functionregStep

Approximation of a general step, such that the approximation is continuous and differentiable

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

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.

Inputs

TypeNameDefaultDescription
RealxAbscissa value
Realy1Ordinate value for x > 0
Realy2Ordinate value for x < 0
Realx_small1e-5Approximation of step for -x_small <= x <= x_small; x_small >= 0 required

Outputs

TypeNameDefaultDescription
RealyOrdinate value to approximate y = if x > 0 then y1 else y2

Revisions

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