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

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Merged
sawyerbfuller 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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z-to-s plane mapping results in small numerical errors so assume s-pl… 
…ane poles near imaginary axis are on imaginary axis
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@sawyerbfuller
sawyerbfuller committed Nov 5, 2021
commit a948186777ef0a80581a9aceea91b22e911e5b1d
20 changes: 13 additions & 7 deletions control/freqplot.py
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Original file line number Diff line number Diff line change
Expand Up @@ -718,16 +718,22 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None,
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 indent_direction != 'none':
if sys.isctime():
splane_poles = sys.pole()
else:
# map z-plane poles to s-plane
splane_poles = np.log(sys.pole())/sys.dt
# 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 0. in splane_poles and not omega_range_given:
and np.any(np.isclose(abs(splane_poles), 0)) \
and not omega_range_given:
# add some points for quarter circle around poles at origin
splane_contour = np.concatenate(
(1j * np.linspace(0., indent_radius, 50),
Expand All @@ -737,13 +743,13 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None,
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
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
splane_contour[i] -= \
np.sqrt(indent_radius ** 2 - (s-p).imag ** 2)
Expand Down