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vol 62 / August, 2019
Article

DOI 10.17586/0021-3454-2017-60-9-863-868

UDC 28.50

MATHEMATICAL MODEL OF HYDROLITHOSPHERIC PROCESSES

S. V. Bystrov
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate professor


V. V. Grigoriev
ITMO University, Saint Petersburg, 197101, Russian Federation; Professor


O. K. Mansurova
University of Mines, Department of Technological Process Automation and Production; Associate Professor


I. M. Pershin
North Caucasus Federal University, Pyatigorsk Institute; Department of Control in Technical and Biomedical Systems; Professor, Head of the Department


M. I. Pershin
NCFU, Branch in Pyatigorsk; Department of Control in Technical and Biotechnical Systems; Post-Graduate Student


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Abstract. It is noted that many of hydrolithospheric processes are described by partial differential equations, and corresponding mathematical models do not have analytical solutions; in several cases, there are no mathematical models, too. Therefore, to solve a practical problem, such as synthesis of control system of flow rate of producing wells or formation of an optimal technological modes of operation field, it is necessary to develop an approximate model. A method of approximating model construction for a hydrolithospheric process is presented. The proposed approach is based on the methods of frequency synthesis and distribution of high-quality modes theory. Design of distributed regulators using the developed method is reported to ensure required quality parameters.
Keywords: hydrolithospheric processes, distributed objects, partial differential equations

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