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662 lines (547 loc) · 22.9 KB
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"""freqresp_test.py - test frequency response functions
RMM, 30 May 2016 (based on timeresp_test.py)
This is a rudimentary set of tests for frequency response functions,
including bode plots.
"""
import matplotlib.pyplot as plt
import numpy as np
from numpy.testing import assert_allclose
import math
import pytest
import control as ctrl
from control.statesp import StateSpace
from control.xferfcn import TransferFunction
from control.matlab import ss, tf, bode, rss
from control.freqplot import bode_plot, nyquist_plot, singular_values_plot
from control.tests.conftest import slycotonly
pytestmark = pytest.mark.usefixtures("mplcleanup")
@pytest.fixture
def ss_siso():
A = np.array([[1, 1], [0, 1]])
B = np.array([[0], [1]])
C = np.array([[1, 0]])
D = 0
return StateSpace(A, B, C, D)
@pytest.fixture
def ss_mimo():
A = np.array([[1, 1], [0, 1]])
B = np.array([[1, 0], [0, 1]])
C = np.array([[1, 0]])
D = np.array([[0, 0]])
return StateSpace(A, B, C, D)
def test_freqresp_siso(ss_siso):
"""Test SISO frequency response"""
omega = np.linspace(10e-2, 10e2, 1000)
# test frequency response
ctrl.freqresp(ss_siso, omega)
@slycotonly
def test_freqresp_mimo(ss_mimo):
"""Test MIMO frequency response calls"""
omega = np.linspace(10e-2, 10e2, 1000)
ctrl.freqresp(ss_mimo, omega)
tf_mimo = tf(ss_mimo)
ctrl.freqresp(tf_mimo, omega)
def test_bode_basic(ss_siso):
"""Test bode plot call (Very basic)"""
# TODO: proper test
tf_siso = tf(ss_siso)
bode(ss_siso)
bode(tf_siso)
assert len(bode_plot(tf_siso, plot=False, omega_num=20)[0] == 20)
omega = bode_plot(tf_siso, plot=False, omega_limits=(1, 100))[2]
assert_allclose(omega[0], 1)
assert_allclose(omega[-1], 100)
assert len(bode_plot(tf_siso, plot=False, omega=np.logspace(-1,1,10))[0])\
== 10
def test_nyquist_basic(ss_siso):
"""Test nyquist plot call (Very basic)"""
# TODO: proper test
tf_siso = tf(ss_siso)
nyquist_plot(ss_siso)
nyquist_plot(tf_siso)
count, contour = nyquist_plot(
tf_siso, plot=False, return_contour=True, omega_num=20)
assert len(contour) == 20
with pytest.warns(UserWarning, match="encirclements was a non-integer"):
count, contour = nyquist_plot(
tf_siso, plot=False, omega_limits=(1, 100), return_contour=True)
assert_allclose(contour[0], 1j)
assert_allclose(contour[-1], 100j)
count, contour = nyquist_plot(
tf_siso, plot=False, omega=np.logspace(-1, 1, 10), return_contour=True)
assert len(contour) == 10
@pytest.mark.filterwarnings("ignore:.*non-positive left xlim:UserWarning")
def test_superimpose():
"""Test superimpose multiple calls.
