Implement Kinsol as non-linear solver for non-linear loops over components

[AnHeuermann]

Related Issues

#812, #808

Purpose

A fixed-point iterations is currently the only solver available to solve algebraic loops over components but not suitable for all problems.
Implementing KINSOL as alternative to the fixed-point iteration will enable more FMUs connected to run smoothly.

[AnHeuermann]

I need some test case to verify that everything is correct.
Do we have some FMUs with non-linear loops over them already? Otherwise I could add a test to OpenModelica or add some generated FMUs this testsuite.

Currently I'm using

loadModel(Modelica);

loadString("model loopsOverFMUsA
  Real a, b, c;
  Modelica.Blocks.Interfaces.RealOutput a_out;
  Modelica.Blocks.Interfaces.RealOutput b_out;
  Modelica.Blocks.Interfaces.RealInput c_in;
equation
  c = c_in;
  // Eq. 1 and 2 of loop
  a + b + c=0;
  2*a - 3*b + 2*c=9;
  a_out = a;
  b_out = b;
end loopsOverFMUsA;
"); getErrorString();

loadString("model loopsOverFMUsB
  Real a, b, c;
  Modelica.Blocks.Interfaces.RealInput a_in;
  Modelica.Blocks.Interfaces.RealInput b_in;
  Modelica.Blocks.Interfaces.RealOutput c_out;
equation
  a = a_in;
  b = b_in;
  // Equation 3 of loop
  a*a + b*b + c*c=5;
  c_out = c;
end loopsOverFMUsB;
"); getErrorString();

buildModelFMU(loopsOverFMUsA, fmuType="me"); getErrorString();
buildModelFMU(loopsOverFMUsB, fmuType="me"); getErrorString();

system("rm -rf FMU_A && unzip -qq loopsOverFMUsA.fmu -d FMU_A"); getErrorString();
system("rm -rf FMU_B && unzip -qq loopsOverFMUsB.fmu -d FMU_B"); getErrorString();

writeFile("loopsOverFMUs.lua","
oms_setTempDirectory(\"./temp/\")
oms_newModel(\"loopsOverFMUs\")
oms_addSystem(\"loopsOverFMUs.root\", oms_system_sc)

-- instantiate FMUs
oms_addSubModel(\"loopsOverFMUs.root.A1\", \"loopsOverFMUsA.fmu\")
oms_addSubModel(\"loopsOverFMUs.root.B1\", \"loopsOverFMUsB.fmu\")
oms_addSubModel(\"loopsOverFMUs.root.A2\", \"loopsOverFMUsA.fmu\")
oms_addSubModel(\"loopsOverFMUs.root.B2\", \"loopsOverFMUsB.fmu\")

-- connections: A1 -> B1
oms_addConnection(\"loopsOverFMUs.root.A1.a_out\", \"loopsOverFMUs.root.B1.a_in\")
oms_addConnection(\"loopsOverFMUs.root.A1.b_out\", \"loopsOverFMUs.root.B1.b_in\")
oms_addConnection(\"loopsOverFMUs.root.A1.c_in\", \"loopsOverFMUs.root.B1.c_out\")

-- connections: A2 -> B2
oms_addConnection(\"loopsOverFMUs.root.A2.a_out\", \"loopsOverFMUs.root.B2.a_in\")
oms_addConnection(\"loopsOverFMUs.root.A2.b_out\", \"loopsOverFMUs.root.B2.b_in\")
oms_addConnection(\"loopsOverFMUs.root.A2.c_in\", \"loopsOverFMUs.root.B2.c_out\")

-- simulation settings
oms_setResultFile(\"loopsOverFMUs\", \"loopsOverFMUs.csv\")
oms_setStartTime(\"loopsOverFMUs\", 0)
oms_setStopTime(\"loopsOverFMUs\", 0.1)

oms_instantiate(\"loopsOverFMUs\")
oms_setReal(\"loopsOverFMUs.root.B1.a_in\", 0.635425)
oms_setReal(\"loopsOverFMUs.root.B1.b_in\", -1.8)
oms_setReal(\"loopsOverFMUs.root.A1.c_in\", 1.16458)
--oms_setReal(\"loopsOverFMUs.root.B2.a_in\", 0.635425)
--oms_setReal(\"loopsOverFMUs.root.B2.b_in\", -1.8)
--oms_setReal(\"loopsOverFMUs.root.A2.c_in\", 1.16458)

oms_initialize(\"loopsOverFMUs\")
oms_simulate(\"loopsOverFMUs\")
oms_terminate(\"loopsOverFMUs\")
oms_delete(\"loopsOverFMUs\")
"); getErrorString();

system("OMSimulator loopsOverFMUs.lua --algLoopSolver=kinsol --logLevel=2"); getErrorString();

But it is a bit to simple to solve for a good test.

Also I'm not sure how to change values for B2.a_in, B2.b_in and A2.c_in in an automated fassion if the fmi2getReal function failed. We could add or substract 10% or something similar. But otherwise we need the user to give initial values that are good enough.

[AnHeuermann]

Okay, here comes an example that is ridiculous simple but impossible to solve for the fixed-point iteration. Just connect FMUA and FMUB in the obvious way:

model FMUA
  Modelica.Blocks.Interfaces.RealInput x_in;
  Modelica.Blocks.Interfaces.RealOutput x_out;
  Real y(fixed=true, start=2);
  parameter Real a = 2;
equation
  der(y) = a*y;
  x_out = 2*x_in-y;
end FMUA;

model FMUB
  Modelica.Blocks.Interfaces.RealInput x_in;
  Modelica.Blocks.Interfaces.RealOutput x_out;
equation
  x_out = x_in;
end FMUB;

But we have a remaining problem: The equation system during initialization

warning: Alg. loop (size 2)                                                                                                                                                 debug:   debug:   Create new KinsolSolver object for algebraic loop number 0
debug:   Solving algebraic loop formed by connections
                A.x_out <-> B.x_in
                B.x_out <-> A.x_in
debug:   Using solver KINSOL
debug:   Solving system 0

is solved correctly, but after initialization the graph or SCC changes and we get a "new" system

warning: Alg. loop (size 2)
debug:   Solving algebraic loop formed by connections
                A.y <-> B.x_in
                B.x_out <->
debug:   Using solver Kinsol
debug:   Solving system 0

which seems a bit odd and results in a segmentation fault.

[AnHeuermann]

I will add a test case to OpenModelica/testsuite/omsimulator, see PR OpenModelica/OpenModelica#6787

Documentation will follow in a separate PR.