functionregStep

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

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

Information

Regularization for step function around zero

Hypothesis and equations

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.

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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Inputs

Type	Name	Default	Description
Real	x		Abscissa value
Real	y1		Ordinate value for x > 0
Real	y2		Ordinate value for x < 0
Real	x_small	1e-5	Approximation of step for -x_small <= x <= x_small; x_small >= 0 required

Outputs

Type	Name	Default	Description
Real	y		Ordinate value to approximate y = if x > 0 then y1 else y2

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.