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首页> 外文会议>2002 ASME International Mechanical Engineering Congress and Exposition , Nov 17-22, 2002, New Orleans, Louisiana >BASIS PROPERTY AND STABILIZATION OF A TRANSLATING TENSIONED BEAM THROUGH A POINTWISE CONTROL FORCE
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BASIS PROPERTY AND STABILIZATION OF A TRANSLATING TENSIONED BEAM THROUGH A POINTWISE CONTROL FORCE

机译：通过点阵控制力实现平移张紧梁的基础性能和稳定化

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摘要

Introducing a recently developed powerful method , Riesz basis method what is so called, and applying to the stabilization of a translating tensioned beam through a pointwise control force are the two purposes of the paper. An asymptotic analysis, which is different from the one in treating the same problem in literature, is used to get a complete asymptotic expansion of the eigenvalues and eigenfunctions for the beam. The controlled system is written as an evolution equation in a state Hilbert space whose energy norm (induced by inner product) is the total energy of the beam. The spectrum-determined growth condition is obtained by showing that there is a set of generalized eigenfunctions of the system, which forms a Riesz basis for the state space. As a consequence, the stability, particularly the exponential stability of the system is developed. The analysis used here can be extended to other distributed systems and the results significantly improve that in [ASME Journal of Dynamic Systems, Measurement, and Control, 122(2000),322-331].
机译：介绍一种最近开发的功能强大的方法，即所谓的Riesz基方法，并通过点控制力将其应用于平移张紧梁的稳定化是本文的两个目的。渐进分析不同于文献中对相同问题的处理，它用于获得光束特征值和特征函数的完整渐近展开。受控系统被写为状态希尔伯特空间中的演化方程，其能量范数（由内积引起）是光束的总能量。频谱确定的生长条件是通过显示系统存在一组广义本征函数而获得的，该函数构成了状态空间的Riesz基础。结果，发展了系统的稳定性，特别是指数稳定性。此处使用的分析可以扩展到其他分布式系统，其结果显着改善了[ASME Journal of Dynamic Systems，Measurement and Control，122（2000），322-331]。

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