Test to make sure that multiple calls to plots superimpose their
data on the same axes unless told to do otherwise
"""
# Generate two plots in a row; should be on the same axes
plt.figure(1)
plt.clf()
ctrl.bode_plot(ctrl.tf([1], [1, 2, 1]))
ctrl.bode_plot(ctrl.tf([5], [1, 1]))
# Check that there are two axes and that each axes has two lines
len(plt.gcf().axes) == 2
for ax in plt.gcf().axes:
# Make sure there are 2 lines in each subplot
assert len(ax.get_lines()) == 2
# Generate two plots as a list; should be on the same axes
plt.figure(2)
plt.clf()
ctrl.bode_plot([ctrl.tf([1], [1, 2, 1]), ctrl.tf([5], [1, 1])])
# Check that there are two axes and that each axes has two lines
assert len(plt.gcf().axes) == 2
for ax in plt.gcf().axes:
# Make sure there are 2 lines in each subplot
assert len(ax.get_lines()) == 2
# Generate two separate plots; only the second should appear
plt.figure(3)
plt.clf()
ctrl.bode_plot(ctrl.tf([1], [1, 2, 1]))
plt.clf()
ctrl.bode_plot(ctrl.tf([5], [1, 1]))
# Check to make sure there are two axes and that each axes has one line
assert len(plt.gcf().axes) == 2
for ax in plt.gcf().axes:
# Make sure there is only 1 line in the subplot
assert len(ax.get_lines()) == 1
# Now add a line to the magnitude plot and make sure if is there
for ax in plt.gcf().axes:
if ax.get_label() == 'control-bode-magnitude':
break
ax.semilogx([1e-2, 1e1], 20 * np.log10([1, 1]), 'k-')
assert len(ax.get_lines()) == 2
def test_doubleint():
"""Test typcast bug with double int
30 May 2016, RMM: added to replicate typecast bug in frequency_response.py
"""
A = np.array([[0, 1], [0, 0]])
B = np.array([[0], [1]])
C = np.array([[1, 0]])
D = 0
sys = ss(A, B, C, D)
bode(sys)
@pytest.mark.parametrize(
"Hz, Wcp, Wcg",
[pytest.param(False, 6.0782869, 10., id="omega"),
pytest.param(True, 0.9673894, 1.591549, id="Hz")])
@pytest.mark.parametrize(
"deg, p0, pm",
[pytest.param(False, -np.pi, -2.748266, id="rad"),
pytest.param(True, -180, -157.46405841, id="deg")])
@pytest.mark.parametrize(
"dB, maginfty1, maginfty2, gminv",
[pytest.param(False, 1, 1e-8, 0.4, id="mag"),
pytest.param(True, 0, -1e+5, -7.9588, id="dB")])
def test_bode_margin(dB, maginfty1, maginfty2, gminv,
deg, p0, pm,
Hz, Wcp, Wcg):
"""Test bode margins"""
num = [1000]
den = [1, 25, 100, 0]
sys = ctrl.tf(num, den)
plt.figure()
ctrl.bode_plot(sys, margins=True, dB=dB, deg=deg, Hz=Hz)
fig = plt.gcf()
allaxes = fig.get_axes()
mag_to_infinity = (np.array([Wcp, Wcp]),
np.array([maginfty1, maginfty2]))
assert_allclose(mag_to_infinity,
allaxes[0].lines[2].get_data(),
rtol=1e-5)
gm_to_infinty = (np.array([Wcg, Wcg]),
np.array([gminv, maginfty2]))
assert_allclose(gm_to_infinty,
allaxes[0].lines[3].get_data(),
rtol=1e-5)
one_to_gm = (np.array([Wcg, Wcg]),
np.array([maginfty1, gminv]))
assert_allclose(one_to_gm, allaxes[0].lines[4].get_data(),
rtol=1e-5)
pm_to_infinity = (np.array([Wcp, Wcp]),
np.array([1e5, pm]))
assert_allclose(pm_to_infinity,
allaxes[1].lines[2].get_data(),
rtol=1e-5)
pm_to_phase = (np.array([Wcp, Wcp]),
np.array([pm, p0]))
assert_allclose(pm_to_phase, allaxes[1].lines[3].get_data(),
rtol=1e-5)
phase_to_infinity = (np.array([Wcg, Wcg]),
np.array([0, p0]))
assert_allclose(phase_to_infinity, allaxes[1].lines[4].get_data(),
rtol=1e-5)
@pytest.fixture
def dsystem_dt(request):
"""Test systems for test_discrete"""
# SISO state space systems with either fixed or unspecified sampling times
sys = rss(3, 1, 1)
# MIMO state space systems with either fixed or unspecified sampling times
A = [[-3., 4., 2.], [-1., -3., 0.], [2., 5., 3.]]
B = [[1., 4.], [-3., -3.], [-2., 1.]]
C = [[4., 2., -3.], [1., 4., 3.]]
