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

2016/07/24 by Stürzer, Dominik, Arnold, Anton, Kugi, Andreas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.07052

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 C₀-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.

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