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discard zero imaginary part for sys.dcgain() #579

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Merged
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Mar 20, 2021
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discard zero imaginary part for sys.dcgain() #579

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8c9e807
discard zero imaginary part for sys.dcgain()
bnavigator Mar 19, 2021
9a54254
Apply review suggestions by @murrayrm: revert comment change, remove …
bnavigator Mar 19, 2021
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7 changes: 7 additions & 0 deletions control/lti.py
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Original file line number Diff line number Diff line change
Expand Up @@ -208,6 +208,13 @@ def dcgain(self):
raise NotImplementedError("dcgain not implemented for %s objects" %
str(self.__class__))

def _dcgain(self, warn_infinite):
zeroresp = self(0 if self.isctime() else 1,
warn_infinite=warn_infinite)
if np.all(np.logical_or(np.isreal(zeroresp), np.isnan(zeroresp.imag))):
return zeroresp.real
else:
return zeroresp

# Test to see if a system is SISO
def issiso(sys, strict=False):
Expand Down
25 changes: 18 additions & 7 deletions control/statesp.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1216,16 +1216,27 @@ def dcgain(self, warn_infinite=False):

.. math: G(1) = C (I - A)^{-1} B + D

Parameters
----------
warn_infinite : bool, optional
By default, don't issue a warning message if the zero-frequency
gain is infinite. Setting `warn_infinite` to generate the warning
message.

Returns
-------
gain : ndarray
An array of shape (outputs,inputs); the array will either be the
zero-frequency (or DC) gain, or, if the frequency response is
singular, the array will be filled with (inf + nanj).

gain : (outputs, inputs) ndarray or scalar
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gain : (noutputs, ninputs) ndarray or scalar

Array or scalar value for SISO systems, depending on
config.defaults['control.squeeze_frequency_response'].
The value of the array elements or the scalar is either the
zero-frequency (or DC) gain, or `inf`, if the frequency response
is singular.

For real valued systems, the empty imaginary part of the
complex zero-frequency response is discarded and a real array or
scalar is returned.
"""
return self(0, warn_infinite=warn_infinite) if self.isctime() \
else self(1, warn_infinite=warn_infinite)
return self._dcgain(warn_infinite)

def _isstatic(self):
"""True if and only if the system has no dynamics, that is,
Expand Down
10 changes: 5 additions & 5 deletions control/tests/freqresp_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -433,9 +433,9 @@ def test_dcgain_consistency():
np.testing.assert_equal(
sys_ss(0j, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_tf.dcgain(warn_infinite=False), complex(np.inf, np.nan))
sys_tf.dcgain(), np.inf)
np.testing.assert_equal(
sys_ss.dcgain(warn_infinite=False), complex(np.inf, np.nan))
sys_ss.dcgain(), np.inf)

# Set up transfer function with pole, zero at the origin
sys_tf = ctrl.tf([1, 0], [1, 0])
Expand All @@ -448,7 +448,7 @@ def test_dcgain_consistency():
np.testing.assert_equal(
sys_tf(0j, warn_infinite=False), complex(np.nan, np.nan))
np.testing.assert_equal(
sys_tf.dcgain(warn_infinite=False), complex(np.nan, np.nan))
sys_tf.dcgain(), np.nan)

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Consider adding a test to show that dcgain() on a system with negative gain at zero frequency returns a negative number.

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Already exists:

