Parameter identification for the fractional order, state space model of heat transfer process using Atangana-Baleanu operator

Abstract

In the paper the parameters identification problem for a new, non integer order, state space model of heat transfer process is presented. The proposed model uses Atangana-Baleanu derivative operator. The analytical formula of step response is proposed. The parameters of the model are estimated via numerical minimization of the Mean Square Error (MSE) cost function. Finally the proposed model is compared to fractional order models using Caputo (C) and Caputo-Fabrizio (CF) operators. Results of numerical tests show, that the accuracy of the proposed model is better than accuracy of CF model, but worse, than accuracy of the C model.