D = [[-2., 4.], [0., 1.]]
dt = request.param
systems = {'sssiso': StateSpace(sys.A, sys.B, sys.C, sys.D, dt),
'ssmimo': StateSpace(A, B, C, D, dt),
'tf': TransferFunction([2, 1], [2, 1, 1], dt)}
return systems
@pytest.fixture
def dsystem_type(request, dsystem_dt):
"""Return system by typekey"""
systype = request.param
return dsystem_dt[systype]
@pytest.mark.parametrize("dsystem_dt", [0.1, True], indirect=True)
@pytest.mark.parametrize("dsystem_type", ['sssiso', 'ssmimo', 'tf'],
indirect=True)
def test_discrete(dsystem_type):
"""Test discrete time frequency response"""
dsys = dsystem_type
# Set frequency range to just below Nyquist freq (for Bode)
omega_ok = np.linspace(10e-4, 0.99, 100) * np.pi / dsys.dt
# Test frequency response
dsys.frequency_response(omega_ok)
# Check for warning if frequency is out of range
with pytest.warns(UserWarning, match="above.*Nyquist"):
# Look for a warning about sampling above Nyquist frequency
omega_bad = np.linspace(10e-4, 1.1, 10) * np.pi / dsys.dt
dsys.frequency_response(omega_bad)
# Test bode plots (currently only implemented for SISO)
if (dsys.ninputs == 1 and dsys.noutputs == 1):
# Generic call (frequency range calculated automatically)
bode(dsys)
# Convert to transfer function and test bode again
systf = tf(dsys)
bode(systf)
# Make sure we can pass a frequency range
bode(dsys, omega_ok)
else:
# Calling bode should generate a not implemented error
with pytest.raises(NotImplementedError):
bode((dsys,))
def test_options(editsdefaults):
"""Test ability to set parameter values"""
# Generate a Bode plot of a transfer function
sys = ctrl.tf([1000], [1, 25, 100, 0])
fig1 = plt.figure()
ctrl.bode_plot(sys, dB=False, deg=True, Hz=False)
# Save the parameter values
left1, right1 = fig1.axes[0].xaxis.get_data_interval()
numpoints1 = len(fig1.axes[0].lines[0].get_data()[0])
# Same transfer function, but add a decade on each end
ctrl.config.set_defaults('freqplot', feature_periphery_decades=2)
fig2 = plt.figure()
ctrl.bode_plot(sys, dB=False, deg=True, Hz=False)
left2, right2 = fig2.axes[0].xaxis.get_data_interval()
# Make sure we got an extra decade on each end
assert_allclose(left2, 0.1 * left1)
assert_allclose(right2, 10 * right1)
# Same transfer function, but add more points to the plot
ctrl.config.set_defaults(
'freqplot', feature_periphery_decades=2, number_of_samples=13)
fig3 = plt.figure()
ctrl.bode_plot(sys, dB=False, deg=True, Hz=False)
numpoints3 = len(fig3.axes[0].lines[0].get_data()[0])
# Make sure we got the right number of points
assert numpoints1 != numpoints3
assert numpoints3 == 13
@pytest.mark.parametrize(
"TF, initial_phase, default_phase, expected_phase",
[pytest.param(ctrl.tf([1], [1, 0]),
None, -math.pi/2, -math.pi/2, id="order1, default"),
pytest.param(ctrl.tf([1], [1, 0]),
180, -math.pi/2, 3*math.pi/2, id="order1, 180"),
pytest.param(ctrl.tf([1], [1, 0, 0]),
None, -math.pi, -math.pi, id="order2, default"),
pytest.param(ctrl.tf([1], [1, 0, 0]),
180, -math.pi, math.pi, id="order2, 180"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0]),
None, -3*math.pi/2, -3*math.pi/2, id="order2, default"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0]),
180, -3*math.pi/2, math.pi/2, id="order2, 180"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0, 0]),
None, 0, 0, id="order4, default"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0, 0]),
180, 0, 0, id="order4, 180"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0, 0]),
-360, 0, -2*math.pi, id="order4, -360"),
