def check_unwrap_array(self, angle, period=None):
if period is None:
angle_mod = angle % (2 * np.pi)
angle_unwrap = unwrap(angle_mod)
else:
angle_mod = angle % period
angle_unwrap = unwrap(angle_mod, period)
np.testing.assert_array_almost_equal(angle_unwrap, angle)
def nichols_plot(syslist, omega=None, grid=True):
"""Nichols plot for a system
Plots a Nichols plot for the system over a (optional) frequency range.
Parameters
----------
syslist : list of Lti, or Lti
List of linear input/output systems (single system is OK)
omega : array_like
Range of frequencies (list or bounds) in rad/sec
grid : boolean, optional
True if the plot should include a Nichols-chart grid. Default is True.
Returns
-------
None
"""
# If argument was a singleton, turn it into a list
if (not getattr(syslist, '__iter__', False)):
syslist = (syslist,)
# Select a default range if none is provided
if omega is None:
omega = default_frequency_range(syslist)
for sys in syslist:
# Get the magnitude and phase of the system
mag_tmp, phase_tmp, omega = sys.freqresp(omega)
mag = np.squeeze(mag_tmp)
phase = np.squeeze(phase_tmp)
# Convert to Nichols-plot format (phase in degrees,
# and magnitude in dB)
x = unwrap(sp.degrees(phase), 360)
y = 20*sp.log10(mag)
# Generate the plot
plt.plot(x, y)
plt.xlabel('Phase (deg)')
plt.ylabel('Magnitude (dB)')
plt.title('Nichols Plot')
# Mark the -180 point
plt.plot([-180], [0], 'r+')
# Add grid
if grid:
nichols_grid()
def plot(self,
syslist,
omega=None,
dB=None,
Hz=None,
deg=None,
Plot=True,
*args,
**kwargs):
self.axes1.clear()
self.axes1.grid(True, color='gray')
self.axes1.set_ylabel("Magnitude (dB)" if dB else "Magnitude")
self.axes2.clear()
self.axes2.grid(True, color='gray')
self.axes2.set_ylabel("Phase (deg)" if deg else "Phase (rad)")
self.axes2.set_xlabel(
"Frequency (Hz)" if Hz else "Frequency (rad/sec)")
if (dB is None):
dB = control.config.bode_dB
if (deg is None):
deg = control.config.bode_deg
if (Hz is None):
Hz = control.config.bode_Hz
if (not getattr(syslist, '__iter__', False)):
syslist = (syslist, )
mags, phases, omegas = [], [], []
if (omega == None):
omega = default_frequency_range(syslist)
mag_tmp, phase_tmp, omega = syslist[0].freqresp(omega)
mag = np.atleast_1d(np.squeeze(mag_tmp))
phase = np.atleast_1d(np.squeeze(phase_tmp))
phase = unwrap(phase)
if Hz: omega = omega / (2 * sp.pi)
if dB: mag = 20 * sp.log10(mag)
if deg: phase = phase * 180 / sp.pi
mags.append(mag)
phases.append(phase)
omegas.append(omega)
if dB:
self.axes1.semilogx(omega, mag, *args, **kwargs)
else:
self.axes1.loglog(omega, mag, *args, **kwargs)
self.axes2.semilogx(omega, phase, *args, **kwargs)
self.canvas = FigCanvas(self, -1, self.fig)
self.canvas.draw()
def plot(self, syslist, omega=None, dB=None, Hz=None, deg=None, Plot=True, *args , **kwargs):
self.axes1.clear()
self.axes1.grid(True , color='gray')
self.axes1.set_ylabel("Magnitude (dB)" if dB else "Magnitude")
self.axes2.clear()
self.axes2.grid(True , color='gray')
self.axes2.set_ylabel("Phase (deg)" if deg else "Phase (rad)")
self.axes2.set_xlabel("Frequency (Hz)" if Hz else "Frequency (rad/sec)")
if (dB is None):
dB = control.config.bode_dB
if (deg is None):
deg = control.config.bode_deg
if (Hz is None):
Hz = control.config.bode_Hz
if (not getattr(syslist, '__iter__', False)):
syslist = (syslist,)
mags, phases, omegas = [], [], []
if (omega == None):
omega = default_frequency_range(syslist)
mag_tmp, phase_tmp, omega = syslist[0].freqresp(omega)
mag = np.atleast_1d(np.squeeze(mag_tmp))
phase = np.atleast_1d(np.squeeze(phase_tmp))
phase = unwrap(phase)
if Hz: omega = omega/(2*sp.pi)
if dB: mag = 20*sp.log10(mag)
if deg: phase = phase * 180 / sp.pi
mags.append(mag)
phases.append(phase)
omegas.append(omega)
if dB:
self.axes1.semilogx(omega,mag,*args,**kwargs)
else:
self.axes1.loglog(omega,mag,*args,**kwargs)
self.axes2.semilogx(omega,phase,*args,**kwargs)
self.canvas = FigCanvas(self, -1, self.fig)
self.canvas.draw()
def bode_plot(mag, phase, f, in_Hz=True, in_dB=True, in_deg=True, label=None,
axes=None, *args, **kwargs):
r"""Create a Bode plot for a system.
