科学基金项目(3ZS051-A25-030;3ZS-042-B25-049)~~

摘　　要：根据拉格朗日运动方程和牛顿力学定律,建立机械式离心调速器的动力学方程,运用数值仿真,研究受外部扰动的离心调速器系统动力学行为,该系统具有较复杂的动力学特性。利用系统的全局分岔图和李雅普诺夫指数谱,准确刻画出系统的局部动力学行为,并讨论离心调速器系统参数变化对机械系统运动状态的影响,由此得知该系统在适当参数下处于混沌运动。运用Poincaré映射图揭示该系统的Hopf分岔与混沌形成过程。基于Lyapunov稳定性理论,采用耦合反馈同步控制方法与自适应同步控制方法实现混沌同步,并给出实现自同步的条件及控制律参数的选取范围。最后运用数值仿真证实同步控制方法的有效性。The dynamic equations of the centrifugal flywheel governor with external disturbance were established according to Lagrange equation of motion and Newton laws of mechanics. The dynamical behaviors of the centrifugal flywheel governor with external disturbance were investigated by numerical simulations, and the system exhibited exceedingly complicated dynamic behaviors. The influence of system parameter on the centrifugal flywheel govemor system was discussed through Lyapunov-exponents spectrum and global bifurcation diagram, which accurately portayed the partial dynamic behavior of the system. This was informed that it was chaotic with proper system parameters. The progress of the Hopf bifurcation and chaos forming of the centrifugal flywheel governor system were revealed by Poincare maps with different system parameters. Based on the Lyapunov stability theory, the chaos synchronization of the centrifugal flywheel governor was controlled by coupled-feedback control scheme and adaptive control scheme, the conditions and the range of controllers＇ parameters for self-synchronization of chaotic systems were obtained. Finally, the numerical illustrations showed the effectiveness of these methods.

关 键 词：调速器 LYAPUNOV指数谱 HOPF分岔 POINCARÉ截面 混沌同步 耦合反馈同步 自适应同步 

分 类 号：O322[理学—一般力学与力学基础]