])
def test_initial_phase(TF, initial_phase, default_phase, expected_phase):
# Check initial phase of standard transfer functions
mag, phase, omega = ctrl.bode(TF)
assert(abs(phase[0] - default_phase) < 0.1)
# Now reset the initial phase to +180 and see if things work
mag, phase, omega = ctrl.bode(TF, initial_phase=initial_phase)
assert(abs(phase[0] - expected_phase) < 0.1)
# Make sure everything works in rad/sec as well
if initial_phase:
plt.xscale('linear') # avoids xlim warning on next line
plt.clf() # clear previous figure (speeds things up)
mag, phase, omega = ctrl.bode(
TF, initial_phase=initial_phase/180. * math.pi, deg=False)
assert(abs(phase[0] - expected_phase) < 0.1)
@pytest.mark.parametrize(
"TF, wrap_phase, min_phase, max_phase",
[pytest.param(ctrl.tf([1], [1, 0]),
None, -math.pi/2, 0, id="order1, default"),
pytest.param(ctrl.tf([1], [1, 0]),
True, -math.pi, math.pi, id="order1, True"),
pytest.param(ctrl.tf([1], [1, 0]),
-270, -3*math.pi/2, math.pi/2, id="order1, -270"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0]),
None, -3*math.pi/2, 0, id="order3, default"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0]),
True, -math.pi, math.pi, id="order3, True"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0]),
-270, -3*math.pi/2, math.pi/2, id="order3, -270"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0, 0, 0]),
True, -3*math.pi/2, 0, id="order5, default"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0, 0, 0]),
True, -math.pi, math.pi, id="order5, True"),
pytest.param(ctrl.tf([1], [1, 0, 0, 0, 0, 0]),
-270, -3*math.pi/2, math.pi/2, id="order5, -270"),
])
def test_phase_wrap(TF, wrap_phase, min_phase, max_phase):
mag, phase, omega = ctrl.bode(TF, wrap_phase=wrap_phase)
assert(min(phase) >= min_phase)
assert(max(phase) <= max_phase)
def test_phase_wrap_multiple_systems():
sys_unstable = ctrl.zpk([],[1,1], gain=1)
mag, phase, omega = ctrl.bode(sys_unstable, plot=False)
assert(np.min(phase) >= -2*np.pi)
assert(np.max(phase) <= -1*np.pi)
mag, phase, omega = ctrl.bode((sys_unstable, sys_unstable), plot=False)
assert(np.min(phase) >= -2*np.pi)
assert(np.max(phase) <= -1*np.pi)
def test_freqresp_warn_infinite():
"""Test evaluation warnings for transfer functions w/ pole at the origin"""
sys_finite = ctrl.tf([1], [1, 0.01])
sys_infinite = ctrl.tf([1], [1, 0.01, 0])
# Transfer function with finite zero frequency gain
np.testing.assert_almost_equal(sys_finite(0), 100)
np.testing.assert_almost_equal(sys_finite(0, warn_infinite=False), 100)
np.testing.assert_almost_equal(sys_finite(0, warn_infinite=True), 100)
# Transfer function with infinite zero frequency gain
with pytest.warns(RuntimeWarning, match="divide by zero"):
np.testing.assert_almost_equal(
sys_infinite(0), complex(np.inf, np.nan))
with pytest.warns(RuntimeWarning, match="divide by zero"):
np.testing.assert_almost_equal(
sys_infinite(0, warn_infinite=True), complex(np.inf, np.nan))
np.testing.assert_almost_equal(
sys_infinite(0, warn_infinite=False), complex(np.inf, np.nan))
# Switch to state space
sys_finite = ctrl.tf2ss(sys_finite)
sys_infinite = ctrl.tf2ss(sys_infinite)
# State space system with finite zero frequency gain
np.testing.assert_almost_equal(sys_finite(0), 100)
np.testing.assert_almost_equal(sys_finite(0, warn_infinite=False), 100)
np.testing.assert_almost_equal(sys_finite(0, warn_infinite=True), 100)
# State space system with infinite zero frequency gain
with pytest.warns(RuntimeWarning, match="singular matrix"):
