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40                          3  MODELLING AND SIMULATION OF MIXED SYSTEMS


               or inductances, the consideration of active components or entire circuits has hith-
               erto only been realised in experiments. One possible reason for this is that when
               developing mechanical parts of the system it is often sufficient to describe the
               electronics in abstract form using controller equations and thereby to avoid the
               circuit level.
                 There are also some approaches that attempt to model the entire electro-
               mechanical system as a unit without any preference for electronics or mechanics.
               These methods include bond graphs, block diagrams, and modelling languages
               such as Modelica. Despite the elegance of these description forms it is generally
               found that neither the electronics nor the mechanics can be modelled with the usual
               standard procedures, see Section 3.4.
                 Finally, the possibility of coupling together simulators for different domains
               represents a further approach to solving the problem. This could, for example,
               occur systematically with the aid of a simulator backplane, as is often created for
               pure electronics. Typical applications for this are the coupling of circuit and logic
               simulators or the distribution of simulations on a parallel computer or a cluster
               of workstations. However, simulator coupling is associated with a whole range of
               problems: Firstly the resulting simulator package is unwieldy, it is often difficult
               to operate, and licences are required for all of the individual simulators. Secondly,
               the problems associated with synchronisation between two very heterogeneous
               simulator cores are even more severe, see Section 3.5.
                 At this point it should be re-emphasised that this work deals with the simulation
               of mixed systems. Electro-mechanical components will be considered only within
               the context of the system.



               3.2     Electronics and Mechanics


               3.2.1    Introduction

               The following section will investigate the common ground and differences between
               electronics and mechanics and the associated models. For this purpose the mod-
               elling of the two domains will be considered on the level of an abstraction, see
               Figure 3.1. On the lowest level we find the consideration of electrical and mag-
               netic fields and of the mechanical continuum. In electronics such considerations
               are required exclusively for the design of components, e.g. transistors, and this
               approach is known as device simulation. In the present context, however, we are
               interested in systems and therefore this type of simulation can be disregarded.
               Above this we find circuit simulation, which considers net lists of electronic com-
               ponents. In digital circuits we can convert continuous voltage levels into discrete
               values, such as 0 and 1, thereby significantly accelerating the simulation. Using
               digital electronics we can build processors on which software runs, which can
               itself act as an abstraction level. In mechanics, on the other hand, it has hitherto
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