非自治旋转机械系统自同步与异结构同步的研究  

Self-synchronization and different structure synchronization for a non-autonomous rotational machine system

作　　者：张建刚[1] 褚衍东[1] 俞建宁[1] 李险峰[1] 杨丽新[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,兰州730070

出　　处：《振动与冲击》2009年第5期35-40,48,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(50475109);甘肃省自然科学基金项目(3ZS-051-A25-030;3ZS-042-B25-049)

摘　　要：研究一类非自治旋转机械系统的复杂动力学行为。通过系统运动的拉格朗日方程和牛顿第二定律,建立了机械式离心调速器系统的动力学方程。通过系统的分岔图和Lyapunov指数研究系统的混沌行为,通过仿真Poincar截面分析系统通向混沌的道路,并且验证该系统的分岔图与Lyapunov指数谱是完全吻合的。基于Lyapunov稳定性理论,采用非线性控制方法进行一类不同阶非自治混沌系统之间的同步控制的研究。通过构造合适的控制函数,成功地实现两个不同阶混沌系统之间的同步控制,并用数值仿真进一步证明该方法的有效性。The complex dynamic behavior of the mechanical centrifugal flywheel governor system was studied.The dynamical equation of the system was established using Lagrangian and Newton's second law.The chaotic behavior of the system was analyzed by means of bifurcation diagram and Lyapunov exponents.The evolution from Hopf bifurcation to chaos was shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters,and the bifurcation diagrams were verified by the related Lyapunov exponent spectra.Based on Lyapunov stability theory,a method of non-linear control was proposed for synchronization between two different non-autonomous chaotic systems.The chaotic synchronization between Duffing system and mechanical centrifugal flywheel governor system was realized by constructing the appropriate non-linear controller.Numerical simulation shows the effectiveness and feasibility of the proposed method.

关 键 词：调速器 Lyapunov指 数混 沌异结构 混沌同步 Poincar截面 

分 类 号：O322[理学—一般力学与力学基础] TB535[理学—力学]