**Arguments:**
- *sys*: Linear input/output system (Lti)
- *freqs*: List or frequencies or tuple of (min, max) frequencies over which
to plot the system response.
If *freqs* is *None*, then an appropriate range will be determined
automatically.
- *in_Hz*: If *True*, the frequencies (*freqs*) are in Hz and should be
plotted in Hz (otherwise, rad/s)
- *in_dB*: If *True*, plot the magnitude in dB
- *in_deg*: If *True*, plot the phase in degrees (otherwise, radians)
- *label*: Label for the legend, if added
- *axes*: Tuple (pair) of axes to plot into
If *None* or (*None*, None*), then axes are created
- *\*args*, *\*\*kwargs*: Additional options to matplotlib (color,
linestyle, etc.)
**Returns:**
1. Axes of the magnitude and phase plots (tuple (pair) of matplotlib axes)
**Example:**
.. plot::
:include-source:
>>> from control.matlab import ss
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> axes = bode_plot(sys)
"""
phase = unwrap(phase)
freq_unit = Hz if in_Hz else rad / s
# Create axes if necessary.
if axes is None or (None, None):
axes = (plt.subplot(211), plt.subplot(212))
# Magnitude plot
axes[0].semilogx(f / freq_unit, to_dB(mag) if in_dB else mag,
label=label, *args, **kwargs)
# Add a grid and labels.
axes[0].grid(True)
axes[0].grid(True, which='minor')
axes[0].set_ylabel("Magnitude in dB" if in_dB else "Magnitude")
# Phase plot
axes[1].semilogx(f / freq_unit, phase / (deg if in_deg else rad),
label=label, *args, **kwargs)
# Add a grid and labels.
axes[1].grid(True)
axes[1].grid(True, which='minor')
axes[1].set_xlabel(number_label("Frequency", "Hz" if in_Hz else "rad/s"))
axes[1].set_ylabel(number_label("Phase", "deg" if in_deg else "rad"))
return axes
def bode_plot(syslist,
omega=None,
dB=None,
Hz=None,
deg=None,
Plot=True,
*args,
**kwargs):
"""Bode plot for a system
Plots a Bode plot for the system over a (optional) frequency range.
Parameters
----------
syslist : linsys
List of linear input/output systems (single system is OK)
omega : freq_range
Range of frequencies (list or bounds) in rad/sec
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
*args, **kwargs:
Additional options to matplotlib (color, linestyle, etc)
Returns
-------
mag : array (list if len(syslist) > 1)
magnitude
phase : array (list if len(syslist) > 1)
phase
omega : array (list if len(syslist) > 1)
frequency
Notes
-----
1. Alternatively, you may use the lower-level method (mag, phase, freq)
= sys.freqresp(freq) to generate the frequency response for a system,
but it returns a MIMO response.
2. If a discrete time model is given, the frequency response is plotted
along the upper branch of the unit circle, using the mapping z = exp(j
\omega dt) where omega ranges from 0 to pi/dt and dt is the discrete
time base. If not timebase is specified (dt = True), dt is set to 1.
