def test_squeeze_exceptions(self, fcn):
if fcn == ct.frd:
sys = fcn(ct.rss(2, 1, 1), [1e-2, 1e-1, 1, 1e1, 1e2])
else:
sys = fcn(ct.rss(2, 1, 1))
with pytest.raises(ValueError, match="unknown squeeze value"):
sys.frequency_response([1], squeeze=1)
with pytest.raises(ValueError, match="unknown squeeze value"):
sys([1j], squeeze='siso')
with pytest.raises(ValueError, match="unknown squeeze value"):
evalfr(sys, [1j], squeeze='siso')
with pytest.raises(ValueError, match="must be 1D"):
sys.frequency_response([[0.1, 1], [1, 10]])
with pytest.raises(ValueError, match="must be 1D"):
sys([[0.1j, 1j], [1j, 10j]])
with pytest.raises(ValueError, match="must be 1D"):
evalfr(sys, [[0.1j, 1j], [1j, 10j]])
with pytest.warns(DeprecationWarning, match="LTI `inputs`"):
ninputs = sys.inputs
assert ninputs == sys.ninputs
with pytest.warns(DeprecationWarning, match="LTI `outputs`"):
noutputs = sys.outputs
assert noutputs == sys.noutputs
if isinstance(sys, ct.StateSpace):
with pytest.warns(DeprecationWarning, match="StateSpace `states`"):
nstates = sys.states
assert nstates == sys.nstates
def test_squeeze(self, fcn, nstate, nout, ninp, omega, squeeze, shape,
omega_type):
"""Test correct behavior of frequencey response squeeze parameter."""
# Create the system to be tested
if fcn == ct.frd:
sys = fcn(ct.rss(nstate, nout, ninp), [1e-2, 1e-1, 1, 1e1, 1e2])
elif fcn == ct.tf and (nout > 1 or ninp > 1) and not slycot_check():
pytest.skip("Conversion of MIMO systems to transfer functions "
"requires slycot.")
else:
sys = fcn(ct.rss(nstate, nout, ninp))
if omega_type == "numpy":
omega = np.asarray(omega)
isscalar = omega.ndim == 0
# keep the ndarray type even for scalars
s = np.asarray(omega * 1j)
else:
isscalar = not hasattr(omega, '__len__')
if isscalar:
s = omega * 1J
else:
s = [w * 1J for w in omega]
# Call the transfer function directly and make sure shape is correct
assert sys(s, squeeze=squeeze).shape == shape
# Make sure that evalfr also works as expected
assert ct.evalfr(sys, s, squeeze=squeeze).shape == shape
# Check frequency response
mag, phase, _ = sys.frequency_response(omega, squeeze=squeeze)
if isscalar and squeeze is not True:
# sys.frequency_response() expects a list as an argument
# Add the shape of the input to the expected shape
assert mag.shape == shape + (1, )
assert phase.shape == shape + (1, )
else:
assert mag.shape == shape
assert phase.shape == shape
# Make sure the default shape lines up with squeeze=None case
if squeeze is None:
assert sys(s).shape == shape
# Changing config.default to False should return 3D frequency response
ct.config.set_defaults('control', squeeze_frequency_response=False)
mag, phase, _ = sys.frequency_response(omega)
if isscalar:
assert mag.shape == (sys.noutputs, sys.ninputs, 1)
assert phase.shape == (sys.noutputs, sys.ninputs, 1)
assert sys(s).shape == (sys.noutputs, sys.ninputs)
assert ct.evalfr(sys, s).shape == (sys.noutputs, sys.ninputs)
else:
assert mag.shape == (sys.noutputs, sys.ninputs, len(omega))
assert phase.shape == (sys.noutputs, sys.ninputs, len(omega))
assert sys(s).shape == \
(sys.noutputs, sys.ninputs, len(omega))
assert ct.evalfr(sys, s).shape == \
(sys.noutputs, sys.ninputs, len(omega))
def testAcker(self, fixedseed):
for states in range(1, self.maxStates):
for i in range(self.maxTries):
