diff --git a/control/rlocus.py b/control/rlocus.py
index 3a3c1c2b6..dbab96f97 100644
--- a/control/rlocus.py
+++ b/control/rlocus.py
@@ -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)
@@ -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
@@ -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):
@@ -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)
@@ -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]
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