Causal Bond Graphs and Forms of Mathematical Models

Abstract

After the discussion of the systematic construction of bond graphs, their causal augmentation and the systematic derivation of equations from a causal bond graph, we are prepared to consider different causal patterns in bond graphs and their relation with different forms of mathematical models in detail. As a general prerequisite, we assume that if controlled sources appear in a bond graph, their modulating signal can be expressed by system inputs or by state variables. Furthermore, if transformers and gyrators are modulated, they are allowed to be modulated only by state variables. The reason for this confinement is that otherwise, algebraic loops may result that are not easily detected by inspection of a causal bond graph as will be explained in more detail in Section 4.8.