.BuildingSystems.Utilities.Math.Functions.powerLinearized

Information

• 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.

Interface

function powerLinearized
  extends Modelica.Icons.Function;
  input Real x "Abscissa value";
  input Real n "Exponent";
  input Real x0 "Abscissa value below which linearization occurs";
  output Real y "Function value";
end powerLinearized;

Revisions

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