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Fractional Modelling and Identification of a Thermal Process

Heat transfer problems are subject to diffusion phenomenon, and can be modelled with the help of fractional systems. The simulation of these particular systems is based on a fractional integrator, where the non-integer behaviour occurs only within a limited spectral band. A first model, based on the use of one fractional integrator, has been already defined and tested on a thermal pilot. Starting from frequency considerations derived from the analysis of a diffusion problem, a more general approximation of the fractional system is proposed here. The new model is based on the use of two fractional integrator operators. This makes it possible to define a state-space model for simulation of transients, and to use an output-error technique in order to estimate the parameters of the model. Experimental results obtained for a thermal process illustrate the improvements obtained using the proposed model.