Page 63 - Mechatronic Systems Modelling and Simulation with HDLs

52 3 MODELLING AND SIMULATION OF MIXED SYSTEMS

For the variant of model transformation on the basis of a FE simulator, the field
of application of a corresponding solution is only a little wider than that of the
FE simulator. This is also emphasised by the fact that there is comparatively little
literature in this field.

3.4 Domain-Independent Description Forms

In this section approaches will be described that cannot be classed as an expansion
of the tools in a certain domain. The most important representatives here are
bond graphs, block diagrams and modelling languages such as Modelica, Dymola
or ACSL.

3.4.1 Bond graphs

The bond graph approach, see for example Karnopp and Rosenberg [180] or Thoma
[398], fundamentally rests upon the same principles as the analogies in electronics
and mechanics, see Section 3.2.2. However, there is one significant difference. In
the analogies, currents were generally identified with forces/moments and voltages
with velocities, so that an analogy in the form of an equivalent circuit has the same
structure as the original system. This is true because according to Kirchhoff’s laws,
currents and forces add up to zero at a node and voltages and relative velocities
add up to zero in a closed loop.
By contrast, in the bond graphs, the following classifications are made. Voltages
are normally associated with forces/moments and called effort, currents are asso-
ciated with velocities/angular velocities and called flow. The elements used in the
bond graph approach can be divided into one, two and three-port networks. The
one-port networks are the so-called C, I and R elements, which in electronics cor-
respond with capacitors, inductors and resistors and in mechanics correspond with
springs, masses and dampers, see Table 3.2. In addition there are sources for effort
and flow. Transmission elements and gyrators are defined as two-port networks.
The former transmit effort to effort or flow to flow in a fixed or variable relation-
ship to one another; the latter put the effort, on the one hand, into a relationship
with the flow, on the other (and vice versa). Transmission elements can thus be
transformers, gears or levers for small deflections. A gyrator could for example
describe a DC motor. The three-port networks finally represent serial or parallel
junctions (s-junction, p-junction). The one, two and three-port networks are linked
together by half arrows, so-called bonds, which each bear an effort and a flow. The
direction of the arrow shows the direction of the positive power flow. The work
done is found by the product of effort and flow. In addition to the half arrows of
the bonds there are also connections with a full arrow, in which either the effort
or the flow is neglected. These connections carry information, but no energy.
The calculation of bond graphs first of all requires the drawing up of a suitable
system of equations, which is generally explicitly formulated. This means that the