Identification of a thermal system using continuous linear parameter-varying fractional modelling

In this study, the authors present an identification procedure of a non-linear thermal system that exhibits a diffusive interface. Indeed, the system deals with heat conduction in a homogeneous material through a wall. Heating front face temperature dynamics when random heat flux is applied to the wall´s front face area are considered. If the thermophysical properties of the material depend on the temperature, the heat equation is not linear anymore. Hence, in order to explicitly take into account the dependence of the system dynamics on the temperature, a fractional continuous linear parameter-varying model is used and determined thanks to a local approach composed of two steps. First, the authors show that for small heating temperature variations, the heat diffusion can be modelled with the help of a local fractional model based on a fractional integrator operator of order (1´2), which acts only over a limited spectral band. The transfer function parameters of this model are estimated thanks to an output-error technique at different initial temperature-operating points. Secondly, the transfer function parameters dependence with respect to the initial temperature of the material is obtained by direct polynomial interpolation. Simulations using ARMCO iron are used to demonstrate the performances of the proposed local approach.