软弹簧Duffing系统的安全盆侵蚀及其时滞位移反馈控制

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (8) : 11-15,2.

论文

软弹簧Duffing系统的安全盆侵蚀及其时滞位移反馈控制

尚慧琳1,文永蓬2

作者信息 +

Erosion of safe basins in a softening duffing system and its control by elayed position feedback

Shang Hui-lin1, wen yong-peng2

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文章历史 +

摘要

对一个软弹簧Duffing系统引入线性时滞位移反馈，研究时滞反馈系统安全盆侵蚀的控制作用。首先通过Melnikov函数法分析了时滞受控系统的安全盆的边界分形条件。发现在弱反馈下，时滞反馈的增大能够提高安全盆边界分形的激励振幅阈值，抑制安全盆的侵蚀。并利用时滞系统无限维初始空间向有限维欧式空间投影的思想给出时滞反馈系统安全盆的定义。再以时滞量为变参数，运用四阶Rung-Kutta方法和点映射方法研究了时间滞后对受控系统安全盆的影响规律。发现在一定的时滞变化范围内，通过增大时滞，可以有效抑制系统的安全盆侵蚀。数值仿真结果与定性分析的一致性证明了理论预测的有效性。该研究结果说明时滞位移反馈是控制系统的安全盆侵蚀的有效策略。

Abstract

Linear delayed position feedback is induced to a softening Duffing system, and its effect on controlling the erosion of safe basins is investigated. Firstly, the condition of fractal erosion of the basin boundary is obtained. The results show that the increasing of time delay can enhance the threshold of the excitation amplitude of the fractal erosion and reduce the erosion under a weak feedback control. Then the definition of safe basin in delayed feedback controlled system is given according to the idea of projecting infinite initial space of delayed system into finite-dimensional Euclidean Space. Finally, considering time delay as a variable parameter and employing the 4th Runge-Kutta and the point mapping methods, evolutions of safe basin with time delay are presented. It is found that the increasing of time delay within a certain range can reduce the erosion of safe basins effectively. The agreement of the theoretical analysis and numerical simulations verifies the validity of the analytical prediction. All the results have an implication that delayed position feedback can be used as a good approach to control the erosion of safe basins.

导出引用

尚慧琳;文永蓬. 软弹簧Duffing系统的安全盆侵蚀及其时滞位移反馈控制[J]. 振动与冲击, 2012, 31(8): 11-15,2

Shang Hui-lin;wen yong-peng. Erosion of safe basins in a softening duffing system and its control by elayed position feedback[J]. Journal of Vibration and Shock, 2012, 31(8): 11-15,2