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Paper details
Number 4 - December 2016
Volume 26 - 2016
Modeling heat distribution with the use of a non-integer order, state space model
Krzysztof Oprzędkiewicz, Edyta Gawin, Wojciech Mitkowski
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
non-integer order systems, heat transfer equation, infinite dimensional systems, Feller semigroups