Effort-controlled fractional derivator (Fracderec)

Effort-controlled fractional derivator from [1] (chap 7):

\begin{equation*} f(s) = g \, s^{alpha} \, e(s). \end{equation*}

Power variables

flux: Not defined \(f\) (None)

effort: Not defined \(e\) (None)

Arguments

label : str: Fracderec label.
nodes : ('N1', 'N2'): Component terminals with positive flux N1->N2.
parameters : keyword arguments: Component parameters

Key	Description	Unit	Default
g	Gain	unknown	1.0
alpha	Derivation order in (0, 1)	d.u.	0.5
NbPoles	Approximation order	d.u.	20
PolesMinMax	Poles modules in \((10^{min}, 10^{max})\)	Hz	(-5, 10)
NbFreqPoints	Number of optimization points	d.u.	200
FreqsMinMax	Optimization interval	Hz	(1, 48000.0)
DoPlot	Plot transfer function	bool	False

Usage

fracder = Fracderec('fracder', ('N1', 'N2'), g=1.0, alpha=0.5, NbPoles=20, PolesMinMax=(-5, 10), NbFreqPoints=200, FreqsMinMax=(1, 48000.0), DoPlot=False)

Netlist line

fraccalc.fracderec fracder ('N1', 'N2'): g=1.0; alpha=0.5; NbPoles=20; PolesMinMax=(-5, 10); NbFreqPoints=200; FreqsMinMax=(1, 48000.0); DoPlot=False;

Example

>>> # Import dictionary
>>> from pyphs.dictionary import fraccalc
>>> # Define component label
>>> label = 'fracder'
>>> # Define component nodes
>>> nodes = ('N1', 'N2')
>>> # Define component parameters
>>> parameters = {'g': 1.0,                     # Gain (unknown)
...               'alpha': 0.5,                 # Derivation order in (0, 1) (d.u.)
...               'NbPoles': 20,                # Approximation order (d.u.)
...               'PolesMinMax': (-5, 10),      # Poles modules in :math:`(10^{min}, 10^{max})` (Hz)
...               'NbFreqPoints': 200,          # Number of optimization points (d.u.)
...               'FreqsMinMax': (1, 48000.0),  # Optimization interval (Hz)
...               'DoPlot': False,              # Plot transfer function (bool)
...              }
>>> # Instanciate component
>>> component = fraccalc.Fracderec(label, nodes, **parameters)
>>> # Graph dimensions
>>> len(component.nodes)
37
>>> len(component.edges)
68

Reference

[1]

(1, 2) Antoine Falaize. Modelisation, simulation, generation de code et correction de systemes multi-physiques audios: Approche par reseau de composants et formulation hamiltonienne a ports. PhD thesis, ecole Doctorale d'Informatique, Telecommunication et electronique de Paris, Universite Pierre et Marie Curie, Paris 6, EDITE UPMC ED130, july 2016.