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1186 lines (1043 loc) · 48.1 KB
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"""timeresp_test.py - test time response functions"""
from copy import copy
from distutils.version import StrictVersion
import numpy as np
import pytest
import scipy as sp
import control as ct
from control import StateSpace, TransferFunction, c2d, isctime, ss2tf, tf2ss
from control.exception import slycot_check
from control.tests.conftest import slycotonly
from control.timeresp import (_default_time_vector, _ideal_tfinal_and_dt,
forced_response, impulse_response,
initial_response, step_info, step_response)
class TSys:
"""Struct of test system"""
def __init__(self, sys=None, call_kwargs=None):
self.sys = sys
self.kwargs = call_kwargs if call_kwargs else {}
def __repr__(self):
"""Show system when debugging"""
return self.sys.__repr__()
class TestTimeresp:
@pytest.fixture
def tsystem(self, request):
"""Define some test systems"""
"""continuous"""
A = np.array([[1., -2.], [3., -4.]])
B = np.array([[5.], [7.]])
C = np.array([[6., 8.]])
D = np.array([[9.]])
siso_ss1 = TSys(StateSpace(A, B, C, D, 0))
siso_ss1.t = np.linspace(0, 1, 10)
siso_ss1.ystep = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234,
39.1165, 42.3227, 44.9694, 47.1599,
48.9776])
siso_ss1.X0 = np.array([[.5], [1.]])
siso_ss1.yinitial = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118,
1.9092, 1.1508, 0.5833, 0.1645, -0.1391])
ss1 = siso_ss1.sys
"""D=0, continuous"""
siso_ss2 = TSys(StateSpace(ss1.A, ss1.B, ss1.C, 0, 0))
siso_ss2.t = siso_ss1.t
siso_ss2.ystep = siso_ss1.ystep - 9
siso_ss2.initial = siso_ss1.yinitial - 9
siso_ss2.yimpulse = np.array([86., 70.1808, 57.3753, 46.9975, 38.5766,
31.7344, 26.1668, 21.6292, 17.9245,
14.8945])
"""System with unspecified timebase"""
siso_ss2_dtnone = TSys(StateSpace(ss1.A, ss1.B, ss1.C, 0, None))
siso_ss2_dtnone.t = np.arange(0, 10, 1.)
siso_ss2_dtnone.ystep = np.array([0., 86., -72., 230., -360., 806.,
-1512., 3110., -6120., 12326.])
siso_tf1 = TSys(TransferFunction([1], [1, 2, 1], 0))
siso_tf2 = copy(siso_ss1)
siso_tf2.sys = ss2tf(siso_ss1.sys)
"""MIMO system, contains ``siso_ss1`` twice"""
mimo_ss1 = copy(siso_ss1)
A = np.zeros((4, 4))
A[:2, :2] = siso_ss1.sys.A
A[2:, 2:] = siso_ss1.sys.A
B = np.zeros((4, 2))
B[:2, :1] = siso_ss1.sys.B
B[2:, 1:] = siso_ss1.sys.B
C = np.zeros((2, 4))
C[:1, :2] = siso_ss1.sys.C
C[1:, 2:] = siso_ss1.sys.C
D = np.zeros((2, 2))
D[:1, :1] = siso_ss1.sys.D
D[1:, 1:] = siso_ss1.sys.D
mimo_ss1.sys = StateSpace(A, B, C, D)
"""MIMO system, contains ``siso_ss2`` twice"""
mimo_ss2 = copy(siso_ss2)
A = np.zeros((4, 4))
A[:2, :2] = siso_ss2.sys.A
A[2:, 2:] = siso_ss2.sys.A
B = np.zeros((4, 2))
B[:2, :1] = siso_ss2.sys.B
B[2:, 1:] = siso_ss2.sys.B
C = np.zeros((2, 4))
C[:1, :2] = siso_ss2.sys.C
C[1:, 2:] = siso_ss2.sys.C
D = np.zeros((2, 2))
mimo_ss2.sys = StateSpace(A, B, C, D, 0)
"""discrete"""
siso_dtf0 = TSys(TransferFunction([1.], [1., 0.], 1.))
siso_dtf0.t = np.arange(4)
siso_dtf0.yimpulse = [0., 1., 0., 0.]
siso_dtf1 = TSys(TransferFunction([1], [1, 1, 0.25], True))
siso_dtf1.t = np.arange(0, 5, 1)
siso_dtf1.ystep = np.array([0. , 0. , 1. , 0. , 0.75])
siso_dtf2 = TSys(TransferFunction([1], [1, 1, 0.25], 0.2))
siso_dtf2.t = np.arange(0, 5, 0.2)
siso_dtf2.ystep = np.array(
[0. , 0. , 1. , 0. , 0.75 , 0.25 ,
0.5625, 0.375 , 0.4844, 0.4219, 0.457 , 0.4375,
0.4482, 0.4424, 0.4456, 0.4438, 0.4448, 0.4443,
0.4445, 0.4444, 0.4445, 0.4444, 0.4445, 0.4444,
0.4444])
"""Time step which leads to rounding errors for time vector length"""
num = [-0.10966442, 0.12431949]
den = [1., -1.86789511, 0.88255018]
dt = 0.12493963338370018
siso_dtf3 = TSys(TransferFunction(num, den, dt))
siso_dtf3.t = np.linspace(0, 9*dt, 10)
siso_dtf3.ystep = np.array(
[ 0. , -0.1097, -0.1902, -0.2438, -0.2729,
-0.2799, -0.2674, -0.2377, -0.1934, -0.1368])
"""dtf1 converted statically, because Slycot and Scipy produce
different realizations, wich means different initial condtions,"""
siso_dss1 = copy(siso_dtf1)
siso_dss1.sys = StateSpace([[-1., -0.25],
[ 1., 0.]],
[[1.],
[0.]],
[[0., 1.]],
[[0.]],
True)
siso_dss1.X0 = [0.5, 1.]