# start with a random SS system and transform to TF then
# back to SS, check that the matrices are the same.
sys = rss(states, 1, 1)
if (self.debug):
print(sys)
# Make sure the system is not degenerate
Cmat = ctrb(sys.A, sys.B)
if np.linalg.matrix_rank(Cmat) != states:
if (self.debug):
print(" skipping (not reachable or ill conditioned)")
continue
# Place the poles at random locations
des = rss(states, 1, 1)
poles = pole(des)
# Now place the poles using acker
K = acker(sys.A, sys.B, poles)
new = ss(sys.A - sys.B * K, sys.B, sys.C, sys.D)
placed = pole(new)
# Debugging code
# diff = np.sort(poles) - np.sort(placed)
# if not all(diff < 0.001):
# print("Found a problem:")
# print(sys)
# print("desired = ", poles)
np.testing.assert_array_almost_equal(np.sort(poles),
np.sort(placed),
decimal=4)
def test_nyquist_exceptions():
# MIMO not implemented
sys = ct.rss(2, 2, 2)
with pytest.raises(ct.exception.ControlMIMONotImplemented,
match="only supports SISO"):
ct.nyquist_plot(sys)
# Legacy keywords for arrow size
sys = ct.rss(2, 1, 1)
with pytest.warns(FutureWarning, match="use `arrow_size` instead"):
ct.nyquist_plot(sys, arrow_width=8, arrow_length=6)
# Unknown arrow keyword
with pytest.raises(ValueError, match="unsupported arrow location"):
ct.nyquist_plot(sys, arrows='uniform')
# Bad value for indent direction
sys = ct.tf([1], [1, 0, 1])
with pytest.raises(ValueError, match="unknown value for indent"):
ct.nyquist_plot(sys, indent_direction='up')
# Discrete time system sampled above Nyquist frequency
sys = ct.drss(2, 1, 1)
sys.dt = 0.01
with pytest.warns(UserWarning, match="above Nyquist"):
ct.nyquist_plot(sys, np.logspace(-2, 3))
def test_interconnect_docstring():
"""Test the examples from the interconnect() docstring"""
# MIMO interconnection (note: use [C, P] instead of [P, C] for state order)
P = ct.LinearIOSystem(
ct.rss(2, 2, 2, strictly_proper=True), name='P')
C = ct.LinearIOSystem(ct.rss(2, 2, 2), name='C')
T = ct.interconnect(
[C, P],
connections = [
['P.u[0]', 'C.y[0]'], ['P.u[1]', 'C.y[1]'],
['C.u[0]', '-P.y[0]'], ['C.u[1]', '-P.y[1]']],
inplist = ['C.u[0]', 'C.u[1]'],
outlist = ['P.y[0]', 'P.y[1]'],
)
T_ss = ct.feedback(P * C, ct.ss([], [], [], np.eye(2)))
np.testing.assert_almost_equal(T.A, T_ss.A)
np.testing.assert_almost_equal(T.B, T_ss.B)
np.testing.assert_almost_equal(T.C, T_ss.C)
np.testing.assert_almost_equal(T.D, T_ss.D)
# Implicit interconnection (note: use [C, P, sumblk] for proper state order)
P = ct.tf2io(ct.tf(1, [1, 0]), inputs='u', outputs='y')
C = ct.tf2io(ct.tf(10, [1, 1]), inputs='e', outputs='u')
sumblk = ct.summing_junction(inputs=['r', '-y'], output='e')
T = ct.interconnect([C, P, sumblk], inplist='r', outlist='y')
T_ss = ct.feedback(P * C, 1)
np.testing.assert_almost_equal(T.A, T_ss.A)
np.testing.assert_almost_equal(T.B, T_ss.B)
np.testing.assert_almost_equal(T.C, T_ss.C)
np.testing.assert_almost_equal(T.D, T_ss.D)
def test_response_copy():
# Generate some initial data to use
sys_siso = ct.rss(4, 1, 1)
response_siso = ct.step_response(sys_siso)
siso_ntimes = response_siso.time.size
sys_mimo = ct.rss(4, 2, 1)
response_mimo = ct.step_response(sys_mimo)
mimo_ntimes = response_mimo.time.size
# Transpose
response_mimo_transpose = response_mimo(transpose=True)
assert response_mimo.outputs.shape == (2, 1, mimo_ntimes)
assert response_mimo_transpose.outputs.shape == (mimo_ntimes, 2, 1)
assert response_mimo.states.shape == (4, 1, mimo_ntimes)
assert response_mimo_transpose.states.shape == (mimo_ntimes, 4, 1)
# Squeeze
response_siso_as_mimo = response_siso(squeeze=False)
assert response_siso_as_mimo.outputs.shape == (1, 1, siso_ntimes)
assert response_siso_as_mimo.states.shape == (4, 1, siso_ntimes)
assert response_siso_as_mimo._legacy_states.shape == (4, siso_ntimes)
response_mimo_squeezed = response_mimo(squeeze=True)
assert response_mimo_squeezed.outputs.shape == (2, mimo_ntimes)
assert response_mimo_squeezed.states.shape == (4, mimo_ntimes)
assert response_mimo_squeezed._legacy_states.shape == (4, 1, mimo_ntimes)
# Squeeze and transpose
response_mimo_sqtr = response_mimo(squeeze=True, transpose=True)
assert response_mimo_sqtr.outputs.shape == (mimo_ntimes, 2)
assert response_mimo_sqtr.states.shape == (mimo_ntimes, 4)
assert response_mimo_sqtr._legacy_states.shape == (mimo_ntimes, 4, 1)
# Return_x
t, y = response_mimo
t, y = response_mimo()
t, y, x = response_mimo(return_x=True)
with pytest.raises(ValueError, match="too many"):
t, y = response_mimo(return_x=True)
with pytest.raises(ValueError, match="not enough"):
t, y, x = response_mimo
# Labels
assert response_mimo.output_labels is None
assert response_mimo.state_labels is None
assert response_mimo.input_labels is None
response = response_mimo(
output_labels=['y1', 'y2'], input_labels='u',
state_labels=["x[%d]" % i for i in range(4)])
assert response.output_labels == ['y1', 'y2']
assert response.state_labels == ['x[0]', 'x[1]', 'x[2]', 'x[3]']
assert response.input_labels == ['u']
# Unknown keyword
with pytest.raises(ValueError, match="Unknown parameter(s)*"):
response_bad_kw = response_mimo(input=0)
def test_duplicate_sysname():
# Start with an unnamed system
sys = ct.rss(4, 1, 1)
# No warnings should be generated if we reuse an an unnamed system
with pytest.warns(None) as record:
res = sys * sys
assert not any([type(msg) == UserWarning for msg in record])
# Generate a warning if the system is named
sys = ct.rss(4, 1, 1, name='sys')
with pytest.warns(UserWarning, match="duplicate object found"):
res = sys * sys
def test_squeeze(self, fcn, nstate, nout, ninp, omega, squeeze, shape):
# Create the system to be tested
if fcn == ct.frd:
sys = fcn(ct.rss(nstate, nout, ninp), [1e-2, 1e-1, 1, 1e1, 1e2])
elif fcn == ct.tf and (nout > 1 or ninp > 1) and not slycot_check():
pytest.skip("Conversion of MIMO systems to transfer functions "
"requires slycot.")
