Bond graph/Digraph matching procedure and symbolic determination of state space descriptor systems

摘要

In the context of structural analysis of descriptor systems (i.e. Ex(t) = Ax(t) + Bu(t), with E singular, also called singular systems, generalized state space systems, or differential-algebraic systems [1, 2, 3]), this paper proposes an extension of existing procedures to determine the state-space descriptor form from the bond graph model, relaxing simplified assumptions. Using this state-space representation, we also propose to build the exact corresponding digraph of a (bi)causal bond graph. This correspondence is used to rigorously adapt, by means of the digraph tool, the graphical computation of the characteristic polynomial det (sE - A) or the determinant of the Rosenbrock matrix det (P(s)) directly from the bond graph model (not presented in this paper).