siso_dss1.yinitial = np.array([1., 0.5, -0.75, 0.625, -0.4375])
siso_dss2 = copy(siso_dtf2)
siso_dss2.sys = tf2ss(siso_dtf2.sys)
mimo_dss1 = TSys(StateSpace(ss1.A, ss1.B, ss1.C, ss1.D, True))
mimo_dss1.t = np.arange(0, 5, 0.2)
mimo_dss2 = copy(mimo_ss1)
mimo_dss2.sys = c2d(mimo_ss1.sys, mimo_ss1.t[1]-mimo_ss1.t[0])
mimo_tf2 = copy(mimo_ss2)
tf_ = ss2tf(siso_ss2.sys)
mimo_tf2.sys = TransferFunction(
[[tf_.num[0][0], [0]], [[0], tf_.num[0][0]]],
[[tf_.den[0][0], [1]], [[1], tf_.den[0][0]]],
0)
mimo_dtf1 = copy(siso_dtf1)
tf_ = siso_dtf1.sys
mimo_dtf1.sys = TransferFunction(
[[tf_.num[0][0], [0]], [[0], tf_.num[0][0]]],
[[tf_.den[0][0], [1]], [[1], tf_.den[0][0]]],
True)
# for pole cancellation tests
pole_cancellation = TSys(TransferFunction(
[1.067e+05, 5.791e+04],
[10.67, 1.067e+05, 5.791e+04]))
no_pole_cancellation = TSys(TransferFunction(
[1.881e+06],
[188.1, 1.881e+06]))
# System Type 1 - Step response not stationary: G(s)=1/s(s+1)
siso_tf_type1 = TSys(TransferFunction(1, [1, 1, 0]))
siso_tf_type1.step_info = {
'RiseTime': np.NaN,
'SettlingTime': np.NaN,
'SettlingMin': np.NaN,
'SettlingMax': np.NaN,
'Overshoot': np.NaN,
'Undershoot': np.NaN,
'Peak': np.Inf,
'PeakTime': np.Inf,
'SteadyStateValue': np.NaN}
# SISO under shoot response and positive final value
# G(s)=(-s+1)/(s²+s+1)
siso_tf_kpos = TSys(TransferFunction([-1, 1], [1, 1, 1]))
siso_tf_kpos.step_info = {
'RiseTime': 1.242,
'SettlingTime': 9.110,
'SettlingMin': 0.90,
'SettlingMax': 1.208,
'Overshoot': 20.840,
'Undershoot': 28.0,
'Peak': 1.208,
'PeakTime': 4.282,
'SteadyStateValue': 1.0}
# SISO under shoot response and negative final value
# k=-1 G(s)=-(-s+1)/(s²+s+1)
siso_tf_kneg = TSys(TransferFunction([1, -1], [1, 1, 1]))
siso_tf_kneg.step_info = {
'RiseTime': 1.242,
'SettlingTime': 9.110,
'SettlingMin': -1.208,
'SettlingMax': -0.90,
'Overshoot': 20.840,
'Undershoot': 28.0,
'Peak': 1.208,
'PeakTime': 4.282,
'SteadyStateValue': -1.0}
siso_tf_asymptotic_from_neg1 = TSys(TransferFunction([-1, 1], [1, 1]))
siso_tf_asymptotic_from_neg1.step_info = {
'RiseTime': 2.197,
'SettlingTime': 4.605,
'SettlingMin': 0.9,
'SettlingMax': 1.0,
'Overshoot': 0,
'Undershoot': 100.0,
'Peak': 1.0,
'PeakTime': 0.0,
'SteadyStateValue': 1.0}
siso_tf_asymptotic_from_neg1.kwargs = {
'step_info': {'T': np.arange(0, 5, 1e-3)}}
# example from matlab online help
# https://www.mathworks.com/help/control/ref/stepinfo.html
siso_tf_step_matlab = TSys(TransferFunction([1, 5, 5],
[1, 1.65, 5, 6.5, 2]))
siso_tf_step_matlab.step_info = {
'RiseTime': 3.8456,
'SettlingTime': 27.9762,
'SettlingMin': 2.0689,
'SettlingMax': 2.6873,
'Overshoot': 7.4915,
'Undershoot': 0,
'Peak': 2.6873,
'PeakTime': 8.0530,
'SteadyStateValue': 2.5}
A = [[0.68, -0.34],
[0.34, 0.68]]
B = [[0.18, -0.05],
[0.04, 0.11]]
C = [[0, -1.53],
[-1.12, -1.10]]
D = [[0, 0],
[0.06, -0.37]]
mimo_ss_step_matlab = TSys(StateSpace(A, B, C, D, 0.2))
mimo_ss_step_matlab.kwargs['step_info'] = {'T': 4.6}
mimo_ss_step_matlab.step_info = [[
{'RiseTime': 0.6000,
'SettlingTime': 3.0000,
'SettlingMin': -0.5999,
'SettlingMax': -0.4689,
'Overshoot': 15.5072,
'Undershoot': 0.,
'Peak': 0.5999,
'PeakTime': 1.4000,
'SteadyStateValue': -0.5193},