np.testing.assert_almost_equal(
sys_infinite(0), complex(np.inf, np.nan))
with pytest.warns(RuntimeWarning, match="singular matrix"):
np.testing.assert_almost_equal(
sys_infinite(0, warn_infinite=True), complex(np.inf, np.nan))
np.testing.assert_almost_equal(sys_infinite(
0, warn_infinite=False), complex(np.inf, np.nan))
def test_dcgain_consistency():
"""Test to make sure that DC gain is consistently evaluated"""
# Set up transfer function with pole at the origin
sys_tf = ctrl.tf([1], [1, 0])
assert 0 in sys_tf.poles()
# Set up state space system with pole at the origin
sys_ss = ctrl.tf2ss(sys_tf)
assert 0 in sys_ss.poles()
# Finite (real) numerator over 0 denominator => inf + nanj
np.testing.assert_equal(
sys_tf(0, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_ss(0, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_tf(0j, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_ss(0j, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_tf.dcgain(), np.inf)
np.testing.assert_equal(
sys_ss.dcgain(), np.inf)
# Set up transfer function with pole, zero at the origin
sys_tf = ctrl.tf([1, 0], [1, 0])
assert 0 in sys_tf.poles()
assert 0 in sys_tf.zeros()
# Pole and zero at the origin should give nan + nanj for the response
np.testing.assert_equal(
sys_tf(0, warn_infinite=False), complex(np.nan, np.nan))
np.testing.assert_equal(
sys_tf(0j, warn_infinite=False), complex(np.nan, np.nan))
np.testing.assert_equal(
sys_tf.dcgain(), np.nan)
# Set up state space version
sys_ss = ctrl.tf2ss(ctrl.tf([1, 0], [1, 1])) * \
ctrl.tf2ss(ctrl.tf([1], [1, 0]))
# Different systems give different representations => test accordingly
if 0 in sys_ss.poles() and 0 in sys_ss.zeros():
# Pole and zero at the origin => should get (nan + nanj)
np.testing.assert_equal(
sys_ss(0, warn_infinite=False), complex(np.nan, np.nan))
np.testing.assert_equal(
sys_ss(0j, warn_infinite=False), complex(np.nan, np.nan))
np.testing.assert_equal(
sys_ss.dcgain(), np.nan)
elif 0 in sys_ss.poles():
# Pole at the origin, but zero elsewhere => should get (inf + nanj)
np.testing.assert_equal(
sys_ss(0, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_ss(0j, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_ss.dcgain(), np.inf)
else:
# Near pole/zero cancellation => nothing sensible to check
pass
# Pole with non-zero, complex numerator => inf + infj
s = ctrl.tf('s')
sys_tf = (s + 1) / (s**2 + 1)
assert 1j in sys_tf.poles()
# Set up state space system with pole on imaginary axis
sys_ss = ctrl.tf2ss(sys_tf)
assert 1j in sys_tf.poles()
# Make sure we get correct response if evaluated at the pole
np.testing.assert_equal(
sys_tf(1j, warn_infinite=False), complex(np.inf, np.inf))
# For state space, numerical errors come into play
resp_ss = sys_ss(1j, warn_infinite=False)
if np.isfinite(resp_ss):
assert abs(resp_ss) > 1e15
else:
if resp_ss != complex(np.inf, np.inf):
pytest.xfail("statesp evaluation at poles not fully implemented")
else:
np.testing.assert_equal(resp_ss, complex(np.inf, np.inf))
# DC gain is finite
np.testing.assert_almost_equal(sys_tf.dcgain(), 1.)
np.testing.assert_almost_equal(sys_ss.dcgain(), 1.)
# Make sure that we get the *signed* DC gain
sys_tf = -1 / (s + 1)
np.testing.assert_almost_equal(sys_tf.dcgain(), -1)
sys_ss = ctrl.tf2ss(sys_tf)
np.testing.assert_almost_equal(sys_ss.dcgain(), -1)
# Testing of the singular_value_plot function
class TSys:
"""Struct of test system"""
def __init__(self, sys=None, call_kwargs=None):
self.sys = sys
