Network-based Modeling and Index Analysis of Coupled Electro-Mechanical Systems

We consider the modeling of multi-physics dynamical systems, in particular the coupling of mechanical and electrical subsystems. The current state of the art in modeling and simulation tools like Dymola or Matlab/Simulink is a network-based modeling via interconnection of several standardized subcomponents. This approach of modeling dynamical systems leads to differential-algebraic equations (DAEs) that can easily be of very high index. In these tools the usual way to deal with high index DAEs is to use computer-algebra packages and symbolic differentiation to identify and resolve the algebraic constraints to obtain a system in minimal coordinates. This approach has several disadvantages. In this contribution we propose a new remodeling approach for coupled electro-mechanical systems. The first step is based on an index reduction formalism for each uni-physics subcomponent by using so-called minimal extension yielding a minimally extended index 1 formulation for each subcomponent. In a second step the index of the overall coupled system is analyzed. We provide conditions for the coupled system to be of index 1.