Clarify the meaning of "top level input variables that are connectors"

[casella]

Section 4.8, Definition 4.4, says that one must count extra local equations for

1. input and flow variables present in each (top-level) public connector component.
2. (top-level) public input variables that neither are connectors nor have binding equations

Consider this simple MWE

model M
  connector RealInput = input Real;
  RealInput u;
end M;

It seems obvious to me that this model is balanced, because the variable u is meant to be computed elsewhere and passed to this model as an input. That's the pattern used in Modelica.Blocks.Interfaces.SISO. In fact, if one looks at the pattern of the SimpleAir example model in Section 4.8, the structure is the same, and indeed in that model the 2 + nXi connector input variables are counted as "variables inside connectors". On the other hand, it also seems to me that u is not an input variable inside a connector component, but rather itself an input variable that is also a connector; hence, according to rule 2., it shouldn't be counted. But that doesn't make sense to me.

What is the meaning of "public input variables that are connectors", and why should they not be counted as extra equations for balanced models?

[henrikt-ma]

Aren't you simply interpreting the present in in a non-favorable way? My understanding is that u is "in" a public connector component.

[casella]

Aren't you simply interpreting the present in in a non-favorable way? My understanding is that u is "in" a public connector component.

I guess so, that's why I'm asking for a clarification 😃

As I wrote, what is not clear to me is in which specific case the input variable should not be counted, i.e., the public top level input variable that is a connector. Could you make a concrete example of that?

[HansOlsson]

The key part is that there are different rules regarding the bindings; so consider:

  input Real u1=2;
  input Real u2;

Here u2 adds an extra equation (similarly as an input connector), but u1 doesn't.

For variables that are part of connectors it can be more complicated, as some of the bindings have reverse causality, like Q_flow in Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPortWithoutT (not input, will have to check if there are any similar for that case).