def test_simple_dlqr():
# Example taken from M. de Oliveira's MAE280B lecture notes
H = State([[0, 0, 1, 0],
[0, 0, 0, 1],
[4.03428022844288e-06, 0, 0, 0.0515652322798669],
[0, 0, -0.000104315254033883, 0]],
[[0, 0], [1e-5/3, 0], [0, 0], [0, 0.01]],
eye(4), dt=0.1)
k, _, _ = lqr(H[:, 1], eye(4))
H.a = H.a.T
f, _, _ = lqr(H[:, 0], block_diag(0, 0, 1e-5, 1e-5), 0.1)
assert_almost_equal(k, array([[0, 0, -2.08727337333631e-06, 0]]))
assert_almost_equal(f, array([[1.71884123e-11, 0, 0, -1.79301359e-15]]))
def test_simple_dlqr():
# Example taken from M. de Oliveira's MAE280B lecture notes
H = State([[0, 0, 1, 0], [0, 0, 0, 1],
[4.03428022844288e-06, 0, 0, 0.0515652322798669],
[0, 0, -0.000104315254033883, 0]],
[[0, 0], [1e-5 / 3, 0], [0, 0], [0, 0.01]],
eye(4),
dt=0.1)
k, _, _ = lqr(H[:, 1], eye(4))
H.a = H.a.T
f, _, _ = lqr(H[:, 0], block_diag(0, 0, 1e-5, 1e-5), 0.1)
assert_almost_equal(k, array([[0, 0, -2.08727337333631e-06, 0]]))
assert_almost_equal(f, array([[1.71884123e-11, 0, 0, -1.79301359e-15]]))
def test_simple_lqr():
# Example taken from M. de Oliveira's MAE280B lecture notes
H = State([[0, 0, 1, 0], [0, 0, 0, 1],
[4.03428022844288e-06, 0, 0, 0.0515652322798669],
[0, 0, -0.000104315254033883, 0]],
[[0, 0], [1e-5 / 3, 0], [0, 0], [0, 0.01]], eye(4))
k, _, _ = lqr(H[:, 1], eye(4))
H.a = H.a.T
f, _, _ = lqr(H[:, 0], block_diag(0, 0, 1e-5, 1e-5), 0.1)
assert_almost_equal(k, array([[1.00554916, -1, 52.52180106, 18.51107167]]))
assert_almost_equal(
f,
array([[-577.370350, 173.600463, 0.383744946, 0.050228534]]),
decimal=5)
def test_simple_lqr():
# Example taken from M. de Oliveira's MAE280B lecture notes
H = State([[0, 0, 1, 0],
[0, 0, 0, 1],
[4.03428022844288e-06, 0, 0, 0.0515652322798669],
[0, 0, -0.000104315254033883, 0]],
[[0, 0], [1e-5/3, 0], [0, 0], [0, 0.01]],
eye(4))
k, _, _ = lqr(H[:, 1], eye(4))
H.a = H.a.T
f, _, _ = lqr(H[:, 0], block_diag(0, 0, 1e-5, 1e-5), 0.1)
assert_almost_equal(k, array([[1.00554916, -1, 52.52180106, 18.51107167]]))
assert_almost_equal(f, array([[-577.370350, 173.600463,
0.383744946, 0.050228534]]), decimal=5)
def test_simple_lqry():
# Scalar matrices
H = State(1, 1, 1, 1)
k, x, e = lqr(H, Q=3, weight_on='output')
assert_almost_equal(array([k[0, 0], x[0, 0], e[0]]), [1.5, 3, -0.5 + 0j])
# Wrong S shape
assert_raises(ValueError, lqr, H, Q=3, S=eye(2), weight_on='output')
def test_simple_lqry():
# Scalar matrices
H = State(1, 1, 1, 1)
k, x, e = lqr(H, Q=3, weight_on='output')
assert_almost_equal(array([k[0, 0], x[0, 0], e[0]]), [1.5, 3, -0.5+0j])
# Wrong S shape
assert_raises(ValueError, lqr, H, Q=3, S=eye(2), weight_on='output')
def test_lqr_arguments():
# First arg is not LTI
assert_raises(ValueError, lqr, 1, 1)
# Static Gain
assert_raises(ValueError, lqr, State(1), 1)
# Wrong string
assert_raises(ValueError, lqr, Transfer(1, [1, 1]), 1, weight_on='asdf')
# scalar matrices
H = Transfer(1, [1, 1])
k, x, e = lqr(H, 3)
assert_almost_equal(array([k[0, 0], x[0, 0], e[0]]), [1, 1, -2 + 0j])
def test_lqr_arguments():
# First arg is not LTI
assert_raises(ValueError, lqr, 1, 1)
# Static Gain
assert_raises(ValueError, lqr, State(1), 1)
# Wrong string
assert_raises(ValueError, lqr, Transfer(1, [1, 1]), 1, weight_on='asdf')
# scalar matrices
H = Transfer(1, [1, 1])
k, x, e = lqr(H, 3)
assert_almost_equal(array([k[0, 0], x[0, 0], e[0]]), [1, 1, -2+0j])
def test_feedback_dynamic_static():
M = array([[2, 2, 1, -1],
[3, 2, -2, 3],
[1, -1, 1, -3],
[0, -1, 2, 0]])
a, b, c, d = matrix_slice(M, [3, 3])
G = State(a, b, eye(3))
H, _, _ = lqr(G, eye(3))
CL = feedback(G, H)
assert_almost_equal(CL.poles,
array([-5.42998305, -3.75504185, -1.55400925]))
G = State(a, b, c, d)
CL = feedback(G, 5+0j)
assert_almost_equal(concatenate_state_matrices(CL),
array([[2., -3., 11., -1.],
[3., 17., -32., 3.],
[1., -16., 31., -3.],
[0., -1., 2., 0.]]))
CL = feedback(5, G)
assert_almost_equal(concatenate_state_matrices(CL),
array([[2., -3., 11., -5.],
[3., 17., -32., 15.],
[1., -16., 31., -15.],
[0., 5., -10., 5.]]))
