functionpowerLinearized

Power function that is linearized below a user-defined threshold

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

Information

Function that approximates y=xn where 0 < n so that
  • the function is defined and monotonically increasing for all x.
  • dy/dx is bounded and continuous everywhere (for n < 1).

For x < x0, this function replaces y=xn by a linear function that is continuously differentiable everywhere.

A typical use of this function is to replace T = T4(1/4) in a radiation balance to ensure that the function is defined everywhere. This can help solving the initialization problem when a solver may be far from a solution and hence T4 < 0.

See the package Examples for the graph.

Inputs

TypeNameDefaultDescription
RealxAbscissa value
RealnExponent
Realx0Abscissa value below which linearization occurs

Outputs

TypeNameDefaultDescription
RealyFunction value

Revisions

  • February 3, 2011, by Michael Wetter:
    First implementation.