Modeling and optimal identification of pseudodifferential electrical dynamics by means of diffusive representation - Part 1: Modeling

We present the concept of "diffusive representation" and show how this notion can beused for modeling purposes in the field of electrical engineering, namely, when some nonrational dynamics are invloved. We examine two significant cases of electrical components, the standard models of which reveal themselves to be insufficiently accurate in several situations: 1) capacitors with dielectric relaxations and 2) an inductor with iron core. According to the diffusive representation approach, such components are modeled by convenient state-space input-output formulations of diffusive nature, well adapted to both analysis and cheap numerical approximations. Concrete numerical examples and simulations in the time domain are given and commented.