On the stabilization of a flexible beam with a tip mass
Date
1998-11
Authors
Conrad, F.
Morgül, Ö.
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Source Title
SIAM Journal on Control and Optimization
Print ISSN
0363-0129
Electronic ISSN
Publisher
Society for Industrial and Applied Mathematics
Volume
36
Issue
6
Pages
1962 - 1986
Language
English
Type
Journal Title
Journal ISSN
Volume Title
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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.
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Keywords
Boundary control, Flexible 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