functionsmoothHeaviside

Twice continuously differentiable approximation to the Heaviside function

Extends from Modelica.Icons.Function (Icon for functions).

Information

Twice Lipschitz continuously differentiable approximation to the Heaviside(.,.) function.
Function is derived from a quintic polynomial going through (0,0) and (1,1), with zero first and second order derivatives at those points.
See Example BuildingSystems.Utilities.Math.Examples.SmoothHeaviside.

Inputs

TypeNameDefaultDescription
RealxArgument
RealdeltaParameter used for scaling

Outputs

TypeNameDefaultDescription
RealyResult

Revisions

  • October 21, 2019:
    Added delta.min attribute to guard against division by zero.
    This is for issue 1202.
  • September 13, 2019, by Kristoff Six and Filip Jorissen:
    Once continuously differentiable replaced by twice continuously differentiable implementation. This is for issue 1202.
  • March 15, 2016, by Michael Wetter:
    Replaced spliceFunction with regStep. This is for issue 300.
  • July 17, 2015, by Marcus Fuchs:
    Add link to example.
  • February 5, 2015, by Filip Jorissen:
    Added smoothOrder = 1.
  • July 14, 2010, by Wangda Zuo, Michael Wetter:
    First implementation.