def setUp(self):
"""Set up some systems for testing out MATLAB functions"""
A = np.matrix("1. -2.; 3. -4.")
B = np.matrix("5.; 7.")
C = np.matrix("6. 8.")
D = np.matrix("9.")
self.siso_ss1 = StateSpace(A, B, C, D)
# Create some transfer functions
self.siso_tf1 = TransferFunction([1], [1, 2, 1])
self.siso_tf2 = _convert_to_transfer_function(self.siso_ss1)
# Create MIMO system, contains ``siso_ss1`` twice
A = np.matrix("1. -2. 0. 0.;"
"3. -4. 0. 0.;"
"0. 0. 1. -2.;"
"0. 0. 3. -4. ")
B = np.matrix("5. 0.;" "7. 0.;" "0. 5.;" "0. 7. ")
C = np.matrix("6. 8. 0. 0.;" "0. 0. 6. 8. ")
D = np.matrix("9. 0.;" "0. 9. ")
self.mimo_ss1 = StateSpace(A, B, C, D)
# Create discrete time systems
self.siso_dtf1 = TransferFunction([1], [1, 1, 0.25], True)
self.siso_dtf2 = TransferFunction([1], [1, 1, 0.25], 0.2)
self.siso_dss1 = tf2ss(self.siso_dtf1)
self.siso_dss2 = tf2ss(self.siso_dtf2)
self.mimo_dss1 = StateSpace(A, B, C, D, True)
self.mimo_dss2 = c2d(self.mimo_ss1, 0.2)
def setUp(self):
"""Set up some systems for testing out MATLAB functions"""
A = np.matrix("1. -2.; 3. -4.")
B = np.matrix("5.; 7.")
C = np.matrix("6. 8.")
D = np.matrix("9.")
self.siso_ss1 = StateSpace(A, B, C, D)
# Create some transfer functions
self.siso_tf1 = TransferFunction([1], [1, 2, 1])
self.siso_tf2 = _convert_to_transfer_function(self.siso_ss1)
# Create MIMO system, contains ``siso_ss1`` twice
A = np.matrix("1. -2. 0. 0.;"
"3. -4. 0. 0.;"
"0. 0. 1. -2.;"
"0. 0. 3. -4. ")
B = np.matrix("5. 0.;"
"7. 0.;"
"0. 5.;"
"0. 7. ")
C = np.matrix("6. 8. 0. 0.;"
"0. 0. 6. 8. ")
D = np.matrix("9. 0.;"
"0. 9. ")
self.mimo_ss1 = StateSpace(A, B, C, D)
# Create discrete time systems
self.siso_dtf1 = TransferFunction([1], [1, 1, 0.25], True)
self.siso_dtf2 = TransferFunction([1], [1, 1, 0.25], 0.2)
self.siso_dss1 = tf2ss(self.siso_dtf1)
self.siso_dss2 = tf2ss(self.siso_dtf2)
self.mimo_dss1 = StateSpace(A, B, C, D, True)
self.mimo_dss2 = c2d(self.mimo_ss1, 0.2)
def test_convert_to_transfer_function(self):
"""Test for correct state space to transfer function conversion."""
A = [[1., -2.], [-3., 4.]]
B = [[6., 5.], [4., 3.]]
C = [[1., -2.], [3., -4.], [5., -6.]]
D = [[1., 0.], [0., 1.], [1., 0.]]
sys = StateSpace(A, B, C, D)
tfsys = _convert_to_transfer_function(sys)
num = [[np.array([1., -7., 10.]),
np.array([-1., 10.])],
[np.array([2., -8.]),
np.array([1., -2., -8.])],
[np.array([1., 1., -30.]),
np.array([7., -22.])]]
den = [[np.array([1., -5., -2.]) for _ in range(sys.ninputs)]
for _ in range(sys.noutputs)]
for i in range(sys.noutputs):
for j in range(sys.ninputs):
np.testing.assert_array_almost_equal(tfsys.num[i][j],
num[i][j])
np.testing.assert_array_almost_equal(tfsys.den[i][j],
den[i][j])
def test_state_space_conversion_mimo(self):
"""Test conversion of a single input, two-output state-space
system against the same TF"""
s = TransferFunction([1, 0], [1])
b0 = 0.2
b1 = 0.1
b2 = 0.5
a0 = 2.3
a1 = 6.3
a2 = 3.6
a3 = 1.0
h = (b0 + b1*s + b2*s**2)/(a0 + a1*s + a2*s**2 + a3*s**3)
H = TransferFunction([[h.num[0][0]], [(h*s).num[0][0]]],
[[h.den[0][0]], [h.den[0][0]]])
sys = _convert_to_statespace(H)
H2 = _convert_to_transfer_function(sys)
np.testing.assert_array_almost_equal(H.num[0][0], H2.num[0][0])
np.testing.assert_array_almost_equal(H.den[0][0], H2.den[0][0])
np.testing.assert_array_almost_equal(H.num[1][0], H2.num[1][0])
np.testing.assert_array_almost_equal(H.den[1][0], H2.den[1][0])
def test_state_space_conversion_mimo(self):
"""Test conversion of a single input, two-output state-space
system against the same TF"""
s = TransferFunction([1, 0], [1])
b0 = 0.2
b1 = 0.1
b2 = 0.5
a0 = 2.3
a1 = 6.3
a2 = 3.6
a3 = 1.0
h = (b0 + b1*s + b2*s**2)/(a0 + a1*s + a2*s**2 + a3*s**3)
H = TransferFunction([[h.num[0][0]], [(h*s).num[0][0]]],
[[h.den[0][0]], [h.den[0][0]]])
sys = _convertToStateSpace(H)
H2 = _convert_to_transfer_function(sys)
np.testing.assert_array_almost_equal(H.num[0][0], H2.num[0][0])
np.testing.assert_array_almost_equal(H.den[0][0], H2.den[0][0])
np.testing.assert_array_almost_equal(H.num[1][0], H2.num[1][0])
np.testing.assert_array_almost_equal(H.den[1][0], H2.den[1][0])
def test_convert_to_transfer_function(self):
"""Test for correct state space to transfer function conversion."""
A = [[1., -2.], [-3., 4.]]
B = [[6., 5.], [4., 3.]]
C = [[1., -2.], [3., -4.], [5., -6.]]
D = [[1., 0.], [0., 1.], [1., 0.]]
sys = StateSpace(A, B, C, D)
tfsys = _convert_to_transfer_function(sys)
num = [[np.array([1., -7., 10.]), np.array([-1., 10.])],
[np.array([2., -8.]), np.array([1., -2., -8.])],
[np.array([1., 1., -30.]), np.array([7., -22.])]]
den = [[np.array([1., -5., -2.]) for _ in range(sys.inputs)]
for _ in range(sys.outputs)]
for i in range(sys.outputs):
for j in range(sys.inputs):
np.testing.assert_array_almost_equal(tfsys.num[i][j], num[i][j])
np.testing.assert_array_almost_equal(tfsys.den[i][j], den[i][j])
