Connecting multiple DAE FMUs

[AnHeuermann]

As soon as we have decided on one or multiple mathematical representations for FMUs the question about connecting FMUs will arise.

How to:

• Connect (classic ODE) 3.0 ME/CS FMU with a new DAE 3.0 ME/CS FMU:
  • What limitations could this face?
  • What would an importing tool need to support this kind of connections?
• Connection of DAE 3.0 ME/CS FMU with another DAE 3.0 ME/CS FMU of the same differential index / class of DAE problem:
  • We need to insure that this still fits the mathematical representation the layered standards aims to support.
• Connection of DAE 3.0 ME/CS FMU with a DAE 3.0 ME/CS FMU of different index / class of DAE problem:
  • Is it possible to combine such FMUs?
  • What limitations could this face?

[ICG2000]

One thing that might be good to keep in mind here is that the combination of two DAEs with a certain index can, in general, yield a coupled system with a different index. For example

d/dt x_1 = y_1
0 = x_1 + y_1 + u_1

d/dt x_2 = y_2
0 = x_2 + y_2 + u_2

Both these systems have index 1 in [x_i, y_i], however, when combined with the coupling equations

u_1 = y_2
u_2 = y_1

The coupled system is not index 1 anymore (the determinant of the algebraic equations with respect to the algebraic variables is 0).

We can just ignore it and leave it to the user, I'm not sure (don't think) there's a way of avoiding it. But I thought it's good to keep it in mind.