def test_discrete_bode(self):
# Create a simple discrete time system and check the calculation
sys = TransferFunction([1], [1, 0.5], 1)
omega = [1, 2, 3]
mag_out, phase_out, omega_out = bode(sys, omega)
H_z = list(map(lambda w: 1./(np.exp(1.j * w) + 0.5), omega))
np.testing.assert_array_almost_equal(omega, omega_out)
np.testing.assert_array_almost_equal(mag_out, np.absolute(H_z))
np.testing.assert_array_almost_equal(mag_out, np.absolute(H_z))
def test_discrete_bode(self):
# Create a simple discrete time system and check the calculation
sys = TransferFunction([1], [1, 0.5], 1)
omega = [1, 2, 3]
mag_out, phase_out, omega_out = bode(sys, omega)
H_z = list(map(lambda w: 1. / (np.exp(1.j * w) + 0.5), omega))
np.testing.assert_array_almost_equal(omega, omega_out)
np.testing.assert_array_almost_equal(mag_out, np.absolute(H_z))
np.testing.assert_array_almost_equal(mag_out, np.absolute(H_z))
def bode(*args, **keywords):
"""Bode plot of the frequency response
Examples
--------
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> mag, phase, omega = bode(sys)
.. todo::
Document these use cases
* >>> bode(sys, w)
* >>> bode(sys1, sys2, ..., sysN)
* >>> bode(sys1, sys2, ..., sysN, w)
* >>> bode(sys1, 'plotstyle1', ..., sysN, 'plotstyleN')
"""
# If the first argument is a list, then assume python-control calling format
if (getattr(args[0], '__iter__', False)):
return freqplot.bode(*args, **keywords)
# Otherwise, run through the arguments and collect up arguments
syslist = []; plotstyle=[]; omega=None;
i = 0;
while i < len(args):
# Check to see if this is a system of some sort
if (ctrlutil.issys(args[i])):
# Append the system to our list of systems
syslist.append(args[i])
i += 1
# See if the next object is a plotsytle (string)
if (i < len(args) and isinstance(args[i], str)):
plotstyle.append(args[i])
i += 1
# Go on to the next argument
continue
# See if this is a frequency list
elif (isinstance(args[i], (list, np.ndarray))):
omega = args[i]
i += 1
break
else:
raise ControlArgument("unrecognized argument type")
# Check to make sure that we processed all arguments
if (i < len(args)):
raise ControlArgument("not all arguments processed")
# Check to make sure we got the same number of plotstyles as systems
if (len(plotstyle) != 0 and len(syslist) != len(plotstyle)):
raise ControlArgument("number of systems and plotstyles should be equal")
# Warn about unimplemented plotstyles
#! TODO: remove this when plot styles are implemented in bode()
#! TODO: uncomment unit test code that tests this out
if (len(plotstyle) != 0):
print("Warning (matabl.bode): plot styles not implemented");
# Call the bode command
return freqplot.bode(syslist, omega, **keywords)
def testConvert(self):
"""Test state space to transfer function conversion."""
verbose = self.debug
# print __doc__
# Machine precision for floats.
# eps = np.finfo(float).eps
for states in range(1, self.maxStates):
for inputs in range(1, self.maxIO):
for outputs in range(1, self.maxIO):
