functionSmoothPower

Limiting the derivative of function y = if x>=0 then x^pow else -(-x)^pow

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

Information

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.

SmoothPower

References

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

Inputs

TypeNameDefaultDescription
RealxInput variable
RealdeltaxRange for interpolation
RealpowExponent for x

Outputs

TypeNameDefaultDescription
RealyOutput variable

Revisions

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