SmoothPowerLimiting the derivative of function y = if x>=0 then x^pow else -(-x)^pow |
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.
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.
x |
Type: Real Description: Input variable |
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deltax |
Type: Real Description: Range for interpolation |
pow |
Type: Real Description: Exponent for x |
y |
Type: Real Description: Output variable |
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