python-control/control/tests/freqresp_test.py

Lines 505 to 507 in 8c9e807

# Make sure that we get the *signed* DC gain
sys_tf = -1 / (s + 1)
np.testing.assert_almost_equal(sys_tf.dcgain(), -1)

# Set up state space version
sys_ss = ctrl.tf2ss(ctrl.tf([1, 0], [1, 1])) * \
Expand All @@ -462,15 +462,15 @@ def test_dcgain_consistency():
np.testing.assert_equal(
sys_ss(0j, warn_infinite=False), complex(np.nan, np.nan))
np.testing.assert_equal(
sys_ss.dcgain(warn_infinite=False), complex(np.nan, np.nan))
sys_ss.dcgain(), np.nan)
elif 0 in sys_ss.pole():
# Pole at the origin, but zero elsewhere => should get (inf + nanj)
np.testing.assert_equal(
sys_ss(0, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_ss(0j, warn_infinite=False), complex(np.inf, np.nan))
np.testing.assert_equal(
sys_ss.dcgain(warn_infinite=False), complex(np.inf, np.nan))
sys_ss.dcgain(), np.inf)
else:
# Near pole/zero cancellation => nothing sensible to check
pass
Expand Down
7 changes: 3 additions & 4 deletions control/tests/statesp_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -498,7 +498,7 @@ def test_dc_gain_cont(self):
np.testing.assert_allclose(sys2.dcgain(), expected)

sys3 = StateSpace(0., 1., 1., 0.)
np.testing.assert_equal(sys3.dcgain(), complex(np.inf, np.nan))
np.testing.assert_equal(sys3.dcgain(), np.inf)

def test_dc_gain_discr(self):
"""Test DC gain for discrete-time state-space systems."""
Expand All @@ -516,7 +516,7 @@ def test_dc_gain_discr(self):

# summer
sys = StateSpace(1, 1, 1, 0, True)
np.testing.assert_equal(sys.dcgain(), complex(np.inf, np.nan))
np.testing.assert_equal(sys.dcgain(), np.inf)

@pytest.mark.parametrize("outputs", range(1, 6))
@pytest.mark.parametrize("inputs", range(1, 6))
Expand All @@ -539,7 +539,7 @@ def test_dc_gain_integrator(self, outputs, inputs, dt):
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, complex(np.inf, np.nan), dtype=complex)
dc = np.full_like(d, np.inf, dtype=float)
if sys.issiso():
dc = dc.squeeze()

Expand Down Expand Up @@ -953,4 +953,3 @@ def test_xferfcn_ndarray_precedence(op, tf, arr):
ss = ct.tf2ss(tf)
result = op(arr, ss)
assert isinstance(result, ct.StateSpace)

6 changes: 3 additions & 3 deletions control/tests/xferfcn_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -807,7 +807,7 @@ def test_dcgain_cont(self):
np.testing.assert_equal(sys2.dcgain(), 2)

sys3 = TransferFunction(6, [1, 0])
np.testing.assert_equal(sys3.dcgain(), complex(np.inf, np.nan))
np.testing.assert_equal(sys3.dcgain(), np.inf)

num = [[[15], [21], [33]], [[10], [14], [22]]]
den = [[[1, 3], [2, 3], [3, 3]], [[1, 5], [2, 7], [3, 11]]]
Expand All @@ -827,13 +827,13 @@ def test_dcgain_discr(self):

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

# differencer, with warning
sys = TransferFunction(1, [1, -1], True)
with pytest.warns(RuntimeWarning, match="divide by zero"):
np.testing.assert_equal(
sys.dcgain(warn_infinite=True), complex(np.inf, np.nan))
sys.dcgain(warn_infinite=True), np.inf)

# summer
sys = TransferFunction([1, -1], [1], True)
Expand Down
15 changes: 11 additions & 4 deletions control/xferfcn.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1070,12 +1070,19 @@ def dcgain(self, warn_infinite=False):

Returns
-------
gain : ndarray
The zero-frequency gain
gain : (outputs, inputs) ndarray or scalar
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gain : (noutputs, ninputs) ndarray or scalar

Array or scalar value for SISO systems, depending on
config.defaults['control.squeeze_frequency_response'].
The value of the array elements or the scalar is either the
zero-frequency (or DC) gain, or `inf`, if the frequency response
is singular.

For real valued systems, the empty imaginary part of the
complex zero-frequency response is discarded and a real array or
scalar is returned.

"""
return self(0, warn_infinite=warn_infinite) if self.isctime() \
else self(1, warn_infinite=warn_infinite)
return self._dcgain(warn_infinite)

def _isstatic(self):
"""returns True if and only if all of the numerator and denominator
Expand Down