# start with a random SS system and transform to TF then
# back to SS, check that the matrices are the same.
ssOriginal = matlab.rss(states, outputs, inputs)
if (verbose):
self.printSys(ssOriginal, 1)
# Make sure the system is not degenerate
Cmat = ctrb(ssOriginal.A, ssOriginal.B)
if (np.linalg.matrix_rank(Cmat) != states):
if (verbose):
print(" skipping (not reachable)")
continue
Omat = obsv(ssOriginal.A, ssOriginal.C)
if (np.linalg.matrix_rank(Omat) != states):
if (verbose):
print(" skipping (not observable)")
continue
tfOriginal = matlab.tf(ssOriginal)
if (verbose):
self.printSys(tfOriginal, 2)
ssTransformed = matlab.ss(tfOriginal)
if (verbose):
self.printSys(ssTransformed, 3)
tfTransformed = matlab.tf(ssTransformed)
if (verbose):
self.printSys(tfTransformed, 4)
# Check to see if the state space systems have same dim
if (ssOriginal.states != ssTransformed.states):
print("WARNING: state space dimension mismatch: " + \
"%d versus %d" % \
(ssOriginal.states, ssTransformed.states))
# Now make sure the frequency responses match
# Since bode() only handles SISO, go through each I/O pair
# For phase, take sine and cosine to avoid +/- 360 offset
for inputNum in range(inputs):
for outputNum in range(outputs):
if (verbose):
print("Checking input %d, output %d" \
% (inputNum, outputNum))
ssorig_mag, ssorig_phase, ssorig_omega = \
bode(_mimo2siso(ssOriginal, \
inputNum, outputNum), \
deg=False, Plot=False)
ssorig_real = ssorig_mag * np.cos(ssorig_phase)
ssorig_imag = ssorig_mag * np.sin(ssorig_phase)
#
# Make sure TF has same frequency response
#
num = tfOriginal.num[outputNum][inputNum]
den = tfOriginal.den[outputNum][inputNum]
tforig = tf(num, den)
tforig_mag, tforig_phase, tforig_omega = \
bode(tforig, ssorig_omega, \
deg=False, Plot=False)
tforig_real = tforig_mag * np.cos(tforig_phase)
tforig_imag = tforig_mag * np.sin(tforig_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tforig_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tforig_imag)
#
# Make sure xform'd SS has same frequency response
#
ssxfrm_mag, ssxfrm_phase, ssxfrm_omega = \
bode(_mimo2siso(ssTransformed, \
inputNum, outputNum), \
ssorig_omega, \
deg=False, Plot=False)
ssxfrm_real = ssxfrm_mag * np.cos(ssxfrm_phase)
ssxfrm_imag = ssxfrm_mag * np.sin(ssxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, ssxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, ssxfrm_imag)
#
# Make sure xform'd TF has same frequency response
#
num = tfTransformed.num[outputNum][inputNum]
den = tfTransformed.den[outputNum][inputNum]
tfxfrm = tf(num, den)
tfxfrm_mag, tfxfrm_phase, tfxfrm_omega = \
bode(tfxfrm, ssorig_omega, \
deg=False, Plot=False)
tfxfrm_real = tfxfrm_mag * np.cos(tfxfrm_phase)
tfxfrm_imag = tfxfrm_mag * np.sin(tfxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tfxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tfxfrm_imag)
def testConvert(self):
"""Test state space to transfer function conversion."""
verbose = self.debug
# print __doc__
# Machine precision for floats.
# eps = np.finfo(float).eps
for states in range(1, self.maxStates):
for inputs in range(1, self.maxIO):
for outputs in range(1, self.maxIO):
# start with a random SS system and transform to TF then
# back to SS, check that the matrices are the same.
ssOriginal = matlab.rss(states, outputs, inputs)
if (verbose):
self.printSys(ssOriginal, 1)
# Make sure the system is not degenerate
Cmat = ctrb(ssOriginal.A, ssOriginal.B)
if (np.linalg.matrix_rank(Cmat) != states):
if (verbose):
print(" skipping (not reachable)")
continue
Omat = obsv(ssOriginal.A, ssOriginal.C)
if (np.linalg.matrix_rank(Omat) != states):
if (verbose):
print(" skipping (not observable)")
continue
tfOriginal = matlab.tf(ssOriginal)
if (verbose):
self.printSys(tfOriginal, 2)
ssTransformed = matlab.ss(tfOriginal)
if (verbose):
self.printSys(ssTransformed, 3)
tfTransformed = matlab.tf(ssTransformed)
if (verbose):
self.printSys(tfTransformed, 4)
