On the stabilization of a flexible beam with a tip mass
Author
Conrad, F.
Morgül, Ö.
Date
1998-11Source Title
SIAM Journal on Control and Optimization
Print ISSN
0363-0129
Publisher
Society for Industrial and Applied Mathematics
Volume
36
Issue
6
Pages
1962 - 1986
Language
English
Type
ArticleItem Usage Stats
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Abstract
We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case.
Keywords
Boundary controlFlexible structures
Infinite dimensional systems
Semigroup theory
Stability
Closed loop control systems
Eigenvalues and eigenfunctions
Equations of motion
Feedback
Mathematical models
Stabilization
Boundary control
Flexible beam
Infinite dimensional systems
Semigroup theory
Tip mass
Asymptotic stability