Page 27 - Mechatronic Systems Modelling and Simulation with HDLs

16 2 PRINCIPLES OF MODELLING AND SIMULATION

All the methods described up to this point relate to the description of an error-
free system. This is worthwhile if the simulation is to contribute to the actual
design. In some cases, however, the aim is to investigate the effect of errors within
the system. In this case error modelling is called for. One application for this is
the evaluation of measures to increase intrinsic safety; another is the evaluation
of test methods for differentiating between functional systems and rejects during
production. In both cases, errors that impair the function of the system under
consideration are modelled. Here too the modelling represents an abstraction of
reality, which in the ideal case covers several error mechanisms. For example,
the stuck-at error model in digital electronics describes the permanent presence
of a logical 0 or logical 1 at a signal of the circuit. Whether this is caused by a
short-circuit with a supply cable or by excessively deep etching of contact holes is
of secondary importance. The decisive point is that the circuit no longer functions
correctly and that this problem can be detected by the tests developed.
Due to their importance, structural, physical and experimental model develop-
ment will be considered in more depth in the following. Finally, we note that
specialist fields, such as modelling with neural networks, fuzzy techniques or
genetic programming, will not be considered.

2.4.2 Structural modelling

Introduction

A structural model is characterised by the basic models used and the connection
structure between these basic models. A module can be composed of basic models
and can itself be again connected to other modules. This can be performed succes-
sively, thus describing complex systems. A structural model can be characterised
on the basis of the following terms: Hierarchy, modularity, regularity and local-
ity. The hierarchy of a model is derived from the call structure of basic models
and modules. So an operational amplifier (=module) can be put together from
MOS transistors (=basic models) and then circuits can be built up from opera-
tional amplifiers. Using graph theory, such a hierarchy can be described as a tree,
in which the roots represent the system as a whole and the leaves represent the
basic models. The number of levels of the hierarchy grow in a logarithmic rela-
tionship to the number of basic elements involved. The modularity of the system
relates to the question of how simple and reasonable it is to divide the system
into modules. Regularity is a measure of how many module types are necessary to
represent the entire system. A low number is beneficial here because it indicates
a compact representation. Finally, locality is a measure of how well a module can
be considered without the context of its installation. Modules with straightforward
interfaces to their outside world are particularly beneficial here.
In the following, models are considered in the form of circuit diagrams, state
graphs, multibody diagrams and finite elements. Further descriptions with structural