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Supervised by Ministry of Industry and Information Technology of The People''s Republic of China Sponsored by Harbin Institute of Technology Editor-in-chief Yu Zhou ISSNISSN 1005-9113 CNCN 23-1378/T

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Related citation:Jilong Wu,Yingfeng Shang.Exponential Stabilization of Euler-Bernoulli Beam with Input Time-Delay in the Boundary Control[J].Journal of Harbin Institute Of Technology(New Series),2019,26(3):20-25.DOI:10.11916/j.issn.1005-9113.17054.
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Exponential Stabilization of Euler-Bernoulli Beam with Input Time-Delay in the Boundary Control
Jilong Wu,Yingfeng Shang
(Department of Mathematics, Tianjin University, Tianjin 300072, China)
Abstract:
The boundary control problem of a cantilever Euler-Bernoulli beam with input time delay is considered. In order to exponentially stabilize the system, a feedback controller is adopted. And we study the well-posedness and exponential stability of the closed-loop system. The approach used in this paper is done by several steps. Firstly, the well-posedness of this system is proved by semi-group theory. Secondly, the asymptotical expression of eigenvalue is investigated by spectral analysis. Thirdly, the exponential stability of the system is studied by multiplier technology. Finally, numerical simulations on the dynamical behavior of the system are given to support the results obtained.
Key words:  feedback control  time delay  Lyapunov function  exponential stability  spectral analysis
DOI:10.11916/j.issn.1005-9113.17054
Clc Number:O231.1
Fund:
Descriptions in Chinese:
  

带有边界控制时滞的欧拉系统的指数稳定

武继龙, 尚应锋

(天津大学 理学院数学系,天津 300072)

创新点说明:

研究了一种带有边界控制时滞的欧拉梁系统的稳定性。为使时滞系统指数稳定, 设计了反馈控制器。在对时滞系统进行反馈控制后,研究了系统的适定性与稳定性。本文主要分成四个部分:1)使用半群理论证明系统可解性; 2)使用谱分析得出系统的特征函数的渐近表达形式;3) 使用乘子法证明了系统的指数稳定;4)对控制策略应用后的系统进行数值模拟,直观上展示了理论的正确性

研究目的:

对带有边界控制时滞的系统,使用相应的反馈控制策略使系统指数稳定

研究方法:

首先使用反馈控制策略,对时滞系统进行反馈控制,然后使用半群理论,谱分析,乘子法证明了系统的指数稳定,并对系统进行了数值模拟,得到好的模拟结果

研究结果:

反馈控制策略在对于带有时滞的系统具有很好的效果,最后的数值模拟进行了直观的展示

结论:

由于时滞问题的多样性,不同的时滞需要设计不同的反馈控制策略。本文中研究的问题只针对边界控制时滞问题。对于其他时滞问题需要进行其他分析。

关键词:反馈控制,时滞,Lyapunov方程,指数稳定,谱分析

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