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root_locus_sketch.py
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root_locus_sketch.py
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from matplotlib.transforms import BlendedGenericTransform
from matplotlib import patches
from matplotlib.patches import Circle, Arc
import matplotlib.pyplot as plt
plt.rcParams['mathtext.fontset'] = 'cm'
import numpy as np
dtr = np.pi/180
import control
mygray = '#808B96'
grid_dict = {'linestyle':'dashed',\
'color':mygray, \
'linewidth':1.0, \
'zorder':0, \
}
class root_locus_sketch(object):
def __init__(self, ax=None, \
xmax=2, xmin=-5.5, ymax=5.5, ymin=-5.5, \
xlims=[-8,4], ylims=[-6,6], \
fontdict = {'size': 20, 'family':'serif'}, \
axis_lw=2, \
):
if ax is None:
fig = plt.figure(figsize=(9,9))
ax = fig.add_subplot(111)
self.ax = ax
self.xmin = xmin
self.xmax = xmax
self.ymin = ymin
self.ymax = ymax
self.xlims = xlims
self.ylims = ylims
self.axis_lw = axis_lw
self.fontdict = fontdict
def draw_arrow(self, start_coords, end_coords, \
fc='k', ec=None, lw=None, **plot_args):
if not hasattr(self, 'hw'):
self.set_arrow_lengths()
if ec is None:
ec = fc
# if lw is None:
# lw = self.arrow_lw
##start_A = transform_coords(start_coords, HT)
##stop_A = transform_coords(end_coords, HT)
dx = end_coords[0]-start_coords[0]
dy = end_coords[1]-start_coords[1]
self.ax.arrow(start_coords[0], start_coords[1], dx, dy, \
lw=lw, fc=fc, ec=ec, \
width=0.01, \
head_width=self.hw, head_length=self.hl, \
#overhang = self.ohg, \
length_includes_head=True, clip_on = False, \
**plot_args)
def draw_axis(self):
self.draw_arrow((0,0), (self.xmax,0), \
lw=self.axis_lw)
#fc=self.axis_color,
#self.place_rotated_text(self.xmax+self.axis_label_shift, 0, xlabel, HT)
self.draw_arrow((0,0), (0,self.ymax), \
lw=self.axis_lw)
self.draw_arrow((0,0), (0,self.ymin), \
lw=self.axis_lw)
#fc=self.axis_color,
#self.place_rotated_text(0, self.ymax+self.axis_label_shift, ylabel, HT)
self.draw_arrow((0,0), (self.xmin,0), \
lw=self.axis_lw)
def set_arrow_lengths(self):
self.hw = 1./30.*(self.ymax-self.ymin)
self.hl = 1./20.*(self.xmax-self.xmin)
self.lw = 2. # axis line width
self.ohg = 0.3 # arrow overhang
def axis_off(self):
self.ax.set_axis_off()
def draw_marker(self, point, style='go', size=12, **plot_kwargs):
self.ax.plot([np.real(point)],[np.imag(point)], \
style, markersize=size, **plot_kwargs)
def draw_markers(self, point_list, style='go', size=12, **plot_kwargs):
for point in point_list:
self.draw_marker(point, style=style, size=size, **plot_kwargs)
def add_text(self, point, text, xoffset=0, yoffset=0, \
fontdict=None):
if fontdict is None:
fontdict = self.fontdict
self.ax.text(np.real(point)+xoffset, np.imag(point)+yoffset, \
text, fontdict=fontdict)
def add_math_text(self, point, text, *args, **kwargs):
if text[0] != '$':
text = '$%s$' % text
self.add_text(point, text, *args, **kwargs)
def draw_point_with_label(self, point, text, style='go', size=12, \
xoffset=0, yoffset=0, \
fontdict=None):
self.draw_marker(point, style=style, size=size)
self.add_text(point, text, xoffset=xoffset, yoffset=yoffset, \
fontdict=fontdict)
def draw_line(self, start, end, linestyle='k--', **plot_kwargs):
self.ax.plot([np.real(start), np.real(end)], \
[np.imag(start), np.imag(end)], \
linestyle, **plot_kwargs)
def draw_lines_to_point(self, point, pole_or_zero_list, \
linestyle='k--', **plot_kwargs):
for pz in pole_or_zero_list:
self.draw_line(pz, point, linestyle=linestyle, **plot_kwargs)
def draw_poles(self, pole_list, style='rX', size=12, **plot_kwargs):
for i, p in enumerate(pole_list):
j = i+1
self.ax.plot([np.real(p)],[np.imag(p)], \
style, markersize=size, **plot_kwargs)
def draw_zeros(self, zero_list, style='ro', size=12, **plot_kwargs):
self.draw_markers(zero_list, style=style, size=size, **plot_kwargs)
