The Fractional Order Models of a Thermal Trace on a Heat-Insulating Surface

eng Article in English DOI: 10.14313/PAR_254/13

send Krzysztof Oprzędkiewicz AGH University of Science and Technology, Department of Automatic Control and Robotics, al. A. Mickiewicza 30, 30-059 Kraków, Poland

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Abstract

The paper deals with a modeling of thermal trace at heat insulating surface with the use of two Fractional Order (FO) state space models. The fundamental distributed-parameter model was compared to simplified, lumped-parameter model, built with the assumption that the spatial heat transfer can be omitted. Such a comparison has not been presented yet. The simplifying assumption was confirmed experimentally in two ways. Firstly, the proposed lumped-parameter model assures the same accuracy in the sense of Integral Absolute Error (IAE) cost function as distributed-parameter model. Next, identified values of the heat transfer coefficient in the heat transfer equation are close to zero.

Keywords

2D heat transfer, Caputo definition, fractional order system, initial problem, thermal camera, thermal trace

Modele ułamkowe rzędu śladu termicznego na powierzchni izolującej ciepło

Streszczenie

W pracy omówiono zagadnienie modelowania śladu termicznego na powierzchni izolującej ciepło z wykorzystaniem modeli ułamkowego rzędu w przestrzeni stanu. Podstawowy model o parametrach rozłożonych porównano z jego uproszczeniem o parametrach skupionych, zbudowanym przy założeniu, że przestrzenne rozchodzenie się ciepła w materiale płyty może być pominięte. Takie porównanie modelu o parametrach rozłożonych z modelem o parametrach skupionych nie było dotąd prezentowane. Założenie upraszczające zostało potwierdzone doświadczalnie dwiema niezależnymi drogami. Po pierwsze, dokładność (w sensie wskaźnika jakości IAE) modelu o parametrach skupionych jest praktycznie taka sama, jak modelu o parametrach rozłożonych. Po drugie, wartości współczynnika przewodnictwa cieplnego otrzymane w wyniku identyfikacji modelu są bliskie zera.

Słowa kluczowe

definicja Caputo, dwuwymiarowe przewodnictwo cieplne, kamera termowizyjna, problem początkowy, ślad termiczny, system rzędu ułamkowego

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