diff --git a/control/statesp.py b/control/statesp.py
index f5b8534c3..27dbdf934 100644
--- a/control/statesp.py
+++ b/control/statesp.py
@@ -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)))
+ 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))
return np.squeeze(gain)
diff --git a/control/tests/statesp_test.py b/control/tests/statesp_test.py
index 8a6617116..245b396c6 100644
--- a/control/tests/statesp_test.py
+++ b/control/tests/statesp_test.py
@@ -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.)
@@ -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?"""
diff --git a/control/tests/xferfcn_test.py b/control/tests/xferfcn_test.py
index 2d114fea6..a6c9ae585 100644
--- a/control/tests/xferfcn_test.py
+++ b/control/tests/xferfcn_test.py
@@ -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)
@@ -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)
diff --git a/control/xferfcn.py b/control/xferfcn.py
index 963329ffb..1559fa047 100644
--- a/control/xferfcn.py
+++ b/control/xferfcn.py
@@ -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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