def plot_branches(self, rmat, **plot_kwargs):
self.ax.plot(np.real(rmat), np.imag(rmat), **plot_kwargs)
def label_axes(self, real_point=None, imag_point=None, fontdict=None):
if real_point is None:
real_point = self.xmax-0.7j
if imag_point is None:
imag_point = 0.3+self.ymax*1j
self.add_text(real_point, 'Re', fontdict=fontdict)
self.add_text(imag_point, 'Im', fontdict=fontdict)
def label_points(self, points, labels, offsets=None, fontdict=None):
N = len(points)
if offsets is None:
offsets = [(0,0)]*N
elif len(offsets) == 1:
offsets = N*offsets
for p, label, offset in zip(points, labels, offsets):
self.add_text(p, label, xoffset=offset[0], yoffset=offset[1], \
fontdict=fontdict)
def draw_vertical_gridlines(self, xlist=None, \
ymin=None, ymax=None, plot_kwargs=None):
if plot_kwargs is None:
plot_kwargs = grid_dict
if ymax is None:
ymax = self.ymax
if ymin is None:
ymin = self.ymin
if xlist is None:
xlist = np.arange(0,self.xmax,1)
for x in xlist:
self.ax.plot([x,x], [ymin,ymax], **plot_kwargs)
def draw_horizontal_gridlines(self, ylist=None, \
xmin=None, xmax=None, plot_kwargs=None):
if plot_kwargs is None:
plot_kwargs = grid_dict
if xmax is None:
xmax = self.xmax
if xmin is None:
xmin = self.xmin
if ylist is None:
ylist = np.arange(self.ymin,self.ymax,1)
for y in ylist:
self.ax.plot([int(xmin),int(xmax)], [y,y], **plot_kwargs)
def draw_xticks(self, ticks=None, dy=0.1, **plot_kwargs):
kwargs = {'color':'k',\
'linewidth':2}
kwargs.update(plot_kwargs)
if ticks is None:
ticks = np.arange(int(self.xmin), int(self.xmax), 1)
for tick in ticks:
start_tick = [tick, dy]
end_tick = [tick, -dy]
self.ax.plot([tick,tick], [dy,-dy], **kwargs)
def draw_yticks(self, ticks=None, dx=0.1, **plot_kwargs):
kwargs = {'color':'k',\
'linewidth':2}
kwargs.update(plot_kwargs)
if ticks is None:
ticks = np.arange(int(self.ymin), int(self.ymax)+1, 1)
for tick in ticks:
self.ax.plot([-dx,dx], [tick,tick], **kwargs)
def main_axis(self, ticks=True):
self.set_arrow_lengths()
self.axis_off()
self.draw_axis()
if ticks:
self.draw_xticks()
self.draw_yticks()
self.label_axes()
self.ax.set_xlim(self.xlims)
self.ax.set_ylim(self.ylims)
plt.tight_layout()
class root_locus_sketch_with_TF(root_locus_sketch):
def __init__(self, G, ax=None, *args, **kwargs):
root_locus_sketch.__init__(self, ax, *args, **kwargs)
self.G = G
def main(self, kvect=None, markerstyle='bX', linecolor='b',
plot_branches=True, ticks=True):
root_locus_sketch.main_axis(self, ticks=ticks)
self.draw_poles(style=markerstyle)
if plot_branches:
self.plot_branches(kvect=kvect,color=linecolor)
self.draw_zeros()
def draw_poles(self, style='rX', size=12, **plot_kwargs):
root_locus_sketch.draw_poles(self, self.G.pole(), style=style, size=size, **plot_kwargs)
def draw_zeros(self, style='ro', size=12, **plot_kwargs):
zlist = self.G.zero()
if len(zlist) > 0:
root_locus_sketch.draw_zeros(self, zlist, style=style, size=size, **plot_kwargs)
def plot_branches(self, kvect=None, **plot_kwargs):
rmat, kout = control.root_locus(self.G, kvect=kvect, Plot=False)
self.ax.plot(np.real(rmat), np.imag(rmat), **plot_kwargs)
def label_axes(self, real_point=None, imag_point=None, fontdict=None):
if real_point is None:
real_point = self.xmax-0.7j
if imag_point is None:
imag_point = 0.3+self.ymax*1j
self.add_text(real_point, 'Re', fontdict=fontdict)
self.add_text(imag_point, 'Im', fontdict=fontdict)
def label_points(self, points, labels, offsets=None, fontdict=None):
N = len(points)
if offsets is None:
offsets = [(0,0)]*N
elif len(offsets) == 1:
offsets = N*offsets
for p, label, offset in zip(points, labels, offsets):
self.add_text(p, label, xoffset=offset[0], yoffset=offset[1], \
fontdict=fontdict)
def draw_vertical_gridlines(self, xlist=None, \
ymin=None, ymax=None, plot_kwargs=None):
if plot_kwargs is None:
plot_kwargs = grid_dict
if ymax is None:
