A Structural-Algebraic Approach for Coupled DAE Systems
Lena Scholz · 2012
Modeling and simulation of multi-physical systems is an important issue in many industrial applications. In modern simulation packages such as DYMOLA or MATLAB/SIMULINK the modeling of multi-physical systems is usually based on a network of subsystems for the different physical domains coupled together via certain interface conditions. This modeling of dynamical systems via interconnected subsystems leads to differential-algebraic equations (DAEs) that require certain regularization techniques to guarantee stable and robust numerical computations [1]. In most simulation environments computer-algebra packages and symbolic differentiation are used to identify the constraints and interface conditions based on generic structural information and to resolve these conditions in order to obtain a system in minimal coordinates. However, even for very simple examples an index reduction based on structural properties, as e.g. used by Pantelides algorithm [3] or in the structural analysis of Pryce [4], can fail if the system is structurally singular.