Nonlinear function blocks in Modelica.Blocks should use homotopy for initialization

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Reported by fcasella on 8 Mar 2013 15:25 UTC
The Modelica.Blocks.Nonlinear.Limiter model contains the following code:

  if initial() and not limitsAtInit then
     y = u;
     assert(u >= uMin - 0.01*abs(uMin) and 
            u <= uMax + 0.01*abs(uMax),
           "Limiter: During initialization the limits have been ignored.\n"+
           "However, the result is that the input u is not within the required limits:\n"+
           "  u = " + String(u) + ", uMin = " + String(uMin) + ", uMax = " + String(uMax));
  else
     y = smooth(0,if u > uMax then uMax else if u < uMin then uMin else u);

this helps the convergence of the nonlinear solver at initialization by not taking into account of the nonlinearities, if they are actually inactive at initialization; otherwise, a slightly messy situation ensues (-> when the simulation starts, the found initial solution is no longer a consistent solution of the dynamic problem).

A cleaner implementation in Modelica >= 3.2 would be:

y = homotopy(
  actual = smooth(0,if u > uMax then uMax else if u < uMin then uMin else u),
  simplified = y);

Similar arguments hold for VariableLimiter and DeadZone.

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Migrated-From: https://trac.modelica.org/Modelica/ticket/1012

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Modified by fcasella on 11 Mar 2013 13:42 UTC

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Comment by otter on 28 Mar 2013 11:19 UTC
This is a good idea. However, before introducing it in MSL, one or more concrete test cases are needed where this can be evaluated that it works as expected.

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Modified by otter on 18 Apr 2013 15:15 UTC

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Modified by beutlich on 6 Oct 2015 21:13 UTC

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Comment by otter on 11 Dec 2015 14:07 UTC
Fixed in 995e959 as suggested.

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Changelog modified by otter on 11 Dec 2015 14:07 UTC
Numerics improved for the Nonlinear blocks Limiter, VariableLimiter, DeadZone by using the homotopy operator