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Fix canonical form 'observable' #200

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Merged
murrayrm merged 2 commits into from
Jul 2, 2018
Merged

Fix canonical form 'observable' #200

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598a91a
Fix canonical form 'observable'
Apr 18, 2018
5009e92
add: test for singularity; unittests
Apr 23, 2018
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5 changes: 4 additions & 1 deletion control/canonical.py
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Original file line number Diff line number Diff line change
Expand Up @@ -133,7 +133,10 @@ def observable_form(xsys):
Wrz = obsv(zsys.A, zsys.C)

# Transformation from one form to another
Tzx = inv(Wrz) * Wrx
Tzx = solve(Wrz, Wrx) # matrix left division, Tzx = inv(Wrz) * Wrx

if matrix_rank(Tzx) != xsys.states:
raise ValueError("Transformation matrix singular to working precision.")

# Finally, compute the output matrix
zsys.B = Tzx * xsys.B
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44 changes: 44 additions & 0 deletions control/tests/canonical_test.py
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Expand Up @@ -52,3 +52,47 @@ def test_unreachable_system(self):

# Check if an exception is raised
np.testing.assert_raises(ValueError, canonical_form, sys, "reachable")

def test_observable_form(self):
"""Test the observable canonical form"""

# Create a system in the observable canonical form
coeffs = [1.0, 2.0, 3.0, 4.0, 1.0]
A_true = np.polynomial.polynomial.polycompanion(coeffs)
A_true = np.fliplr(np.flipud(A_true))
B_true = np.matrix("1.0 1.0 1.0 1.0").T
C_true = np.matrix("1.0 0.0 0.0 0.0")
D_true = 42.0

# Perform a coordinate transform with a random invertible matrix
T_true = np.matrix([[-0.27144004, -0.39933167, 0.75634684, 0.44135471],
[-0.74855725, -0.39136285, -0.18142339, -0.50356997],
[-0.40688007, 0.81416369, 0.38002113, -0.16483334],
[-0.44769516, 0.15654653, -0.50060858, 0.72419146]])
A = np.linalg.solve(T_true, A_true)*T_true
B = np.linalg.solve(T_true, B_true)
C = C_true*T_true
D = D_true

# Create a state space system and convert it to the observable canonical form
sys_check, T_check = canonical_form(ss(A, B, C, D), "observable")

# Check against the true values
np.testing.assert_array_almost_equal(sys_check.A, A_true)
np.testing.assert_array_almost_equal(sys_check.B, B_true)
np.testing.assert_array_almost_equal(sys_check.C, C_true)
np.testing.assert_array_almost_equal(sys_check.D, D_true)
np.testing.assert_array_almost_equal(T_check, T_true)

def test_unobservable_system(self):
"""Test observable canonical form with an unobservable system"""

# Create an unobservable system
A = np.matrix("1.0 2.0 2.0; 4.0 5.0 5.0; 7.0 8.0 8.0")
B = np.matrix("1.0 1.0 1.0").T
C = np.matrix("1.0 1.0 1.0")
D = 42.0
sys = ss(A, B, C, D)

# Check if an exception is raised
np.testing.assert_raises(ValueError, canonical_form, sys, "observable")