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murrayrmmurrayrm
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Merge pull request #264 from don4get/refactor/cleaning-nichols
Clean up nichols.py
2 parents 5ff1184 + 9179e89 commit be59f62

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Lines changed: 34 additions & 22 deletions

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‎control/nichols.py‎

Lines changed: 34 additions & 22 deletions
Original file line numberDiff line numberDiff line change
@@ -1,3 +1,13 @@
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"""nichols.py
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Functions for plotting Black-Nichols charts.
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Routines in this module:
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nichols.nichols_plot aliased as nichols.nichols
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nichols.nichols_grid
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"""
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# nichols.py - Nichols plot
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#
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# Contributed by Allan McInnes <Allan.McInnes@canterbury.ac.nz>
@@ -45,17 +55,17 @@
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from .ctrlutil import unwrap
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from .freqplot import default_frequency_range
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48-
__all__ = ['nichols_plot', 'nichols']
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__all__ = ['nichols_plot', 'nichols', 'nichols_grid']
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# Nichols plot
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def nichols_plot(syslist, omega=None, grid=True):
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def nichols_plot(sys_list, omega=None, grid=True):
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"""Nichols plot for a system
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Plots a Nichols plot for the system over a (optional) frequency range.
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Parameters
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----------
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syslist : list of LTI, or LTI
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sys_list : list of LTI, or LTI
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List of linear input/output systems (single system is OK)
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omega : array_like
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Range of frequencies (list or bounds) in rad/sec
@@ -68,14 +78,14 @@ def nichols_plot(syslist, omega=None, grid=True):
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"""
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# If argument was a singleton, turn it into a list
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if (not getattr(syslist, '__iter__', False)):
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syslist = (syslist,)
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if not getattr(sys_list, '__iter__', False):
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sys_list = (sys_list,)
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# Select a default range if none is provided
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if omega is None:
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omega = default_frequency_range(syslist)
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omega = default_frequency_range(sys_list)
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for sys in syslist:
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for sys in sys_list:
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# Get the magnitude and phase of the system
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mag_tmp, phase_tmp, omega = sys.freqresp(omega)
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mag = np.squeeze(mag_tmp)
@@ -100,9 +110,8 @@ def nichols_plot(syslist, omega=None, grid=True):
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if grid:
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nichols_grid()
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# Nichols grid
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#! TODO: Consider making linestyle configurable
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def nichols_grid(cl_mags=None, cl_phases=None):
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def nichols_grid(cl_mags=None, cl_phases=None, line_style='dotted'):
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"""Nichols chart grid
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Plots a Nichols chart grid on the current axis, or creates a new chart
@@ -116,6 +125,8 @@ def nichols_grid(cl_mags=None, cl_phases=None):
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cl_phases : array-like (degrees), optional
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Array of closed-loop phases defining the iso-phase lines on a custom
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Nichols chart. Must be in the range -360 < cl_phases < 0
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line_style : string, optional
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.. seealso:: https://matplotlib.org/gallery/lines_bars_and_markers/linestyles.html
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Returns
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-------
@@ -137,12 +148,12 @@ def nichols_grid(cl_mags=None, cl_phases=None):
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# The key set of magnitudes are always generated, since this
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# guarantees a recognizable Nichols chart grid.
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key_cl_mags = np.array([-40.0, -20.0, -12.0, -6.0, -3.0, -1.0, -0.5, 0.0,
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0.25, 0.5, 1.0, 3.0, 6.0, 12.0])
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0.25, 0.5, 1.0, 3.0, 6.0, 12.0])
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# Extend the range of magnitudes if necessary. The extended arange
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# will end up empty if no extension is required. Assumes that closed-loop
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# magnitudes are approximately aligned with open-loop magnitudes beyond
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# the value of np.min(key_cl_mags)
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cl_mag_step = -20.0 # dB
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cl_mag_step = -20.0 # dB
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extended_cl_mags = np.arange(np.min(key_cl_mags),
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ol_mag_min + cl_mag_step, cl_mag_step)
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cl_mags = np.concatenate((extended_cl_mags, key_cl_mags))
@@ -163,12 +174,12 @@ def nichols_grid(cl_mags=None, cl_phases=None):
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# Find the M-contours
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m = m_circles(cl_mags, phase_min=np.min(cl_phases), phase_max=np.max(cl_phases))
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m_mag = 20*sp.log10(np.abs(m))
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m_phase = sp.mod(sp.degrees(sp.angle(m)), -360.0) # Unwrap
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m_phase = sp.mod(sp.degrees(sp.angle(m)), -360.0) # Unwrap
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# Find the N-contours
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n = n_circles(cl_phases, mag_min=np.min(cl_mags), mag_max=np.max(cl_mags))
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n_mag = 20*sp.log10(np.abs(n))
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n_phase = sp.mod(sp.degrees(sp.angle(n)), -360.0) # Unwrap
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n_phase = sp.mod(sp.degrees(sp.angle(n)), -360.0) # Unwrap
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# Plot the contours behind other plot elements.
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# The "phase offset" is used to produce copies of the chart that cover
@@ -182,10 +193,10 @@ def nichols_grid(cl_mags=None, cl_phases=None):
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for phase_offset in phase_offsets:
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# Draw M and N contours
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plt.plot(m_phase + phase_offset, m_mag, color='gray',
186-
linestyle='dotted', zorder=0)
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plt.plot(n_phase + phase_offset, n_mag, color='gray',
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linestyle='dotted', zorder=0)
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plt.plot(m_phase + phase_offset, m_mag, color='lightgray',
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linestyle=line_style, zorder=0)
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plt.plot(n_phase + phase_offset, n_mag, color='lightgray',
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linestyle=line_style, zorder=0)
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# Add magnitude labels
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for x, y, m in zip(m_phase[:][-1] + phase_offset, m_mag[:][-1], cl_mags):
@@ -203,7 +214,7 @@ def nichols_grid(cl_mags=None, cl_phases=None):
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# generating Nichols plots
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#
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206-
# Compute contours of a closed-loop transfer function
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def closed_loop_contours(Gcl_mags, Gcl_phases):
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"""Contours of the function Gcl = Gol/(1+Gol), where
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Gol is an open-loop transfer function, and Gcl is a corresponding
@@ -229,7 +240,7 @@ def closed_loop_contours(Gcl_mags, Gcl_phases):
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# Invert Gcl = Gol/(1+Gol) to map the contours into the open-loop space
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return Gcl/(1.0 - Gcl)
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232-
# M-circle
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def m_circles(mags, phase_min=-359.75, phase_max=-0.25):
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"""Constant-magnitude contours of the function Gcl = Gol/(1+Gol), where
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Gol is an open-loop transfer function, and Gcl is a corresponding
@@ -255,7 +266,7 @@ def m_circles(mags, phase_min=-359.75, phase_max=-0.25):
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Gcl_mags, Gcl_phases = sp.meshgrid(10.0**(mags/20.0), phases)
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return closed_loop_contours(Gcl_mags, Gcl_phases)
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# N-circle
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def n_circles(phases, mag_min=-40.0, mag_max=12.0):
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"""Constant-phase contours of the function Gcl = Gol/(1+Gol), where
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Gol is an open-loop transfer function, and Gcl is a corresponding
@@ -281,5 +292,6 @@ def n_circles(phases, mag_min=-40.0, mag_max=12.0):
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Gcl_phases, Gcl_mags = sp.meshgrid(sp.radians(phases), mags)
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return closed_loop_contours(Gcl_mags, Gcl_phases)
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# Function aliases
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nichols = nichols_plot

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