# Check to see if the state space systems have same dim
if (ssOriginal.states != ssTransformed.states):
print("WARNING: state space dimension mismatch: " + \
"%d versus %d" % \
(ssOriginal.states, ssTransformed.states))
# Now make sure the frequency responses match
# Since bode() only handles SISO, go through each I/O pair
# For phase, take sine and cosine to avoid +/- 360 offset
for inputNum in range(inputs):
for outputNum in range(outputs):
if (verbose):
print("Checking input %d, output %d" \
% (inputNum, outputNum))
ssorig_mag, ssorig_phase, ssorig_omega = \
bode(_mimo2siso(ssOriginal, \
inputNum, outputNum), \
deg=False, plot=False)
ssorig_real = ssorig_mag * np.cos(ssorig_phase)
ssorig_imag = ssorig_mag * np.sin(ssorig_phase)
#
# Make sure TF has same frequency response
#
num = tfOriginal.num[outputNum][inputNum]
den = tfOriginal.den[outputNum][inputNum]
tforig = tf(num, den)
tforig_mag, tforig_phase, tforig_omega = \
bode(tforig, ssorig_omega, \
deg=False, plot=False)
tforig_real = tforig_mag * np.cos(tforig_phase)
tforig_imag = tforig_mag * np.sin(tforig_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tforig_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tforig_imag)
#
# Make sure xform'd SS has same frequency response
#
ssxfrm_mag, ssxfrm_phase, ssxfrm_omega = \
bode(_mimo2siso(ssTransformed, \
inputNum, outputNum), \
ssorig_omega, \
deg=False, plot=False)
ssxfrm_real = ssxfrm_mag * np.cos(ssxfrm_phase)
ssxfrm_imag = ssxfrm_mag * np.sin(ssxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, ssxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, ssxfrm_imag)
#
# Make sure xform'd TF has same frequency response
#
num = tfTransformed.num[outputNum][inputNum]
den = tfTransformed.den[outputNum][inputNum]
tfxfrm = tf(num, den)
tfxfrm_mag, tfxfrm_phase, tfxfrm_omega = \
bode(tfxfrm, ssorig_omega, \
deg=False, plot=False)
tfxfrm_real = tfxfrm_mag * np.cos(tfxfrm_phase)
tfxfrm_imag = tfxfrm_mag * np.sin(tfxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tfxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tfxfrm_imag)
def bode(self, axes=None, pairs=None, label='bode',
title=None, colors=['b', 'g', 'r', 'c', 'm', 'y', 'k'],
styles=[(None,None), (3,3), (1,1), (3,2,1,2)], **kwargs):
"""Create a Bode plot of the system's response.
The Bode plots of a MIMO system are overlayed. This is different than
MATLAB\ :sup:`®`, which creates an array of subplots.
**Arguments:**
- *axes*: Tuple (pair) of axes for the magnitude and phase plots
If *axes* 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 *axes* 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 "Bode Plot
of *fbase*", where *fbase* is the base filename of the data. Use
'' for no title.
- *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
- *styles*: Line/dash style or list of line/dash styles that will be
used sequentially
Each style is a string representing a linestyle (e.g., "--") or a
tuple of on/off lengths representing dashes. Use "" for no line
and "-" for a solid line.
.. Seealso::
http://matplotlib.sourceforge.net/api/collections_api.html
- *\*\*kwargs*: Additional arguments for :meth:`control.freqplot.bode`
**Returns:**
1. *axes*: Tuple (pair) of axes for the magnitude and phase plots
**Example:**
.. code-block:: python
>>> from modelicares import LinRes, save
>>> from numpy import pi, logspace
>>> lin = LinRes('examples/PID.mat')
>>> lin.bode(label='examples/PID-bode', omega=2*pi*logspace(-2, 3),
... title="Bode Plot of Modelica.Blocks.Continuous.PID") # doctest: +ELLIPSIS
(<matplotlib.axes._subplots.AxesSubplot object at 0x...>, <matplotlib.axes._subplots.AxesSubplot object at 0x...>)
>>> save()
Saved examples/PID-bode.pdf
Saved examples/PID-bode.png
.. only:: html
.. image:: ../examples/PID-bode.png
:scale: 70 %
:alt: example for LinRes.bode()
.. only:: latex
.. figure:: ../examples/PID-bode.pdf
:scale: 80 %
Results of example for :meth:`LinRes.bode`.
