.FractionalOrder.UsersGuide.QuickStartGuide .FractionalOrder.UsersGuide.QuickStartGuideThe most important block for most users will be FractionalOrder.Approximations.OustaloupOperator.
This block applies an approximated fractional differential operation to the input u.
The user can specify the fitting frequency interval, approximation order and fraction of differentiation (e.g., 0.5 for a half-differentiation or -1 for normal integration).
The approximation is more or less exact contingent on the following conditions:
1) the relevant dynamics of the simulated model are inside the specified fitting frequency interval
2) the fitting frequency interval (measured in orders of magnitude) is not too large
3) the approximation order is high enough
4) the absolute value of the differentiation fraction is low enough
Points 2-4 are interdependent on each other. For a large frequency interval and a large fraction of differentiation, a high approximation order is needed.
If in doubt, it is suggested to open the
FractionalOrder.Approximations.OustaloupOperator-model, type in the needed parameters,
and use the LinearSystems.Bodeplot function to check the accuracy of the resulting Approximation.
Also, the predefined values are quite sensible.
Developed 2015 at the DLR Institute of System Dynamics and Control