Exponential stabilization of an axially moving string with geometrical nonlinearity by linear boundary feedback
Exponential stabilization of an axially moving string with geometrical nonlinearity by linear boundary feedback
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DOI：
10.1016/j.jsv.2006.03.012
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发表时间：
2006-10
影响因子：
4.7
通讯作者：
Tiecheng Li;Z. Hou
中科院分区：
文献类型：
--
作者：
Tiecheng Li;Z. Hou
本文利用边界控制解决了轴向移动弦的振动抑制问题。 Taking into account large transverse motion of the string via the second-order component of Lagrangian strain, a nonlinear oscillation equation is derived for the problem by employing the Hamilton's Principle.然后采用直接李亚普诺夫方法证明了负速度反馈的线性边界控制确保了运动弦的振动响应指数稳定。主要贡献是控制器增益参数方面的新稳定性条件，以及对应用控制的边界处的平衡条件的详细演示。
This paper addresses the vibration suppression problem of an axially moving string using boundary control. Taking into account large transverse motion of the string via the second-order component of Lagrangian strain, a nonlinear oscillation equation is derived for the problem by employing the Hamilton's Principle. Direct Lyapunov method is then adopted to demonstrate that a linear boundary control of negative speed feedback ensures the vibration response of the moving string exponentially stable. The main contributions are a new stability condition in terms of controller gain parameter, and a detailed demonstration on the equilibrium condition at the boundary where the control is applied.