Examples
--------
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> mag, phase, omega = bode(sys)
"""
# Set default values for options
import control.config
if (dB is None): dB = control.config.bode_dB
if (deg is None): deg = control.config.bode_deg
if (Hz is None): Hz = control.config.bode_Hz
# If argument was a singleton, turn it into a list
if (not getattr(syslist, '__iter__', False)):
syslist = (syslist, )
mags, phases, omegas = [], [], []
for sys in syslist:
if (sys.inputs > 1 or sys.outputs > 1):
#TODO: Add MIMO bode plots.
raise NotImplementedError(
"Bode is currently only implemented for SISO systems.")
else:
if (omega == None):
# Select a default range if none is provided
omega = default_frequency_range(syslist)
# Get the magnitude and phase of the system
mag_tmp, phase_tmp, omega = sys.freqresp(omega)
mag = np.atleast_1d(np.squeeze(mag_tmp))
phase = np.atleast_1d(np.squeeze(phase_tmp))
phase = unwrap(phase)
if Hz: omega = omega / (2 * sp.pi)
if dB: mag = 20 * sp.log10(mag)
if deg: phase = phase * 180 / sp.pi
mags.append(mag)
phases.append(phase)
omegas.append(omega)
# Get the dimensions of the current axis, which we will divide up
#! TODO: Not current implemented; just use subplot for now
if (Plot):
# Magnitude plot
plt.subplot(211)
if dB:
plt.semilogx(omega, mag, *args, **kwargs)
else:
plt.loglog(omega, mag, *args, **kwargs)
plt.hold(True)
# Add a grid to the plot + labeling
plt.grid(True)
plt.grid(True, which='minor')
plt.ylabel("Magnitude (dB)" if dB else "Magnitude")
# Phase plot
plt.subplot(212)
plt.semilogx(omega, phase, *args, **kwargs)
plt.hold(True)
# Add a grid to the plot + labeling
plt.grid(True)
plt.grid(True, which='minor')
plt.ylabel("Phase (deg)" if deg else "Phase (rad)")
# Label the frequency axis
plt.xlabel("Frequency (Hz)" if Hz else "Frequency (rad/sec)")
if len(syslist) == 1:
return mags[0], phases[0], omegas[0]
else:
return mags, phases, omegas
def test_unwrap_list(self):
angle = [0, 2.2, 5.4, -0.4]
angle_unwrapped = [0, 0.2, 0.4, 0.6]
np.testing.assert_array_almost_equal(unwrap(angle, 1.0), angle_unwrapped)
def test_unwrap_large_skips(self):
angle = np.array([0., 4 * np.pi, -2 * np.pi])
np.testing.assert_array_almost_equal(unwrap(angle), [0., 0., 0.])
def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
Plot=True, *args, **kwargs):
"""Bode plot for a system
Plots a Bode plot for the system over a (optional) frequency range.
Parameters
----------
syslist : linsys
List of linear input/output systems (single system is OK)
omega : freq_range
Range of frequencies (list or bounds) in rad/sec
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
*args, **kwargs:
Additional options to matplotlib (color, linestyle, etc)
Returns
-------
mag : array (list if len(syslist) > 1)
magnitude
phase : array (list if len(syslist) > 1)
phase
omega : array (list if len(syslist) > 1)
frequency
Notes
-----
1. Alternatively, you may use the lower-level method (mag, phase, freq)
= sys.freqresp(freq) to generate the frequency response for a system,
but it returns a MIMO response.
2. If a discrete time model is given, the frequency response is plotted
along the upper branch of the unit circle, using the mapping z = exp(j
\omega dt) where omega ranges from 0 to pi/dt and dt is the discrete
time base. If not timebase is specified (dt = True), dt is set to 1.
Examples
--------
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> mag, phase, omega = bode(sys)
"""
# Set default values for options
import control.config
if (dB is None): dB = control.config.bode_dB
if (deg is None): deg = control.config.bode_deg
if (Hz is None): Hz = control.config.bode_Hz
# If argument was a singleton, turn it into a list
if (not getattr(syslist, '__iter__', False)):
syslist = (syslist,)
mags, phases, omegas = [], [], []
for sys in syslist:
if (sys.inputs > 1 or sys.outputs > 1):
#TODO: Add MIMO bode plots.
raise NotImplementedError("Bode is currently only implemented for SISO systems.")
