非线性振动系统极限环振幅与频率的控制  

Control of amplitude and frequency of limit cycles in nonlinear oscillatory systems

作　　者：沈建和[1,2] 陈树辉[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275 [2]福建师范大学数学与计算机科学学院,福州350007

出　　处：《振动与冲击》2009年第6期90-92,117,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10672193)

摘　　要：研究非线性振动系统极限环振幅与频率的控制。利用多尺度法,计算了动力系统Hopf分岔点附近的正规型,获得极限环振幅及频率与反馈系数的近似解析关系。通过选择适当的反馈系数,可对极限环的振幅与频率进行控制。选取一类三维系统作为算例,讨论并比较了几类线性、非线性反馈控制器的控制效果,所得的解析结果与数值模拟的结果基本吻合。The multiple scales method was used to calculate the normal forms of dynamical systems near the Hopf bifurcation point and the analytical formula regarding the amplitude and frequency of the controlled limit cycles and the feedback gains was obtained. Thus, the control of amplitude and frequency of limit cycles was realized by choosing the suitable feedback gains. A three-dimensional system was chosen as an illustrated example. The efficiencies of some linear or nonlinear state feedback controllers were discussed and compared. The obtained analytical conclusions were verified by numerical simulations.

关 键 词：极限环 振幅控制 频率控制 

分 类 号：O322[理学—一般力学与力学基础]