else:
sys = fcn(ct.rss(nstate, nout, ninp))
# Convert the frequency list to an array for easy of use
isscalar = not hasattr(omega, '__len__')
omega = np.array(omega)
# Call the transfer function directly and make sure shape is correct
assert sys(omega * 1j, squeeze=squeeze).shape == shape
# Make sure that evalfr also works as expected
assert ct.evalfr(sys, omega * 1j, squeeze=squeeze).shape == shape
# Check frequency response
mag, phase, _ = sys.frequency_response(omega, squeeze=squeeze)
if isscalar and squeeze is not True:
# sys.frequency_response() expects a list as an argument
# Add the shape of the input to the expected shape
assert mag.shape == shape + (1, )
assert phase.shape == shape + (1, )
else:
assert mag.shape == shape
assert phase.shape == shape
# Make sure the default shape lines up with squeeze=None case
if squeeze is None:
assert sys(omega * 1j).shape == shape
# Changing config.default to False should return 3D frequency response
ct.config.set_defaults('control', squeeze_frequency_response=False)
mag, phase, _ = sys.frequency_response(omega)
if isscalar:
assert mag.shape == (sys.noutputs, sys.ninputs, 1)
assert phase.shape == (sys.noutputs, sys.ninputs, 1)
assert sys(omega * 1j).shape == (sys.noutputs, sys.ninputs)
assert ct.evalfr(sys,
omega * 1j).shape == (sys.noutputs, sys.ninputs)
else:
assert mag.shape == (sys.noutputs, sys.ninputs, len(omega))
assert phase.shape == (sys.noutputs, sys.ninputs, len(omega))
assert sys(omega * 1j).shape == \
(sys.noutputs, sys.ninputs, len(omega))
assert ct.evalfr(sys, omega * 1j).shape == \
(sys.noutputs, sys.ninputs, len(omega))
def test_init_namedif():
# Set up the initial system
sys = ct.rss(2, 1, 1)
# Rename the system, inputs, and outouts
sys_new = sys.copy()
ct.StateSpace.__init__(sys_new, sys, inputs='u', outputs='y', name='new')
assert sys_new.name == 'new'
assert sys_new.input_labels == ['u']
assert sys_new.output_labels == ['y']
# Call constructor without re-initialization
sys_keep = sys.copy()
ct.StateSpace.__init__(sys_keep, sys, init_namedio=False)
assert sys_keep.name == sys_keep.name
assert sys_keep.input_labels == sys_keep.input_labels
assert sys_keep.output_labels == sys_keep.output_labels
# Make sure that passing an unrecognized keyword generates an error
with pytest.raises(TypeError, match="unrecognized keyword"):
ct.StateSpace.__init__(sys_keep,
sys,
inputs='u',
outputs='y',
init_namedio=False)
def test_response_transpose(self, nstate, nout, ninp, squeeze, ysh_in,
ysh_no, xsh_in):
sys = ct.rss(nstate, nout, ninp)
T = np.linspace(0, 1, 8)
# Step response - input indexed
t, y, x = ct.step_response(sys,
T,
transpose=True,
return_x=True,
squeeze=squeeze)
assert t.shape == (T.size, )
assert y.shape == ysh_in
assert x.shape == xsh_in
# Initial response - no input indexing
t, y, x = ct.initial_response(sys,
T,
1,
transpose=True,
return_x=True,
squeeze=squeeze)
assert t.shape == (T.size, )
assert y.shape == ysh_no
assert x.shape == (T.size, sys.nstates)
def tsys(self):
"""Create some systems for testing"""
class Tsys:
pass
T = Tsys()
# Single input, single output continuous and discrete time systems
sys = rss(3, 1, 1)
T.siso_ss1 = StateSpace(sys.A, sys.B, sys.C, sys.D, None)
T.siso_ss1c = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.0)
T.siso_ss1d = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.1)
T.siso_ss2d = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.2)
T.siso_ss3d = StateSpace(sys.A, sys.B, sys.C, sys.D, True)
# Two input, two output continuous time system
A = [[-3., 4., 2.], [-1., -3., 0.], [2., 5., 3.]]
B = [[1., 4.], [-3., -3.], [-2., 1.]]
C = [[4., 2., -3.], [1., 4., 3.]]
