Page 44 - Mechatronic Systems Modelling and Simulation with HDLs

2.7 SIMULATORS AND SIMULATION 33

The third point recommends the coarsening of the value range of variables, such
as occurs in electronics in the transition from an analogue to a digital consideration.
In this approach, the variables, and of course also the components and interaction
rules, are initially retained. But one value now covers a whole value interval in
the original model, the individual value of which can no longer be activated. This
may lead to changes in the formulation of interaction rules.
Finally, the fourth principle is based upon the combination of components and
variables. For example, the distortion of a capacitive pressure element in space
can be determined by a large number of positional variables. From an electrical
point of view, however, only the resulting capacitance of the structure is of interest
and not the strain. The capacitance, on the other hand, represents a single numeric
value which is, however, partially determined by the mechanical strain.
All these methods thus serve to obtain a simulatable description from the more
theoretical basis of a conceptual model without, in the process, losing the validity
of the application cases of interest.

2.7 Simulators and Simulation

2.7.1 Introduction

The models introduced in the previous sections can be automatically evaluated in
3
numerous ways. This is called simulation. Before electronics came into being,
attempts were made to construct mechanical equipment that displayed the same
relationships between the variables as was the case in the model. Worth mentioning
in this context is, for example, the tide prediction device (1879) by Lord Kelvin
or the mechanical differential analyzer (1930) by Vannevar Busch. After the sec-
ond world war the development of electronics resulted in the analogue computer,
which was successfully implemented in the aircraft industry, for example. The
field of simulation gained new impetus with the introduction of the digital com-
puter, which brought the advantage that adaptation to a new simulation problem
did not require changes to the hardware, but only different software. Today we
differentiate between a whole range of simulator classes in the field of application
of mechatronics and micromechatronics, the most important of which are listed in
Table 2.1.

2.7.2 Circuit simulation

A circuit simulation considers networks of components such as transistors, diodes,
resistors, capacitors, coils, etc. The variables that are of interest here are gener-
ally voltages and currents. These are represented in continuous form. Nonlinear,
differential-algebraic equation systems have to be solved, which arise as a result

3 The word simulation is derived from the Latin verb simulare, which means to feign.