def test_damp(self):
# Test the continuous time case.
zeta = 0.1
wn = 42
p = -wn * zeta + 1j * wn * np.sqrt(1 - zeta**2)
sys = tf(1, [1, 2 * zeta * wn, wn**2])
expected = ([wn, wn], [zeta, zeta], [p, p.conjugate()])
np.testing.assert_allclose(sys.damp(), expected)
np.testing.assert_allclose(damp(sys), expected)
# Also test the discrete time case.
dt = 0.001
sys_dt = c2d(sys, dt, method='matched')
p_zplane = np.exp(p * dt)
expected_dt = ([wn, wn], [zeta,
zeta], [p_zplane,
p_zplane.conjugate()])
np.testing.assert_almost_equal(sys_dt.damp(), expected_dt)
np.testing.assert_almost_equal(damp(sys_dt), expected_dt)
#also check that for a discrete system with a negative real pole the damp function can extract wn and zeta.
p2_zplane = -0.2
sys_dt2 = tf(1, [1, -p2_zplane], dt)
wn2, zeta2, p2 = sys_dt2.damp()
p2_splane = -wn2 * zeta2 + 1j * wn2 * np.sqrt(1 - zeta2**2)
p2_zplane = np.exp(p2_splane * dt)
np.testing.assert_almost_equal(p2, p2_zplane)
def test_damp(self):
# Test the continuous time case.
zeta = 0.1
wn = 42
p = -wn * zeta + 1j * wn * np.sqrt(1 - zeta**2)
sys = tf(1, [1, 2 * zeta * wn, wn**2])
expected = ([wn, wn], [zeta, zeta], [p, p.conjugate()])
np.testing.assert_equal(sys.damp(), expected)
np.testing.assert_equal(damp(sys), expected)
# Also test the discrete time case.
dt = 0.001
sys_dt = c2d(sys, dt, method='matched')
p_zplane = np.exp(p*dt)
expected_dt = ([wn, wn], [zeta, zeta],
[p_zplane, p_zplane.conjugate()])
np.testing.assert_almost_equal(sys_dt.damp(), expected_dt)
np.testing.assert_almost_equal(damp(sys_dt), expected_dt)