Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system

This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers satisfying the nonlinear KYP lemma as well as the interaction with a...

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Bibliographic Details
Published in:arXiv.org 2015-10
Main Authors: Miletić, Maja, Stürzer, Dominik, Arnold, Anton, Kugi, Andreas
Format: Article
Language:English
Subjects:
Dynamic stability
Dynamical systems
Euler-Bernoulli beams
Feedback
Nonlinear control
Nonlinear dynamics
Stability analysis
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Summary:This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers satisfying the nonlinear KYP lemma as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability is rigorously proven for the resulting closed-loop PDE-ODE system. The analysis is based on semigroup theory for the corresponding first order evolution problem. For the large-time analysis, precompactness of the trajectories is shown by deriving uniform-in-time bounds on the solution and its time derivatives.
ISSN:2331-8422