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ArticleOriginal scientific text

Title

Modeling heat distribution with the use of a non-integer order, state space model

Authors 1, 2, 1

Affiliations

  1. Department of Automatics and Biomedical Engineering, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-079 Kraków, Poland
  2. Department of Computer Sciences, High Vocational School in Tarnów, al. A Mickiewicza 8, 33-100 Tarnów, Poland

Abstract

A new, state space, non-integer order model for the heat transfer process is presented. The proposed model is based on a Feller semigroup one, the derivative with respect to time is expressed by the non-integer order Caputo operator, and the derivative with respect to length is described by the non-integer order Riesz operator. Elementary properties of the state operator are proven and a formula for the step response of the system is also given. The proposed model is applied to the modeling of temperature distribution in a one dimensional plant. Results of experiments show that the proposed model is more accurate than the analogical integer order model in the sense of the MSE cost function.

Keywords

ENG
POL
non-integer order system, heat transfer equation, infinite dimensional system, Feller semigroups

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Additional information

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

International Journal of Applied Mathematics and Computer Science
2016/26/4
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Pages:
749-756
Main language of publication
English
Published
2016

DOI: 10.1515/amcs-2016-0052

Exact and natural sciences