def testBalredMatchDC(self, matarrayin):
# controlable canonical realization computed in matlab for the transfer
# function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin(
[[-15., -7.5, -6.25, -1.875],
[8., 0., 0., 0.],
[0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = matarrayin([[2.], [0.], [0.], [0.]])
C = matarrayin([[0.5, 0.6875, 0.7031, 0.5]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
orders = 2
rsys = balred(sys,orders,method='matchdc')
Artrue = np.array(
[[-4.43094773, -4.55232904],
[-4.55232904, -5.36195206]])
Brtrue = np.array([[1.36235673], [1.03114388]])
Crtrue = np.array([[1.36235673, 1.03114388]])
Drtrue = np.array([[-0.08383902]])
np.testing.assert_array_almost_equal(rsys.A, Artrue, decimal=2)
np.testing.assert_array_almost_equal(rsys.B, Brtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.C, Crtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.D, Drtrue, decimal=4)
def testModredUnstable(self, matarrayin):
"""Check if an error is thrown when an unstable system is given"""
A = matarrayin([[4.5418, 3.3999, 5.0342, 4.3808],
[0.3890, 0.3599, 0.4195, 0.1760],
[-4.2117, -3.2395, -4.6760, -4.2180],
[0.0052, 0.0429, 0.0155, 0.2743]])
B = matarrayin([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
C = matarrayin([[1.0, 2.0, 3.0, 4.0], [1.0, 2.0, 3.0, 4.0]])
D = matarrayin([[0.0, 0.0], [0.0, 0.0]])
sys = StateSpace(A, B, C, D)
np.testing.assert_raises(ValueError, modred, sys, [2, 3])
def testHSVD(self, matarrayout, matarrayin):
A = matarrayin([[1., -2.], [3., -4.]])
B = matarrayin([[5.], [7.]])
C = matarrayin([[6., 8.]])
D = matarrayin([[9.]])
sys = StateSpace(A, B, C, D)
hsv = hsvd(sys)
hsvtrue = np.array([24.42686, 0.5731395]) # from MATLAB
np.testing.assert_array_almost_equal(hsv, hsvtrue)
# test for correct return type: ALWAYS return ndarray, even when
# use_numpy_matrix(True) was used
assert isinstance(hsv, np.ndarray)
assert not isinstance(hsv, np.matrix)
def testMarkovSignature(self, matarrayout, matarrayin):
U = matarrayin([[1., 1., 1., 1., 1.]])
Y = U
m = 3
H = markov(Y, U, m, transpose=False)
Htrue = np.array([[1., 0., 0.]])
np.testing.assert_array_almost_equal(H, Htrue)
# Make sure that transposed data also works
H = markov(np.transpose(Y), np.transpose(U), m, transpose=True)
np.testing.assert_array_almost_equal(H, np.transpose(Htrue))
# Generate Markov parameters without any arguments
H = markov(Y, U, m)
np.testing.assert_array_almost_equal(H, Htrue)
# Test example from docstring
T = np.linspace(0, 10, 100)
U = np.ones((1, 100))
T, Y = forced_response(tf([1], [1, 0.5], True), T, U)
H = markov(Y, U, 3, transpose=False)
# Test example from issue #395
inp = np.array([1, 2])
outp = np.array([2, 4])
mrk = markov(outp, inp, 1, transpose=False)
# Make sure MIMO generates an error
U = np.ones((2, 100)) # 2 inputs (Y unchanged, with 1 output)
with pytest.raises(ControlMIMONotImplemented):
markov(Y, U, m)
def testBalredTruncate(self, matarrayin):
# controlable canonical realization computed in matlab for the transfer
# function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin([[-15., -7.5, -6.25, -1.875], [8., 0., 0., 0.],
[0., 4., 0., 0.], [0., 0., 1., 0.]])
B = matarrayin([[2.], [0.], [0.], [0.]])
C = matarrayin([[0.5, 0.6875, 0.7031, 0.5]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
orders = 2
rsys = balred(sys, orders, method='truncate')
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[0.9057], [0.4068]])
Crtrue = np.array([[0.9057, 0.4068]])
Drtrue = np.array([[0.]])
np.testing.assert_array_almost_equal(rsys.A, Artrue, decimal=2)
np.testing.assert_array_almost_equal(rsys.B, Brtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.C, Crtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.D, Drtrue, decimal=4)
def testModredTruncate(self, matarrayin):
#balanced realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin([[-1.958, -1.194, 1.824, -1.464],
[-1.194, -0.8344, 2.563, -1.351],
[-1.824, -2.563, -1.124, 2.704],
[-1.464, -1.351, -2.704, -11.08]])
B = matarrayin([[-0.9057], [-0.4068], [-0.3263], [-0.3474]])
C = matarrayin([[-0.9057, -0.4068, 0.3263, -0.3474]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
rsys = modred(sys, [2, 3], 'truncate')
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[-0.9057], [-0.4068]])
Crtrue = np.array([[-0.9057, -0.4068]])
Drtrue = np.array([[0.]])
np.testing.assert_array_almost_equal(rsys.A, Artrue)
np.testing.assert_array_almost_equal(rsys.B, Brtrue)
np.testing.assert_array_almost_equal(rsys.C, Crtrue)
np.testing.assert_array_almost_equal(rsys.D, Drtrue)