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[python-control-discuss] SF.net SVN: python-control:[135] trunk/src/freqplot.py
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From: <all...@us...> - 2011-02-14 07:49:12
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Revision: 135
http://python-control.svn.sourceforge.net/python-control/?rev=135&view=rev
Author: allanmcinnes
Date: 2011-02-14 07:49:05 +0000 (Mon, 14 Feb 2011)
Log Message:
-----------
Add the ability to define custom Nichols charts by passing magnitude and/or phase arrays to nichols_grid. Also some tweaks to the chart grid generation and axis configuration, and further clean-up of documentation and naming.
Modified Paths:
--------------
trunk/src/freqplot.py
Modified: trunk/src/freqplot.py
===================================================================
--- trunk/src/freqplot.py 2011-02-13 16:49:58 UTC (rev 134)
+++ trunk/src/freqplot.py 2011-02-14 07:49:05 UTC (rev 135)
@@ -181,7 +181,7 @@
# Nichols plot
# Contributed by Allan McInnes <All...@ca...>
#! TODO: need unit test code
-def nichols(syslist, omega=None):
+def nichols(syslist, omega=None, grid=True):
"""Nichols plot for a system
Usage
@@ -196,6 +196,8 @@
List of linear input/output systems (single system is OK)
omega : freq_range
Range of frequencies (list or bounds) in rad/sec
+ grid : boolean
+ True if the plot should include a Nichols-chart grid
Return values
-------------
@@ -228,88 +230,114 @@
# Mark the -180 point
plt.plot([-180], [0], 'r+')
+
+ # Add grid
+ if grid:
+ nichols_grid()
# Nichols grid
-def nichols_grid():
+def nichols_grid(**kwargs):
"""Nichols chart grid
Usage
=====
nichols_grid()
- Plots a Nichols chart grid on the current axis.
+ Plots a Nichols chart grid on the current axis, or creates a new chart
+ if no plot already exists.
Parameters
----------
- None
+ cl_mags : array-like (dB)
+ Array of closed-loop magnitudes defining the iso-gain lines on a
+ custom Nichols chart.
+ cl_phases : array-like (degrees)
+ Array of closed-loop phases defining the iso-phase lines on a custom
+ Nichols chart. Must be in the range -360 < cl_phases < 0
Return values
-------------
None
"""
- mag_min_default = -40.0 # dB
- mag_step = 20.0 # dB
+ # Default chart size
+ ol_phase_min = -359.99
+ ol_phase_max = 0.0
+ ol_mag_min = -40.0
+ ol_mag_max = default_ol_mag_max = 50.0
+
+ # Find bounds of the current dataset, if there is one.
+ if plt.gcf().gca().has_data():
+ ol_phase_min, ol_phase_max, ol_mag_min, ol_mag_max = plt.axis()
- # Chart defaults
- phase_min, phase_max, mag_min, mag_max = -360.0, 0.0, mag_min_default, 40.0
-
- # Set actual chart bounds based on current plot
- if plt.gcf().gca().has_data():
- phase_min, phase_max, mag_min, mag_max = plt.axis()
-
# M-circle magnitudes.
- # The "fixed" set are always generated, since this guarantees a recognizable
- # Nichols chart grid.
- mags_fixed = np.array([-40.0, -20.0, -12.0, -6.0, -3.0, -1.0, -0.5, 0.0,
- 0.25, 0.5, 1.0, 3.0, 6.0, 12.0])
-
- if mag_min < mag_min_default:
- # Outside the "fixed" set of magnitudes, the generated M-circles
- # are extended in steps of 'mag_step' dB to cover anything made
- # visible by the range of the existing plot
- mags_adjust = np.arange(mag_step*np.floor(mag_min/mag_step),
- mag_min_default, mag_step)
- mags = np.concatenate((mags_adjust, mags_fixed))
+ if kwargs.has_key('cl_mags'):
+ # Custom chart
+ cl_mags = kwargs['cl_mags']
else:
- mags = mags_fixed
+ # Default chart magnitudes
+ # The key set of magnitudes are always generated, since this
+ # guarantees a recognizable Nichols chart grid.
