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fix rlocus plotting problem in Jupyter notebooks + comments, PEP8 #503

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Jan 14, 2021
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fix rlocus plotting problem in Jupyter notebooks + comments, PEP8 #503

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108 changes: 82 additions & 26 deletions control/rlocus.py
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Original file line number Diff line number Diff line change
Expand Up @@ -222,6 +222,14 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
ax.set_xlabel('Real')
ax.set_ylabel('Imaginary')

# Set up the limits for the plot
# Note: need to do this before computing grid lines
if xlim:
ax.set_xlim(xlim)
if ylim:
ax.set_ylim(ylim)

# Draw the grid
if grid and sisotool:
if isdtime(sys, strict=True):
zgrid(ax=ax)
Expand All @@ -236,14 +244,9 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
ax.axhline(0., linestyle=':', color='k', zorder=-20)
ax.axvline(0., linestyle=':', color='k', zorder=-20)
if isdtime(sys, strict=True):
ax.add_patch(plt.Circle((0,0), radius=1.0,
linestyle=':', edgecolor='k', linewidth=1.5,
fill=False, zorder=-20))

if xlim:
ax.set_xlim(xlim)
if ylim:
ax.set_ylim(ylim)
ax.add_patch(plt.Circle(
(0, 0), radius=1.0, linestyle=':', edgecolor='k',
linewidth=1.5, fill=False, zorder=-20))

return mymat, kvect

Expand Down Expand Up @@ -642,16 +645,21 @@ def _sgrid_func(fig=None, zeta=None, wn=None):
ax = fig.gca()
else:
ax = fig.axes[1]

# Get locator function for x-axis tick marks
xlocator = ax.get_xaxis().get_major_locator()

# Decide on the location for the labels (?)
ylim = ax.get_ylim()
ytext_pos_lim = ylim[1] - (ylim[1] - ylim[0]) * 0.03
xlim = ax.get_xlim()
xtext_pos_lim = xlim[0] + (xlim[1] - xlim[0]) * 0.0

# Create a list of damping ratios, if needed
if zeta is None:
zeta = _default_zetas(xlim, ylim)

# Figure out the angles for the different damping ratios
angles = []
for z in zeta:
if (z >= 1e-4) and (z <= 1):
Expand All @@ -661,11 +669,8 @@ def _sgrid_func(fig=None, zeta=None, wn=None):
y_over_x = np.tan(angles)

# zeta-constant lines

index = 0

for yp in y_over_x:
ax.plot([0, xlocator()[0]], [0, yp*xlocator()[0]], color='gray',
for index, yp in enumerate(y_over_x):
ax.plot([0, xlocator()[0]], [0, yp * xlocator()[0]], color='gray',
linestyle='dashed', linewidth=0.5)
ax.plot([0, xlocator()[0]], [0, -yp * xlocator()[0]], color='gray',
linestyle='dashed', linewidth=0.5)
Expand All @@ -679,45 +684,96 @@ def _sgrid_func(fig=None, zeta=None, wn=None):
ytext_pos = ytext_pos_lim
ax.annotate(an, textcoords='data', xy=[xtext_pos, ytext_pos],
fontsize=8)
index += 1
ax.plot([0, 0], [ylim[0], ylim[1]],
color='gray', linestyle='dashed', linewidth=0.5)

angles = np.linspace(-90, 90, 20)*np.pi/180
# omega-constant lines
angles = np.linspace(-90, 90, 20) * np.pi/180
if wn is None:
wn = _default_wn(xlocator(), ylim)

for om in wn:
if om < 0:
yp = np.sin(angles)*np.abs(om)
xp = -np.cos(angles)*np.abs(om)
ax.plot(xp, yp, color='gray',
linestyle='dashed', linewidth=0.5)
an = "%.2f" % -om
ax.annotate(an, textcoords='data', xy=[om, 0], fontsize=8)
# Generate the lines for natural frequency curves
yp = np.sin(angles) * np.abs(om)
xp = -np.cos(angles) * np.abs(om)

# Plot the natural frequency contours
ax.plot(xp, yp, color='gray', linestyle='dashed', linewidth=0.5)

# Annotate the natural frequencies by listing on x-axis
# Note: need to filter values for proper plotting in Jupyter
if (om > xlim[0]):
an = "%.2f" % -om
ax.annotate(an, textcoords='data', xy=[om, 0], fontsize=8)


def _default_zetas(xlim, ylim):
"""Return default list of damping coefficients"""
sep1 = -xlim[0]/4
"""Return default list of damping coefficients

This function computes a list of damping coefficients based on the limits
of the graph. A set of 4 damping coefficients are computed for the x-axis
and a set of three damping coefficients are computed for the y-axis
(corresponding to the normal 4:3 plot aspect ratio in `matplotlib`?).

Parameters
----------
xlim : array_like
List of x-axis limits [min, max]
ylim : array_like
List of y-axis limits [min, max]

Returns
-------
zeta : list
List of default damping coefficients for the plot

"""
# Damping coefficient lines that intersect the x-axis
sep1 = -xlim[0] / 4
ang1 = [np.arctan((sep1*i)/ylim[1]) for i in np.arange(1, 4, 1)]

# Damping coefficient lines that intersection the y-axis
sep2 = ylim[1] / 3
ang2 = [np.arctan(-xlim[0]/(ylim[1]-sep2*i)) for i in np.arange(1, 3, 1)]

# Put the lines together and add one at -pi/2 (negative real axis)
angles = np.concatenate((ang1, ang2))
angles = np.insert(angles, len(angles), np.pi/2)

# Return the damping coefficients corresponding to these angles
zeta = np.sin(angles)
return zeta.tolist()


def _default_wn(xloc, ylim):
"""Return default wn for root locus plot"""
"""Return default wn for root locus plot

This function computes a list of natural frequencies based on the grid
parameters of the graph.

Parameters
----------
xloc : array_like
List of x-axis tick values
ylim : array_like
List of y-axis limits [min, max]

Returns
-------
wn : list
List of default natural frequencies for the plot

"""

wn = xloc # one frequency per x-axis tick mark
sep = xloc[1]-xloc[0] # separation between ticks

wn = xloc
sep = xloc[1]-xloc[0]
# Insert additional frequencies to span the y-axis
while np.abs(wn[0]) < ylim[1]:
wn = np.insert(wn, 0, wn[0]-sep)

# If there are too many values, cut them in half
while len(wn) > 7:
wn = wn[0:-1:2]

Expand Down