def test_06(self):
# Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = u(t)
# The exact step response is 1 - (1 + t)*exp(-t).
system = ([1.0], [1.0, 2.0, 1.0])
tout, y = step2(system, atol=1e-10, rtol=1e-8)
expected_y = 1 - (1 + tout) * np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_01(self):
# First order system: x'(t) + x(t) = u(t)
# Exact step response is x(t) = 1 - exp(-t).
system = ([1.0],[1.0,1.0])
tout, y = step2(system)
expected_y = 1.0 - np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_05(self):
# Simple integrator: x'(t) = u(t)
# Exact step response is x(t) = t.
system = ([1.0],[1.0,0.0])
tout, y = step2(system, atol=1e-10, rtol=1e-8)
expected_y = tout
assert_almost_equal(y, expected_y)
def test_06(self):
# Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = u(t)
# The exact step response is 1 - (1 + t)*exp(-t).
system = ([1.0], [1.0, 2.0, 1.0])
tout, y = step2(system, atol=1e-10, rtol=1e-8)
expected_y = 1 - (1 + tout) * np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_05(self):
# Simple integrator: x'(t) = u(t)
# Exact step response is x(t) = t.
system = ([1.0],[1.0,0.0])
tout, y = step2(system, atol=1e-10, rtol=1e-8)
expected_y = tout
assert_almost_equal(y, expected_y)
def test_01(self):
# First order system: x'(t) + x(t) = u(t)
# Exact step response is x(t) = 1 - exp(-t).
system = ([1.0],[1.0,1.0])
tout, y = step2(system)
expected_y = 1.0 - np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_04(self):
"""Specify an initial condition as a list."""
# First order system: x'(t) + x(t) = u(t), x(0)=3.0
# Exact step response is x(t) = 1 + 2*exp(-t).
system = ([1.0],[1.0,1.0])
tout, y = step2(system, X0=[3.0])
expected_y = 1 + 2.0*np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_04(self):
"""Specify an initial condition as a list."""
# First order system: x'(t) + x(t) = u(t), x(0)=3.0
# Exact step response is x(t) = 1 + 2*exp(-t).
system = ([1.0],[1.0,1.0])
tout, y = step2(system, X0=[3.0])
expected_y = 1 + 2.0*np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_02(self):
"""Specify the desired time values for the output."""
# First order system: x'(t) + x(t) = u(t)
# Exact step response is x(t) = 1 - exp(-t).
system = ([1.0],[1.0,1.0])
n = 21
t = np.linspace(0, 2.0, n)
tout, y = step2(system, T=t)
assert_equal(tout.shape, (n,))
assert_almost_equal(tout, t)
expected_y = 1 - np.exp(-t)
assert_almost_equal(y, expected_y)
def test_02(self):
"""Specify the desired time values for the output."""
# First order system: x'(t) + x(t) = u(t)
# Exact step response is x(t) = 1 - exp(-t).
system = ([1.0],[1.0,1.0])
n = 21
t = np.linspace(0, 2.0, n)
tout, y = step2(system, T=t)
assert_equal(tout.shape, (n,))
assert_almost_equal(tout, t)
expected_y = 1 - np.exp(-t)
assert_almost_equal(y, expected_y)