Approximation of a thermal diffusive interface fractional-order system — Part 1: Application to a semi-infinite plane

Abstract

As in the first part, the main purpose of this work is to derive some models used to the design and the validation of an automatic control system of temperature. After presenting, in the first part, the modelling and the approximation of the diffusive interface in the homogeneous semi-infinite plane medium, this second part deals with homogeneous finite plane medium. From partial differential equations that govern one-dimensional heat transfer, the transfer function of the medium is first computed considering the boundary conditions and the initial time temperature value. As for the semi-infinite plane medium, the fractional integrator of order 0.5 appears. However, for this case, it shows up for a limited frequency range. Then, a condition that permits to consider a finite medium as a semiinfinite medium around the crossover frequency of the control loop is proposed. If this condition is respected, then the method presented in the first part to approximate the fractional model by a rational model can be used to time simulation.