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BugFix: DC gain for discrete-time systems #126

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Merged
merged 1 commit into from
Jan 6, 2017
Merged

BugFix: DC gain for discrete-time systems #126

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11 changes: 7 additions & 4 deletions control/statesp.py
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Original file line number Diff line number Diff line change
Expand Up @@ -612,11 +612,14 @@ def dcgain(self):
at the origin
"""
try:
gain = np.asarray(self.D -
self.C.dot(np.linalg.solve(self.A, self.B)))
if self.isctime():
gain = np.asarray(self.D -
self.C.dot(np.linalg.solve(self.A, self.B)))
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Indentation is off alignment here. This is a small matter of style; OK for someone to fix it directly on master branch if there are not other issues with this PR.

else:
gain = self.horner(1)
except LinAlgError:
# zero eigenvalue: singular matrix
return np.nan
# eigenvalue at DC
gain = np.tile(np.nan,(self.outputs,self.inputs))
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blank line deletion here does not seem to be relevant to the other changes in this commit.

return np.squeeze(gain)


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40 changes: 39 additions & 1 deletion control/tests/statesp_test.py
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Expand Up @@ -228,7 +228,8 @@ def testArrayAccessSS(self):

assert sys1.dt == sys1_11.dt

def test_dcgain(self):
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.)

Expand All @@ -239,6 +240,43 @@ def test_dcgain(self):
sys3 = StateSpace(0., 1., 1., 0.)
np.testing.assert_equal(sys3.dcgain(), np.nan)

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_scalarStaticGain(self):
"""Regression: can we create a scalar static gain?"""
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23 changes: 22 additions & 1 deletion control/tests/xferfcn_test.py
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Expand Up @@ -524,7 +524,8 @@ def testMatrixMult(self):
np.testing.assert_array_almost_equal(H.num[1][0], H2.num[0][0])
np.testing.assert_array_almost_equal(H.den[1][0], H2.den[0][0])

def test_dcgain(self):
def test_dcgain_cont(self):
"""Test DC gain for continuous-time transfer functions"""
sys = TransferFunction(6, 3)
np.testing.assert_equal(sys.dcgain(), 2)

Expand All @@ -540,6 +541,26 @@ def test_dcgain(self):
expected = [[5, 7, 11], [2, 2, 2]]
np.testing.assert_array_equal(sys4.dcgain(), expected)

def test_dcgain_discr(self):
"""Test DC gain for discrete-time transfer functions"""
# static gain
sys = TransferFunction(6, 3, True)
np.testing.assert_equal(sys.dcgain(), 2)

# averaging filter
sys = TransferFunction(0.5, [1, -0.5], True)
np.testing.assert_almost_equal(sys.dcgain(), 1)

# differencer
sys = TransferFunction(1, [1, -1], True)
np.testing.assert_equal(sys.dcgain(), np.inf)

# summer
# causes a RuntimeWarning due to the divide by zero
sys = TransferFunction([1,-1], [1], True)
np.testing.assert_equal(sys.dcgain(), 0)


def suite():
return unittest.TestLoader().loadTestsFromTestCase(TestXferFcn)

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12 changes: 11 additions & 1 deletion control/xferfcn.py
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Expand Up @@ -945,13 +945,23 @@ def sample(self, Ts, method='zoh', alpha=None):
def dcgain(self):
"""Return the zero-frequency (or DC) gain

For a transfer function G(s), the DC gain is G(0)
For a continous-time transfer function G(s), the DC gain is G(0)
For a discrete-time transfer function G(z), the DC gain is G(1)

Returns
-------
gain : ndarray
The zero-frequency gain
"""
if self.isctime():
return self._dcgain_cont()
else:
return self(1)

def _dcgain_cont(self):
"""_dcgain_cont() -> DC gain as matrix or scalar

Special cased evaluation at 0 for continuous-time systems"""
gain = np.empty((self.outputs, self.inputs), dtype=float)
for i in range(self.outputs):
for j in range(self.inputs):
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