Title | On control of dynamic of a pipeline in the case of its dynamic instability |
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Authors | P. A. Velmisov^{1}, A. V. Gladun^{2}^{1}Ulyanovsk State Technical University ^{2}Ulyanovsk Civil Aviation Institute named after
Chief Marshal of Aviation B.P. Bugaev |

Annotation | The problem of control of a mechanical system, which is a hollow elastic rod with a fluid or gas, flowing inside it (pipeline), is investigated. The case of dynamic instability of a mechanical system is considered. The controllability of the system is determined by linear approximation. The controls are constructed to ensure the damping of the pipeline oscillations. The results of numerical simulation of the behavior of the mechanical system under the action of constructed controls with given parameters are presented. |

Keywords | elastic pipeline, dynamics, controllability, control, partial differential equations, Galerkin method, a linear approximation |

Citation | Velmisov P. A., Gladun A. V. ''On control of dynamic of a pipeline in the case of its dynamic instability'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 381-390. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper54.pdf. - Date of access: 03.12.2021. |

**© SVMO, National Research Mordovia State University, 2021**

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