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improved default time vector for time response functions that takes zeros into account.#454

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Merged
murrayrm merged 7 commits intopython-control:masterfromsawyerbfuller:better-tfinal
Oct 17, 2020
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4 changes: 4 additions & 0 deletionscontrol/statesp.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -944,6 +944,10 @@ def dcgain(self):
gain = np.tile(np.nan, (self.outputs, self.inputs))
return np.squeeze(gain)

def is_static_gain(self):
"""True if and only if the system has no dynamics, that is,
if A and B are zero. """
return not np.any(self.A) and not np.any(self.B)

# TODO: add discrete time check
def _convertToStateSpace(sys, **kw):
Expand Down
14 changes: 10 additions & 4 deletionscontrol/tests/sisotool_test.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -32,9 +32,12 @@ def test_sisotool(self):
initial_point_2, 4)

# Check the step response before moving the point
# new array needed because change in compute step response default time
step_response_original = np.array(
[0., 0.0217, 0.1281, 0.3237, 0.5797, 0.8566, 1.116,
1.3261, 1.4659, 1.526])
[0. , 0.0069, 0.0448, 0.124 , 0.2427, 0.3933, 0.5653, 0.7473,
0.928 , 1.0969])
#old: np.array([0., 0.0217, 0.1281, 0.3237, 0.5797, 0.8566, 1.116,
# 1.3261, 1.4659, 1.526])
assert_array_almost_equal(
ax_step.lines[0].get_data()[1][:10], step_response_original, 4)

Expand DownExpand Up@@ -77,9 +80,12 @@ def test_sisotool(self):
bode_mag_moved, 4)

# Check if the step response has changed
# new array needed because change in compute step response default time
step_response_moved = np.array(
[0., 0.0239, 0.161 , 0.4547, 0.8903, 1.407,
1.9121, 2.2989, 2.4686, 2.353])
[0. , 0.0072, 0.0516, 0.1554, 0.3281, 0.5681, 0.8646, 1.1987,
1.5452, 1.875 ])
#old: array([0., 0.0239, 0.161 , 0.4547, 0.8903, 1.407,
# 1.9121, 2.2989, 2.4686, 2.353])
assert_array_almost_equal(
ax_step.lines[0].get_data()[1][:10], step_response_moved, 4)

Expand Down
65 changes: 41 additions & 24 deletionscontrol/tests/timeresp_test.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -29,6 +29,12 @@ def setUp(self):
# Create some transfer functions
self.siso_tf1 = TransferFunction([1], [1, 2, 1])
self.siso_tf2 = _convert_to_transfer_function(self.siso_ss1)

# tests for pole cancellation
self.pole_cancellation = TransferFunction([1.067e+05, 5.791e+04],
[10.67, 1.067e+05, 5.791e+04])
self.no_pole_cancellation = TransferFunction([1.881e+06],
[188.1, 1.881e+06])

# Create MIMO system, contains ``siso_ss1`` twice
A = np.matrix("1. -2. 0. 0.;"
Expand DownExpand Up@@ -167,6 +173,14 @@ def test_step_info(self):
2.50,
rtol=rtol)

# confirm that pole-zero cancellation doesn't perturb results
# https://github.com/python-control/python-control/issues/440
step_info_no_cancellation = step_info(self.no_pole_cancellation)
step_info_cancellation = step_info(self.pole_cancellation)
for key in step_info_no_cancellation:
np.testing.assert_allclose(step_info_no_cancellation[key],
step_info_cancellation[key], rtol=1e-4)

def test_impulse_response(self):
# Test SISO system
sys = self.siso_ss1
Expand DownExpand Up@@ -348,33 +362,41 @@ def test_step_robustness(self):
sys2 = TransferFunction(num, den2)

# Compute step response from input 1 to output 1, 2
t1, y1 = step_response(sys1, input=0, T_num=100)
t2, y2 = step_response(sys2, input=0, T_num=100)
t1, y1 = step_response(sys1, input=0,T=2,T_num=100)
t2, y2 = step_response(sys2, input=0,T=2,T_num=100)
np.testing.assert_array_almost_equal(y1, y2)

def test_auto_generated_time_vector(self):
# confirm a TF with a pole at p simulates for7.0/p seconds
# confirm a TF with a pole at p simulates forratio/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],
(7/p))
(ratio/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 for7.0/p seconds
(ratio2/p))
# confirm a TF with poles at 0 and p simulates forratio/p seconds
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, .5, 0]))[0],
(7/p))
(ratio2/p))

# confirm a TF with a natural frequency of wn rad/s gets a
# dt of 1/(7.0*wn)
# 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/(7.0*wn))
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/(7.0*wn))
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],
Expand All@@ -384,37 +406,32 @@ def test_auto_generated_time_vector(self):
.1)
np.testing.assert_array_almost_equal(
_ideal_tfinal_and_dt(TransferFunction(1, [1, 2*zeta*wn, wn**2]))[1],
1/(7.0*wn))
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)))
# 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 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,
step_response(sys, 100)[0][-1],
decimal=.5)
np.ceil(step_response(sys, 100)[0][-1]))
np.testing.assert_array_almost_equal(
100,
step_response(sysdt, 100)[0][-1],
decimal=.5)
np.ceil(step_response(sysdt, 100)[0][-1]))
np.testing.assert_array_almost_equal(
100,
impulse_response(sys, 100)[0][-1],
decimal=.5)
np.ceil(impulse_response(sys, 100)[0][-1]))
np.testing.assert_array_almost_equal(
100,
initial_response(sys, 100)[0][-1],
decimal=.5)
np.ceil(initial_response(sys, 100)[0][-1]))


def test_time_vector(self):
Expand Down
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