def testBalredMatchDC(self, matarrayin):
# controlable canonical realization computed in matlab for the transfer
# function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin(
[[-15., -7.5, -6.25, -1.875],
[8., 0., 0., 0.],
[0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = matarrayin([[2.], [0.], [0.], [0.]])
C = matarrayin([[0.5, 0.6875, 0.7031, 0.5]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
orders = 2
rsys = balred(sys,orders,method='matchdc')
Artrue = np.array(
[[-4.43094773, -4.55232904],
[-4.55232904, -5.36195206]])
Brtrue = np.array([[1.36235673], [1.03114388]])
Crtrue = np.array([[1.36235673, 1.03114388]])
Drtrue = np.array([[-0.08383902]])
np.testing.assert_array_almost_equal(rsys.A, Artrue, decimal=2)
np.testing.assert_array_almost_equal(rsys.B, Brtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.C, Crtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.D, Drtrue, decimal=4)
def testBalredTruncate(self, matarrayin):
# controlable canonical realization computed in matlab for the transfer
# function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = matarrayin([[-15., -7.5, -6.25, -1.875], [8., 0., 0., 0.],
[0., 4., 0., 0.], [0., 0., 1., 0.]])
B = matarrayin([[2.], [0.], [0.], [0.]])
C = matarrayin([[0.5, 0.6875, 0.7031, 0.5]])
D = matarrayin([[0.]])
sys = StateSpace(A, B, C, D)
orders = 2
rsys = balred(sys, orders, method='truncate')
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[0.9057], [0.4068]])
Crtrue = np.array([[0.9057, 0.4068]])
Drtrue = np.array([[0.]])
np.testing.assert_array_almost_equal(rsys.A, Artrue, decimal=2)
np.testing.assert_array_almost_equal(rsys.B, Brtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.C, Crtrue, decimal=4)
np.testing.assert_array_almost_equal(rsys.D, Drtrue, decimal=4)
plt.close('all')
# controllable canonical realization computed in MATLAB for the
# transfer function: num = [1 11 45 32], den = [1 15 60 200 60]
A = np.array([[-15., -7.5, -6.25, -1.875], [8., 0., 0., 0.], [0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = np.array([[2.], [0.], [0.], [0.]])
C = np.array([[0.5, 0.6875, 0.7031, 0.5]])
D = np.array([[0.]])
# The full system
fsys = StateSpace(A, B, C, D)
# The reduced system, truncating the order by 1
n = 3
rsys = msimp.balred(fsys, n, method='truncate')
# Comparison of the step responses of the full and reduced systems
plt.figure(1)
y, t = mt.step(fsys)
yr, tr = mt.step(rsys)
plt.plot(t.T, y.T)
plt.plot(tr.T, yr.T)
# Repeat balanced reduction, now with 100-dimensional random state space
sysrand = mt.rss(100, 1, 1)
rsysrand = msimp.balred(sysrand, 10, method='truncate')
# Comparison of the impulse responses of the full and reduced random systems
plt.figure(2)
yrand, trand = mt.impulse(sysrand)
#controlable canonical realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = np.matrix('-15., -7.5, -6.25, -1.875; \
8., 0., 0., 0.; \
0., 4., 0., 0.; \
0., 0., 1., 0.')
B = np.matrix('2.; 0.; 0.; 0.')
C = np.matrix('0.5, 0.6875, 0.7031, 0.5')
D = np.matrix('0.')
# The full system
fsys = StateSpace(A,B,C,D)
# The reduced system, truncating the order by 1
ord = 3
rsys = msimp.balred(fsys,ord, method = 'truncate')
# Comparison of the step responses of the full and reduced systems
plt.figure(1)
y, t = mt.step(fsys)
yr, tr = mt.step(rsys)
plt.plot(t.T, y.T)
plt.plot(tr.T, yr.T)
# Repeat balanced reduction, now with 100-dimensional random state space
sysrand = mt.rss(100, 1, 1)
rsysrand = msimp.balred(sysrand,10,method ='truncate')
# Comparison of the impulse responses of the full and reduced random systems
plt.figure(2)
yrand, trand = mt.impulse(sysrand)