{'RiseTime': 0.,
'SettlingTime': 3.6000,
'SettlingMin': -0.2797,
'SettlingMax': -0.1043,
'Overshoot': 118.9918,
'Undershoot': 0,
'Peak': 0.2797,
'PeakTime': .6000,
'SteadyStateValue': -0.1277}],
[{'RiseTime': 0.4000,
'SettlingTime': 2.8000,
'SettlingMin': -0.6724,
'SettlingMax': -0.5188,
'Overshoot': 24.6476,
'Undershoot': 11.1224,
'Peak': 0.6724,
'PeakTime': 1,
'SteadyStateValue': -0.5394},
{'RiseTime': 0.0000, # (*)
'SettlingTime': 3.4000,
'SettlingMin': -0.4350, # (*)
'SettlingMax': -0.1485,
'Overshoot': 132.0170,
'Undershoot': 0.,
'Peak': 0.4350,
'PeakTime': .2,
'SteadyStateValue': -0.1875}]]
# (*): MATLAB gives 0.4 for RiseTime and -0.1034 for
# SettlingMin, but it is unclear what 10% and 90% of
# the steady state response mean, when the step for
# this channel does not start a 0.
siso_ss_step_matlab = copy(mimo_ss_step_matlab)
siso_ss_step_matlab.sys = siso_ss_step_matlab.sys[1, 0]
siso_ss_step_matlab.step_info = siso_ss_step_matlab.step_info[1][0]
Ta = [[siso_tf_kpos, siso_tf_kneg, siso_tf_step_matlab],
[siso_tf_step_matlab, siso_tf_kpos, siso_tf_kneg]]
mimo_tf_step_info = TSys(TransferFunction(
[[Ti.sys.num[0][0] for Ti in Tr] for Tr in Ta],
[[Ti.sys.den[0][0] for Ti in Tr] for Tr in Ta]))
mimo_tf_step_info.step_info = [[Ti.step_info for Ti in Tr]
for Tr in Ta]
# enforce enough sample points for all channels (they have different
# characteristics)
mimo_tf_step_info.kwargs['step_info'] = {'T_num': 2000}
systems = locals()
if isinstance(request.param, str):
return systems[request.param]
else:
return [systems[sys] for sys in request.param]
@pytest.mark.parametrize(
"kwargs",
[{},
{'X0': 0},
{'X0': np.array([0, 0])},
{'X0': 0, 'return_x': True},
])
@pytest.mark.parametrize("tsystem", ["siso_ss1"], indirect=True)
def test_step_response_siso(self, tsystem, kwargs):
"""Test SISO system step response"""
sys = tsystem.sys
t = tsystem.t
yref = tsystem.ystep
# SISO call
out = step_response(sys, T=t, **kwargs)
tout, yout = out[:2]
assert len(out) == 3 if ('return_x', True) in kwargs.items() else 2
np.testing.assert_array_almost_equal(tout, t)
np.testing.assert_array_almost_equal(yout, yref, decimal=4)
@pytest.mark.parametrize("tsystem", ["mimo_ss1"], indirect=True)
def test_step_response_mimo(self, tsystem):
"""Test MIMO system, which contains ``siso_ss1`` twice."""
sys = tsystem.sys
t = tsystem.t
yref = tsystem.ystep
_t, y_00 = step_response(sys, T=t, input=0, output=0)
_t, y_11 = step_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, yref, decimal=4)
np.testing.assert_array_almost_equal(y_11, yref, decimal=4)
@pytest.mark.parametrize("tsystem", ["mimo_ss1"], indirect=True)
def test_step_response_return(self, tsystem):
"""Verify continuous and discrete time use same return conventions."""
sysc = tsystem.sys
sysd = c2d(sysc, 1) # discrete time system
Tvec = np.linspace(0, 10, 11) # make sure to use integer times 0..10
Tc, youtc = step_response(sysc, Tvec, input=0)
Td, youtd = step_response(sysd, Tvec, input=0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
@pytest.mark.parametrize("dt", [0, 1], ids=["continuous", "discrete"])
def test_step_nostates(self, dt):
"""Constant system, continuous and discrete time.
