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### Integer order vs fractional order temperature models in the forced air heating system DOI:10.15199/48.2019.11.09

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The use of electric heating in building automation and air conditioning systems has many advantages. Electric heaters are easy to control and they allow to fast obtain preset temperature. The electric heating has been discussed by many Authors, e.g. the dynamics of electric floor heating systems is analyzed in the paper [6], the energy-efficient electric heating is discussed in [8]. The construction of control algorithm requires to know the model of a process. The heat processes inside buildings can be described by different models. For example the paper [7] analyzed transfer function models of electrically heated room, the paper [4] proposes transfer function, non integer order models of room heating with the use of radiator. The fractional calculus is a very useful tool to describe many physical phenomena. Fractional Order (FO) or equivalently noninteger order models for different physical phenomena are presented by many Authors, e.g. [1], [3], [5], [13],[18], [19]. It is also well known that heat processes can be described using FO approach. This issue has been investigated e.g. by [12], [13], [15], [14]. The models can have a form of a FO transfer function, a FO partial differential equation or a FO state equation. This paper is intented to compare integer order (IO) vs FO transfer function models of the forced electric heating system. The considered system works in a pharmaceutical factory. It is required to keep predefined, constant, relatively high temperature in insulated room with cubature about 75m3. The paper is organized as follows: at the beginning, some elementary ideas from FO calculus are presented. Next, the considered heating system is described and the FO transfer function models with suitable approximations are proposed. Finally the models are verified with the use of experimental data obtained from SCADA system. Preliminaries 0.1 Basic ideas from fractional calculus A presentation of elementary ideas[...]

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