else:
if (omega == None):
# Select a default range if none is provided
omega = default_frequency_range(syslist)
# Get the magnitude and phase of the system
mag_tmp, phase_tmp, omega = sys.freqresp(omega)
mag = np.atleast_1d(np.squeeze(mag_tmp))
phase = np.atleast_1d(np.squeeze(phase_tmp))
phase = unwrap(phase)
if Hz: omega = omega/(2*sp.pi)
if dB: mag = 20*sp.log10(mag)
if deg: phase = phase * 180 / sp.pi
mags.append(mag)
phases.append(phase)
omegas.append(omega)
# Get the dimensions of the current axis, which we will divide up
#! TODO: Not current implemented; just use subplot for now
if (Plot):
# Magnitude plot
plt.subplot(211);
if dB:
plt.semilogx(omega, mag, *args, **kwargs)
else:
plt.loglog(omega, mag, *args, **kwargs)
plt.hold(True);
# Add a grid to the plot + labeling
plt.grid(True)
plt.grid(True, which='minor')
plt.ylabel("Magnitude (dB)" if dB else "Magnitude")
# Phase plot
plt.subplot(212);
plt.semilogx(omega, phase, *args, **kwargs)
plt.hold(True);
# Add a grid to the plot + labeling
plt.grid(True)
plt.grid(True, which='minor')
plt.ylabel("Phase (deg)" if deg else "Phase (rad)")
# Label the frequency axis
plt.xlabel("Frequency (Hz)" if Hz else "Frequency (rad/sec)")
if len(syslist) == 1:
return mags[0], phases[0], omegas[0]
else:
return mags, phases, omegas
def bode_plot(mag,
phase,
f,
in_Hz=True,
in_dB=True,
in_deg=True,
label=None,
axes=None,
*args,
**kwargs):
r"""Create a Bode plot for a system.
**Parameters:**
- *sys*: Linear input/output system (Lti)
- *freqs*: List or frequencies or tuple of (min, max) frequencies over which
to plot the system response.
If *freqs* is *None*, then an appropriate range will be determined
automatically.
- *in_Hz*: If *True*, the frequencies (*freqs*) are in Hz and should be
plotted in Hz (otherwise, rad/s)
- *in_dB*: If *True*, plot the magnitude in dB
- *in_deg*: If *True*, plot the phase in degrees (otherwise, radians)
- *label*: Label for the legend, if added
- *axes*: Tuple (pair) of axes to plot into
If *None* or (*None*, None*), then axes are created
- *\*args*, *\*\*kwargs*: Additional options to matplotlib (color,
linestyle, etc.)
**Returns:**
1. Axes of the magnitude and phase plots (tuple (pair) of matplotlib axes)
**Example:**
.. plot::
:include-source:
>>> from control.matlab import ss
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> axes = bode_plot(sys)
"""
phase = unwrap(phase)
freq_unit = Hz if in_Hz else rad / s
# Create axes if necessary.
if axes is None or (None, None):
axes = (plt.subplot(211), plt.subplot(212))
# Magnitude plot
axes[0].semilogx(f / freq_unit,
to_dB(mag) if in_dB else mag,
label=label,
*args,
**kwargs)
# Add a grid and labels.
axes[0].grid(True)
axes[0].grid(True, which='minor')
axes[0].set_ylabel("Magnitude in dB" if in_dB else "Magnitude")
# Phase plot
axes[1].semilogx(f / freq_unit,
phase / (deg if in_deg else rad),
label=label,
*args,
**kwargs)
# Add a grid and labels.
axes[1].grid(True)
axes[1].grid(True, which='minor')
axes[1].set_xlabel(number_label("Frequency", "Hz" if in_Hz else "rad/s"))
axes[1].set_ylabel(number_label("Phase", "deg" if in_deg else "rad"))
return axes
def bode_plot(syslist, omega=None, dB=False, Hz=False, deg=True,
# ModelicaRes 7/2/13:
# Plot=True, *args, **kwargs):
Plot=True, style='-', label=None, axes=None, *args, **kwargs):
# ModelicaRes 7/5/13: Added description of axes argument and output
"""Bode plot for a system
Plots a Bode plot for the system over a (optional) frequency range.
Parameters
----------
syslist : linsys
List of linear input/output systems (single system is OK)
omega : freq_range
Range of frequencies (list or bounds) in rad/sec
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
axes : tuple (pair) of axes to plot into
If None or (None, None), then axes are created
*args, **kwargs:
Additional options to matplotlib (color, linestyle, etc)
Returns
-------
mag : array (list if len(syslist) > 1)
magnitude
phase : array (list if len(syslist) > 1)
phase
omega : array (list if len(syslist) > 1)
frequency
axes
tuple (pair) of axes for the magnitude and phase plots
Notes
-----
1. Alternatively, you may use the lower-level method (mag, phase, freq)
= sys.freqresp(freq) to generate the frequency response for a system,
but it returns a MIMO response.
