We present a numerical analysis on a control for the time evolution of a model of an overhead crane. This closed-loop system consists of a platform, which moves horizontally along a rail, a cable attached to the platform, and a load at its end. In the literature, it is known that it is asymptotically stable (cf. Saouri [#!saou!#]). This numerical analysis concerns the dissipative finite elements method (cf. Miletic [#!maja!#]) based on the P2 Lagrangian polynomials and a Crank-Nicholson time discretization. We prove that the numerical method dissipates the energy, analogous to the continuous case, for both discretizations semi and fully. Finally, we derive error bounds for both discretizations.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 1
Year: 2018

DOI: 10.12732/ijam.v31i1.8

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