Abstract
This contribution starts from two benchmark control problems that are quite close as mathematical models: the overhead crane with flexible cable and the flexible marine riser. A unified model for these controlled objects is obtained by applying an adapted version of the Hamilton variational principle. To this model it is associated the so called energy identity which suggests a Liapunov functional incorporating a prime integral of the system. This functional is used for feedback controller synthesis. In order to prove stabilization of the closed loop system, there is associated a system of functional differential equation s of neutral type for which both basic theory (existence, uniqueness, data dependence) and stability theory are well established. It is discussed under what conditions asymptotic stability may be proved using the Barbašin Krasovskii LaSalle invariance principle.
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Acknowledgments
The work was supported by the project CNCS-Romania PN-II-ID-PCE-3-0198.
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Răsvan, V. (2016). Models and Stabilization for Mechanical Systems with Propagation and Linear Motion Coordinates. In: Witrant, E., Fridman, E., Sename, O., Dugard, L. (eds) Recent Results on Time-Delay Systems. Advances in Delays and Dynamics, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-26369-4_8
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