+ key_cl_mags = np.array([-40.0, -20.0, -12.0, -6.0, -3.0, -1.0, -0.5, 0.0,
+ 0.25, 0.5, 1.0, 3.0, 6.0, 12.0])
+ # Extend the range of magnitudes if necessary. The extended arange
+ # will end up empty if no extension is required. Assumes that closed-loop
+ # magnitudes are approximately aligned with open-loop magnitudes beyond
+ # the value of np.min(key_cl_mags)
+ cl_mag_step = -20.0 # dB
+ extended_cl_mags = np.arange(np.min(key_cl_mags),
+ ol_mag_min + cl_mag_step, cl_mag_step)
+ cl_mags = np.concatenate((extended_cl_mags, key_cl_mags))
# N-circle phases (should be in the range -360 to 0)
- phases = np.array([-0.25, -10.0, -20.0, -30.0, -45.0, -60.0, -90.0,
- -120.0, -150.0, -180.0, -210.0, -240.0, -270.0,
- -310.0, -325.0, -340.0, -350.0, -359.75])
+ if kwargs.has_key('cl_phases'):
+ # Custom chart
+ cl_phases = kwargs['cl_phases']
+ assert ((-360.0 < np.min(cl_phases)) and (np.max(cl_phases) < 0.0))
+ else:
+ # Choose a reasonable set of default phases (denser if the open-loop
+ # data is restricted to a relatively small range of phases).
+ key_cl_phases = np.array([-0.25, -45.0, -90.0, -180.0, -270.0, -325.0, -359.75])
+ if np.abs(ol_phase_max - ol_phase_min) < 90.0:
+ other_cl_phases = np.arange(-10.0, -360.0, -10.0)
+ else:
+ other_cl_phases = np.arange(-10.0, -360.0, -20.0)
+ cl_phases = np.concatenate((key_cl_phases, other_cl_phases))
# Find the M-contours
- m = m_circles(mags, phase_min=np.min(phases), phase_max=np.max(phases))
+ m = m_circles(cl_mags, phase_min=np.min(cl_phases), phase_max=np.max(cl_phases))
m_mag = 20*sp.log10(np.abs(m))
m_phase = sp.mod(sp.degrees(sp.angle(m)), -360.0) # Unwrap
# Find the N-contours
- n = n_circles(phases, mag_min=np.min(mags), mag_max=np.max(mags))
+ n = n_circles(cl_phases, mag_min=np.min(cl_mags), mag_max=np.max(cl_mags))
n_mag = 20*sp.log10(np.abs(n))
n_phase = sp.mod(sp.degrees(sp.angle(n)), -360.0) # Unwrap
# Plot the contours behind other plot elements.
# The "phase offset" is used to produce copies of the chart that cover
# the entire range of the plotted data, starting from a base chart computed
- # over the range -360 < phase < 0 (see above). Given the range
+ # over the range -360 < phase < 0. Given the range
# the base chart is computed over, the phase offset should be 0
- # for -360 < phase_min < 0.
- phase_offset_min = 360.0*np.ceil(phase_min/360.0)
- phase_offset_max = 360.0*np.ceil(phase_max/360.0) + 360.0
+ # for -360 < ol_phase_min < 0.
+ phase_offset_min = 360.0*np.ceil(ol_phase_min/360.0)
+ phase_offset_max = 360.0*np.ceil(ol_phase_max/360.0) + 360.0
phase_offsets = np.arange(phase_offset_min, phase_offset_max, 360.0)
+
for phase_offset in phase_offsets:
+ # Draw M and N contours
plt.plot(m_phase + phase_offset, m_mag, color='gray',
linestyle='dashed', zorder=0)
plt.plot(n_phase + phase_offset, n_mag, color='gray',
linestyle='dashed', zorder=0)
- # Add magnitude labels
- for x, y, m in zip(m_phase[:][-1], m_mag[:][-1], mags):
- align = 'right' if m < 0.0 else 'left'
- plt.text(x, y, str(m) + ' dB', size='small', ha=align)
+ # Add magnitude labels
+ for x, y, m in zip(m_phase[:][-1] + phase_offset, m_mag[:][-1], cl_mags):
+ align = 'right' if m < 0.0 else 'left'
+ plt.text(x, y, str(m) + ' dB', size='small', ha=align)
- # Make sure axes conform to any pre-existing plot.
