Structural Decomposition of Process Models Described by Higher Index DAE Systems

Abstract

Abstract A graph-theoretical method for the structural analysis of dynamic lumped process models described by differential and algebraic equations (DAEs) is applied in this paper in order to determine the most important solvability properties (degree of freedom, structural solvability, model decomposition, dynamic degree of freedom, differential index, e.g.) of these models by using the so-called dynamic representation graph. The structure of the dynamic representation graph is suitable for the determination of the mentioned solvability properties. The aim of our work is to show a decomposition procedure in case of higher index models. This method shows the subpart which causes the higher index and the position of this part in the hierarchy of structurally solvable submodels. Using this procedure we can answer the generally not simple question that in case of large process models which submodel or submodels cause the higher index and what the positions of these submodels are in relation to the other, structurally solvable submodels in the model.