时滞速度反馈对软弹簧Duffing系统安全盆的控制研究

尚慧琳

振动与冲击 ›› 2011, Vol. 30 ›› Issue (5) : 54-58.

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (5) : 54-58.
论文

时滞速度反馈对软弹簧Duffing系统安全盆的控制研究

  • 尚慧琳
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Control of Erosion of Safe Basins in a Softening Duffing Oscillator by Velocity Delayed Feedback

  • Huilin Shang

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摘要

摘 要:为了利用时滞反馈对于非线性系统实施安全盆侵蚀控制,以一个软弹簧Duffing系统为例,对系统引入线性时滞速度反馈,研究时滞速度反馈对系统安全盆侵蚀的控制作用。首先通过Melnikov函数法分析时滞受控系统的安全盆的边界分形条件;再以时间滞后量为变参数,通过四阶龙格-库塔法和蒙特-卡罗方法,刻画安全盆形态,计算安全盆面积。发现时滞速度反馈对影响安全盆边界有着重要作用,通过增大时滞量,可以对系统的安全盆侵蚀进行有效抑制。该研究结果说明时滞速度反馈是控制系统的安全盆侵蚀的有效手段。



Abstract

Abstract: In order to apply delayed feedback controlling the erosion of safe basins in nonlinear systems, a softening Duffing oscillator is considered in the paper as an example, a linear delayed velocity feedback is induced to the system, and the effects of delayed velocity feedback on controlling the basin erosion are investigated. Firstly, the condition of fractal erosion of safe basin’s boundary of the delayed controlled system is obtained by the Melnikov method. Then considering time delay as a variable parameter and employing the 4th-order Runge-Kutta and the Monte-Carlo methods, the evolutions of boundaries and area of safe basins with the delay are presented. It is found that the delayed velocity feedback can greatly affect the safe basin, and the erosion of safe basin can be reduced by the increase of the delay effectively. It follows that the delayed velocity feedback can be used as a good approach to control the erosion of safe basins.

关键词

软弹簧duffing振子 / 安全盆侵蚀 / 时滞 / 反馈增益 / 分形

Key words

softening Duffing oscillator / erosion of safe basin / time delay / feedback / fractal

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导出引用
尚慧琳. 时滞速度反馈对软弹簧Duffing系统安全盆的控制研究[J]. 振动与冲击, 2011, 30(5): 54-58
Huilin Shang. Control of Erosion of Safe Basins in a Softening Duffing Oscillator by Velocity Delayed Feedback[J]. Journal of Vibration and Shock, 2011, 30(5): 54-58

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