D = [[-2., 4.], [0., 1.]]
T.mimo_ss1 = StateSpace(A, B, C, D, None)
T.mimo_ss1c = StateSpace(A, B, C, D, 0)
# Two input, two output discrete time system
T.mimo_ss1d = StateSpace(A, B, C, D, 0.1)
# Same system, but with a different sampling time
T.mimo_ss2d = StateSpace(A, B, C, D, 0.2)
# Single input, single output continuus and discrete transfer function
T.siso_tf1 = TransferFunction([1, 1], [1, 2, 1], None)
T.siso_tf1c = TransferFunction([1, 1], [1, 2, 1], 0)
T.siso_tf1d = TransferFunction([1, 1], [1, 2, 1], 0.1)
T.siso_tf2d = TransferFunction([1, 1], [1, 2, 1], 0.2)
T.siso_tf3d = TransferFunction([1, 1], [1, 2, 1], True)
return T
def test_size_mismatch(self):
sys1 = FRD(ct.rss(2, 2, 2), np.logspace(-1, 1, 10))
# Different number of inputs
sys2 = FRD(ct.rss(3, 1, 2), np.logspace(-1, 1, 10))
self.assertRaises(ValueError, FRD.__add__, sys1, sys2)
# Different number of outputs
sys2 = FRD(ct.rss(3, 2, 1), np.logspace(-1, 1, 10))
self.assertRaises(ValueError, FRD.__add__, sys1, sys2)
# Inputs and outputs don't match
self.assertRaises(ValueError, FRD.__mul__, sys2, sys1)
# Feedback mismatch
self.assertRaises(ValueError, FRD.feedback, sys2, sys1)
def test_lqe_discrete():
"""Test overloading of lqe operator for discrete time systems"""
csys = ct.rss(2, 1, 1)
dsys = ct.drss(2, 1, 1)
Q = np.eye(1)
R = np.eye(1)
# Calling with a system versus explicit A, B should be the sam
K_csys, S_csys, E_csys = ct.lqe(csys, Q, R)
K_expl, S_expl, E_expl = ct.lqe(csys.A, csys.B, csys.C, Q, R)
np.testing.assert_almost_equal(K_csys, K_expl)
np.testing.assert_almost_equal(S_csys, S_expl)
np.testing.assert_almost_equal(E_csys, E_expl)
# Calling lqe() with a discrete time system should call dlqe()
K_lqe, S_lqe, E_lqe = ct.lqe(dsys, Q, R)
K_dlqe, S_dlqe, E_dlqe = ct.dlqe(dsys, Q, R)
np.testing.assert_almost_equal(K_lqe, K_dlqe)
np.testing.assert_almost_equal(S_lqe, S_dlqe)
np.testing.assert_almost_equal(E_lqe, E_dlqe)
# Calling lqe() with no timebase should call lqe()
asys = ct.ss(csys.A, csys.B, csys.C, csys.D, dt=None)
K_asys, S_asys, E_asys = ct.lqe(asys, Q, R)
K_expl, S_expl, E_expl = ct.lqe(csys.A, csys.B, csys.C, Q, R)
np.testing.assert_almost_equal(K_asys, K_expl)
np.testing.assert_almost_equal(S_asys, S_expl)
np.testing.assert_almost_equal(E_asys, E_expl)
# Calling dlqe() with a continuous time system should raise an error
with pytest.raises(ControlArgument, match="called with a continuous"):
K, S, E = ct.dlqe(csys, Q, R)
def test_interconnect_exceptions():
# First make sure the docstring example works
P = ct.tf2io(ct.tf(1, [1, 0]), input='u', output='y')
C = ct.tf2io(ct.tf(10, [1, 1]), input='e', output='u')
sumblk = ct.summing_junction(inputs=['r', '-y'], output='e')
T = ct.interconnect((P, C, sumblk), input='r', output='y')
assert (T.ninputs, T.noutputs, T.nstates) == (1, 1, 2)
# Unrecognized arguments
# LinearIOSystem
with pytest.raises(TypeError, match="unknown parameter"):
P = ct.LinearIOSystem(ct.rss(2, 1, 1), output_name='y')
# Interconnect
with pytest.raises(TypeError, match="unknown parameter"):
T = ct.interconnect((P, C, sumblk), input_name='r', output='y')
# Interconnected system
with pytest.raises(TypeError, match="unknown parameter"):
T = ct.InterconnectedSystem((P, C, sumblk), input_name='r', output='y')
# NonlinearIOSytem
with pytest.raises(TypeError, match="unknown parameter"):
nlios = ct.NonlinearIOSystem(
None, lambda t, x, u, params: u*u, input_count=1, output_count=1)
# Summing junction
with pytest.raises(TypeError, match="input specification is required"):
sumblk = ct.summing_junction()
with pytest.raises(TypeError, match="unknown parameter"):
sumblk = ct.summing_junction(input_count=2, output_count=2)
def test_size_mismatch(self):
sys1 = FRD(ct.rss(2, 2, 2), np.logspace(-1, 1, 10))
# Different number of inputs
sys2 = FRD(ct.rss(3, 1, 2), np.logspace(-1, 1, 10))
self.assertRaises(ValueError, FRD.__add__, sys1, sys2)
# Different number of outputs
sys2 = FRD(ct.rss(3, 2, 1), np.logspace(-1, 1, 10))
self.assertRaises(ValueError, FRD.__add__, sys1, sys2)
# Inputs and outputs don't match
self.assertRaises(ValueError, FRD.__mul__, sys2, sys1)
# Feedback mismatch
self.assertRaises(ValueError, FRD.feedback, sys2, sys1)
def test_named_ss():
