Page 19 - Mechatronic Systems Modelling and Simulation with HDLs

8 2 PRINCIPLES OF MODELLING AND SIMULATION

generation of the behaviour at the pins. This is the highest level of validity and this
level in particular is required in order to understand the real system. A structurally
valid system is also predictively valid.

2.2 Model Categories

We can obtain an initial classification of models by considering the range of values
of the system variables, see for example Zeigler [435]. These may be continuous
or discrete. A range of values is continuous if it covers real numbers or an interval
of them. For example, a mechanical position has a continuous range of values. In
a discrete range of values, on the other hand, the system variable takes on a value
from a finite (or at least countable) quantity of values, as is the case for digital,
electronic signals. The states of the model take on a discrete, continuous or mixed
form depending upon the system variables.
Time is explicitly removed from the system variables and investigated in a
similar manner with respect to its value range. In the discrete case time proceeds
in leaps; valid time points are calculated as the product of a whole number and a
basic time span. This may, for example, be suitable if a gate simulation is run with
unit delays. By contrast, we can also consider models in which time is continuous.
These can be divided into two categories: event-oriented models and differential
equation models. In the former case each change of state of the model is triggered
by an event, so that the trajectory of system states proceeds in leaps. The events
themselves can occur at arbitrary points in time; their number in relation to a
predetermined time interval is however finite. By contrast, in models based upon
differential equations the trajectory of system states is continuous. Changes are
described on the basis of the system variables and their rate of change.
A further possibility for differentiating between models is based upon whether
the description uses concentrated or distributed parameters. Examples of the for-
mer case are electronic components or the fixed and elastic bodies of the multibody
representation of a mechanical system. Distributed parameters should be used in
the consideration of a mechanical continuum, for example.
Models may furthermore be of a static or dynamic nature. In the former case,
in electronics for example, when determining the operating point of a circuit it
is sufficient to represent capacitors as open circuits and coils as short-circuits. In
multibody mechanics stationary systems can be analysed. Dynamic models are
required in electronics for transient simulations, i.e. for those over a time range,
whereas in mechanics we can differentiate between two application cases: kine-
matics and kinetics, see for example Nikravesh [299]. Kinematics relates to the
investigation of positions, speeds and accelerations without taking into account
the forces that cause the movement they describe. Kinetics also considers the
acting forces.
In some cases a model cannot be described in a purely deterministic manner,
meaning that at least one random variable must be included. As an example, a