def test_05(self):
"""Test that bode() finds a reasonable frequency range."""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
n = 10
# Expected range is from 0.01 to 10.
expected_w = np.logspace(-2, 1, n)
w, mag, phase = bode(system, n=n)
assert_almost_equal(w, expected_w)
def test_05(self):
# Test that bode() finds a reasonable frequency range.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
n = 10
# Expected range is from 0.01 to 10.
expected_w = np.logspace(-2, 1, n)
w, mag, phase = bode(system, n=n)
assert_almost_equal(w, expected_w)
def test_04(self):
# Test bode() phase calculation.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, mag, phase = bode(system, w=w)
jw = w * 1j
y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
expected_phase = np.arctan2(y.imag, y.real) * 180.0 / np.pi
assert_almost_equal(phase, expected_phase)
def test_03(self):
"""Test bode() magnitude calculation."""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, mag, phase = bode(system, w=w)
jw = w * 1j
y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
expected_mag = 20.0 * np.log10(abs(y))
assert_almost_equal(mag, expected_mag)
def test_04(self):
"""Test bode() phase calculation."""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, mag, phase = bode(system, w=w)
jw = w * 1j
y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
expected_phase = np.arctan2(y.imag, y.real) * 180.0 / np.pi
assert_almost_equal(phase, expected_phase)
def test_03(self):
# Test bode() magnitude calculation.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, mag, phase = bode(system, w=w)
jw = w * 1j
y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
expected_mag = 20.0 * np.log10(abs(y))
assert_almost_equal(mag, expected_mag)
def test_02(self):
"""Test bode() phase calculation (manual sanity check)."""
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# angle(H(s=0.1)) ~= -5.7 deg
# angle(H(s=1)) ~= -45 deg
# angle(H(s=10)) ~= -84.3 deg
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, mag, phase = bode(system, w=w)
expected_phase = [-5.7, -45, -84.3]
assert_almost_equal(phase, expected_phase, decimal=1)
def test_02(self):
# Test bode() phase calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# angle(H(s=0.1)) ~= -5.7 deg
# angle(H(s=1)) ~= -45 deg
# angle(H(s=10)) ~= -84.3 deg
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, mag, phase = bode(system, w=w)
expected_phase = [-5.7, -45, -84.3]
assert_almost_equal(phase, expected_phase, decimal=1)
def test_05(self):
"""Test that bode() finds a reasonable frequency range."""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
vals = linalg.eigvals(system.A)
minpole = min(abs(np.real(vals)))
maxpole = max(abs(np.real(vals)))
n = 10
# Expected range is from 0.01 to 10.
expected_w = np.logspace(-2, 1, n)
w, mag, phase = bode(system, n=n)
assert_almost_equal(w, expected_w)
def test_05(self):
"""Test that bode() finds a reasonable frequency range."""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
vals = linalg.eigvals(system.A)
minpole = min(abs(np.real(vals)))
maxpole = max(abs(np.real(vals)))
n = 10
# Expected range is from 0.01 to 10.
expected_w = np.logspace(-2, 1, n)
w, mag, phase = bode(system, n=n)
assert_almost_equal(w, expected_w)
def test_01(self):
"""Test bode() magnitude calculation (manual sanity check)."""
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# cutoff: 1 rad/s, slope: -20 dB/decade
# H(s=0.1) ~= 0 dB
# H(s=1) ~= -3 dB
# H(s=10) ~= -20 dB
# H(s=100) ~= -40 dB
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, mag, phase = bode(system, w=w)
expected_mag = [0, -3, -20, -40]
assert_almost_equal(mag, expected_mag, decimal=1)
def test_01(self):
# Test bode() magnitude calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# cutoff: 1 rad/s, slope: -20 dB/decade
# H(s=0.1) ~= 0 dB
# H(s=1) ~= -3 dB
# H(s=10) ~= -20 dB
# H(s=100) ~= -40 dB
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, mag, phase = bode(system, w=w)
expected_mag = [0, -3, -20, -40]
assert_almost_equal(mag, expected_mag, decimal=1)
def test_05(self):
"""Test that bode() finds a reasonable frequency range.
A reasonable frequency range is two orders of magnitude before the
minimum (slowest) pole and two orders of magnitude after the maximum
(fastest) pole.
