Page 62 - Mechatronic Systems Modelling and Simulation with HDLs

3.3 MODEL TRANSFORMATION 51

suitable tool, e.g. MATLAB/Simulink. In this connection a class of controllers
is prepared in [346] that includes continuous, proportional, discrete and mixed
controllers. Simple, electronic components can also be described on the same basis.
The underlying equations are added to the equations of motion of mechanics, and
the equations of sensors and actuators, and are then solved as a whole.

3.3.5 Finite-element simulation

One possibility for system simulation using a FE simulator is to fuse the equation
system of electronics together with the equation system of finite elements. The
resulting equations include the sought-after unknowns from electronics and me-
chanics. The complete system can thus be processed using a standard solver.
Particularly important in this context is the work of Bedrosian [22], who ex-
panded a finite element simulator for the calculation of electromagnetic fields so
that it could process both analogue circuits and also the kinematics of rigid bodies.
A significant aspect of this is to obtain a few desirable properties of FE matrices.
So in contrast to the matrix for the finite elements, the system matrix would be
neither positive definite nor sparse. Bedrosian therefore insists upon a separate
consideration of the matrices for the individual domains, which requires a suitable
iteration in order to obtain a consistent solution for the system as a whole.

3.3.6 Evaluation of the model transformation

The introduction of analogue hardware description languages has caused interest
in equivalent circuits for mechanical components to fall sharply. This is primarily
because a hardware description language is significantly more flexible in its for-
mulation. This is true particularly for components for which the analogies provide
no direct parallel. Furthermore, the overview is quickly lost if it is unclear what
the equivalent voltages and currents represent.
In principle, the modelling of continuous relationships on an event-oriented
basis — for example using digital logic or a Pr/T network — is nothing unusual.
Every simulator for analogue processes that is run on a digital computer has the
same fundamental problem to solve. The difference in the present case is that the
basic functions of the simulation, such as the integration procedure or the automated
selection of a suitable step size, have to be modelled fully by the user, which firstly
can be very cumbersome and secondly presumably raises a performance problem.
When discussing the simulation of mechatronic systems in a multibody simula-
tor it is particularly worth mentioning the elegant solution of Maißer [253], which
models the electronics according to the Lagrange principle, so that the resulting
equations are compatible with multibody simulation, which is also based upon
the Lagrange approach. However, the lack of any significant libraries of transis-
tor models and the fact that digital electronics and software are disregarded, are
problematic.