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_forced_response(self):
t = np.linspace(0, 1, 10)
# compute step response - test with state space, and transfer function
# objects
u = np.array([1., 1, 1, 1, 1, 1, 1, 1, 1, 1])
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
tout, yout, _xout = forced_response(self.siso_ss1, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
_t, yout, _xout = forced_response(self.siso_tf2, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# test with initial value and special algorithm for ``U=0``
u = 0
x0 = np.matrix(".5; 1.")
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
_t, yout, _xout = forced_response(self.siso_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# Test MIMO system, which contains ``siso_ss1`` twice
# first system: initial value, second system: step response
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.array([[.5], [1], [0], [0]])
youttrue = np.array([[11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391],
[9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776]])
_t, yout, _xout = forced_response(self.mimo_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# Test discrete MIMO system to use correct convention for input
sysc = self.mimo_ss1
dt=t[1]-t[0]
sysd = c2d(sysc, dt) # discrete time system
Tc, youtc, _xoutc = forced_response(sysc, t, u, x0)
Td, youtd, _xoutd = forced_response(sysd, t, u, x0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
np.testing.assert_array_almost_equal(youtc, youtd, decimal=4)
# Test discrete MIMO system without default T argument
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.array([[.5], [1], [0], [0]])
youttrue = np.array([[11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391],
[9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776]])
_t, yout, _xout = forced_response(sysd, U=u, X0=x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
def test_step_response(self):
# Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
youttrue = np.array([
9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165, 42.3227, 44.9694,
47.1599, 48.9776
])
# SISO call
tout, yout = step_response(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Play with arguments
tout, yout = step_response(sys, T=t, X0=0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
X0 = np.array([0, 0])
tout, yout = step_response(sys, T=t, X0=X0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
tout, yout, xout = step_response(sys, T=t, X0=0, return_x=True)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
_t, y_00 = step_response(sys, T=t, input=0, output=0)
_t, y_11 = step_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
# Make sure continuous and discrete time use same return conventions
sysc = self.mimo_ss1
sysd = c2d(sysc, 1) # discrete time system
Tvec = np.linspace(0, 10, 11) # make sure to use integer times 0..10
Tc, youtc = step_response(sysc, Tvec, input=0)
Td, youtd = step_response(sysd, Tvec, input=0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
def test_forced_response(self):
t = np.linspace(0, 1, 10)
# compute step response - test with state space, and transfer function
# objects
u = np.array([1., 1, 1, 1, 1, 1, 1, 1, 1, 1])
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
tout, yout, _xout = forced_response(self.siso_ss1, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
_t, yout, _xout = forced_response(self.siso_tf2, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# test with initial value and special algorithm for ``U=0``
u = 0
x0 = np.matrix(".5; 1.")
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
_t, yout, _xout = forced_response(self.siso_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# Test MIMO system, which contains ``siso_ss1`` twice
# first system: initial value, second system: step response
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.matrix(".5; 1; 0; 0")
youttrue = np.array([[11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391],
[9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776]])
_t, yout, _xout = forced_response(self.mimo_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# Test discrete MIMO system to use correct convention for input
sysc = self.mimo_ss1
dt=t[1]-t[0]
sysd = c2d(sysc, dt) # discrete time system
Tc, youtc, _xoutc = forced_response(sysc, t, u, x0)
Td, youtd, _xoutd = forced_response(sysd, t, u, x0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
np.testing.assert_array_almost_equal(youtc, youtd, decimal=4)
def test_step_response(self):
# Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
# SISO call
tout, yout = step_response(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Play with arguments
tout, yout = step_response(sys, T=t, X0=0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
X0 = np.array([0, 0])
tout, yout = step_response(sys, T=t, X0=X0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
tout, yout, xout = step_response(sys, T=t, X0=0, return_x=True)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
_t, y_00 = step_response(sys, T=t, input=0, output=0)
_t, y_11 = step_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
# Make sure continuous and discrete time use same return conventions
sysc = self.mimo_ss1
sysd = c2d(sysc, 1) # discrete time system
Tvec = np.linspace(0, 10, 11) # make sure to use integer times 0..10
Tc, youtc = step_response(sysc, Tvec, input=0)
Td, youtd = step_response(sysd, Tvec, input=0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
