Thermal Modeling Using Two-Port Network Impedance Fractional-Order Approximations

Abstract

Sufficiently accurate thermal modeling is necessary for many applications such as heat dissipation, melting processes, building design or even bio-heat transfers in surgery. Circuit models help modeling heat transfer dynamics: this method is simple and is often used to model thermal phenomena. However, such models well approximates low and high frequency behavior but they are not accurate enough in the middle band of interest, thus lacking of precision in dynamical terms. A more complete and accurate description of conductive heat transfer can be obtained by using a two-port network. The resulting analytical expressions are complex and nonlinear in the frequency ω. This complexity in the frequency domain is difficult to handle when it comes to control applications and more specifically in real-time applications such as surgery. Consequently, an analysis of this thermal two-port network in the frequency domain directly leads to fractional-order systems. A frequency domain analysis of the series and shunt impedances will be presented and different approximations will be explored in order to obtain simple but sufficiently precise linear fractional transfer function models. The series impedances are approximated by using asymptotic and pole-zero approximations and the shunt impedance is approximated by using a capacitance approximation and two fractional model approximations.