ymax = self.ymax
if ymin is None:
ymin = self.ymin
if xlist is None:
xlist = np.arange(0,self.xmax,1)
for x in xlist:
self.ax.plot([x,x], [ymin,ymax], **plot_kwargs)
def draw_horizontal_gridlines(self, ylist=None, \
xmin=None, xmax=None, plot_kwargs=None):
if plot_kwargs is None:
plot_kwargs = grid_dict
if xmax is None:
xmax = self.xmax
if xmin is None:
xmin = self.xmin
if ylist is None:
ylist = np.arange(self.ymin,self.ymax,1)
for y in ylist:
self.ax.plot([int(xmin),int(xmax)], [y,y], **plot_kwargs)
def draw_xticks(self, ticks=None, dy=0.1, **plot_kwargs):
kwargs = {'color':'k',\
'linewidth':2}
kwargs.update(plot_kwargs)
if ticks is None:
ticks = np.arange(int(self.xmin), int(self.xmax), 1)
for tick in ticks:
start_tick = [tick, dy]
end_tick = [tick, -dy]
self.ax.plot([tick,tick], [dy,-dy], **kwargs)
def draw_yticks(self, ticks=None, dx=0.1, **plot_kwargs):
kwargs = {'color':'k',\
'linewidth':2}
kwargs.update(plot_kwargs)
if ticks is None:
ticks = np.arange(int(self.ymin), int(self.ymax), 1)
for tick in ticks:
self.ax.plot([-dx,dx], [tick,tick], **kwargs)
class root_locus_sketch_with_TF_2(root_locus_sketch):
def __init__(self, ax, G, *args, **kwargs):
root_locus_sketch.__init__(self, ax, *args, **kwargs)
self.G = G
def draw_poles(self, style='rX', size=12, zorder=10, **kwargs):
root_locus_sketch.draw_poles(self, self.G.pole(), style=style, \
size=size, zorder=zorder, **kwargs)
def draw_zeros(self, style='ro', size=12, zorder=10, **kwargs):
root_locus_sketch.draw_poles(self, self.G.zero(), style=style, \
size=size, zorder=zorder, \
**kwargs)
def add_test_point(self, point, style='go', size=12, \
label=None, label_offset=0+0j, \
**plot_kwargs):
self.s0 = point
self.draw_marker(point, style=style, size=size, **plot_kwargs)
if label is not None:
self.add_math_text(self.s0+label_offset, label)
def draw_lines_to_test_point(self, linestyle='k--', **plot_kwargs):
self.draw_lines_to_point(self.s0, self.G.pole(), \
linestyle=linestyle, **plot_kwargs)
self.draw_lines_to_point(self.s0, self.G.zero(), \
linestyle=linestyle, **plot_kwargs)
def build_label_list(self, N, pat):
labels = []
for i in range(N):
j = i+1
cur_str = pat % j
labels.append(cur_str)
return labels
def make_phi_labels(self):
N = len(self.G.pole())
phi_labels = self.build_label_list(N, '\\phi_{%i}')
return phi_labels
def make_psi_labels(self):
N = len(self.G.zero())
psi_labels = self.build_label_list(N, '\\psi_{%i}')
return psi_labels
def label_angles_to_point(self, phi_labels, psi_labels, \
phi_offsets=None, psi_offsets=None, \
**kwargs):
if phi_offsets is None:
np = len(self.G.pole())
phi_offsets = [0]*np
if psi_offsets is None:
nz = len(self.G.zero())
psi_offsets = [0]*nz
for p, label, po in zip(self.G.pole(), phi_labels, phi_offsets):
self.add_math_text(p+po, label, **kwargs)
for z, label, zo in zip(self.G.zero(), psi_labels, psi_offsets):
self.add_math_text(z+zo, label, **kwargs)
class root_locus_sketch_two_pole_locations(root_locus_sketch):
"""A class for generating pole locations plots for comparing two
TFs and their step responses."""
def __init__(self, G1, G2, label_offsets=[0.2+0.2j, 0.2+0.2j], \
markers=['bo','g^'], inds=[1,2], \
**kwargs):
root_locus_sketch.__init__(self, **kwargs)
self.G1 = G1
self.G2 = G2
self.label_offsets = label_offsets
self.markers = markers
self.inds = inds
def draw_and_label_poles(self):
# get poles and force the imaginary part to be positive
p1 = self.G1.pole()[0]
p2 = self.G2.pole()[0]
for p, m, lo, ind in zip([p1,p2], self.markers, \
self.label_offsets, self.inds):
p = np.real(p) + 1j*np.abs(np.imag(p))
self.draw_marker(p, style=m)
self.draw_marker(np.conj(p), style=m)
mytext = '$G_{%i}$' % ind
self.add_text(p, mytext, xoffset=np.real(lo), yoffset=np.imag(lo))
def main(self, ticks=True):
self.main_axis(ticks=ticks)
self.draw_and_label_poles()