"""
# Create axes if necessary.
if axes is None or (None, None):
fig = base.figure(label)
axes = (fig.add_subplot(211), fig.add_subplot(212))
# Create a title if necessary.
if title is None:
title = r"Bode Plot of %s" % self.fbase
# Set up the color(s) and line style(s).
if not iterable(colors):
# Use the single color for all plots.
colors = (colors,)
if not iterable(styles):
# Use the single line style for all plots.
styles = [styles]
elif type(styles[0]) is int:
# One dashes tuple has been provided; use its value for all plots.
styles = [styles]
n_colors = len(colors)
n_styles = len(styles)
# 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])
bode(sys, Hz=True, label=r'$Y_{%i}/U_{%i}$' % (i_y, i_u),
color=colors[np.mod(i, n_colors)], axes=axes,
style=styles[np.mod(i, n_styles)], **kwargs)
# Note: controls.freqplot.bode() is currently only implemented for
# SISO systems.
# 5/23/11: Since controls.freqplot.bode() already uses subplots for
# the magnitude and phase plots, it would be difficult to modify
# the code to put the Bode plots of a MIMO system into an array of
# subfigures like MATLAB does.
# Decorate and finish.
axes[0].set_title(title)
if len(pairs) > 1:
axes[0].legend()
axes[1].legend()
return axes
def stability_margins(sysdata, deg=True):
"""Calculate gain, phase and stability margins and associated
crossover frequencies.
Usage
-----
gm, pm, sm, wg, wp, ws = stability_margins(sysdata, deg=True)
Parameters
----------
sysdata: linsys or (mag, phase, omega) sequence
sys : linsys
Linear SISO system
mag, phase, omega : sequence of array_like
Input magnitude, phase, and frequencies (rad/sec) sequence from
bode frequency response data
deg=True: boolean
If true, all input and output phases in degrees, else in radians
Returns
-------
gm, pm, sm, wg, wp, ws: float
Gain margin gm, phase margin pm, stability margin sm, and
associated crossover
frequencies wg, wp, and ws of SISO open-loop. If more than
one crossover frequency is detected, returns the lowest corresponding
margin.
"""
#TODO do this precisely without the effects of discretization of frequencies?
#TODO assumes SISO
#TODO unit tests, margin plot
if (not getattr(sysdata, '__iter__', False)):
sys = sysdata
# TODO: implement for discrete time systems
if (isdtime(sys, strict=True)):
raise NotImplementedError("Function not implemented in discrete time")
mag, phase, omega = bode(sys, deg=deg, Plot=False)
elif len(sysdata) == 3:
# TODO: replace with FRD object type?
mag, phase, omega = sysdata
else:
raise ValueError("Margin sysdata must be either a linear system or a 3-sequence of mag, phase, omega.")
if deg:
cycle = 360.
crossover = 180.
else:
cycle = 2 * np.pi
crossover = np.pi
wrapped_phase = -np.mod(phase, cycle)
# phase margin from minimum phase among all gain crossovers
neg_mag_crossings_i = np.nonzero(np.diff(mag < 1) > 0)[0]
mag_crossings_p = wrapped_phase[neg_mag_crossings_i]
if len(neg_mag_crossings_i) == 0:
if mag[0] < 1: # gain always less than one
wp = np.nan
pm = np.inf
else: # gain always greater than one
print("margin: no magnitude crossings found")
wp = np.nan
pm = np.nan
else:
min_mag_crossing_i = neg_mag_crossings_i[np.argmin(mag_crossings_p)]
wp = omega[min_mag_crossing_i]
pm = crossover + phase[min_mag_crossing_i]
if pm < 0:
print("warning: system unstable: negative phase margin")
# gain margin from minimum gain margin among all phase crossovers
neg_phase_crossings_i = np.nonzero(np.diff(wrapped_phase < -crossover) > 0)[0]
neg_phase_crossings_g = mag[neg_phase_crossings_i]
if len(neg_phase_crossings_i) == 0:
wg = np.nan
gm = np.inf
else:
min_phase_crossing_i = neg_phase_crossings_i[
np.argmax(neg_phase_crossings_g)]
wg = omega[min_phase_crossing_i]
gm = abs(1/mag[min_phase_crossing_i])
if gm < 1:
print("warning: system unstable: gain margin < 1")
# stability margin from minimum abs distance from -1 point
if deg:
phase_rad = phase * np.pi / 180.
else:
phase_rad = phase
L = mag * np.exp(1j * phase_rad) # complex loop response to -1 pt
min_Lplus1_i = np.argmin(np.abs(L + 1))
sm = np.abs(L[min_Lplus1_i] + 1)
ws = phase[min_Lplus1_i]
return gm, pm, sm, wg, wp, ws
def testConvert(self, fixedseed, states, inputs, outputs):
"""Test state space to transfer function conversion.
start with a random SS system and transform to TF then
back to SS, check that the matrices are the same.