# Create a system to play with
sys = ct.rss(2, 2, 2)
assert sys.input_labels == ['u[0]', 'u[1]']
assert sys.output_labels == ['y[0]', 'y[1]']
assert sys.state_labels == ['x[0]', 'x[1]']
# Get the state matrices for later use
A, B, C, D = sys.A, sys.B, sys.C, sys.D
# Set up a named state space systems with default names
ct.namedio.NamedIOSystem._idCounter = 0
sys = ct.ss(A, B, C, D)
assert sys.name == 'sys[0]'
assert sys.input_labels == ['u[0]', 'u[1]']
assert sys.output_labels == ['y[0]', 'y[1]']
assert sys.state_labels == ['x[0]', 'x[1]']
assert repr(sys) == \
"<LinearIOSystem:sys[0]:['u[0]', 'u[1]']->['y[0]', 'y[1]']>"
# Pass the names as arguments
sys = ct.ss(A,
B,
C,
D,
name='system',
inputs=['u1', 'u2'],
outputs=['y1', 'y2'],
states=['x1', 'x2'])
assert sys.name == 'system'
assert ct.namedio.NamedIOSystem._idCounter == 1
assert sys.input_labels == ['u1', 'u2']
assert sys.output_labels == ['y1', 'y2']
assert sys.state_labels == ['x1', 'x2']
assert repr(sys) == \
"<LinearIOSystem:system:['u1', 'u2']->['y1', 'y2']>"
# Do the same with rss
sys = ct.rss(['x1', 'x2', 'x3'], ['y1', 'y2'], 'u1', name='random')
assert sys.name == 'random'
assert ct.namedio.NamedIOSystem._idCounter == 1
assert sys.input_labels == ['u1']
assert sys.output_labels == ['y1', 'y2']
assert sys.state_labels == ['x1', 'x2', 'x3']
assert repr(sys) == \
"<LinearIOSystem:random:['u1']->['y1', 'y2']>"
def test_nyquist_exceptions():
# MIMO not implemented
sys = ct.rss(2, 2, 2)
with pytest.raises(ct.exception.ControlMIMONotImplemented,
match="only supports SISO"):
ct.nyquist_plot(sys)
# Legacy keywords for arrow size
sys = ct.rss(2, 1, 1)
with pytest.warns(FutureWarning, match="use `arrow_size` instead"):
ct.nyquist_plot(sys, arrow_width=8, arrow_length=6)
# Discrete time system sampled above Nyquist frequency
sys = ct.drss(2, 1, 1)
sys.dt = 0.01
with pytest.warns(UserWarning, match="above Nyquist"):
ct.nyquist_plot(sys, np.logspace(-2, 3))
def test_string_inputoutput():
# regression test for gh-692
P1 = ct.rss(2, 1, 1)
P1_iosys = ct.LinearIOSystem(P1, inputs='u1', outputs='y1')
P2 = ct.rss(2, 1, 1)
P2_iosys = ct.LinearIOSystem(P2, inputs='y1', outputs='y2')
P_s1 = ct.interconnect([P1_iosys, P2_iosys], inputs='u1', outputs=['y2'])
assert P_s1.input_index == {'u1' : 0}
P_s2 = ct.interconnect([P1_iosys, P2_iosys], input='u1', outputs=['y2'])
assert P_s2.input_index == {'u1' : 0}
P_s1 = ct.interconnect([P1_iosys, P2_iosys], inputs=['u1'], outputs='y2')
assert P_s1.output_index == {'y2' : 0}
P_s2 = ct.interconnect([P1_iosys, P2_iosys], inputs=['u1'], output='y2')
assert P_s2.output_index == {'y2' : 0}
def test_printing(self):
"""Print SISO"""
sys = ss2tf(rss(4, 1, 1))
assert isinstance(str(sys), str)
assert isinstance(sys._repr_latex_(), str)
# SISO, discrete time
sys = sample_system(sys, 1)
assert isinstance(str(sys), str)
assert isinstance(sys._repr_latex_(), str)
def test_frequency_response():
# Create an SISO frequence response
sys = ct.rss(2, 2, 2)
omega = np.logspace(-2, 2, 20)
resp = ct.frequency_response(sys, omega)
eval = sys(omega * 1j)
# Make sure we get the right answers in various ways
np.testing.assert_equal(resp.magnitude, np.abs(eval))
np.testing.assert_equal(resp.phase, np.angle(eval))
np.testing.assert_equal(resp.omega, omega)
# Make sure that we can change the properties of the response
sys = ct.rss(2, 1, 1)
resp_default = ct.frequency_response(sys, omega)
mag_default, phase_default, omega_default = resp_default
assert mag_default.ndim == 1
assert phase_default.ndim == 1
assert omega_default.ndim == 1
assert mag_default.shape[0] == omega_default.shape[0]
assert phase_default.shape[0] == omega_default.shape[0]
resp_nosqueeze = ct.frequency_response(sys, omega, squeeze=False)
mag_nosqueeze, phase_nosqueeze, omega_nosqueeze = resp_nosqueeze
assert mag_nosqueeze.ndim == 3
assert phase_nosqueeze.ndim == 3
assert omega_nosqueeze.ndim == 1
assert mag_nosqueeze.shape[2] == omega_nosqueeze.shape[0]
assert phase_nosqueeze.shape[2] == omega_nosqueeze.shape[0]
# Try changing the response
resp_def_nosq = resp_default(squeeze=False)
mag_def_nosq, phase_def_nosq, omega_def_nosq = resp_def_nosq
assert mag_def_nosq.shape == mag_nosqueeze.shape
assert phase_def_nosq.shape == phase_nosqueeze.shape