2. If a discrete time model is given, the frequency response is plotted
along the upper branch of the unit circle, using the mapping z = exp(j
\omega dt) where omega ranges from 0 to pi/dt and dt is the discrete
time base. If not timebase is specified (dt = True), dt is set to 1.
Examples
--------
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
>>> mag, phase, omega = bode(sys)
"""
# If argument was a singleton, turn it into a list
if (not getattr(syslist, '__iter__', False)):
syslist = (syslist,)
mags, phases, omegas = [], [], []
for sys in syslist:
if (sys.inputs > 1 or sys.outputs > 1):
#TODO: Add MIMO bode plots.
raise NotImplementedError("Bode is currently only implemented for SISO systems.")
else:
if (omega == None):
# Select a default range if none is provided
omega = default_frequency_range(syslist)
# Get the magnitude and phase of the system
mag_tmp, phase_tmp, omega = sys.freqresp(omega)
mag = np.atleast_1d(np.squeeze(mag_tmp))
phase = np.atleast_1d(np.squeeze(phase_tmp))
phase = unwrap(phase)
if Hz: omega = omega/(2*sp.pi)
if dB: mag = 20*sp.log10(mag)
if deg: phase = phase * 180 / sp.pi
mags.append(mag)
phases.append(phase)
omegas.append(omega)
# Get the dimensions of the current axis, which we will divide up
#! TODO: Not current implemented; just use subplot for now
if (Plot):
# ModelicaRes 7/5/13:
# Create axes if necessary.
if axes is None or (None, None):
axes = (plt.subplot(211), plt.subplot(212))
# Magnitude plot
# ModelicaRes 7/5/13:
#plt.subplot(211);
if dB:
# ModelicaRes 7/5/13:
#plt.semilogx(omega, mag, *args, **kwargs)
if type(style) is str:
axes[0].semilogx(omega, mag, linestyle=style, label=label, *args, **kwargs)
else:
axes[0].semilogx(omega, mag, dashes=style, label=label, *args, **kwargs)
else:
# ModelicaRes 7/5/13:
#plt.loglog(omega, mag, *args, **kwargs)
if type(style) is str:
axes[0].loglog(omega, mag, linestyle=style, label=label, *args, **kwargs)
else:
axes[0].loglog(omega, mag, dashes=style, label=label, *args, **kwargs)
# ModelicaRes 7/5/13:
#plt.hold(True);
# Add a grid to the plot + labeling
# ModelicaRes 7/5/13:
#plt.grid(True)
#plt.grid(True, which='minor')
#plt.ylabel("Magnitude (dB)" if dB else "Magnitude")
axes[0].grid(True)
axes[0].grid(True, which='minor')
axes[0].set_ylabel("Magnitude in dB" if dB else "Magnitude")
# Phase plot
# ModelicaRes 7/5/13:
#plt.subplot(212);
# ModelicaRes 7/5/13:
#plt.semilogx(omega, phase, *args, **kwargs)
if type(style) is str:
axes[1].semilogx(omega, phase, linestyle=style, label=label, *args, **kwargs)
else:
axes[1].semilogx(omega, phase, dashes=style, label=label, *args, **kwargs)
# ModelicaRes 7/5/13:
#plt.hold(True);
# Add a grid to the plot + labeling
# ModelicaRes 7/2/13:
#plt.grid(True)
#plt.grid(True, which='minor')
#plt.ylabel("Phase (deg)" if deg else "Phase (rad)")
axes[1].grid(True)
axes[1].grid(True, which='minor')
axes[1].set_ylabel("Phase / deg" if deg else "Phase / rad")
# Label the frequency axis
# ModelicaRes 7/5/13:
#plt.xlabel("Frequency (Hz)" if Hz else "Frequency (rad/sec)")
axes[1].set_xlabel("Frequency / Hz" if Hz else "Frequency / rad s$^{-1}$")
if len(syslist) == 1:
# ModelicaRes 7/5/13:
#return mags[0], phases[0], omegas[0]
return mags[0], phases[0], omegas[0], axes
else:
# ModelicaRes 7/5/13:
#return mags, phases, omegas
return mags, phases, omegas, axes