.BuildSysPro.Utilities.Math.regStep

Information

Regularization for step function around zero

Hypothesis and equations

    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.

Bibliography

Based on the regStep fucntion from Modelica Standard Library and recommandation in IEA ANNEX 60 to inline the function.

Instructions for use

none

Known limits / Use precautions

none

Validations

Validated function - Gilles PLESSIS 07/2016

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Licensed by EDF under a 3-clause BSD-license
Copyright © EDF 2009 - 2023
BuildSysPro version 3.6.0
Initial model : regStep, Martin Otter, Copyright © 2002-2016, ABB, DLR, Dassault Systèmes AB, Modelon, TU Braunschweig, TU Hamburg-Harburg, Politecnico di Milano.
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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

• July18, 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.