Using delayed state feedback to stabilize periodic motions of an oscillator
Using delayed state feedback to stabilize periodic motions of an oscillator
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DOI：
10.1016/j.jsv.2003.07.006
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发表时间：
2004-08
影响因子：
4.7
通讯作者：
Haiyan Hu
中科院分区：
文献类型：
--
作者：
Haiyan Hu
本文讨论了如何用时滞状态反馈镇定线性非正阻尼单自由度系统的周期运动。研究表明，延迟状态反馈在一定的频率范围内起作用。对于单自由度线性无阻尼系统，只要系统的基频高于系统的固有频率，延迟位移反馈几乎能镇定系统的所有周期运动，但它只在一系列越来越窄的低于系统固有频率的频带内起作用。延迟速度反馈的引入可以显著地扩大延迟位移反馈的工作频率范围。然而，如果系统的周期是系统固有周期的整数倍，则即使是时滞状态反馈也不能镇定周期运动。稳定开关判据是分析线性系统镇定问题的有力工具。然而，单自由度线性无阻尼系统的时滞速度反馈的稳定化是一个退化的情况下，现有的稳定开关的标准不能提供任何有用的信息。本文的详细研究揭示了退化情形的复杂性，其中镇定条件可以根据任意特征根的真实的部分的二阶导数来确定。
The paper states how to stabilize the periodic motions of a linear, non-positively damped system of single degree of freedom through the use of delayed state feedback. The study indicates that the delayed state feedback works in certain frequency ranges. For a linear undamped system of single degree of freedom, the delayed displacement feedback is able to stabilize almost all periodic motions of the system provided that their fundamental frequencies are higher than the natural frequency of the system, but it only works in a series of narrower and narrower frequency bands lower than the natural frequency. The introduction of delayed velocity feedback can remarkably enlarge the working frequency ranges of delayed displacement feedback. However, even the delayed state feedback cannot stabilize a periodic motion if the corresponding period is an integral multiple of the natural period of system. The criteria of stability switches prove to be a powerful tool to analyze the stabilization problem of a linear system. However, the stabilization of a linear undamped system of single degree of freedom with delayed velocity feedback only is a degenerate case where the available criteria of stability switches fail to offer any useful information. A detailed study in the paper reveals the complexity of the degenerated case, where the stabilization conditions can be identified according to the second order derivative of the real part of an arbitrary characteristic root.