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On the Construction of Stabilizing Control for a Pipeline System
| Title | On the Construction of Stabilizing Control for a Pipeline System |
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| Authors | A. V. Gladun1, P. A. Velmisov2 1Ulyanovsk Civil Aviation Institute named after Chief Marshal of Aviation B.P. Bugaev 2Ulyanovsk State Technical University |
| Annotation | The paper considers the problem of constructing stabilizing control that suppresses the longitudinal-transverse vibrations of an elastic pipeline conveying fluid. The mathematical model is a system of nonlinear partial differential equations accounting for the longitudinal and transverse deformations of the pipeline interacting with the moving fluid. The Galerkin method is used to reduce the original system to a finite-dimensional system of nonlinear ordinary differential equations. For the case of two basis functions, controllability conditions for the linear approximation are obtained, and a Lyapunov-function-based feedback control is constructed that ensures asymptotic stability of the zero solution. Results of numerical simulation of the pipeline-system dynamics under the constructed control are presented. |
| Keywords | elastic pipeline, longitudinal and transverse vibrations, partial differential equations, Galerkin method, controllability, feedback control, Lyapunov function, asymptotic stability. |
| Citation | Gladun A. V., Velmisov P. A. ''On the Construction of Stabilizing Control for a Pipeline System'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 56-60. Available at: https://conf.svmo.ru/files/2026/papers/paper73.pdf. - Date of access: 25.09.2026. |
© SVMO, National Research Mordovia State University, 2026
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