gh-374 "Bug in step_response()"
"""
sys = TransferFunction([1], [1], dt)
t, y = step_response(sys)
np.testing.assert_allclose(y, np.ones(len(t)))
def assert_step_info_match(self, sys, info, info_ref):
"""Assert reasonable step_info accuracy."""
if sys.isdtime(strict=True):
dt = sys.dt
else:
_, dt = _ideal_tfinal_and_dt(sys, is_step=True)
for k in ['RiseTime', 'SettlingTime', 'PeakTime']:
np.testing.assert_allclose(info[k], info_ref[k], atol=dt,
err_msg=f"{k} does not match")
for k in ['Overshoot', 'Undershoot', 'Peak', 'SteadyStateValue']:
np.testing.assert_allclose(info[k], info_ref[k], rtol=5e-3,
err_msg=f"{k} does not match")
# steep gradient right after RiseTime
absrefinf = np.abs(info_ref['SteadyStateValue'])
if info_ref['RiseTime'] > 0:
y_next_sample_max = 0.8*absrefinf/info_ref['RiseTime']*dt
else:
y_next_sample_max = 0
for k in ['SettlingMin', 'SettlingMax']:
if (np.abs(info_ref[k]) - 0.9 * absrefinf) > y_next_sample_max:
# local min/max peak well after signal has risen
np.testing.assert_allclose(info[k], info_ref[k], rtol=1e-3)
@pytest.mark.parametrize(
"yfinal", [True, False], ids=["yfinal", "no yfinal"])
@pytest.mark.parametrize(
"systype, time_2d",
[("ltisys", False),
("time response", False),
("time response", True),
],
ids=["ltisys", "time response (n,)", "time response (1,n)"])
@pytest.mark.parametrize(
"tsystem",
["siso_tf_step_matlab",
"siso_ss_step_matlab",
"siso_tf_kpos",
"siso_tf_kneg",
"siso_tf_type1",
"siso_tf_asymptotic_from_neg1"],
indirect=["tsystem"])
def test_step_info(self, tsystem, systype, time_2d, yfinal):
"""Test step info for SISO systems."""
step_info_kwargs = tsystem.kwargs.get('step_info', {})
if systype == "time response":
# simulate long enough for steady state value
tfinal = 3 * tsystem.step_info['SettlingTime']
if np.isnan(tfinal):
pytest.skip("test system does not settle")
t, y = step_response(tsystem.sys, T=tfinal, T_num=5000)
sysdata = y
step_info_kwargs['T'] = t[np.newaxis, :] if time_2d else t
else:
sysdata = tsystem.sys
if yfinal:
step_info_kwargs['yfinal'] = tsystem.step_info['SteadyStateValue']
info = step_info(sysdata, **step_info_kwargs)
self.assert_step_info_match(tsystem.sys, info, tsystem.step_info)
@pytest.mark.parametrize(
"yfinal", [True, False], ids=["yfinal", "no_yfinal"])
@pytest.mark.parametrize(
"systype", ["ltisys", "time response"])
@pytest.mark.parametrize(
"tsystem",
['mimo_ss_step_matlab',
pytest.param('mimo_tf_step_info', marks=slycotonly)],
indirect=["tsystem"])
def test_step_info_mimo(self, tsystem, systype, yfinal):
"""Test step info for MIMO systems."""
step_info_kwargs = tsystem.kwargs.get('step_info', {})
if systype == "time response":
tfinal = 3 * max([S['SettlingTime']
for Srow in tsystem.step_info for S in Srow])
t, y = step_response(tsystem.sys, T=tfinal, T_num=5000)
sysdata = y
step_info_kwargs['T'] = t
else:
sysdata = tsystem.sys
if yfinal:
step_info_kwargs['yfinal'] = [[S['SteadyStateValue']
for S in Srow]
for Srow in tsystem.step_info]
info_dict = step_info(sysdata, **step_info_kwargs)
for i, row in enumerate(info_dict):
for j, info in enumerate(row):
self.assert_step_info_match(tsystem.sys,
info, tsystem.step_info[i][j])
def test_step_info_invalid(self):
"""Call step_info with invalid parameters."""
with pytest.raises(ValueError, match="time series data convention"):
step_info(["not numeric data"])
with pytest.raises(ValueError, match="time series data convention"):
step_info(np.ones((10, 15))) # invalid shape
with pytest.raises(ValueError, match="matching time vector"):
step_info(np.ones(15), T=np.linspace(0, 1, 20)) # time too long
with pytest.raises(ValueError, match="matching time vector"):
step_info(np.ones((2, 2, 15))) # no time vector
@pytest.mark.parametrize("tsystem",
[("no_pole_cancellation", "pole_cancellation")],
indirect=True)
def test_step_pole_cancellation(self, tsystem):
# confirm that pole-zero cancellation doesn't perturb results
# https://github.com/python-control/python-control/issues/440
step_info_no_cancellation = step_info(tsystem[0].sys)
step_info_cancellation = step_info(tsystem[1].sys)
self.assert_step_info_match(tsystem[0].sys,
step_info_no_cancellation,
step_info_cancellation)
@pytest.mark.parametrize(
"tsystem, kwargs",
[("siso_ss2", {}),
("siso_ss2", {'X0': 0}),
("siso_ss2", {'X0': np.array([0, 0])}),
("siso_ss2", {'X0': 0, 'return_x': True}),
("siso_dtf0", {})],
indirect=["tsystem"])
def test_impulse_response_siso(self, tsystem, kwargs):
"""Test impulse response of SISO systems."""