assert omega_def_nosq.shape == omega_nosqueeze.shape
resp_nosq_sq = resp_nosqueeze(squeeze=True)
mag_nosq_sq, phase_nosq_sq, omega_nosq_sq = resp_nosq_sq
assert mag_nosq_sq.shape == mag_default.shape
assert phase_nosq_sq.shape == phase_default.shape
assert omega_nosq_sq.shape == omega_default.shape
def test_lqr_call_format(self, cdlqr):
# Create a random state space system for testing
sys = rss(2, 3, 2)
sys.dt = None # treat as either continuous or discrete time
# Weighting matrices
Q = np.eye(sys.nstates)
R = np.eye(sys.ninputs)
N = np.zeros((sys.nstates, sys.ninputs))
# Standard calling format
Kref, Sref, Eref = cdlqr(sys.A, sys.B, Q, R)
# Call with system instead of matricees
K, S, E = cdlqr(sys, Q, R)
np.testing.assert_array_almost_equal(Kref, K)
np.testing.assert_array_almost_equal(Sref, S)
np.testing.assert_array_almost_equal(Eref, E)
# Pass a cross-weighting matrix
K, S, E = cdlqr(sys, Q, R, N)
np.testing.assert_array_almost_equal(Kref, K)
np.testing.assert_array_almost_equal(Sref, S)
np.testing.assert_array_almost_equal(Eref, E)
# Inconsistent system dimensions
with pytest.raises(ct.ControlDimension, match="Incompatible dimen"):
K, S, E = cdlqr(sys.A, sys.C, Q, R)
# Incorrect covariance matrix dimensions
with pytest.raises(ct.ControlDimension, match="Q must be a square"):
K, S, E = cdlqr(sys.A, sys.B, sys.C, R, Q)
# Too few input arguments
with pytest.raises(ct.ControlArgument, match="not enough input"):
K, S, E = cdlqr(sys.A, sys.B)
# First argument is the wrong type (use SISO for non-slycot tests)
sys_tf = tf(rss(3, 1, 1))
sys_tf.dt = None # treat as either continuous or discrete time
with pytest.raises(ct.ControlArgument, match="LTI system must be"):
K, S, E = cdlqr(sys_tf, Q, R)
def test_size_mismatch(self):
"""Test size mismacht"""
sys1 = ss2tf(rss(2, 2, 2))
# Different number of inputs
sys2 = ss2tf(rss(3, 1, 2))
with pytest.raises(ValueError):
TransferFunction.__add__(sys1, sys2)
# Different number of outputs
sys2 = ss2tf(rss(3, 2, 1))
with pytest.raises(ValueError):
TransferFunction.__add__(sys1, sys2)
# Inputs and outputs don't match
with pytest.raises(ValueError):
TransferFunction.__mul__(sys2, sys1)
# Feedback mismatch (MIMO not implemented)
with pytest.raises(NotImplementedError):
TransferFunction.feedback(sys2, sys1)
def test_squeeze_0_8_4(self, nstate, nout, ninp, squeeze, shape):
# Set defaults to match release 0.8.4
ct.config.use_legacy_defaults('0.8.4')
ct.config.use_numpy_matrix(False)
# Generate system, time, and input vectors
sys = ct.rss(nstate, nout, ninp, strictly_proper=True)
tvec = np.linspace(0, 1, 8)
uvec =np.ones((sys.ninputs, 1)) @ np.reshape(np.sin(tvec), (1, 8))
_, yvec = ct.initial_response(sys, tvec, 1, squeeze=squeeze)
assert yvec.shape == shape
def test_lqe_call_format(cdlqe):
# Create a random state space system for testing
sys = rss(4, 3, 2)
sys.dt = None # treat as either continuous or discrete time
# Covariance matrices
Q = np.eye(sys.ninputs)
R = np.eye(sys.noutputs)
N = np.zeros((sys.ninputs, sys.noutputs))
# Standard calling format
Lref, Pref, Eref = cdlqe(sys.A, sys.B, sys.C, Q, R)
# Call with system instead of matricees
L, P, E = cdlqe(sys, Q, R)
np.testing.assert_almost_equal(Lref, L)
np.testing.assert_almost_equal(Pref, P)
np.testing.assert_almost_equal(Eref, E)
# Make sure we get an error if we specify N
with pytest.raises(ct.ControlNotImplemented):
L, P, E = cdlqe(sys, Q, R, N)
# Inconsistent system dimensions
with pytest.raises(ct.ControlDimension, match="Incompatible"):
L, P, E = cdlqe(sys.A, sys.C, sys.B, Q, R)
# Incorrect covariance matrix dimensions
with pytest.raises(ct.ControlDimension, match="Incompatible"):
L, P, E = cdlqe(sys.A, sys.B, sys.C, R, Q)
# Too few input arguments
with pytest.raises(ct.ControlArgument, match="not enough input"):
L, P, E = cdlqe(sys.A, sys.C)
# First argument is the wrong type (use SISO for non-slycot tests)
sys_tf = tf(rss(3, 1, 1))
sys_tf.dt = None # treat as either continuous or discrete time
with pytest.raises(ct.ControlArgument, match="LTI system must be"):
L, P, E = cdlqe(sys_tf, Q, R)
def test_mpc_iosystem_continuous():
# Create a random state space system
sys = ct.rss(2, 1, 1)
T, _ = ct.step_response(sys)
