Approximation methods to embed the non-integer order models in bond graphs

In this paper, a methodology to approximate a class of in3nite dimensional models by a bond graph model is investigated. This procedure is designed to preserve the passivity of the initial model. Through interconnections of passive elementary blocks (passivity is stable under interconnections), a 3nite dimensional passive approximate model is constructed. This 3nite dimensional model, if need be, is reduced thanks to a Krylov–Lanczos process. Finally, a bond graph realization of this reduced-order model is given. An example (a fractional power pole model) and an application (the CRONE suspension) demonstrate the usefulness of the whole approximation procedure. The paper ends with the discussion of the reduced-order model initial conditions determination problem in the non-integer order case. ? 2003 Published by Elsevier B.V.