Page 47 - Mechatronic Systems Modelling and Simulation with HDLs

36 2 PRINCIPLES OF MODELLING AND SIMULATION

2.7.5 Block diagram simulation

5
A block diagram describes the structure of a system of mathematical equations in
graphical form. All connections between blocks are set up so that the causality of
the system can be determined in advance. This facilitates the creation of a simulator
for block diagrams that explicitly builds up system equations. Thus a sequence of
instructions can be processed during the simulation. This is more efficient than
an implicit formulation using ‘genuine’ equations. However, the causality must be
determined in advance and must not change during the course of the simulation,
which may well occur, depending upon the system.

2.7.6 Finite element simulation

Every finite element is characterised by its mass, damping and elasticity matrices.
These matrices are square; the number of rows and columns corresponds with the
number of degrees of freedom of the element. For small deflections the movement
of the mechanics can still be considered as linear. In this case it is sufficient to
establish the element matrices once at the beginning of the simulation. Otherwise,
the element matrices must be calculated afresh for every time increment.
In order to determine the behaviour of the entire structure, the element matrices
are now converted to system matrices. If two suitable degrees of freedom of two
neighbouring finite elements are linked together, then on the system level they
come together into one degree of freedom. In this manner, various degrees of
freedom are dispensed with on the element level. The resulting system matrices
have a band structure, for which certain solution procedures, e.g. the Cholesky
method, are particularly suitable.

2.7.7 Software simulation

The most obvious form of software simulation is performing it on a computer.
A debugger is generally available for this, which displays the processing of pro-
gramme instructions and the current variable value and outputs. The timing of
processing naturally varies according to the computer used, so that at this level
only functional investigations tend to be performed.
Furthermore, there are also so-called command set simulators, which consider
the software processing for a certain processor at assembler level. Timing can be
determined on the basis of the timing cycles that have elapsed. This is only the case,
however, if access to external resources, e.g. to a hard disk, can also be precisely
specified in the timing, which is rarely the case. For embedded processors such
resources are often not available, which means that in this case precise values can
often be obtained for the timing.

5 See also Section 3.4.2.