.IDEAS.Utilities.Math.Functions.regStep

Information

This function is used to approximate the equation

    y = if x > 0 then y1 else y2;

by a smooth characteristic, so that the expression is continuous and differentiable:

   y = smooth(1, if x >  x_small then y1 else
                 if x < -x_small then y2 else f(y1, y2));

In the region -x_small < x < x_small a 2nd order polynomial is used for a smooth transition from y1 to y2.

Interface

function regStep
  extends Modelica.Icons.Function;
  input Real x "Abscissa value";
  input Real y1 "Ordinate value for x > 0";
  input Real y2 "Ordinate value for x < 0";
  input Real x_small(min = 0) = 1e-5 "Approximation of step for -x_small <= x <= x_small; x_small >= 0 required";
  output Real y "Ordinate value to approximate y = if x > 0 then y1 else y2";
end regStep;

Revisions

• February 18, 2016 by Marcus Fuchs:
  Add function with Inline = true in annotations to package for better performance, as suggested in #300 .
• April 29, 2008 by Martin Otter:
  Designed and implemented.
• August 12, 2008 by Michael Sielemann:
  Minor modification to cover the limit case x_small -> 0 without division by zero.