Page 58 - Mechatronic Systems Modelling and Simulation with HDLs

3.3 MODEL TRANSFORMATION 47

Integrator Differentiator
U = dx/dt U = x U = x U = dx/dt
C diff = 1F
U* G int I = I
in
U in I D D
C = 1uF R*I D
G int = 1uS int R = 1Ohm
U = 0V
D

Figure 3.3 Equivalent circuits for integrator and differentiator

right-hand side of Figure 3.3 to the value f(x, ˙x, t). The circuit simulator ensures
that no current flows into the differentiator and thus solves the differential equation.
It is also worth mentioning that the, somewhat tiresome, process of converting
a system of differential equations has been automated using the MEXEL CAE tool,
see Pelz et al. [322]. A model transformer reads in the differential equation system,
simplifies it if necessary, and then writes out a Spice net list in explicit or implicit
formulation.

3.3.3 Logic/Petri net simulation
Introduction

Predicate/transition networks (Pr/T networks), see [115] represent an extension of
Petri nets and are often used for the modelling of software and/or digital elec-
tronics. They permit a system description on a very abstract level in which the
use of hierarchies permits particularly compact representations. The strength of
Pr/T networks lies in the effective consideration of parallel processes. Brielmann
et al. [46], [47], [48] and Kleinjohann et al. [199] introduce methods for describ-
ing mechanics and other physical domains, plus the associated interfaces using
the resources of the Pr/T networks. Such model transformations thus provide the
option of describing and simulating mixed systems in a consistent manner. The
representation of the hardware description language VHDL in a coloured Petri net
by Olcoz and Colom in [301] shows that Petri net simulation and logic simulation
are not so very different from each other, which means that the events portrayed
in the following section could well be achieved on the basis of digital hardware
description languages.

Definition of Predicate/Transition nets

Pr/T nets consist of places, transitions, and directional edges between these. Places
can contain identifiable markings, which represent the state of the network. If a
marking is sufficiently high at the inputs of a transition and if these satisfy any
additional conditions, then the transition can ‘fire’. In this case the markings in