def test_dcgain(self):
sys = StateSpace(-2., 6., 5., 0)
np.testing.assert_equal(sys.dcgain(), 15.)
sys2 = StateSpace(-2, [6., 4.], [[5.], [7.], [11]], np.zeros((3, 2)))
expected = np.array([[15., 10.], [21., 14.], [33., 22.]])
np.testing.assert_array_equal(sys2.dcgain(), expected)
sys3 = StateSpace(0., 1., 1., 0.)
np.testing.assert_equal(sys3.dcgain(), np.nan)
def test_dcgain(self):
sys = StateSpace(-2.,6.,5.,0)
np.testing.assert_equal(sys.dcgain(), 15.)
sys2 = StateSpace(-2, [6., 4.], [[5.],[7.],[11]], np.zeros((3,2)))
expected = np.array([[15., 10.], [21., 14.], [33., 22.]])
np.testing.assert_array_equal(sys2.dcgain(), expected)
sys3 = StateSpace(0., 1., 1., 0.)
np.testing.assert_equal(sys3.dcgain(), np.nan)
def test_dcgain_cont(self):
"""Test DC gain for continuous-time state-space systems"""
sys = StateSpace(-2.,6.,5.,0)
np.testing.assert_equal(sys.dcgain(), 15.)
sys2 = StateSpace(-2, [6., 4.], [[5.],[7.],[11]], np.zeros((3,2)))
expected = np.array([[15., 10.], [21., 14.], [33., 22.]])
np.testing.assert_array_equal(sys2.dcgain(), expected)
sys3 = StateSpace(0., 1., 1., 0.)
np.testing.assert_equal(sys3.dcgain(), np.nan)
def test_dc_gain_integrator(self, outputs, inputs, dt):
"""DC gain w/ pole at origin returns appropriately sized array of inf.
the SISO case is also tested in test_dc_gain_{cont,discr}
time systems (dt=0)
"""
states = max(inputs, outputs)
# a matrix that is singular at DC, and has no "useless" states as in
# _remove_useless_states
a = np.triu(np.tile(2, (states, states)))
# eigenvalues all +2, except for ...
a[0, 0] = 0 if dt in [0, None] else 1
b = np.eye(max(inputs, states))[:states, :inputs]
c = np.eye(max(outputs, states))[:outputs, :states]
d = np.zeros((outputs, inputs))
sys = StateSpace(a, b, c, d, dt)
dc = np.full_like(d, np.inf, dtype=float)
if sys.issiso():
dc = dc.squeeze()
try:
np.testing.assert_array_equal(dc, sys.dcgain())
except NotImplementedError:
# Skip MIMO tests if there is no slycot
pytest.skip("slycot required for MIMO dcgain")
def test_dcgain_discr(self):
"""Test DC gain for discrete-time state-space systems"""
# static gain
sys = StateSpace([], [], [], 2, True)
np.testing.assert_equal(sys.dcgain(), 2)
# averaging filter
sys = StateSpace(0.5, 0.5, 1, 0, True)
np.testing.assert_almost_equal(sys.dcgain(), 1)
# differencer
sys = StateSpace(0, 1, -1, 1, True)
np.testing.assert_equal(sys.dcgain(), 0)
# summer
sys = StateSpace(1, 1, 1, 0, True)
np.testing.assert_equal(sys.dcgain(), np.nan)
def test_dcgain_integrator(self):
"""DC gain when eigenvalue at DC returns appropriately sized array of nan"""
# the SISO case is also tested in test_dc_gain_{cont,discr}
import itertools
# iterate over input and output sizes, and continuous (dt=None) and discrete (dt=True) time
for inputs,outputs,dt in itertools.product(range(1,6),range(1,6),[None,True]):
states = max(inputs,outputs)
# a matrix that is singular at DC, and has no "useless" states as in _remove_useless_states
a = np.triu(np.tile(2,(states,states)))
# eigenvalues all +2, except for ...
a[0,0] = 0 if dt is None else 1
b = np.eye(max(inputs,states))[:states,:inputs]
c = np.eye(max(outputs,states))[:outputs,:states]
d = np.zeros((outputs,inputs))
sys = StateSpace(a,b,c,d,dt)
dc = np.squeeze(np.tile(np.nan,(outputs,inputs)))
np.testing.assert_array_equal(dc, sys.dcgain())
def test_dc_gain_integrator(self, outputs, inputs, dt):
"""DC gain when eigenvalue at DC returns appropriately sized array of nan.
the SISO case is also tested in test_dc_gain_{cont,discr}
time systems (dt=0)
"""
states = max(inputs, outputs)
# a matrix that is singular at DC, and has no "useless" states as in
# _remove_useless_states
a = np.triu(np.tile(2, (states, states)))
# eigenvalues all +2, except for ...
a[0, 0] = 0 if dt in [0, None] else 1
b = np.eye(max(inputs, states))[:states, :inputs]
c = np.eye(max(outputs, states))[:outputs, :states]
d = np.zeros((outputs, inputs))
sys = StateSpace(a, b, c, d, dt)
dc = np.squeeze(np.full_like(d, np.nan))
np.testing.assert_array_equal(dc, sys.dcgain())
