Optimal control of fluctuations of the “liquid substance - pipeline” system in terms of speed during transportation of a liquid substance

The process of transporting a liquid substance (oil, petroleum products, gas mixtures) the pipeline network and related engineering facilities, being a dynamically non-equilibrium physical system, are often carried out in extreme modes, which can form dangerous wave phenomena accompanied by various instabilities, generating undesirable consequences and even catastrophes. Similar phenomena can occur in technical devices and apparatuses containing in their design hydraulic networks for the transfer of continuous media (aircraft, energy objects). Eliminate (extinguish or reduce the intensity) such phenomena are possible in the shortest possible time by making additional structural changes to the pipeline network, which make it possible to use external devices for dynamic influence on the “liquid substance – pipeline” system and eliminate (or minimize) the possibility of negative wave effects. The paper is devoted to the problem of eliminating dangerous vibrations initiated by a liquid substance transported through a pipeline network, provided that time resources are spent minimally. A mathematical model of the wave process and the problem of optimal control over the speed of such a model are considered. The control effect on the “liquid substance-pipeline” system is carried out at the initial and final points of the pipeline network, while the necessary information about the state of the system is used in a finite number of points distributed along the entire length of the pipeline, which makes it possible to calculate external influences on the system. In order to simplify the presentation of the results, a linear carrier of a liquid substance is used (in applications, a pipeline without branches) and a one-dimensional wave equation – the length of the pipeline is much larger than its diameter.