Design of controllers and compensators for a serially connected string system and its Riesz basis

被引：0
|
作者：
Liu, Dong-Yi [1 ,2 ]
Shang, Ying-Feng [1 ,2 ]
Xu, Gen-Qi [1 ]
机构：
[1] Department of Mathematics, Science School, Tianjin University, Tianjin 300072, China
[2] Department of Automation, Electrical Engineering and Automation School, Tianjin University, Tianjin 300072, China
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2008年 / 25卷 / 05期
关键词：
Control theory - Feedback - Control system stability - Eigenvalues and eigenfunctions - Asymptotic stability - Closed loop control systems - Controllers;
D O I：
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学科分类号：
摘要：
Under free boundary conditions, for a serially connected string system with continuity of vertical force and discontinuity of displacement at the interior nodes, compensators are designed at the interior nodes to compensate the displacement, and controllers are placed on both endpoints to control the system. Thus, a closed loop control system is established. Its well-posedness is then shown via the semigroup theory. From spectrum analysis of operators, it is known that the spectrum of the system is composed of isolated eigenvalues with finite multiplicity, and its spectrum is located in a strip parallel to the imaginary axis in the left half complex plane. Hence, the existence of the Riesz basis is derived and the spectrum-determined growth condition is concluded. The asymptotic stability of the system is thus proved.
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页码：815 / 818
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