"""
ssOriginal = rss(states, outputs, inputs)
if verbose:
self.printSys(ssOriginal, 1)
# Make sure the system is not degenerate
Cmat = ctrb(ssOriginal.A, ssOriginal.B)
if (np.linalg.matrix_rank(Cmat) != states):
pytest.skip("not reachable")
Omat = obsv(ssOriginal.A, ssOriginal.C)
if (np.linalg.matrix_rank(Omat) != states):
pytest.skip("not observable")
tfOriginal = tf(ssOriginal)
if (verbose):
self.printSys(tfOriginal, 2)
ssTransformed = ss(tfOriginal)
if (verbose):
self.printSys(ssTransformed, 3)
tfTransformed = tf(ssTransformed)
if (verbose):
self.printSys(tfTransformed, 4)
# Check to see if the state space systems have same dim
if (ssOriginal.nstates != ssTransformed.nstates) and verbose:
print("WARNING: state space dimension mismatch: %d versus %d" %
(ssOriginal.nstates, ssTransformed.nstates))
# Now make sure the frequency responses match
# Since bode() only handles SISO, go through each I/O pair
# For phase, take sine and cosine to avoid +/- 360 offset
for inputNum in range(inputs):
for outputNum in range(outputs):
if (verbose):
print("Checking input %d, output %d"
% (inputNum, outputNum))
ssorig_mag, ssorig_phase, ssorig_omega = \
bode(_mimo2siso(ssOriginal, inputNum, outputNum),
deg=False, plot=False)
ssorig_real = ssorig_mag * np.cos(ssorig_phase)
ssorig_imag = ssorig_mag * np.sin(ssorig_phase)
#
# Make sure TF has same frequency response
#
num = tfOriginal.num[outputNum][inputNum]
den = tfOriginal.den[outputNum][inputNum]
tforig = tf(num, den)
tforig_mag, tforig_phase, tforig_omega = \
bode(tforig, ssorig_omega,
deg=False, plot=False)
tforig_real = tforig_mag * np.cos(tforig_phase)
tforig_imag = tforig_mag * np.sin(tforig_phase)
np.testing.assert_array_almost_equal(
ssorig_real, tforig_real)
np.testing.assert_array_almost_equal(
ssorig_imag, tforig_imag)
#
# Make sure xform'd SS has same frequency response
#
ssxfrm_mag, ssxfrm_phase, ssxfrm_omega = \
bode(_mimo2siso(ssTransformed,
inputNum, outputNum),
ssorig_omega,
deg=False, plot=False)
ssxfrm_real = ssxfrm_mag * np.cos(ssxfrm_phase)
ssxfrm_imag = ssxfrm_mag * np.sin(ssxfrm_phase)
np.testing.assert_array_almost_equal(
ssorig_real, ssxfrm_real, decimal=5)
np.testing.assert_array_almost_equal(
ssorig_imag, ssxfrm_imag, decimal=5)
# Make sure xform'd TF has same frequency response
#
num = tfTransformed.num[outputNum][inputNum]
den = tfTransformed.den[outputNum][inputNum]
tfxfrm = tf(num, den)
tfxfrm_mag, tfxfrm_phase, tfxfrm_omega = \
bode(tfxfrm, ssorig_omega,
deg=False, plot=False)
tfxfrm_real = tfxfrm_mag * np.cos(tfxfrm_phase)
tfxfrm_imag = tfxfrm_mag * np.sin(tfxfrm_phase)
np.testing.assert_array_almost_equal(
ssorig_real, tfxfrm_real, decimal=5)
np.testing.assert_array_almost_equal(
ssorig_imag, tfxfrm_imag, decimal=5)
def bode(*args, **keywords):
"""Bode plot of the frequency response
Plots a bode gain and phase diagram
Parameters
----------
sys : Lti, or list of Lti
System for which the Bode response is plotted and give. Optionally
a list of systems can be entered, or several systems can be
specified (i.e. several parameters). The sys arguments may also be
interspersed with format strings. A frequency argument (array_like)
may also be added, some examples:
* >>> bode(sys, w) # one system, freq vector
* >>> bode(sys1, sys2, ..., sysN) # several systems
* >>> bode(sys1, sys2, ..., sysN, w)
* >>> bode(sys1, 'plotstyle1', ..., sysN, 'plotstyleN') # + plot formats
omega: freq_range
Range of frequencies in rad/s
dB : boolean
If True, plot result in dB
Hz : boolean
If True, plot frequency in Hz (omega must be provided in rad/sec)
deg : boolean
If True, return phase in degrees (else radians)
Plot : boolean
If True, plot magnitude and phase