sys = tsystem.sys
t = tsystem.t
yref = tsystem.yimpulse
out = impulse_response(sys, T=t, **kwargs)
tout, yout = out[:2]
assert len(out) == 3 if ('return_x', True) in kwargs.items() else 2
np.testing.assert_array_almost_equal(tout, t)
np.testing.assert_array_almost_equal(yout, yref, decimal=4)
@pytest.mark.parametrize("tsystem", ["mimo_ss2"], indirect=True)
def test_impulse_response_mimo(self, tsystem):
""""Test impulse response of MIMO systems."""
sys = tsystem.sys
t = tsystem.t
yref = tsystem.yimpulse
_t, y_00 = impulse_response(sys, T=t, input=0, output=0)
np.testing.assert_array_almost_equal(y_00, yref, decimal=4)
_t, y_11 = impulse_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_11, yref, decimal=4)
yref_notrim = np.zeros((2, len(t)))
yref_notrim[:1, :] = yref
_t, yy = impulse_response(sys, T=t, input=0)
np.testing.assert_array_almost_equal(yy[:,0,:], yref_notrim, decimal=4)
@pytest.mark.skipif(StrictVersion(sp.__version__) < "1.3",
reason="requires SciPy 1.3 or greater")
@pytest.mark.parametrize("tsystem", ["siso_tf1"], indirect=True)
def test_discrete_time_impulse(self, tsystem):
# discrete time impulse sampled version should match cont time
dt = 0.1
t = np.arange(0, 3, dt)
sys = tsystem.sys
sysdt = sys.sample(dt, 'impulse')
np.testing.assert_array_almost_equal(impulse_response(sys, t)[1],
impulse_response(sysdt, t)[1])
@pytest.mark.parametrize("tsystem", ["siso_ss1"], indirect=True)
def test_impulse_response_warnD(self, tsystem):
"""Test warning about direct feedthrough"""
with pytest.warns(UserWarning, match="System has direct feedthrough"):
_ = impulse_response(tsystem.sys, tsystem.t)
@pytest.mark.parametrize(
"kwargs",
[{},
{'X0': 0},
{'X0': np.array([0.5, 1])},
{'X0': np.array([[0.5], [1]])},
{'X0': np.array([0.5, 1]), 'return_x': True},
])
@pytest.mark.parametrize("tsystem", ["siso_ss1"], indirect=True)
def test_initial_response(self, tsystem, kwargs):
"""Test initial response of SISO system"""
sys = tsystem.sys
t = tsystem.t
x0 = kwargs.get('X0', 0)
yref = tsystem.yinitial if np.any(x0) else np.zeros_like(t)
out = initial_response(sys, T=t, **kwargs)
tout, yout = out[:2]
assert len(out) == 3 if ('return_x', True) in kwargs.items() else 2
np.testing.assert_array_almost_equal(tout, t)
np.testing.assert_array_almost_equal(yout, yref, decimal=4)
@pytest.mark.parametrize("tsystem", ["mimo_ss1"], indirect=True)
def test_initial_response_mimo(self, tsystem):
"""Test initial response of MIMO system"""
sys = tsystem.sys
t = tsystem.t
x0 = np.array([[.5], [1.], [.5], [1.]])
yref = tsystem.yinitial
yref_notrim = np.broadcast_to(yref, (2, len(t)))
_t, y_00 = initial_response(sys, T=t, X0=x0, input=0, output=0)
np.testing.assert_array_almost_equal(y_00, yref, decimal=4)
_t, y_11 = initial_response(sys, T=t, X0=x0, input=0, output=1)
np.testing.assert_array_almost_equal(y_11, yref, decimal=4)
_t, yy = initial_response(sys, T=t, X0=x0)
np.testing.assert_array_almost_equal(yy, yref_notrim, decimal=4)
@pytest.mark.parametrize("tsystem",
["siso_ss1", "siso_tf2"],
indirect=True)
def test_forced_response_step(self, tsystem):
"""Test forced response of SISO systems as step response"""
sys = tsystem.sys
t = tsystem.t
u = np.ones_like(t, dtype=float)
yref = tsystem.ystep
tout, yout = forced_response(sys, t, u)
np.testing.assert_array_almost_equal(tout, t)
np.testing.assert_array_almost_equal(yout, yref, decimal=4)
@pytest.mark.parametrize("u",
[np.zeros((10,), dtype=float),
0] # special algorithm
)
@pytest.mark.parametrize("tsystem", ["siso_ss1", "siso_tf2"],
indirect=True)
def test_forced_response_initial(self, tsystem, u):
"""Test forced response of SISO system as intitial response."""
