Analysis of the bond graph model of hybrid physical systems with ideal switches

This paper deals with the modelling of hybrid physical systems. The bond graph technique is used to establish their knowledge model, based upon an ideal representation of the switches. These components are modelled either by flow or by effort sources according to their state and therefore modify the circuit topology at switching times. The paper shows the usefulness of the implicit representation to derive a unique implicit state equation with jumping parameters, to analyse the model properties, to derive an implicit state equation with nilpotency index one for each configuration and to compute the discontinuities. Also, a comparison between the chosen ideal modelling approach and the more common non-ideal approach is carried out using singular perturbations theory. After a presentation of the whole study in the most general context, its results are applied to power converters. which constitute a particular class of hybrid physical systems where switches only commutate in pairs. Finally, an example is developed.