def test_scalar_static_gain(self):
"""Regression: can we create a scalar static gain?
make sure StateSpace internals, specifically ABC matrix
sizes, are OK for LTI operations
"""
g1 = StateSpace([], [], [], [2])
g2 = StateSpace([], [], [], [3])
assert g1.dt == None
assert g2.dt == None
g3 = g1 * g2
assert 6 == g3.D[0, 0]
assert g3.dt == None
g4 = g1 + g2
assert 5 == g4.D[0, 0]
assert g4.dt == None
g5 = g1.feedback(g2)
np.testing.assert_allclose(2. / 7, g5.D[0, 0])
assert g5.dt == None
g6 = g1.append(g2)
np.testing.assert_allclose(np.diag([2, 3]), g6.D)
assert g6.dt == None
def testMIMOfb(self):
sys = StateSpace([[-0.5, 0.0], [0.0, -1.0]], [[1.0, 0.0], [0.0, 1.0]],
[[1.0, 0.0], [0.0, 1.0]], [[0.0, 0.0], [0.0, 0.0]])
omega = np.logspace(-1, 2, 10)
f1 = FRD(sys, omega).feedback([[0.1, 0.3], [0.0, 1.0]])
f2 = FRD(sys.feedback([[0.1, 0.3], [0.0, 1.0]]), omega)
np.testing.assert_array_almost_equal(
f1.frequency_response([0.1, 1.0, 10])[0],
f2.frequency_response([0.1, 1.0, 10])[0])
np.testing.assert_array_almost_equal(
f1.frequency_response([0.1, 1.0, 10])[1],
f2.frequency_response([0.1, 1.0, 10])[1])
def testMIMOfb2(self):
sys = StateSpace(np.array([[-2.0, 0, 0], [0, -1, 1], [0, 0, -3]]),
np.array([[1.0, 0], [0, 0], [0, 1]]), np.eye(3),
np.zeros((3, 2)))
omega = np.logspace(-1, 2, 10)
K = np.array([[1, 0.3, 0], [0.1, 0, 0]])
f1 = FRD(sys, omega).feedback(K)
f2 = FRD(sys.feedback(K), omega)
np.testing.assert_array_almost_equal(
f1.frequency_response([0.1, 1.0, 10])[0],
f2.frequency_response([0.1, 1.0, 10])[0])
np.testing.assert_array_almost_equal(
f1.frequency_response([0.1, 1.0, 10])[1],
f2.frequency_response([0.1, 1.0, 10])[1])
def testMIMOfb2(self):
sys = StateSpace(np.matrix('-2.0 0 0; 0 -1 1; 0 0 -3'),
np.matrix('1.0 0; 0 0; 0 1'),
np.eye(3), np.zeros((3,2)))
omega = np.logspace(-1, 2, 10)
K = np.matrix('1 0.3 0; 0.1 0 0')
f1 = FRD(sys, omega).feedback(K)
f2 = FRD(sys.feedback(K), omega)
np.testing.assert_array_almost_equal(
f1.freqresp([0.1, 1.0, 10])[0],
f2.freqresp([0.1, 1.0, 10])[0])
np.testing.assert_array_almost_equal(
f1.freqresp([0.1, 1.0, 10])[1],
f2.freqresp([0.1, 1.0, 10])[1])
def testMIMOfb(self):
sys = StateSpace([[-0.5, 0.0], [0.0, -1.0]],
[[1.0, 0.0], [0.0, 1.0]],
[[1.0, 0.0], [0.0, 1.0]],
[[0.0, 0.0], [0.0, 0.0]])
omega = np.logspace(-1, 2, 10)
f1 = FRD(sys, omega).feedback([[0.1, 0.3],[0.0, 1.0]])
f2 = FRD(sys.feedback([[0.1, 0.3],[0.0, 1.0]]), omega)
np.testing.assert_array_almost_equal(
f1.freqresp([0.1, 1.0, 10])[0],
f2.freqresp([0.1, 1.0, 10])[0])
np.testing.assert_array_almost_equal(
f1.freqresp([0.1, 1.0, 10])[1],
f2.freqresp([0.1, 1.0, 10])[1])
def testMIMOfb2(self):
sys = StateSpace(np.matrix('-2.0 0 0; 0 -1 1; 0 0 -3'),
np.matrix('1.0 0; 0 0; 0 1'), np.eye(3),
np.zeros((3, 2)))
omega = np.logspace(-1, 2, 10)
K = np.matrix('1 0.3 0; 0.1 0 0')
f1 = FRD(sys, omega).feedback(K)
f2 = FRD(sys.feedback(K), omega)
np.testing.assert_array_almost_equal(
f1.freqresp([0.1, 1.0, 10])[0],
f2.freqresp([0.1, 1.0, 10])[0])
np.testing.assert_array_almost_equal(
f1.freqresp([0.1, 1.0, 10])[1],
f2.freqresp([0.1, 1.0, 10])[1])
def test_scalarStaticGain(self):
"""Regression: can we create a scalar static gain?"""
g1=StateSpace([],[],[],[2])
g2=StateSpace([],[],[],[3])
# make sure StateSpace internals, specifically ABC matrix
# sizes, are OK for LTI operations
g3 = g1*g2
self.assertEqual(6, g3.D[0,0])
g4 = g1+g2
self.assertEqual(5, g4.D[0,0])
g5 = g1.feedback(g2)
self.assertAlmostEqual(2./7, g5.D[0,0])
g6 = g1.append(g2)
np.testing.assert_array_equal(np.diag([2,3]),g6.D)
def test_matrixStaticGain(self):
"""Regression: can we create matrix static gains?"""
d1 = np.matrix([[1,2,3],[4,5,6]])
d2 = np.matrix([[7,8],[9,10],[11,12]])
g1=StateSpace([],[],[],d1)
# _remove_useless_states was making A = [[0]]
self.assertEqual((0,0), g1.A.shape)
g2=StateSpace([],[],[],d2)
g3=StateSpace([],[],[],d2.T)
h1 = g1*g2
np.testing.assert_array_equal(d1*d2, h1.D)
h2 = g1+g3
np.testing.assert_array_equal(d1+d2.T, h2.D)
h3 = g1.feedback(g2)
np.testing.assert_array_almost_equal(solve(np.eye(2)+d1*d2,d1), h3.D)
h4 = g1.append(g2)
np.testing.assert_array_equal(block_diag(d1,d2),h4.D)