sys = tsystem.sys
t = tsystem.t
x0 = tsystem.X0
yref = tsystem.yinitial
if isinstance(sys, StateSpace):
tout, yout = forced_response(sys, t, u, X0=x0)
np.testing.assert_array_almost_equal(tout, t)
np.testing.assert_array_almost_equal(yout, yref, decimal=4)
else:
with pytest.warns(UserWarning, match="Non-zero initial condition "
"given for transfer function"):
tout, yout = forced_response(sys, t, u, X0=x0)
@pytest.mark.parametrize("tsystem, useT",
[("mimo_ss1", True),
("mimo_dss2", True),
("mimo_dss2", False)],
indirect=["tsystem"])
def test_forced_response_mimo(self, tsystem, useT):
"""Test forced response of MIMO system"""
# first system: initial value, second system: step response
sys = tsystem.sys
t = tsystem.t
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.array([[.5], [1], [0], [0]])
yref = np.vstack([tsystem.yinitial, tsystem.ystep])
if useT:
_t, yout = forced_response(sys, t, u, x0)
else:
_t, yout = forced_response(sys, U=u, X0=x0)
np.testing.assert_array_almost_equal(yout, yref, decimal=4)
@pytest.mark.usefixtures("editsdefaults")
def test_forced_response_legacy(self):
# Define a system for testing
sys = ct.rss(2, 1, 1)
T = np.linspace(0, 10, 10)
U = np.sin(T)
"""Make sure that legacy version of forced_response works"""
ct.config.use_legacy_defaults("0.8.4")
# forced_response returns x by default
t, y = ct.step_response(sys, T)
t, y, x = ct.forced_response(sys, T, U)
ct.config.use_legacy_defaults("0.9.0")
# forced_response returns input/output by default
t, y = ct.step_response(sys, T)
t, y = ct.forced_response(sys, T, U)
t, y, x = ct.forced_response(sys, T, U, return_x=True)
@pytest.mark.parametrize(
"tsystem, fr_kwargs, refattr",
[pytest.param("siso_ss1",
{'T': np.linspace(0, 1, 10)}, 'yinitial',
id="ctime no U"),
pytest.param("siso_dss1",
{'T': np.arange(0, 5, 1,)}, 'yinitial',
id="dt=True, no U"),
pytest.param("siso_dtf1",
{'U': np.ones(5,)}, 'ystep',
id="dt=True, no T"),
pytest.param("siso_dtf2",
{'U': np.ones(25,)}, 'ystep',
id="dt=0.2, no T"),
pytest.param("siso_ss2_dtnone",
{'U': np.ones(10,)}, 'ystep',
id="dt=None, no T"),
pytest.param("siso_dtf3",
{'U': np.ones(10,)}, 'ystep',
id="dt with rounding error, no T"),
],
indirect=["tsystem"])
def test_forced_response_T_U(self, tsystem, fr_kwargs, refattr):
"""Test documented forced_response behavior for parameters T and U."""
if refattr == 'yinitial':
fr_kwargs['X0'] = tsystem.X0
t, y = forced_response(tsystem.sys, **fr_kwargs)
np.testing.assert_allclose(t, tsystem.t)
np.testing.assert_allclose(y, getattr(tsystem, refattr),
rtol=1e-3, atol=1e-5)
@pytest.mark.parametrize("tsystem", ["siso_ss1"], indirect=True)
def test_forced_response_invalid_c(self, tsystem):
"""Test invalid parameters."""
with pytest.raises(TypeError,
match="StateSpace.*or.*TransferFunction"):
forced_response("not a system")
with pytest.raises(ValueError, match="T.*is mandatory for continuous"):
forced_response(tsystem.sys)
with pytest.raises(ValueError, match="time values must be equally "
"spaced"):
forced_response(tsystem.sys, [0, 0.1, 0.12, 0.4])
@pytest.mark.parametrize("tsystem", ["siso_dss2"], indirect=True)
def test_forced_response_invalid_d(self, tsystem):
"""Test invalid parameters dtime with sys.dt > 0."""
with pytest.raises(ValueError, match="can't both be zero"):
forced_response(tsystem.sys)
with pytest.raises(ValueError, match="must have same elements"):
forced_response(tsystem.sys,
T=tsystem.t, U=np.random.randn(1, 12))
with pytest.raises(ValueError, match="must have same elements"):
forced_response(tsystem.sys,
T=tsystem.t, U=np.random.randn(12))
with pytest.raises(ValueError, match="must match sampling time"):
forced_response(tsystem.sys, T=tsystem.t*0.9)
with pytest.raises(ValueError, match="must be multiples of "
"sampling time"):
forced_response(tsystem.sys, T=tsystem.t*1.1)
# but this is ok
forced_response(tsystem.sys, T=tsystem.t*2)
@pytest.mark.parametrize("u, x0, xtrue",
[(np.zeros((10,)),
np.array([2., 3.]),
np.vstack([np.linspace(2, 5, 10),
np.full((10,), 3)])),
(np.ones((10,)),
np.array([0., 0.]),
np.vstack([0.5 * np.linspace(0, 1, 10)**2,
np.linspace(0, 1, 10)])),
(np.linspace(0, 1, 10),
np.array([0., 0.]),
np.vstack([np.linspace(0, 1, 10)**3 / 6.,
np.linspace(0, 1, 10)**2 / 2.]))],
ids=["zeros", "ones", "linear"])
def test_lsim_double_integrator(self, u, x0, xtrue):
"""Test forced response of double integrator"""
# Note: scipy.signal.lsim fails if A is not invertible
A = np.array([[0., 1.],
[0., 0.]])
