On extending transitions logic in hybrid dynamic systems based on bond graph and Petri nets combination

Abstract

In order to better take into account complexity of the heterogeneous dynamics in hybrid dynamic systems (HDS); we propose an unified and integrated fuzzy logic hybrid approach extending the concept of a classical switch bond graph modelling to a logical transition that takes into account a gradation instead of abrupt behavioural changes. It allows extension of the reachable states space where we propose real physical intermediate states (fluidification) that can be maintained with a sense. We also modify the mathematical structure of ideal primitive switching element (PSTS) by proposing a formula based on predictive and effective notions that fully comply with standard bond graph syntax and semantics as well as the Petri Nets, grants a freedom of the sampling instants according to the solver. We demonstrate the effectiveness of our approach on a flow control bi-tank and its usefulness both in academia and industrial field. Finally, we discuss some ideas about discrepancy between the level of mathematical abstraction and that of the physical level.