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modify discrete-time contour for nyquist plots to indent around poles #668

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Merged
merged 2 commits into from
Nov 5, 2021
Merged

modify discrete-time contour for nyquist plots to indent around poles #668

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aa92e43
initial commit that performs indents in the z-plane
sawyerbfuller Nov 5, 2021
a948186
z-to-s plane mapping results in small numerical errors so assume s-pl…
sawyerbfuller Nov 5, 2021
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52 changes: 32 additions & 20 deletions control/freqplot.py
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Original file line number Diff line number Diff line change
Expand Up @@ -714,41 +714,53 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None,
if np.any(omega_sys * sys.dt > np.pi) and warn_nyquist:
warnings.warn("evaluation above Nyquist frequency")

# Transform frequencies to continuous domain
contour = np.exp(1j * omega * sys.dt)
else:
contour = 1j * omega_sys
# do indentations in s-plane where it is more convenient
splane_contour = 1j * omega_sys

# Bend the contour around any poles on/near the imaginary axis
# TODO: smarter indent radius that depends on dcgain of system
# and timebase of discrete system.
if isinstance(sys, (StateSpace, TransferFunction)) \
and sys.isctime() and indent_direction != 'none':
poles = sys.pole()
if contour[1].imag > indent_radius \
and 0. in poles and not omega_range_given:
and indent_direction != 'none':
if sys.isctime():
splane_poles = sys.pole()
else:
# map z-plane poles to s-plane, ignoring any at the origin
# because we don't need to indent for them
zplane_poles = sys.pole()
zplane_poles = zplane_poles[~np.isclose(abs(zplane_poles), 0.)]
splane_poles = np.log(zplane_poles)/sys.dt

if splane_contour[1].imag > indent_radius \
and np.any(np.isclose(abs(splane_poles), 0)) \
and not omega_range_given:
# add some points for quarter circle around poles at origin
contour = np.concatenate(
splane_contour = np.concatenate(
(1j * np.linspace(0., indent_radius, 50),
contour[1:]))
for i, s in enumerate(contour):
splane_contour[1:]))
for i, s in enumerate(splane_contour):
# Find the nearest pole
p = poles[(np.abs(poles - s)).argmin()]

p = splane_poles[(np.abs(splane_poles - s)).argmin()]
# See if we need to indent around it
if abs(s - p) < indent_radius:
if p.real < 0 or \
(p.real == 0 and indent_direction == 'right'):
if p.real < 0 or (np.isclose(p.real, 0) \
and indent_direction == 'right'):
# Indent to the right
contour[i] += \
splane_contour[i] += \
np.sqrt(indent_radius ** 2 - (s-p).imag ** 2)
elif p.real > 0 or \
(p.real == 0 and indent_direction == 'left'):
elif p.real > 0 or (np.isclose(p.real, 0) \
and indent_direction == 'left'):
# Indent to the left
contour[i] -= \
splane_contour[i] -= \
np.sqrt(indent_radius ** 2 - (s-p).imag ** 2)
else:
ValueError("unknown value for indent_direction")

# TODO: add code to indent around discrete poles on unit circle
# change contour to z-plane if necessary
if sys.isctime():
contour = splane_contour
else:
contour = np.exp(splane_contour * sys.dt)

# Compute the primary curve
resp = sys(contour)
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