.Buildings.Utilities.Math.Functions.smoothHeaviside

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 Buildings.Utilities.Math.Examples.SmoothHeaviside.

Interface

function smoothHeaviside
  extends Modelica.Icons.Function;
  input Real x "Argument";
  input Real delta(min = Modelica.Constants.eps) "Parameter used for scaling";
  output Real y "Result";
end smoothHeaviside;

Revisions

• July 21, 2025 by Hongxiang Fu:
  Made the function inlined.
  This is for #4278.
• 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.