def test_lti_instantiation(self):
# Test that lti can be instantiated with sequences, scalars.
# See PR-225.
# TransferFunction
s = lti([1], [-1])
assert_(isinstance(s, TransferFunction))
assert_(isinstance(s, lti))
assert_(not isinstance(s, dlti))
assert_(s.dt is None)
# ZerosPolesGain
s = lti(np.array([]), np.array([-1]), 1)
assert_(isinstance(s, ZerosPolesGain))
assert_(isinstance(s, lti))
assert_(not isinstance(s, dlti))
assert_(s.dt is None)
# StateSpace
s = lti([], [-1], 1)
s = lti([1], [-1], 1, 3)
assert_(isinstance(s, StateSpace))
assert_(isinstance(s, lti))
assert_(not isinstance(s, dlti))
assert_(s.dt is None)
def test_from_zpk(self):
# 4th order low-pass filter: H(s) = 1 / (s + 1)
system = lti([], [-1] * 4, [1])
w = [0.1, 1, 10, 100]
w, H = freqresp(system, w=w)
s = w * 1j
expected = 1 / (s + 1)**4
assert_almost_equal(H.real, expected.real)
assert_almost_equal(H.imag, expected.imag)
def test_freq_range(self):
# Test that freqresp() finds a reasonable frequency range.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
# Expected range is from 0.01 to 10.
system = lti([1], [1, 1])
n = 10
expected_w = np.logspace(-2, 1, n)
w, H = freqresp(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_output(self):
# Test freqresp() output calculation.
# 1st order low-pass filter: H(s) = 1 / (s + 1)
system = lti([1], [1, 1])
w = [0.1, 1, 10, 100]
w, H = freqresp(system, w=w)
s = w * 1j
expected = np.polyval(system.num, s) / np.polyval(system.den, s)
assert_almost_equal(H.real, expected.real)
assert_almost_equal(H.imag, expected.imag)
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_output_manual(self):
# Test freqresp() output calculation (manual sanity check).
# 1st order low-pass filter: H(s) = 1 / (s + 1),
# re(H(s=0.1)) ~= 0.99
# re(H(s=1)) ~= 0.5
# re(H(s=10)) ~= 0.0099
system = lti([1], [1, 1])
w = [0.1, 1, 10]
w, H = freqresp(system, w=w)
expected_re = [0.99, 0.5, 0.0099]
expected_im = [-0.099, -0.5, -0.099]
assert_almost_equal(H.real, expected_re, decimal=1)
assert_almost_equal(H.imag, expected_im, 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_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 = 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 suppress_warnings() as sup:
sup.filter(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_from_state_space(self):
# Ensure that freqresp 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 = 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 suppress_warnings() as sup:
sup.filter(BadCoefficients)
system = lti(A, B, C, D)
w, H = freqresp(system, n=100)
s = w * 1j
expected = (1.0 / (1.0 + 2 * s + 2 * s**2 + s**3))
assert_almost_equal(H.real, expected.real)
assert_almost_equal(H.imag, expected.imag)
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_pole_zero(self):
# Test that freqresp() 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, H = freqresp(system, n=2)
assert_equal(w[0], 0.01) # a fail would give not-a-number
def test_08(self):
# Test that bode() return continuous phase, issues/2331.
system = lti([], [-10, -30, -40, -60, -70], 1)
w, mag, phase = system.bode(w=np.logspace(-3, 40, 100))
assert_almost_equal(min(phase), -450, decimal=15)
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 lti_nowarn(self, *args):
with suppress_warnings() as sup:
sup.filter(BadCoefficients)
system = lti(*args)
return system