<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Department of Automatics and Biomedical Engineering AGH University of Science and Technology, al. A. Mickiewicza 30, 30-079 Kraków,

Department of Computer Sciences High Vocational School in Tarnów, al. A Mickiewicza 8, 33-100 Tarnów,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Article Category: Individual Article Information

Published Online: Dec 30, 2016

Page range: 749 - 756

Received: Dec 15, 2015

Accepted: Aug 28, 2016

DOI: https://doi.org/10.1515/amcs-2016-0052

© by Krzysztof Oprzędkiewicz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.