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1 International Journal of Applied Mathematics and Computer Science

1 2016

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

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Oprzędkiewicz K. , Gawin E. , Mitkowski W.

tom 26

nr 4

749-756

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.