GenerationOfFMUs examples in the MSL are broken because of unrecognized redundant initial equations

[Francesco Casella]

The four GenerationOfFMU models in the MSL 3.2.3:
​Modelica.Electrical.Analog.Examples.GenerationOfFMUs
​Modelica.Mechanics.Rotational.Examples.GenerationOfFMUs
​Modelica.Mechanics.Translational.Examples.GenerationOfFMUs
​Modelica.Thermal.HeatTransfer.Examples.GenerationOfFMUs
all share the same issue. They involve the initialization of high-index systems with redundant and consistent initial equations. All of them fail during analyzeInitialSystem with this kind of error

Error: The given system is mixed-determined.   [index > 3]
Please checkout the option "--maxMixedDeterminedIndex".
Error: No system for the symbolic initialization was generated

I prepared a reduced model that replicates the issue, please find it attached. It contains the following two variable declarations with fixed = true

Real directCapacity.heatCapacitor.T(quantity = "ThermodynamicTemperature", unit = "K", displayUnit = "degC", min = 0.0, start = 293.15, fixed = true, nominal = 300.0) "Temperature of element";
Real inverseCapacity.mass.T(quantity = "ThermodynamicTemperature", unit = "K", displayUnit = "degC", min = 0.0, start = 293.15, fixed = true, nominal = 300.0) "Temperature of element";

and the following chain of equalities

directCapacity.heatCapacitor.T = directCapacity.heatCapacitor.port.T;
directCapacity.heatCapacitor.port.T = directCapacity.heatFlowToTemperature.heatPort.T;
directCapacity.heatFlowToTemperature.y = directCapacity.heatFlowToTemperature.heatPort.T
directCapacity.heatFlowToTemperature.y = directCapacity.heatFlowToTemperature.p;
directCapacity.heatFlowToTemperature.p = directCapacity.T;
directCapacity.T = inverseCapacity.T;
inverseCapacity.temperatureToHeatFlow.p = inverseCapacity.T;
inverseCapacity.temperatureToHeatFlow.u = Modelica.Blocks.Interfaces.Adaptors.Functions.state1({inverseCapacity.temperatureToHeatFlow.p, inverseCapacity.temperatureToHeatFlow.u1}, time);
inverseCapacity.temperatureToHeatFlow.u = inverseCapacity.temperatureToHeatFlow.heatPort.T
inverseCapacity.temperatureToHeatFlow.heatPort.T = inverseCapacity.mass.port.T;
inverseCapacity.mass.T = inverseCapacity.mass.port.T;

which is ultimately equivalent to

directCapacity.heatCapacitor.T = inverseCapacity.mass.T

that involves two differentiated variables, thus leading to an index-2 problem with overdetermined and consistent initial equations.

We do have algorithms in OMC to deal with this case (see ​paper). The chain of equality equations is trivial and handled by alias elimination, except for the equation

inverseCapacity.temperatureToHeatFlow.u = Modelica.Blocks.Interfaces.Adaptors.Functions.state1({inverseCapacity.temperatureToHeatFlow.p, inverseCapacity.temperatureToHeatFlow.u1}, time);

The function state1() has lateInline = true, so it should be eventually eliminated once the index has been analyzed. By turning on -d=optdaedump this seems to be the case: the pre-optimization phase ends with the state1() function call still in place

7/7 (1): inverseCapacity.mass.T = Modelica.Blocks.Interfaces.Adaptors.Functions.state1({directCapacity.heatFlowToTemperature.y, directCapacity.derT}, time)   [dynamic |0|0|0|0|] 

but then, the next time the dynamic equations are printed out, it shows up (correctly) as

7/7 (1): inverseCapacity.mass.T = directCapacity.heatFlowToTemperature.y   [dynamic |0|0|0|0|] 

However, for some reason the redundant equation is ultimately not eliminated, leading to a mixed-determined initialization problem.

I tentatively assign this issue to @Karim.Abdelhak, since he's working on index reduction. You may co-ordinate with @lochel, who wrote the algorithm to remove the redundant initial equations.