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Abstract

Nowadays, non-integer systems are a widely researched problem. One of the questions that is of great importance, is the use of mathematical theory of a non-integer order system to the description of supercapacitors (capacitors with very high capacitance). In the description of electronic systems built on a microscale, there are models with dis- tributed parameters of fractional derivatives, which can be successfully approximated by finite-dimensional structures, e.g, in the form of various types of ladder systems (chain). In this paper, we will analyze a ladder system of an RC type consisting of supercapacitors.
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Authors and Affiliations

Waldemar Bauer
Wojciech Mitkowski
Marta Zagórowska
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Abstract

In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.

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Authors and Affiliations

Krzysztof Oprzędkiewicz
Edyta Gawin
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Abstract

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.
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Authors and Affiliations

Krzysztof Oprzędkiewicz
1
ORCID: ORCID
Klaudia Dziedzic
1

  1. AGH University of Science and Technology in Krakow, Faculty of Electrical Engineering, Automatics, Computer Science and Robotics, Department of Automatics and Biomedical Engineering, Kraków, Poland

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