def test_nonzero_initial_time(self):
system = self.lti_nowarn(-1.,1.,1.,0.)
t = np.linspace(1,2)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0])
expected_y = np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_integrator(self):
# integrator: y' = u
system = self.lti_nowarn(0., 1., 1., 0.)
t = np.linspace(0,5)
u = t
tout, y, x = lsim(system, u, t)
expected_x = 0.5 * tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_x)
def test_first_order(self):
# y' = -y
# exact solution is y(t) = exp(-t)
system = self.lti_nowarn(-1.,1.,1.,0.)
t = np.linspace(0,5)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0])
expected_x = np.exp(-tout)
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_x)
def test_double_integrator(self):
# double integrator: y'' = 2u
A = np.mat("0. 1.; 0. 0.")
B = np.mat("0.; 1.")
C = np.mat("2. 0.")
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0,5)
u = np.ones_like(t)
tout, y, x = lsim(system, u, t)
expected_x = np.transpose(np.array([0.5 * tout**2, tout]))
expected_y = tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_y)
def test_jordan_block(self):
# Non-diagonalizable A matrix
# x1' + x1 = x2
# x2' + x2 = u
# y = x1
# Exact solution with u = 0 is y(t) = t exp(-t)
A = np.mat("-1. 1.; 0. -1.")
B = np.mat("0.; 1.")
C = np.mat("1. 0.")
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0,5)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[0.0, 1.0])
expected_y = tout * np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_miso(self):
# A system with two state variables, two inputs, and one output.
A = np.array([[-1.0, 0.0], [0.0, -2.0]])
B = np.array([[1.0, 0.0], [0.0, 1.0]])
C = np.array([1.0, 0.0])
D = np.zeros((1,2))
system = self.lti_nowarn(A, B, C, D)
t = np.linspace(0, 5.0, 101)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0, 1.0])
expected_y = np.exp(-tout)
expected_x0 = np.exp(-tout)
expected_x1 = np.exp(-2.0*tout)
assert_almost_equal(y, expected_y)
assert_almost_equal(x[:,0], expected_x0)
assert_almost_equal(x[:,1], expected_x1)
def sim(self, t, U=[]):
"""
Simulate the PLL with a input
Parameters
----------
t : array_like
Vector with the time
U: array_like
Input to the block with the same lenght of t, if a empty is given
Return
------
out : array like response to U
error : error
"""
if not len(U):
U = np.ones_like(t)
t, signal_out, X = lti.lsim(self.H, U=U, T=t)
error_out = signal_out - U * self.Navg
return signal_out, error_out
def sim(self, t, U = []):
"""
Simulate the PLL with a input
Parameters
----------
t : array_like
Vector with the time
U: array_like
Input to the block with the same lenght of t, if a empty is given
Return
------
out : array like response to U
error : error
"""
if not len(U):
U = np.ones_like(t)
t, signal_out, X = lti.lsim(self.H, U=U, T=t)
error_out = signal_out - U * self.Navg
return signal_out, error_out
