def test_default_timevector_long(self):
"""Test long time vector"""
# TF with fast oscillations simulates only 5000 time steps
# even with long tfinal
wn = 100
tfsys = TransferFunction(1, [1, 0, wn**2])
tout = _default_time_vector(tfsys, tfinal=100)
assert len(tout) == 5000
def test_auto_generated_time_vector(self):
# confirm a TF with a pole at p simulates for ratio/p seconds
p = 0.5
ratio = 9.21034*p # taken from code
ratio2 = 25*p
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5]))[0],
(ratio/p))
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5]).sample(.1))[0],
(ratio2/p))
# confirm a TF with poles at 0 and p simulates for ratio/p seconds
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5, 0]))[0],
(ratio2/p))
# confirm a TF with a natural frequency of wn rad/s gets a
# dt of 1/(ratio*wn)
wn = 10
ratio_dt = 1/(0.025133 * ratio * wn)
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 0, wn**2]))[1],
1/(ratio_dt*ratio*wn))
wn = 100
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 0, wn**2]))[1],
1/(ratio_dt*ratio*wn))
zeta = .1
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 2*zeta*wn, wn**2]))[1],
1/(ratio_dt*ratio*wn))
# but a smapled one keeps its dt
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 2*zeta*wn, wn**2]).sample(.1))[1],
.1)
np.testing.assert_array_almost_equal(
np.diff(initial_response(TransferFunction(1, [1, 2*zeta*wn, wn**2]).sample(.1))[0][0:2]),
.1)
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 2*zeta*wn, wn**2]))[1],
1/(ratio_dt*ratio*wn))
# TF with fast oscillations simulates only 5000 time steps even with long tfinal
self.assertEqual(5000,
len(_default_time_vector(TransferFunction(1, [1, 0, wn**2]),tfinal=100)))
sys = TransferFunction(1, [1, .5, 0])
sysdt = TransferFunction(1, [1, .5, 0], .1)
# test impose number of time steps
self.assertEqual(10, len(step_response(sys, T_num=10)[0]))
# test that discrete ignores T_num
self.assertNotEqual(15, len(step_response(sysdt, T_num=15)[0]))
# test impose final time
np.testing.assert_array_almost_equal(
100,
np.ceil(step_response(sys, 100)[0][-1]))
np.testing.assert_array_almost_equal(
100,
np.ceil(step_response(sysdt, 100)[0][-1]))
np.testing.assert_array_almost_equal(
100,
np.ceil(impulse_response(sys, 100)[0][-1]))
np.testing.assert_array_almost_equal(
100,
np.ceil(initial_response(sys, 100)[0][-1]))
def test_auto_generated_time_vector_tfinal(self, tfsys, tfinal):
"""Confirm a TF with a pole at p simulates for tfinal seconds"""
ideal_tfinal, ideal_dt = _ideal_tfinal_and_dt(tfsys)
np.testing.assert_allclose(ideal_tfinal, tfinal, rtol=1e-4)
T = _default_time_vector(tfsys)
np.testing.assert_allclose(T[-1], tfinal, atol=0.5*ideal_dt)
def test_auto_generated_time_vector(self):
# confirm a TF with a pole at p simulates for 7.0/p seconds
p = 0.5
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5]))[0], (7 / p))
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5]).sample(.1))[0],
(7 / p))
# confirm a TF with poles at 0 and p simulates for 7.0/p seconds
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5, 0]))[0], (7 / p))
# confirm a TF with a natural frequency of wn rad/s gets a
# dt of 1/(7.0*wn)
wn = 10
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 0, wn**2]))[1],
1 / (7.0 * wn))
zeta = .1
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(
1, [1, 2 * zeta * wn, wn**2]))[1], 1 / (7.0 * wn))
# but a smapled one keeps its dt
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(
TransferFunction(1, [1, 2 * zeta * wn, wn**2]).sample(.1))[1],
.1)
np.testing.assert_array_almost_equal(
np.diff(
initial_response(
TransferFunction(
1, [1, 2 * zeta * wn, wn**2]).sample(.1))[0][0:2]), .1)
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(
1, [1, 2 * zeta * wn, wn**2]))[1], 1 / (7.0 * wn))
# TF with fast oscillations simulates only 5000 time steps even with long tfinal
self.assertEqual(
5000,
len(
_default_time_vector(TransferFunction(1, [1, 0, wn**2]),
tfinal=100)))
# and simulates for 7.0/dt time steps
self.assertEqual(
len(_default_time_vector(TransferFunction(1, [1, 0, wn**2]))),
int(7.0 / (1 / (7.0 * wn))))
sys = TransferFunction(1, [1, .5, 0])
sysdt = TransferFunction(1, [1, .5, 0], .1)
# test impose number of time steps
self.assertEqual(10, len(step_response(sys, T_num=10)[0]))
self.assertEqual(10, len(step_response(sysdt, T_num=10)[0]))
# test impose final time
np.testing.assert_array_almost_equal(100,
step_response(sys, 100)[0][-1],
decimal=.5)
np.testing.assert_array_almost_equal(100,
step_response(sysdt, 100)[0][-1],
decimal=.5)
np.testing.assert_array_almost_equal(100,
impulse_response(sys, 100)[0][-1],
decimal=.5)
np.testing.assert_array_almost_equal(100,
initial_response(sys, 100)[0][-1],
decimal=.5)