Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Bulletin of the Polish Academy of Sciences. Technical Sciences

3 Oprzędkiewicz Krzysztof

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: równanie stanu rzędu ułamkowego

Sortuj według:

Ogranicz wyniki do:

The discrete, fractional order model of a two-dimensional temperature field using Grünwald-Letnikov definition

Oprzędkiewicz Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

2024

Vol. 72, nr 4

art. no. e150332

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

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

Oprzędkiewicz Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

2023

Vol. 71, nr 4

art. no. e145675

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.

Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator

Oprzędkiewicz Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

2021

Vol. 69, nr 1

art. no. e135843

In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.