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Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 7, pp. 445452
DOI: 10.17587/mau.17.445-452


Qualitative Distribution of Modes in the Systems with Distributed Parameters

V. V. Grigoriev, grigw@yandex.ru, S. V. Bystrov, sbystrov@mail.ru, ITMO University, St.Petersburg, 197101, Russian Federation, O. K. Mansurova, erke7@mail.ru, National Mineral Resources University (Mining University), St. Petersburg, 199106, Russian Federation, I. M. Pershin, ivmp@yandex.ru, North-Caucasian Federal University, Pyatigorsk Branch, Pyatigorsk, 357501, Russian Federation, M. I. Pershin, Pershinmaksim1992@yandex.ru, Southern Federal University, Taganrog, 347928, Russian Federation


Corresponding author: Grigoriev V. V., D. Sc., Professor, ITMO University, St. Petersburg, 197101, Russian Federation
e-mail: grigvv@yandex.ru

Received on November 11, 2016
Accepted on February 24, 2016

There are many continuous technological processes of high power, with huge material and energy flows. Their parameters can change not only in time, but also in space. The hydrolithospheric processes, the processes connected with heat treatment, diffusion, etc. (in the control theory this class of processes is called objects with the distributed parameters), can serve as an example. Mathematical models of such processes either are not known, or described by the equations in private derivatives. The main approaches, used for analysis of the linear objects with the distributed parameters [614] are based on the theory of differential equations in private derivatives and frequency methods. Without a loss of the linear objects with the distributed parameters we will set the task of application of the qualitative theory [1519] for a synthesis of the control systems with the distributed parameters. We should note that for the distributed objects a decomposition of their mathematical models on the own vector functions of the operators of objects, the own movement of which is described by large dimensional differential equations, takes place. The technique of synthesis of the distributed regulators using the qualitative theory is considered on the example of construction of the closed control systems of the heat distribution process in a plate of the final sizes.

Keywords: distributed systems, areas location parameters, Nyquist criterion, qualitative distribution


Acknowledgements: This work was supported by the leading universities of Russian Federation (grant 074-U01) the Ministry of Education and Science of the Russian Federation, Project no. 14.Z50.31.0031.

For citation:
Grigoriev V. V., Bystrov S. V., Mansurova O. K., Pershin I. M., Pershin M. I. Qualitative Distribution of Modes in the Systems with Distributed Parameters, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 7, pp. 445452.
DOI: 10.17587/mau.17.445-452

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