- plt.axis([phase_min, phase_max, mag_min, mag_max])
+ # Fit axes to generated chart
+ plt.axis([phase_offset_min - 360.0, phase_offset_max - 360.0,
+ np.min(cl_mags), np.max([ol_mag_max, default_ol_mag_max])])
# Gang of Four
#! TODO: think about how (and whether) to handle lists of systems
@@ -417,38 +445,44 @@
return omega
# Compute contours of a closed-loop transfer function
-def closed_loop_contours(Hmag, Hphase):
- """Contours of the function H = G/(1+G).
+def closed_loop_contours(Gcl_mags, Gcl_phases):
+ """Contours of the function Gcl = Gol/(1+Gol), where
+ Gol is an open-loop transfer function, and Gcl is a corresponding
+ closed-loop transfer function.
Usage
=====
- contours = closed_loop_contours(mags, phases)
+ contours = closed_loop_contours(Gcl_mags, Gcl_phases)
Parameters
----------
- mags : array-like
- Meshgrid array of magnitudes of the contours
- phases : array-like
- Meshgrid array of phases in radians of the contours
+ Gcl_mags : array-like
+ Array of magnitudes of the contours
+ Gcl_phases : array-like
+ Array of phases in radians of the contours
Return values
-------------
contours : complex array
Array of complex numbers corresponding to the contours.
"""
- # Compute the contours in H-space
- H = Hmag*sp.exp(1.j*Hphase)
+ # Compute the contours in Gcl-space. Since we're given closed-loop
+ # magnitudes and phases, this is just a case of converting them into
+ # a complex number.
+ Gcl = Gcl_mags*sp.exp(1.j*Gcl_phases)
- # Invert H = G/(1+G) to get an expression for the contours in G-space
- return H/(1.0 - H)
+ # Invert Gcl = Gol/(1+Gol) to map the contours into the open-loop space
+ return Gcl/(1.0 - Gcl)
# M-circle
def m_circles(mags, phase_min=-359.75, phase_max=-0.25):
- """Constant-magnitude contours of the function H = G/(1+G).
+ """Constant-magnitude contours of the function Gcl = Gol/(1+Gol), where
+ Gol is an open-loop transfer function, and Gcl is a corresponding
+ closed-loop transfer function.
Usage
=====
- contours = m_circles(mags)
+ contours = m_circles(mags, phase_min, phase_max)
Parameters
----------
@@ -467,16 +501,18 @@
# Convert magnitudes and phase range into a grid suitable for
# building contours
phases = sp.radians(sp.linspace(phase_min, phase_max, 500))
- Hmag, Hphase = sp.meshgrid(10.0**(mags/20.0), phases)
- return closed_loop_contours(Hmag, Hphase)
+ Gcl_mags, Gcl_phases = sp.meshgrid(10.0**(mags/20.0), phases)
+ return closed_loop_contours(Gcl_mags, Gcl_phases)
# N-circle
def n_circles(phases, mag_min=-40.0, mag_max=12.0):
- """Constant-phase contours of the function H = G/(1+G).
+ """Constant-phase contours of the function Gcl = Gol/(1+Gol), where
+ Gol is an open-loop transfer function, and Gcl is a corresponding
+ closed-loop transfer function.
Usage
=====
- contour = n_circles(angles)
+ contours = n_circles(phases, mag_min, mag_max)
Parameters
----------
@@ -495,5 +531,5 @@
# Convert phases and magnitude range into a grid suitable for
# building contours
mags = sp.linspace(10**(mag_min/20.0), 10**(mag_max/20.0), 2000)
- Hphase, Hmag = sp.meshgrid(sp.radians(phases), mags)
- return closed_loop_contours(Hmag, Hphase)
+ Gcl_phases, Gcl_mags = sp.meshgrid(sp.radians(phases), mags)
+ return closed_loop_contours(Gcl_mags, Gcl_phases)
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