def testNyquist(self):
h1 = TransferFunction([1], [1, 2, 2])
omega = np.logspace(-1, 2, 40)
f1 = FRD(h1, omega, smooth=True)
freqplot.nyquist(f1, np.logspace(-1, 2, 100))
# plt.savefig('/dev/null', format='svg')
plt.figure(2)
freqplot.nyquist(f1, f1.omega)
def testNyquist(self):
h1 = TransferFunction([1], [1, 2, 2])
omega = np.logspace(-1, 2, 40)
f1 = FRD(h1, omega, smooth=True)
freqplot.nyquist(f1, np.logspace(-1, 2, 100))
# plt.savefig('/dev/null', format='svg')
plt.figure(2)
freqplot.nyquist(f1, f1.omega)
def nyquist(self, ax=None, pairs=None, label="nyquist", title=None,
xlabel="Real Axis", ylabel="Imaginary Axis",
colors=['b','g','r','c','m','y','k'], **kwargs):
"""Create a Nyquist plot of the system's response.
The Nyquist plots of a MIMO system are overlayed. This is different
than MATLAB\ :sup:`®`, which creates an array of subplots.
**Arguments:**
- *ax*: Axes onto which the Nyquist diagram should be plotted
If *ax* is not provided, then axes will be created in a new figure.
- *pairs*: List of (input index, output index) tuples of each transfer
function to be evaluated
If not provided, all of the transfer functions will be plotted.
- *label*: Label for the figure (ignored if ax is provided)
This will be used as the base filename if the figure is saved.
- *title*: Title for the figure
If *title* is *None* (default), then the title will be "Nyquist
Plot of *fbase*", where *fbase* is the base filename of the data.
Use '' for no title.
- *xlabel*: x-axis label
- *ylabel*: y-axis label
- *colors*: Color or list of colors that will be used sequentially
Each may be a character, grayscale, or rgb value.
.. Seealso:: http://matplotlib.sourceforge.net/api/colors_api.html
- *\*\*kwargs*: Additional arguments for
:meth:`control.freqplot.nyquist`
**Returns:**
1. *ax*: Axes of the Nyquist plot
**Example:**
.. testsetup::
>>> from modelicares import closeall
>>> closeall()
.. code-block:: python
>>> from modelicares import LinRes, save
>>> from numpy import pi, logspace
>>> lin = LinRes('examples/PID.mat')
>>> lin.nyquist(label='examples/PID-nyquist',
... omega=2*pi*logspace(0, 3, 61), labelFreq=20,
... title="Nyquist Plot of Modelica.Blocks.Continuous.PID") # doctest: +ELLIPSIS
<matplotlib.axes._subplots.AxesSubplot object at 0x...>
>>> save()
Saved examples/PID-nyquist.pdf
Saved examples/PID-nyquist.png
.. only:: html
.. image:: ../examples/PID-nyquist.png
:scale: 70 %
:alt: example for LinRes.nyquist()
.. only:: latex
.. figure:: ../examples/PID-nyquist.pdf
:scale: 70 %
Results of example for :meth:`LinRes.nyquist`.
"""
# Create axes if necessary.
if not ax:
fig = base.figure(label)
ax = fig.add_subplot(111, aspect='equal')
# Create a title if necessary.
if title is None:
title = r"Nyquist Plot of %s" % self.fbase
# Set up the color(s).
if not iterable(colors):
# Use the single color for all plots.
colors = (colors,)
n_colors = len(colors)
# If input/output pair(s) aren't specified, generate a list of all
# pairs.
if not pairs:
pairs = [(i_u, i_y) for i_u in range(self.sys.inputs)
for i_y in range(self.sys.outputs)]
# Create the plots.
for i, (i_u, i_y) in enumerate(pairs):
# Extract the SISO TF. TODO: Is there a better way to do this?
sys = ss(self.sys.A, self.sys.B[:, i_u], self.sys.C[i_y, :],
self.sys.D[i_y, i_u])
nyquist(sys, mark=False, label=r'$Y_{%i}/U_{%i}$' % (i_y, i_u),
color=colors[np.mod(i, n_colors)], ax=ax, **kwargs)
# Note: controls.freqplot.nyquist() is currently only implemented
# for SISO systems.
# Decorate and finish.
if len(pairs) > 1:
ax.legend()
base.add_hlines(ax, color='k', linestyle='--', linewidth=0.5)
base.add_vlines(ax, color='k', linestyle='--', linewidth=0.5)
ax.set_title(title)
if xlabel: # Without this check, xlabel=None will give a label of "None".
ax.set_xlabel(xlabel)
if ylabel: # Same purpose
ax.set_ylabel(ylabel)
return ax
def multinyquist(lins, ax=None, pair=(0, 0), label='nyquist',
title="Nyquist Plot", xlabel="Real Axis",
ylabel="Imaginary Axis", labels='',
colors=['b', 'g', 'r', 'c', 'm', 'y', 'k'],
leg_kwargs={}, **kwargs):
"""Plot multiple linearizations onto a single Nyquist diagram.