Examples
--------
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> mag, phase, omega = bode(sys)
.. todo::
Document these use cases
* >>> bode(sys, w)
* >>> bode(sys1, sys2, ..., sysN)
* >>> bode(sys1, sys2, ..., sysN, w)
* >>> bode(sys1, 'plotstyle1', ..., sysN, 'plotstyleN')
"""
# If the first argument is a list, then assume python-control calling format
if (getattr(args[0], '__iter__', False)):
return freqplot.bode(*args, **keywords)
# Otherwise, run through the arguments and collect up arguments
syslist = []; plotstyle=[]; omega=None;
i = 0;
while i < len(args):
# Check to see if this is a system of some sort
if (ctrlutil.issys(args[i])):
# Append the system to our list of systems
syslist.append(args[i])
i += 1
# See if the next object is a plotsytle (string)
if (i < len(args) and isinstance(args[i], str)):
plotstyle.append(args[i])
i += 1
# Go on to the next argument
continue
# See if this is a frequency list
elif (isinstance(args[i], (list, np.ndarray))):
omega = args[i]
i += 1
break
else:
raise ControlArgument("unrecognized argument type")
# Check to make sure that we processed all arguments
if (i < len(args)):
raise ControlArgument("not all arguments processed")
# Check to make sure we got the same number of plotstyles as systems
if (len(plotstyle) != 0 and len(syslist) != len(plotstyle)):
raise ControlArgument("number of systems and plotstyles should be equal")
# Warn about unimplemented plotstyles
#! TODO: remove this when plot styles are implemented in bode()
#! TODO: uncomment unit test code that tests this out
if (len(plotstyle) != 0):
print("Warning (matabl.bode): plot styles not implemented");
# Call the bode command
return freqplot.bode(syslist, omega, **keywords)
def bode(*args, **keywords):
"""Bode plot of the frequency response
Plots a bode gain and phase diagram
Parameters
----------
sys : Lti, or list of Lti
System for which the Bode response is plotted and give. Optionally
a list of systems can be entered, or several systems can be
specified (i.e. several parameters). The sys arguments may also be
interspersed with format strings. A frequency argument (array_like)
may also be added, some examples:
* >>> bode(sys, w) # one system, freq vector
* >>> bode(sys1, sys2, ..., sysN) # several systems
* >>> bode(sys1, sys2, ..., sysN, w)
* >>> bode(sys1, 'plotstyle1', ..., sysN, 'plotstyleN') # + plot formats
omega: freq_range
Range of frequencies in rad/s
dB : boolean
If True, plot result in dB
Hz : boolean
If True, plot frequency in Hz (omega must be provided in rad/sec)
deg : boolean
If True, return phase in degrees (else radians)
Plot : boolean
If True, plot magnitude and phase
Examples
--------
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> mag, phase, omega = bode(sys)
.. todo::
Document these use cases
* >>> bode(sys, w)
* >>> bode(sys1, sys2, ..., sysN)
* >>> bode(sys1, sys2, ..., sysN, w)
* >>> bode(sys1, 'plotstyle1', ..., sysN, 'plotstyleN')
"""
# If the first argument is a list, then assume python-control calling format
if (getattr(args[0], '__iter__', False)):
return freqplot.bode(*args, **keywords)
# Otherwise, run through the arguments and collect up arguments
syslist = []; plotstyle=[]; omega=None;
i = 0;
while i < len(args):
# Check to see if this is a system of some sort
if (ctrlutil.issys(args[i])):
# Append the system to our list of systems
syslist.append(args[i])
i += 1
# See if the next object is a plotsytle (string)
if (i < len(args) and isinstance(args[i], str)):
plotstyle.append(args[i])
i += 1
# Go on to the next argument
continue
# See if this is a frequency list
elif (isinstance(args[i], (list, np.ndarray))):
omega = args[i]
