Page 176 - Mechatronic Systems Modelling and Simulation with HDLs

8.1 MODELLING MICROMECHATRONIC SYSTEMS 165

developed in recent years for the solution of this problem. Firstly, we can consider
2
the various domains using coupled FE or BE simulators, see, for example, Cai
et al. [57], Gilbert et al. [119] or Senturia et al. [381]. The other possibility is to
accommodate the various domains in one FE simulator on the basis of appropriate
finite elements, such as, for example, in Funk et al. [108]. In the first case the
participating simulators are called up sequentially until a state is reached that is
both stable and also compatible with all domains. Such a state is also called self-
consistent. In the other case, the analyses of the various domains within a simulator
are iterated, with a self-consistent solution only being reached after a while.
In addition to the analysis of the predetermined design, the exploration of the
design space is also supported in some cases. For example, Lee et al. [223] propose
a technique called ‘Design-Window’, which replaces the single passage through all
predetermined parameter combinations with a search led by a neural network. The
number of iterations through automatic 3D modelling, meshing, and FE simulation
operations run by the system, is thereby minimised.

8.1.3 System design

In contrast to the previous section, in system design the environment of the com-
ponents has to be taken into account. In our context this is normally a circuit that
either effects the triggering of a micromechanical actuator or the read-out of a
micromechanical sensor.
Which models are suitable for describing the mechanics in a MEMS? A whole
range of criteria can be drawn up here, which should ideally be fulfilled. In most
cases, however, we are still a long way removed from this. In our context a
mechanics model should:

• be sufficiently precise to correctly represent reality;

• be efficiently simulatable, so that the computing time remains within reason-
able limits;

• not cause numerical problems;
• permit the setting of all significant design and technology parameters, in order
to thus ensure the general applicability of the model;
• describe (quasi-)static and dynamic behaviour;

• be able to formulate the retention and dissipation of energy in relation to the
application.

In addition, there is also the problem of determining the main material and
technological parameters. Examples of these parameters are fabrication-related

2 FE: finite elements, BE: boundary elements.