**Arguments:**
- *lins*: Linearization result or list of results (instances of
:class:`linres.LinRes`)
- *ax*: Axes onto which the Nyquist diagrams should be plotted
If *ax* is not provided, then axes will be created in a new figure.
- *pair*: Tuple of (input index, output index) for the transfer function
to be chosen from each system (applied to all)
This is ignored if the system is SISO.
- *label*: Label for the figure (ignored if axes is provided)
This will be used as the base filename if the figure is saved.
- *title*: Title for the figure
- *xlabel*: x-axis label
- *ylabel*: y-axis label
- *labels*: Label or list of labels for the legends
If *labels* is *None*, then no label will be used. If it is an
empty string (''), then the base filenames will be used.
- *colors*: Color or list of colors that will be used sequentially
Each may be a character, grayscale, or rgb value.
.. Seealso:: http://matplotlib.sourceforge.net/api/colors_api.html
- *leg_kwargs*: Dictionary of keyword arguments for
:meth:`matplotlib.pyplot.legend`
If *leg_kwargs* is *None*, then no legend will be shown.
- *\*\*kwargs*: Additional arguments for :meth:`control.freqplot.nyquist`
If *textFreq* is not specified, then only the frequency points of the
first system will have text labels.
**Returns:**
1. *ax*: Axes of the Nyquist plot
**Example:**
.. testsetup::
>>> from modelicares import closeall
>>> closeall()
.. code-block:: python
>>> import os
>>> from glob import glob
>>> from modelicares import LinRes, multinyquist, save, read_params
>>> from numpy import pi, logspace
>>> lins = map(LinRes, glob('examples/PID/*/*.mat'))
>>> labels = ["Td=%g" % read_params('Td', os.path.join(lin.dir, 'dsin.txt'))
... for lin in lins]
>>> multinyquist(lins,
... title="Nyquist Plot of Modelica.Blocks.Continuous.PID",
... label='examples/PIDs-nyquist', textFreq=True,
... omega=2*pi*logspace(-1, 3, 81), labelFreq=20,
... labels=labels) # doctest: +ELLIPSIS
<matplotlib.axes._subplots.AxesSubplot object at 0x...>
>>> save()
Saved examples/PIDs-nyquist.pdf
Saved examples/PIDs-nyquist.png
.. only:: html
.. image:: ../examples/PIDs-nyquist.png
:scale: 70 %
:alt: Nyquist plot of PID with varying parameters
.. only:: latex
.. figure:: ../examples/PIDs-nyquist.pdf
:scale: 70 %
Nyquist plot of PID with varying parameters
"""
# Create axes if necessary.
if not ax:
fig = figure(label)
ax = fig.add_subplot(111, aspect='equal')
# Process the lins input.
if not iterable(lins):
lins = [lins]
# Process the labels input.
if labels == '':
labels = [lin.fbase for lin in lins]
elif labels == None:
labels = ['']*len(lins)
# Set up the color(s).
if not iterable(colors):
# Use the single color for all plots.
colors = (colors,)
n_colors = len(colors)
# Create the plots.
textFreq = kwargs.pop('textFreq', None)
for i, (lin, label) in enumerate(zip(lins, labels)):
if lin.sys.inputs > 1 or lin.sys.outputs > 1:
# Extract the SISO TF. TODO: Is there a better way to do this?
sys = ss(self.sys.A, self.sys.B[:, pair[0]], self.sys.C[pair[1], :],
self.sys.D[pair[1], pair[0]])
else:
sys = lin.sys
nyquist(sys, mark=False, label=label, ax=ax,
textFreq=i==0 if textFreq is None else textFreq,
color=colors[np.mod(i, n_colors)], **kwargs)
# Decorate and finish.
add_hlines(ax, color='k', linestyle='--', linewidth=0.5)
add_vlines(ax, color='k', linestyle='--', linewidth=0.5)
ax.set_title(title)
if xlabel: # Without this check, xlabel=None will give a label of "None".
ax.set_xlabel(xlabel)
if ylabel: # Same purpose
ax.set_ylabel(ylabel)
if leg_kwargs is not None:
loc = leg_kwargs.pop('loc', 'best')
ax.legend(loc=loc, **leg_kwargs)
return ax