B = np.array([[0.],
[1.]])
C = np.array([[1., 0.]])
D = 0.
sys = StateSpace(A, B, C, D)
t = np.linspace(0, 1, 10)
_t, yout, xout = forced_response(sys, t, u, x0, return_x=True)
np.testing.assert_array_almost_equal(xout, xtrue, decimal=6)
ytrue = np.squeeze(np.asarray(C.dot(xtrue)))
np.testing.assert_array_almost_equal(yout, ytrue, decimal=6)
@slycotonly
def test_step_robustness(self):
"Test robustness os step_response against denomiantors: gh-240"
# Create 2 input, 2 output system
num = [[[0], [1]], [[1], [0]]]
den1 = [[[1], [1,1]], [[1, 4], [1]]]
sys1 = TransferFunction(num, den1)
den2 = [[[1], [1e-10, 1, 1]], [[1, 4], [1]]] # slight perturbation
sys2 = TransferFunction(num, den2)
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)
@pytest.mark.parametrize(
"tfsys, tfinal",
[(TransferFunction(1, [1, .5]), 13.81551), # pole at 0.5
(TransferFunction(1, [1, .5]).sample(.1), 25), # discrete pole at 0.5
(TransferFunction(1, [1, .5, 0]), 25)]) # poles at 0.5 and 0
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)
@pytest.mark.parametrize("wn, zeta", [(10, 0), (100, 0), (100, .1)])
def test_auto_generated_time_vector_dt_cont1(self, wn, zeta):
"""Confirm a TF with a natural frequency of wn rad/s gets a
dt of 1/(ratio*wn)"""
dtref = 0.25133 / wn
tfsys = TransferFunction(1, [1, 2*zeta*wn, wn**2])
np.testing.assert_almost_equal(_ideal_tfinal_and_dt(tfsys)[1], dtref,
decimal=5)
def test_auto_generated_time_vector_dt_cont2(self):
"""A sampled tf keeps its dt"""
wn = 100
zeta = .1
tfsys = TransferFunction(1, [1, 2*zeta*wn, wn**2]).sample(.1)
tfinal, dt = _ideal_tfinal_and_dt(tfsys)
np.testing.assert_almost_equal(dt, .1)
T, _ = initial_response(tfsys)
np.testing.assert_almost_equal(np.diff(T[:2]), [.1])
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
@pytest.mark.parametrize("fun", [step_response,
impulse_response,
initial_response])
def test_default_timevector_functions_c(self, fun):
"""Test that functions can calculate the time vector automatically"""
sys = TransferFunction(1, [1, .5, 0])
_tfinal, _dt = _ideal_tfinal_and_dt(sys)
# test impose number of time steps
tout, _ = fun(sys, T_num=10)
assert len(tout) == 10
# test impose final time
tout, _ = fun(sys, T=100.)
np.testing.assert_allclose(tout[-1], 100., atol=0.5*_dt)
@pytest.mark.parametrize("fun", [step_response,
impulse_response,
initial_response])
@pytest.mark.parametrize("dt", [0.1, 0.112])
def test_default_timevector_functions_d(self, fun, dt):
"""Test that functions can calculate the time vector automatically"""
sys = TransferFunction(1, [1, .5, 0], dt)
# test impose number of time steps is ignored with dt given
tout, _ = fun(sys, T_num=15)
assert len(tout) != 15
# test impose final time
tout, _ = fun(sys, 100)
np.testing.assert_allclose(tout[-1], 100., atol=0.5*dt)
@pytest.mark.parametrize("tsystem",
["siso_ss2", # continuous
"siso_tf1",
"siso_dss1", # unspecified sampling time
"siso_dtf1",
"siso_dss2", # matching timebase
"siso_dtf2",
"siso_ss2_dtnone", # undetermined timebase
"mimo_ss2", # MIMO
pytest.param("mimo_tf2", marks=slycotonly),
"mimo_dss1",
pytest.param("mimo_dtf1", marks=slycotonly),
],
indirect=True)
@pytest.mark.parametrize("fun", [step_response,
impulse_response,
initial_response,
forced_response])
@pytest.mark.parametrize("squeeze", [None, True, False])
def test_time_vector(self, tsystem, fun, squeeze, matarrayout):
"""Test time vector handling and correct output convention
gh-239, gh-295
"""
sys = tsystem.sys
kw = {}
if hasattr(tsystem, "t"):
t = tsystem.t
kw['T'] = t
if fun == forced_response:
kw['U'] = np.vstack([np.sin(t) for i in range(sys.ninputs)])
elif fun == forced_response and isctime(sys, strict=True):
pytest.skip("No continuous forced_response without time vector.")