# provide penalties on the system signals
Q = np.eye(sys.nstates)
R = np.eye(sys.ninputs)
cost = opt.quadratic_cost(sys, Q, R)
# Continuous time MPC controller not implemented
with pytest.raises(NotImplementedError):
ctrl = opt.create_mpc_iosystem(sys, T, cost)
def test_statefbk_errors(self):
sys = ct.rss(4, 4, 2, strictly_proper=True)
K, _, _ = ct.lqr(sys, np.eye(sys.nstates), np.eye(sys.ninputs))
with pytest.raises(ControlArgument, match="must be I/O system"):
sys_tf = ct.tf([1], [1, 1])
ctrl, clsys = ct.create_statefbk_iosystem(sys_tf, K)
with pytest.raises(ControlArgument, match="output size must match"):
est = ct.rss(3, 3, 2)
ctrl, clsys = ct.create_statefbk_iosystem(sys, K, estimator=est)
with pytest.raises(ControlArgument, match="must be the full state"):
sys_nf = ct.rss(4, 3, 2, strictly_proper=True)
ctrl, clsys = ct.create_statefbk_iosystem(sys_nf, K)
with pytest.raises(ControlArgument, match="gain must be an array"):
ctrl, clsys = ct.create_statefbk_iosystem(sys, "bad argument")
with pytest.raises(ControlArgument, match="unknown type"):
ctrl, clsys = ct.create_statefbk_iosystem(sys, K, type=1)
# Errors involving integral action
C_int = np.eye(2, 4)
K_int, _, _ = ct.lqr(sys,
np.eye(sys.nstates + C_int.shape[0]),
np.eye(sys.ninputs),
integral_action=C_int)
with pytest.raises(ControlArgument, match="must pass an array"):
ctrl, clsys = ct.create_statefbk_iosystem(
sys, K_int, integral_action="bad argument")
with pytest.raises(ControlArgument, match="must be an array of size"):
ctrl, clsys = ct.create_statefbk_iosystem(sys,
K,
integral_action=C_int)
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)
def test_convert_to_statespace():
# Set up the initial system
sys = ct.tf(ct.rss(2, 1, 1))
# Make sure we can rename system name, inputs, outputs
sys_new = ct.ss(sys, inputs='u', outputs='y', name='new')
assert sys_new.name == 'new'
assert sys_new.input_labels == ['u']
assert sys_new.output_labels == ['y']
# Try specifying the state names (via low level test)
with pytest.warns(UserWarning, match="non-unique state space realization"):
sys_new = ct.ss(sys, inputs='u', outputs='y', states=['x1', 'x2'])
assert sys_new.input_labels == ['u']
assert sys_new.output_labels == ['y']
assert sys_new.state_labels == ['x1', 'x2']
def testMinrealBrute(self):
# depending on the seed and minreal performance, a number of
# reductions is produced. If random gen or minreal change, this
# will be likely to fail
nreductions = 0
for n, m, p in permutations(range(1, 6), 3):
s = rss(n, p, m)
sr = s.minreal()
if s.states > sr.states:
nreductions += 1
else:
# Check to make sure that poles and zeros match
# For poles, just look at eigenvalues of A
np.testing.assert_array_almost_equal(np.sort(eigvals(s.A)),
np.sort(eigvals(sr.A)))
# For zeros, need to extract SISO systems
for i in range(m):
for j in range(p):
# Extract SISO dynamixs from input i to output j
s1 = ss(s.A, s.B[:, i], s.C[j, :], s.D[j, i])
s2 = ss(sr.A, sr.B[:, i], sr.C[j, :], sr.D[j, i])
# Check that the zeros match
# Note: sorting doesn't work => have to do the hard way
z1 = zero(s1)
z2 = zero(s2)
# Start by making sure we have the same # of zeros
assert len(z1) == len(z2)
# Make sure all zeros in s1 are in s2
for z in z1:
# Find the closest zero TODO: find proper bounds
assert min(abs(z2 - z)) <= 1e-7
# Make sure all zeros in s2 are in s1
for z in z2:
# Find the closest zero
assert min(abs(z1 - z)) <= 1e-7
# Make sure that the number of systems reduced is as expected
# (Need to update this number if you change the seed at top of file)
assert nreductions == 2
def test_linestyle_checks():
sys = ct.rss(2, 1, 1)
# Things that should work
ct.nyquist_plot(sys, primary_style=['-', '-'], mirror_style=['-', '-'])
ct.nyquist_plot(sys, mirror_style=None)
with pytest.raises(ValueError, match="invalid 'primary_style'"):
ct.nyquist_plot(sys, primary_style=False)
with pytest.raises(ValueError, match="invalid 'mirror_style'"):
ct.nyquist_plot(sys, mirror_style=0.2)
# If only one line style is given use, the default value for the other
# TODO: for now, just make sure the signature works; no correct check yet
with pytest.warns(PendingDeprecationWarning, match="single string"):
ct.nyquist_plot(sys, primary_style=':', mirror_style='-.')
