In
industrial applications, the automatic modeling of systems
consisting of mechanical or electrical devices or couplings thereof
leads to differentialalgebraic equations  DAEs. Besides the large
scale, these systems usually are of high
index,
which is, roughly speaking, a measure of the order of the derivative of
a perturbation that enters the solution of a perturbed DAE. A high
index causes severe problems in the numerical solution of DAEs
like for example the reduction of convergence order; therefore it is
necessary to
remodel
the system as an equivalent but indexreduced DAE. In general, this
remodeling leads to an
unstructured model that, at first glance, has no reinterpretation as an
electrical or mechanical system. Since common simulation packages like
SIMPACK, Modelica and SPICE do not require a DAE model
but a socalled
network list, which is a special data format
containing information about the interconnection structure of the sytem
components, this is a great disadvantage.
For
electrical systems though, there is an index reduction technique
developed in the Matheon project D5
that obeys the structure of
the
specific network. In this
approach,
the index of the corresponding DAE is reduced by a
pure topological
analysis of the network, that detects the index
increasing sets,
i.e., loops of voltage sources and capacitances as
well as cutsets
consisting of current sources and inductances
and replaces them with equivalent structures of lower
index.


Correspondence of
mechanical and electrical quantities 
Mechanical 
~

Electrical 
Force 
~

Current 
Velocitiy 
~

Node Potential 
Impulse 
~

Charge 
Position 
~

Magnetic Flux 
Kinetic Energy 
~

Electrical Energy 
Potential Energy 
~

Magnetic Energy 

The aim of this project is to extend this graphtheoretical approach to
mechanical networks and thus to establish a structurepreserving
indexreduction of mechanical systems. Furthermore, exploiting the
equivalences between electrical and
mechanical systems, we aim to derive a nonindexincreasing
coupling procedure of electrical and mechanical structures to develope
a remodeling strategy for mechatronic systems.

Correspondence of
mechanical and electrical devices 
Spring 
~

Inductor 
Inerter 
~

Capacitor 
Damper 
~

Resistor 
Mechanical Ground 
~

Electrical Ground 