self.kwargs = call_kwargs if call_kwargs else {}
def __repr__(self):
"""Show system when debugging"""
return self.sys.__repr__()
@pytest.fixture
def ss_mimo_ct():
A = np.diag([-1/75.0, -1/75.0])
B = np.array([[87.8, -86.4],
[108.2, -109.6]])/75.0
C = np.eye(2)
D = np.zeros((2, 2))
T = TSys(ss(A, B, C, D))
T.omegas = [0.0, [0.0], np.array([0.0, 0.01])]
T.sigmas = [np.array([[197.20868123], [1.39141948]]),
np.array([[197.20868123], [1.39141948]]),
np.array([[197.20868123, 157.76694498], [1.39141948, 1.11313558]])
]
return T
@pytest.fixture
def ss_miso_ct():
A = np.diag([-1 / 75.0])
B = np.array([[87.8, -86.4]]) / 75.0
C = np.array([[1]])
D = np.zeros((1, 2))
T = TSys(ss(A, B, C, D))
T.omegas = [0.0, np.array([0.0, 0.01])]
T.sigmas = [np.array([[123.1819792]]),
np.array([[123.1819792, 98.54558336]])]
return T
@pytest.fixture
def ss_simo_ct():
A = np.diag([-1 / 75.0])
B = np.array([[1.0]]) / 75.0
C = np.array([[87.8], [108.2]])
D = np.zeros((2, 1))
T = TSys(ss(A, B, C, D))
T.omegas = [0.0, np.array([0.0, 0.01])]
T.sigmas = [np.array([[139.34159465]]),
np.array([[139.34159465, 111.47327572]])]
return T
@pytest.fixture
def ss_siso_ct():
A = np.diag([-1 / 75.0])
B = np.array([[1.0]]) / 75.0
C = np.array([[87.8]])
D = np.zeros((1, 1))
T = TSys(ss(A, B, C, D))
T.omegas = [0.0, np.array([0.0, 0.01])]
T.sigmas = [np.array([[87.8]]),
np.array([[87.8, 70.24]])]
return T
@pytest.fixture
def ss_mimo_dt():
A = np.array([[0.98675516, 0.],
[0., 0.98675516]])
B = np.array([[1.16289679, -1.14435402],
[1.43309149, -1.45163427]])
C = np.eye(2)
D = np.zeros((2, 2))
T = TSys(ss(A, B, C, D, dt=1.0))
T.omegas = [0.0, np.array([0.0, 0.001, 0.01])]
T.sigmas = [np.array([[197.20865428], [1.39141936]]),
np.array([[197.20865428, 196.6563423, 157.76758858],
[1.39141936, 1.38752248, 1.11314018]])]
return T
@pytest.fixture
def tsystem(request, ss_mimo_ct, ss_miso_ct, ss_simo_ct, ss_siso_ct, ss_mimo_dt):
systems = {"ss_mimo_ct": ss_mimo_ct,
"ss_miso_ct": ss_miso_ct,
"ss_simo_ct": ss_simo_ct,
"ss_siso_ct": ss_siso_ct,
"ss_mimo_dt": ss_mimo_dt
}
return systems[request.param]
@pytest.mark.parametrize("tsystem",
["ss_mimo_ct", "ss_miso_ct", "ss_simo_ct", "ss_siso_ct", "ss_mimo_dt"], indirect=["tsystem"])
def test_singular_values_plot(tsystem):
sys = tsystem.sys
for omega_ref, sigma_ref in zip(tsystem.omegas, tsystem.sigmas):
sigma, _ = singular_values_plot(sys, omega_ref, plot=False)
np.testing.assert_almost_equal(sigma, sigma_ref)
def test_singular_values_plot_mpl_base(ss_mimo_ct, ss_mimo_dt):
sys_ct = ss_mimo_ct.sys
sys_dt = ss_mimo_dt.sys
plt.figure()
singular_values_plot(sys_ct, plot=True)
fig = plt.gcf()
allaxes = fig.get_axes()
assert(len(allaxes) == 1)
assert(allaxes[0].get_label() == 'control-sigma')
plt.figure()
singular_values_plot([sys_ct, sys_dt], plot=True, Hz=True, dB=True, grid=False)
fig = plt.gcf()
allaxes = fig.get_axes()
assert(len(allaxes) == 1)
assert(allaxes[0].get_label() == 'control-sigma')
def test_singular_values_plot_mpl_superimpose_nyq(ss_mimo_ct, ss_mimo_dt):
sys_ct = ss_mimo_ct.sys
sys_dt = ss_mimo_dt.sys
omega_all = np.logspace(-3, 2, 1000)
plt.figure()
singular_values_plot(sys_ct, omega_all, plot=True)
singular_values_plot(sys_dt, omega_all, plot=True)
fig = plt.gcf()
allaxes = fig.get_axes()
assert(len(allaxes) == 1)
assert (allaxes[0].get_label() == 'control-sigma')
nyquist_line = allaxes[0].lines[-1].get_data()
assert(len(nyquist_line[0]) == 2)
assert(nyquist_line[0][0] == nyquist_line[0][1])
assert(nyquist_line[0][0] == np.pi/sys_dt.dt)