Modelica library for simulating fractional differential equations.
This library contains approximation models for simulating fractional differential operators (for example half-differentiators, i.e., s^0.5). These are used in several physical domains like electrochemistry, viscoelasticity, or heat transfer. An exact representation would use infinite memory, therefore only approximations are used, that cover a certain frequency interval.
The library contains the following elements:
- a block model to approximate the transient behavior of fractional differential operators, using Oustaloup's method
- block models to approximate the transient behavior of fractional differential operators, using Xue's and Carlson's method (discouraged)
- test cases
- examples for applications
Main features of the elements provided are:
- user-defined trade-off between accuracy and simulation speed, by selecting an appropriate approximation order and fitting frequency interval
- good rejection of rounding errors, using a series of first-order elements to approximate the fractional differential operator
Potential applications of the provided elements are:
- modelling the relationship between heat transfer and temperature at the border of a semi-infinite domain
- simulating the transient response of a viscoelastic block, subjected to tension
- tuning fractional PID controllers
The original version of this library was released before the Modelica conference 2015 in Versailles:
Download FractionalOrder (2015-07-28)
This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the Modelica License 2.
Copyright (C) 2015, DLR German Aerospace Center
The library is developed by:
- Alexander Pollok
- Dirk Zimmer
from the German Aerospace Center (DLR) and
- Francesco Casella
from the Politecnico di Milano.
You may report any issues with using the Issues button.
Contributions in the form of Pull Requests are always welcome.