Adds input/output meta data

[ValentinKaisermayer]

Removes pesky warnings that the connector contains (non-flow, non-stream, non-input, non-output) variables but no flow variable.

[ValentinKaisermayer]

Can we please separate the irreducability from the inputs?
It can not be that this simple system with one state has five states in MTK.

@named c = Constant(; k=2)
@named gain = Gain(1;)
@named int = Integrator(; k=1)
@named fb = Feedback(;)
@named model = ODESystem(
    [
        connect(c.output, fb.input1), 
        connect(fb.input2, int.output), 
        connect(fb.output, gain.input),
        connect(gain.output, int.input),
    ], 
    t, 
    systems=[int, gain, c, fb]
)
sys = structural_simplify(model)

julia> sys
Model model with 5 equations
States (5):
  int₊x(t) [defaults to 0.0]
  int₊input₊u(t) [defaults to 0.0]
  gain₊input₊u(t) [defaults to 0.0]
⋮
Parameters (3):
  int₊k [defaults to 1]
  gain₊k [defaults to 1]
  c₊k [defaults to 2]
Incidence matrix:5×6 SparseArrays.SparseMatrixCSC{Num, Int64} with 10 stored entries:
 ×  ⋅  ×  ⋅  ⋅  ⋅
 ⋅  ⋅  ⋅  ⋅  ⋅  ×
 ⋅  ×  ⋅  ⋅  ×  ⋅
 ⋅  ⋅  ⋅  ×  ×  ×
 ⋅  ⋅  ×  ×  ⋅  ⋅

@YingboMa

[codecov]

Codecov Report

Merging #81 (e4eb600) into main (c9af29e) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main      #81   +/-   ##
=======================================
  Coverage   69.06%   69.06%           
=======================================
  Files          23       23           
  Lines         931      931           
=======================================
  Hits          643      643           
  Misses        288      288           

Impacted Files	Coverage Δ
src/Blocks/math.jl	100.00% <100.00%> (ø)
src/Blocks/utils.jl	61.53% <100.00%> (ø)
src/Thermal/HeatTransfer/ideal_components.jl	100.00% <100.00%> (ø)

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[baggepinnen]

The input should only be considered irreducible if !is_bound(state)

[ValentinKaisermayer]

The input should only be considered irreducible if !is_bound(state)

https://github.com/SciML/ModelingToolkit.jl/blob/fd279c0377da50331fe920d6dd62f2816e60b02d/src/variables.jl#L30

isirreducible(x) = isvarkind(VariableIrreducible, x) || (isinput(x) && !is_bound(x))

[ValentinKaisermayer]

SciML/ModelingToolkit.jl#1577