i += 1
break
else:
raise ControlArgument("unrecognized argument type")
# Check to make sure that we processed all arguments
if (i < len(args)):
raise ControlArgument("not all arguments processed")
# Check to make sure we got the same number of plotstyles as systems
if (len(plotstyle) != 0 and len(syslist) != len(plotstyle)):
raise ControlArgument("number of systems and plotstyles should be equal")
# Warn about unimplemented plotstyles
#! TODO: remove this when plot styles are implemented in bode()
#! TODO: uncomment unit test code that tests this out
if (len(plotstyle) != 0):
print("Warning (matabl.bode): plot styles not implemented");
# Call the bode command
return freqplot.bode(syslist, omega, **keywords)
def multibode(lins, axes=None, pair=(0, 0), label='bode', title="Bode Plot",
labels='', colors=['b', 'g', 'r', 'c', 'm', 'y', 'k'],
styles=[(None,None), (3,3), (1,1), (3,2,1,2)], leg_kwargs={},
**kwargs):
r"""Plot multiple linearizations onto a single Bode diagram.
**Arguments:**
- *lins*: Linearization result or list of results (instances of
:class:`linres.LinRes`)
- *axes*: Tuple (pair) of axes for the magnitude and phase plots
If *axes* 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
- *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
- *styles*: Line/dash style or list of line/dash styles that will be
used sequentially
Each style is a string representing a linestyle (e.g., "--") or a
tuple of on/off lengths representing dashes. Use "" for no line
and "-" for a solid line.
.. Seealso::
http://matplotlib.sourceforge.net/api/collections_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.bode`
**Returns:**
1. *axes*: Tuple (pair) of axes for the magnitude and phase plots
**Example:**
.. testsetup::
>>> from modelicares import closeall
>>> closeall()
.. code-block:: python
>>> import os
>>> from glob import glob
>>> from modelicares import LinRes, multibode, save, read_params
>>> from numpy import pi, logspace
>>> lins = map(LinRes, glob('examples/PID/*/*.mat'))
>>> labels = ["Ti=%g" % read_params('Ti', os.path.join(lin.dir, 'dsin.txt'))
... for lin in lins]
>>> multibode(lins,
... title="Bode Plot of Modelica.Blocks.Continuous.PID",
... label='examples/PIDs-bode', omega=2*pi*logspace(-2, 3),
... labels=labels, leg_kwargs=dict(loc='lower right')) # doctest: +ELLIPSIS
(<matplotlib.axes._subplots.AxesSubplot object at 0x...>, <matplotlib.axes._subplots.AxesSubplot object at 0x...>)
>>> save()
Saved examples/PIDs-bode.pdf
Saved examples/PIDs-bode.png
.. only:: html
.. image:: ../examples/PIDs-bode.png
:scale: 70 %
:alt: Bode plot of PID with varying parameters
.. only:: latex
.. figure:: ../examples/PIDs-bode.pdf
:scale: 70 %
Bode plot of PID with varying parameters
"""
# Create axes if necessary.
if not axes:
fig = figure(label)
axes = (fig.add_subplot(211), fig.add_subplot(212))
# 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) and line style(s).
if not iterable(colors):
# Use the single color for all plots.
colors = (colors,)
if not iterable(styles):
# Use the single line style for all plots.
styles = [styles]
elif type(styles[0]) is int:
# One dashes tuple has been provided; use its value for all plots.
styles = [styles]
n_colors = len(colors)
n_styles = len(styles)
# Create the plots.
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
bode(sys, Hz=True, label=label,
color=colors[np.mod(i, n_colors)], axes=axes,
style=styles[np.mod(i, n_styles)], **kwargs)
# Decorate and finish.
axes[0].set_title(title)
if leg_kwargs is not None:
loc = leg_kwargs.pop('loc', 'best')
axes[0].legend(loc=loc, **leg_kwargs)
axes[1].legend(loc=loc, **leg_kwargs)
return axes
