.ThermoCycle.Functions.transition_factor

Information

DESCRIPTION:

This function returns a value between 1 and 0. A smooth transition is achieved by means of defining the position and the transition intervall from start to stop parameter. Outside this intervall, the 1 and the 0 are returned, respectively. This transition function with up to two smooth derivatives was taken from [1]. If you provide an order higher than 2, the generalised logistic function[2] will be used to calculated the transition curve.

OUTPUT:

tFactor = smooth transition between 0 and 1 from start to stop [-]

Use tFactor in an equation like this:

tFactor = transition_factor(start=start,stop=stop,position=position);
smoothed = tFactor*1stValue + (1 - tFactor)*2ndValue;

REFERENCES:

[1] Christoph C Richter, Proposal of New Object-Oriented Equation-Based Model Libraries for Thermodynamic Systems, PhD thesis, Technical University Carolo-Wilhelmina Braunschweig, 2008

[2] Generalised logistic function on Wikipedia

IMPLEMENTATION:

Implemented in 2012 for Technical University of Denmark, DTU Mechanical Engineering, Kongens Lyngby, Denmark by Jorrit Wronski (jowr@mek.dtu.dk)

Interface

function transition_factor
  extends Modelica.Icons.Function;
  import Modelica.Constants.pi;
  import Modelica.Constants.e;
  input Real start = 0.25 "start of transition interval";
  input Real stop = 0.75 "end of transition interval";
  input Real position = 0.0 "current position";
  input Integer order = 2 "Smooth up to which derivative?";
  output Real tFactor "weighting factor";
end transition_factor;