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Mathematics > Analysis of PDEs

arXiv:1607.07052 (math)
[Submitted on 24 Jul 2016 (v1), last revised 23 May 2017 (this version, v2)]

Title:Closed-loop Stability Analysis of a Gantry Crane with Heavy Chain

Authors:Dominik Stürzer, Anton Arnold, Andreas Kugi
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Abstract:In this paper, we analyze a systematically designed and easily tunable backstepping-based boundary control concept developed by Thull, Wild, and Kugi (2006) for a gantry crane with heavy chain and payload. The corresponding closed-loop system is formulated as an abstract evolution equation in an appropriate Hilbert space. Non-restrictive conditions for the controller coefficients are derived, under which the solutions are described by a $C_0$-semigroup of contractions, and are asymptotically stable. Moreover, by applying Huang's theorem we can finally even show that under these conditions the controller renders the closed-loop system exponentially stable.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1607.07052 [math.AP]
  (or arXiv:1607.07052v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1607.07052

Submission history

From: Anton Arnold [view email]
[v1] Sun, 24 Jul 2016 14:59:34 UTC (1,386 KB)
[v2] Tue, 23 May 2017 21:37:09 UTC (1,389 KB)
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