"""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
vals = linalg.eigvals(system.A)
minpole = min(abs(np.real(vals)))
maxpole = max(abs(np.real(vals)))
n = 10;
expected_w = np.logspace(np.log10(minpole) - 2, np.log10(maxpole) + 2, n)
w, mag, phase = bode(system, n=n)
assert_almost_equal(w, expected_w)
def test_from_state_space(self):
# Ensure that bode works with a system that was created from the
# state space representation matrices A, B, C, D. In this case,
# system.num will be a 2-D array with shape (1, n+1), where (n,n)
# is the shape of A.
# A Butterworth lowpass filter is used, so we know the exact
# frequency response.
a = np.array([1.0, 2.0, 2.0, 1.0])
A = linalg.companion(a).T
B = np.array([[0.0], [0.0], [1.0]])
C = np.array([[1.0, 0.0, 0.0]])
D = np.array([[0.0]])
with warnings.catch_warnings():
warnings.simplefilter("ignore", BadCoefficients)
system = lti(A, B, C, D)
w, mag, phase = bode(system, n=100)
expected_magnitude = 20 * np.log10(np.sqrt(1.0 / (1.0 + w**6)))
assert_almost_equal(mag, expected_magnitude)
def test_05(self):
"""Test that bode() finds a reasonable frequency range.
A reasonable frequency range is two orders of magnitude before the
minimum (slowest) pole and two orders of magnitude after the maximum
(fastest) pole.
"""
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
vals = linalg.eigvals(system.A)
minpole = min(abs(np.real(vals)))
maxpole = max(abs(np.real(vals)))
n = 10
expected_w = np.logspace(
np.log10(minpole) - 2,
np.log10(maxpole) + 2, n)
w, mag, phase = bode(system, n=n)
assert_almost_equal(w, expected_w)
def test_from_state_space(self):
# Ensure that bode works with a system that was created from the
# state space representation matrices A, B, C, D. In this case,
# system.num will be a 2-D array with shape (1, n+1), where (n,n)
# is the shape of A.
# A Butterworth lowpass filter is used, so we know the exact
# frequency response.
a = np.array([1.0, 2.0, 2.0, 1.0])
A = linalg.companion(a).T
B = np.array([[0.0],[0.0],[1.0]])
C = np.array([[1.0, 0.0, 0.0]])
D = np.array([[0.0]])
with warnings.catch_warnings():
warnings.simplefilter("ignore", BadCoefficients)
system = lti(A, B, C, D)
w, mag, phase = bode(system, n=100)
expected_magnitude = 20 * np.log10(np.sqrt(1.0 / (1.0 + w**6)))
assert_almost_equal(mag, expected_magnitude)
def test_07(self):
"""bode() should not fail on a system with pure imaginary poles."""
# The test passes if bode doesn't raise an exception.
system = lti([1], [1, 0, 100])
w, mag, phase = bode(system, n=2)
def test_06(self):
"""Test that bode() doesn't fail on a system with a pole at 0."""
# integrator, pole at zero: H(s) = 1 / s
system = lti([1], [1, 0])
w, mag, phase = bode(system, n=2)
assert_equal(w[0], 0.01) # a fail would give not-a-number
def test_06(self):
# Test that bode() doesn't fail on a system with a pole at 0.
# integrator, pole at zero: H(s) = 1 / s
system = lti([1], [1, 0])
w, mag, phase = bode(system, n=2)
assert_equal(w[0], 0.01) # a fail would give not-a-number
def test_07(self):
# bode() should not fail on a system with pure imaginary poles.
# The test passes if bode doesn't raise an exception.
system = lti([1], [1, 0, 100])
w, mag, phase = bode(system, n=2)
print(G)
data_freq = numpy.array([
50, 100, 200, 400, 600, 800, 1 * pow(10, 3), 2 * pow(10, 3),
3 * pow(10, 3), 5 * pow(10, 3), 10 * pow(10, 3), 50 * pow(10, 3),
100 * pow(10, 3), 200 * pow(10, 3), 500 * pow(10, 3), 600 * pow(10, 3),
700 * pow(10, 3), 800 * pow(10, 3), 900 * pow(10, 3), 1 * pow(10, 6),
2 * pow(10, 6)
])
data_Av = numpy.array([
14, 28, 46, 58, 64, 65, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70,
70, 70
])
w, mag, phase = bode(G, numpy.logspace(1, 9).tolist())
f = w / (2 * numpy.pi)
pyplot.figure(figsize=(15, 10))
pyplot.subplot(211)
pyplot.title("Ex25_4_a_Bode_Mag")
pyplot.semilogx(f, mag, lw=5, label="Formula") # Bode magnitude plot
pyplot.plot(data_freq,
20 * numpy.log10(data_Av),
'.--',
lw=5,
label="Experiment_Data")
pyplot.ylim([-40, 40])
pyplot.ylabel('Magnitude (dB)')
pyplot.xlabel("Frequency (Hz)")
pyplot.legend()
pyplot.grid(True)
