Vibration Control of an Axially Moving String by Boundary Control
Vibration Control of an Axially Moving String by Boundary Control
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DOI：
10.1115/1.2801153
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发表时间：
1996-03
影响因子：
1.7
通讯作者：
Seung-Yop Lee;C. D. Mote
中科院分区：
文献类型：
--
作者：
Seung-Yop Lee;C. D. Mote
通过对边界横向运动或外部边界力的时变控制，实现了轴向运动弦横向振动的稳定。平移弦的总机械能是李雅普诺夫函数，边界控制律被设计用来耗散弦在左边界和/或右边界的总振动能量。通过最小化从边界反射的能量来确定的最佳反馈增益是张力与入射波到边界控制的传播速度之比。此外，对于任何初始扰动，稳定系统所有振动能量所需的最大时间是波在到达边界控制之前传播到管柱跨度所需的时间。利用半群理论，利用能量范数的衰减率分析验证了边界控制下轴向运动弦的渐近稳定性和指数稳定性。通过仿真验证了理论预测的最优边界控制对平移管柱稳定性的影响。
The stabilization of the transverse vibration ofan axially moving string is implemented using time-varying control of either the boundary transverse motion or the external boundary forces. The total mechanical energy of the translating string is a Lyapunov functional and boundary control laws are designed to dissipate the total vibration energy of the string at the left and/or right boundary. An optimal feedback gain determined by minimizing the energy reflected from the boundaries, is the ratio of tension to the propagation velocity of an incident wave to the boundary control. Also the maximum time required to stabilize all vibration energy of the system for any initial disturbance is the time required for a wave to propagate the span of the string before hitting boundary control. Asymptotic and exponential stability of the axially moving string under boundary control are verified analytically through the decay rate of the energy norm and the use of semigroup theory. Simulations are used to verify the theoretically predicted, optimal boundary control for the stabilization of the translating string.