Merge pull request python-control#200 from ipa-lth/master

murrayrm · web-flow · commit 077a8bcc2a79 · 2018-07-01T20:06:05.000-07:00
Fix canonical form 'observable'
diff --git a/control/canonical.py b/control/canonical.py
@@ -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
diff --git a/control/tests/canonical_test.py b/control/tests/canonical_test.py
@@ -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")
