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Fractional discrete-continuous model of heat transfer process

Oprzędkiewicz Krzysztof, Dziedzic Klaudia

Archives of Control Sciences

2021

Vol. 31, No. 2

287--306

The paper proposes a new, state space, finite dimensional, fractional order model of a heat transfer in one dimensional body. The time derivative is described by Caputo operator. The second order central difference describes the derivative along the length. The analytical formulae of the model responses are proved. The stability, convergence, and positivity of the model are also discussed. Theoretical results are verified by experiments.

Non integer order, state space model of heat transfer process using Atangana-Baleanu operator

Oprzędkiewicz K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2020

Vol. 68, nr 1

43--50

In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.

Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator

Oprzędkiewicz K., Dziedzic K., Więckowski Ł.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 5

905--914

The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.