Support conditional equations in tearing

[Francesco Casella]

Consider the following model, already discussed in #5206

model NonSatIntEq
  Real x;
  Real y;
  Real usat;
  Real u;
  parameter Real y0(fixed = false, start = 8);
  parameter Real T = 1;
  parameter Real k = 10;
  parameter Real uMin = 0;
  parameter Real uMax = 1;
parameter Real y_ref = 8;
initial equation
  der(x) = 0;
  if u > usat then
    u = usat + 1;
  else
    y = y_ref;
  end if;
equation
  T * der(x) = usat - x;
  y = k * x;
  usat = homotopy(actual = smooth(0, if u > uMax then uMax else if u < uMin then uMin else u), simplified = u);
  u = y0 - y;
end NonSatIntEq;

The back-end could select u as a tearing variable to solve the initialization problem. Unfortunately, the following warnings are issued

[1] 00:44:12 Scripting Notification
 
The selection of a new tearing variable failed. 


[2] 00:44:12 Translation Warning
Function Tearing.selectTearingVar failed at least once. Use -d=tearingdump or -d=tearingdumpV for more information.

[3] 00:44:12 Translation Warning
Iteration variables with default zero start attribute in equation system with analytic Jacobian:
         usat:VARIABLE() .NonSatIntEq type: Real 
         u:VARIABLE() .NonSatIntEq type: Real 
         y:VARIABLE() .NonSatIntEq type: Real 
         x:VARIABLE() .NonSatIntEq type: Real 

The transformational debugger shows a system of four implicit equations, but only shows three residuals. Lots of Matrix Singular messages are issued, and eventually a wrong initial solution (not in steady-state) is accepted at the beginning of the simulation.

If the conditional equation is manually converted to this equation

(if u > usat then u - (usat + 1) else y - y_ref) = 0;

then the tearing is applied successfully and the initialization problem is solved correctly.

Please fix the back-end to process these conditional equations correctly as far as tearing is concerned.

[Francesco Casella]

Rescheduled to 1.14.0 after 1.13.0 releasee

[Francesco Casella]

Karim, are you or some of your colleagues interested in looking into this issue?

[Karim Adbdelhak]

It seems like the simplifyIfEquations module in BackendDAEOptimize is only used on the simulation DAE and not the initial system. If applied, it should do exactly the transformation from

  if u > usat then
    u = usat + 1;
  else
    y = y_ref;
  end if;

to

(if u > usat then u - (usat + 1) else y - y_ref) = 0;

I am not quite sure where and at what time during the optimization this step should be called. I tried adding "simplifyIfEquations" to ConfigFlag INIT_OPT_MODULES in Flags.mo, which is a viable flag according to omc --help=optmodules, but i get following error:

"Error: 'simplifyIfEquations' is not a valid optimization module. Please check the flags carefully.

Any suggestions where this configuration has to be added?

[Karim Adbdelhak]

fixed with ​PR

[Francesco Casella]

Thanks Karim!