Page 30 - Mechatronic Systems Modelling and Simulation with HDLs

2.4 MODEL DEVELOPMENT 19

number of basic models is small. But object-orientation is also becoming increas-
ingly prevalent in digital design using hardware description languages, although in
this context it should be regarded more in the context of an increase in efficiency
in the development of text-based, software-like models, see for example Ecker and
Mrva [93].
In mechanics object-orientation has only recently been implemented in order to
make modelling easier, whereby the work of Otter [308] and Kecskem´ ethy [185]
in particular, are worth mentioning. One explanation for this is the fact that the
number of basic elements and the associated variation in mechanics is significantly
greater than is the case in electronics. Furthermore, the classic modelling methods
of mechanical engineering often lead to descriptions in the form of generalised
2
coordinates, which are again incompatible with object-oriented modelling. The
advantage of the generalised coordinates is that the resulting equation system has a
minimum number of equations and, furthermore, the constraints can be disregarded
for holonomous systems. This is attractive from a numerical point of view. How-
ever, generalised coordinates can only be specified by drawing upon knowledge of
the entire system and not from the mole-hill perspective of a component.

Resulting equations

In this section we will investigate the equations that result from the various mod-
elling forms. From a mathematical point of view, a digital gate or the setting of
a digital signal in a hardware description language gives an instruction, which is
executed after the passage of a predetermined time period. This period corresponds
with the time delay of the described block. If the block is defined without a delay,
then a virtual period of time still passes, the delta time, in which although the sim-
ulation time does not proceed, a check is made to ensure that the right-hand sides
of all assignments have already been evaluated before the new value of the assign-
ment under consideration becomes effective. Otherwise the parallel processing of
instructions would not be possible.
In the case of an analogue circuit, the modified node voltage analysis is generally
used, see Vlach and Singhal [410] for a good overview. This establishes differ-
ential equations for capacitances and inductances. Transistor models can include
one or more parasitic capacitances. Otherwise the heart of transistor models, like
diode models, is made up of a parallel circuit consisting of a resistor and a current
source, the parameters of which have to be set for each new time interval. This
corresponds with an arbitrary linear characteristic that can be placed as a tangent
at the current working point on the nonlinear characteristic of the transistor. Volt-
age and current sources each correspond with constraints that are formulated in
algebraic equations. Resistors are also expressed in algebraic equations. Overall
a differential-algebraic equation system is established that is also known as DAE

2 See Section 6.2.