def test_trdata_labels():
# Create an I/O system with labels
sys = ct.rss(4, 3, 2)
iosys = ct.LinearIOSystem(sys)
T = np.linspace(1, 10, 10)
U = [np.sin(T), np.cos(T)]
# Create a response
response = ct.input_output_response(iosys, T, U)
# Make sure the labels got created
np.testing.assert_equal(
response.output_labels, ["y[%d]" % i for i in range(sys.noutputs)])
np.testing.assert_equal(
response.state_labels, ["x[%d]" % i for i in range(sys.nstates)])
np.testing.assert_equal(
response.input_labels, ["u[%d]" % i for i in range(sys.ninputs)])
def test_operator_conversion(self):
sys_tf = ct.tf([1], [1, 2, 1])
frd_tf = FRD(sys_tf, np.logspace(-1, 1, 10))
frd_2 = FRD(2 * np.ones(10), np.logspace(-1, 1, 10))
# Make sure that we can add, multiply, and feedback constants
sys_add = frd_tf + 2
chk_add = frd_tf + frd_2
np.testing.assert_array_almost_equal(sys_add.omega, chk_add.omega)
np.testing.assert_array_almost_equal(sys_add.fresp, chk_add.fresp)
sys_radd = 2 + frd_tf
chk_radd = frd_2 + frd_tf
np.testing.assert_array_almost_equal(sys_radd.omega, chk_radd.omega)
np.testing.assert_array_almost_equal(sys_radd.fresp, chk_radd.fresp)
sys_sub = frd_tf - 2
chk_sub = frd_tf - frd_2
np.testing.assert_array_almost_equal(sys_sub.omega, chk_sub.omega)
np.testing.assert_array_almost_equal(sys_sub.fresp, chk_sub.fresp)
sys_rsub = 2 - frd_tf
chk_rsub = frd_2 - frd_tf
np.testing.assert_array_almost_equal(sys_rsub.omega, chk_rsub.omega)
np.testing.assert_array_almost_equal(sys_rsub.fresp, chk_rsub.fresp)
sys_mul = frd_tf * 2
chk_mul = frd_tf * frd_2
np.testing.assert_array_almost_equal(sys_mul.omega, chk_mul.omega)
np.testing.assert_array_almost_equal(sys_mul.fresp, chk_mul.fresp)
sys_rmul = 2 * frd_tf
chk_rmul = frd_2 * frd_tf
np.testing.assert_array_almost_equal(sys_rmul.omega, chk_rmul.omega)
np.testing.assert_array_almost_equal(sys_rmul.fresp, chk_rmul.fresp)
sys_rdiv = 2 / frd_tf
chk_rdiv = frd_2 / frd_tf
np.testing.assert_array_almost_equal(sys_rdiv.omega, chk_rdiv.omega)
np.testing.assert_array_almost_equal(sys_rdiv.fresp, chk_rdiv.fresp)
sys_pow = frd_tf**2
chk_pow = FRD(sys_tf**2, np.logspace(-1, 1, 10))
np.testing.assert_array_almost_equal(sys_pow.omega, chk_pow.omega)
np.testing.assert_array_almost_equal(sys_pow.fresp, chk_pow.fresp)
sys_pow = frd_tf**-2
chk_pow = FRD(sys_tf**-2, np.logspace(-1, 1, 10))
np.testing.assert_array_almost_equal(sys_pow.omega, chk_pow.omega)
np.testing.assert_array_almost_equal(sys_pow.fresp, chk_pow.fresp)
# Assertion error if we try to raise to a non-integer power
self.assertRaises(ValueError, FRD.__pow__, frd_tf, 0.5)
# Selected testing on transfer function conversion
sys_add = frd_2 + sys_tf
chk_add = frd_2 + frd_tf
np.testing.assert_array_almost_equal(sys_add.omega, chk_add.omega)
np.testing.assert_array_almost_equal(sys_add.fresp, chk_add.fresp)
# Input/output mismatch size mismatch in rmul
sys1 = FRD(ct.rss(2, 2, 2), np.logspace(-1, 1, 10))
self.assertRaises(ValueError, FRD.__rmul__, frd_2, sys1)
# Make sure conversion of something random generates exception
self.assertRaises(TypeError, FRD.__add__, frd_tf, 'string')