if hasattr(sys, "nstates"):
kw['X0'] = np.arange(sys.nstates) + 1
if sys.ninputs > 1 and fun in [step_response, impulse_response]:
kw['input'] = 1
if squeeze is not None:
kw['squeeze'] = squeeze
out = fun(sys, **kw)
tout, yout = out[:2]
assert tout.ndim == 1
if hasattr(tsystem, 't'):
# tout should always match t, which has shape (n, )
np.testing.assert_allclose(tout, tsystem.t)
elif fun == forced_response and sys.dt in [None, True]:
np.testing.assert_allclose(np.diff(tout), 1.)
if squeeze is False or not sys.issiso():
assert yout.shape[0] == sys.noutputs
assert yout.shape[-1] == tout.shape[0]
else:
assert yout.shape == tout.shape
if sys.isdtime(strict=True) and sys.dt is not True and not \
np.isclose(sys.dt, 0.5):
kw['T'] = np.arange(0, 5, 0.5) # incompatible timebase
with pytest.raises(ValueError):
fun(sys, **kw)
@pytest.mark.parametrize("squeeze", [None, True, False])
@pytest.mark.parametrize("tsystem", ["siso_dtf2"], indirect=True)
def test_time_vector_interpolation(self, tsystem, squeeze):
"""Test time vector handling in case of interpolation.
Interpolation of the input (to match scipy.signal.dlsim)
gh-239, gh-295
"""
sys = tsystem.sys
t = np.arange(0, 10, 1.)
u = np.sin(t)
x0 = 0
squeezekw = {} if squeeze is None else {"squeeze": squeeze}
tout, yout = forced_response(sys, t, u, x0,
interpolate=True, **squeezekw)
if squeeze is False or sys.noutputs > 1:
assert yout.shape[0] == sys.noutputs
assert yout.shape[1] == tout.shape[0]
else:
assert yout.shape == tout.shape
assert np.allclose(tout[1:] - tout[:-1], sys.dt)
@pytest.mark.parametrize("tsystem", ["siso_dtf2"], indirect=True)
def test_discrete_time_steps(self, tsystem):
"""Make sure rounding errors in sample time are handled properly
These tests play around with the input time vector to make sure that
small rounding errors don't generate spurious errors.
gh-332
"""
sys = tsystem.sys
# Set up a time range and simulate
T = np.arange(0, 100, 0.2)
tout1, yout1 = step_response(sys, T)
# Simulate every other time step
T = np.arange(0, 100, 0.4)
tout2, yout2 = step_response(sys, T)
np.testing.assert_array_almost_equal(tout1[::2], tout2)
np.testing.assert_array_almost_equal(yout1[::2], yout2)
# Add a small error into some of the time steps
T = np.arange(0, 100, 0.2)
T[1:-2:2] -= 1e-12 # tweak second value and a few others
tout3, yout3 = step_response(sys, T)
np.testing.assert_array_almost_equal(tout1, tout3)
np.testing.assert_array_almost_equal(yout1, yout3)
# Add a small error into some of the time steps (w/ skipping)
T = np.arange(0, 100, 0.4)
T[1:-2:2] -= 1e-12 # tweak second value and a few others
tout4, yout4 = step_response(sys, T)
np.testing.assert_array_almost_equal(tout2, tout4)
np.testing.assert_array_almost_equal(yout2, yout4)
# Make sure larger errors *do* generate an error
T = np.arange(0, 100, 0.2)
T[1:-2:2] -= 1e-3 # change second value and a few others
with pytest.raises(ValueError):
step_response(sys, T)
@pytest.mark.parametrize("tsystem", ["siso_ss1"], indirect=True)
def test_time_series_data_convention_2D(self, tsystem):
"""Allow input time as 2D array (output should be 1D)"""
tin = np.array(np.linspace(0, 10, 100), ndmin=2)
t, y = step_response(tsystem.sys, tin)
assert isinstance(t, np.ndarray) and not isinstance(t, np.matrix)
assert t.ndim == 1
assert y.ndim == 1 # SISO returns "scalar" output
assert t.shape == y.shape # Allows direct plotting of output
@pytest.mark.usefixtures("editsdefaults")
@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.ss2io])
@pytest.mark.parametrize("nstate, nout, ninp, squeeze, shape1, shape2", [
# state out in squeeze in/out out-only
[1, 1, 1, None, (8,), (8,)],
[2, 1, 1, True, (8,), (8,)],
[3, 1, 1, False, (1, 1, 8), (1, 8)],
[3, 2, 1, None, (2, 1, 8), (2, 8)],
[4, 2, 1, True, (2, 8), (2, 8)],
[5, 2, 1, False, (2, 1, 8), (2, 8)],
[3, 1, 2, None, (1, 2, 8), (1, 8)],
[4, 1, 2, True, (2, 8), (8,)],
[5, 1, 2, False, (1, 2, 8), (1, 8)],
[4, 2, 2, None, (2, 2, 8), (2, 8)],
[5, 2, 2, True, (2, 2, 8), (2, 8)],
[6, 2, 2, False, (2, 2, 8), (2, 8)],
])
def test_squeeze(self, fcn, nstate, nout, ninp, squeeze, shape1, shape2):