This information is part of the Modelica Standard Library maintained by the Modelica Association.

The function is used to limit the derivative of the following function at x=0:

y = if x ≥ 0 then xpow else -(-x)pow;  // pow > 0

by approximating the function in the range -deltax< x < deltax with a third order polynomial that has the same derivative at abs(x)=deltax, as the function above.

Example

In the picture below the input x is increased from -1 to 1. The range of interpolation is defined by the same range. Displayed is the output of the function SmoothPower compared to

y=x*|x|

For |x| > 1 both functions return identical results.

References

ThermoFluid Library

http://sourceforge.net/projects/thermofluid/

y = SmoothPower(x, deltax, pow)

x	Type: Real Description: Input variable
deltax	Type: Real Description: Range for interpolation
pow	Type: Real Description: Exponent for x

y	Type: Real Description: Output variable

2014-04-29 Stefan Wischhusen: Introduced deltax and pow as zero derivatives.