The positivity of the fractional order model of a two-dimensional temperature field

• Autorzy: Oprzędkiewicz Krzysztof

Identyfikatory

DOI

10.24425/bpasts.2023.145675

• Języki publikacji: EN

Abstrakty

EN

The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.

Słowa kluczowe

EN

heat transfer equation; fractional order state equation; Caputo operator; positivity; thermal camera; non-integer order systems

PL

równanie wymiany ciepła; równanie stanu rzędu ułamkowego; operator Caputo; kamera termowizyjna; systemy niecałkowitego rzędu; dodatniość

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 4
• Strony: art. no. e145675
• Opis fizyczny: Bibliogr. 40 poz., rys., tab.

Twórcy

autor

Oprzędkiewicz Krzysztof

• AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Kraków, Poland

• https://orcid.org/0000-0002-8162-0011

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).