| 非线性振动系统极限环振幅与频率的控制 |
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| 引用本文： | 沈建和,陈树辉.非线性振动系统极限环振幅与频率的控制[J].振动与冲击,2009,28(6):90. |
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| 作者姓名： | 沈建和 陈树辉 |
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| 作者单位： | (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) |
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| 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.
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| 关 键 词： | 极限环 振幅控制 频率控制 |
Control of amplitude and frequency of limit cycles in nonlinear oscillatory systems |
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| SHEN Jian-he,CHEN Shu-hui.Control of amplitude and frequency of limit cycles in nonlinear oscillatory systems[J].Journal of Vibration and Shock,2009,28(6):90. |
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| Authors: | SHEN Jian-he CHEN Shu-hui |
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| Affiliation: | (1. Department of Applied Mechanics and Engineering, Sun Yat-sen University, Gaungzhou 510275, China;2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China) |
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| Abstract: | 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 thefeedback gains was obtained. Thus, the control of amplitude and frequency of limit cycleswas 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 bynumerical simulations. |
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| Keywords: | limit cycles amplitude contro l frequency control |
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