Deriving simulation models from bond graphs with algebraic loops. The extension to multibond graph systems

The first part of this paper makes an introduction to the causal problems r aised in some bond graph models when implementing causality. As a consequen ce, zero-order causal paths (ZCPs) provided of algebraic loops appear. Vari ables involved in these loops are related themselves by means of algebraic assignments. An algorithm to detect and open all the zero-order causal path s existing in any bond graph model is described. Opening of topological loo ps will be the employed method. Break variables will be the key to open the loops. The algorithm selects in an optimized way the number of variables n ecessary to open all the topological loops corresponding to the ZCPs existi ng in the model. The result is a set of differential-algebraic equations so lved using a backward-differential formulae numerical method. How to solve multibond graph systems including zero-order causal paths is the subject of the second part of this paper. The constitutive relationships of multibond resistors, transformers and gyrators give way to a new class of zero-order causal paths whose most important characteristic is that their associated topological loops involve more than one direction. In medium-large models t hese relationships produce a combinatory explosion of causal paths only tre atable via software. The same presented algorithms will be able to analyze and optimally choose the appropriate break variables to open all the zero-o rder causal paths. (C) 2000 The Franklin Institute. Published by Elsevier S cience Ltd. All rights reserved.