352 lines
13 KiB
Python
352 lines
13 KiB
Python
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#!/usr/bin/env python
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#
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# statefbk_test.py - test state feedback functions
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# RMM, 30 Mar 2011 (based on TestStatefbk from v0.4a)
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from __future__ import print_function
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import unittest
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import numpy as np
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from control.statefbk import ctrb, obsv, place, place_varga, lqr, lqe, gram, acker
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from control.matlab import *
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from control.exception import slycot_check, ControlDimension
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from control.mateqn import care, dare
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class TestStatefbk(unittest.TestCase):
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"""Test state feedback functions"""
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def setUp(self):
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# Maximum number of states to test + 1
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self.maxStates = 5
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# Maximum number of inputs and outputs to test + 1
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self.maxTries = 4
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# Set to True to print systems to the output.
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self.debug = False
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# get consistent test results
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np.random.seed(0)
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def testCtrbSISO(self):
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A = np.matrix("1. 2.; 3. 4.")
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B = np.matrix("5.; 7.")
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Wctrue = np.matrix("5. 19.; 7. 43.")
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Wc = ctrb(A,B)
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np.testing.assert_array_almost_equal(Wc, Wctrue)
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def testCtrbMIMO(self):
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A = np.matrix("1. 2.; 3. 4.")
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B = np.matrix("5. 6.; 7. 8.")
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Wctrue = np.matrix("5. 6. 19. 22.; 7. 8. 43. 50.")
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Wc = ctrb(A,B)
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np.testing.assert_array_almost_equal(Wc, Wctrue)
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def testObsvSISO(self):
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A = np.matrix("1. 2.; 3. 4.")
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C = np.matrix("5. 7.")
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Wotrue = np.matrix("5. 7.; 26. 38.")
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Wo = obsv(A,C)
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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def testObsvMIMO(self):
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A = np.matrix("1. 2.; 3. 4.")
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C = np.matrix("5. 6.; 7. 8.")
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Wotrue = np.matrix("5. 6.; 7. 8.; 23. 34.; 31. 46.")
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Wo = obsv(A,C)
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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def testCtrbObsvDuality(self):
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A = np.matrix("1.2 -2.3; 3.4 -4.5")
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B = np.matrix("5.8 6.9; 8. 9.1")
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Wc = ctrb(A,B);
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A = np.transpose(A)
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C = np.transpose(B)
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Wo = np.transpose(obsv(A,C));
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np.testing.assert_array_almost_equal(Wc,Wo)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramWc(self):
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A = np.matrix("1. -2.; 3. -4.")
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B = np.matrix("5. 6.; 7. 8.")
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C = np.matrix("4. 5.; 6. 7.")
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D = np.matrix("13. 14.; 15. 16.")
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sys = ss(A, B, C, D)
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Wctrue = np.matrix("18.5 24.5; 24.5 32.5")
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Wc = gram(sys,'c')
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np.testing.assert_array_almost_equal(Wc, Wctrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramRc(self):
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A = np.matrix("1. -2.; 3. -4.")
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B = np.matrix("5. 6.; 7. 8.")
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C = np.matrix("4. 5.; 6. 7.")
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D = np.matrix("13. 14.; 15. 16.")
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sys = ss(A, B, C, D)
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Rctrue = np.matrix("4.30116263 5.6961343; 0. 0.23249528")
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Rc = gram(sys,'cf')
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np.testing.assert_array_almost_equal(Rc, Rctrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramWo(self):
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A = np.matrix("1. -2.; 3. -4.")
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B = np.matrix("5. 6.; 7. 8.")
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C = np.matrix("4. 5.; 6. 7.")
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D = np.matrix("13. 14.; 15. 16.")
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sys = ss(A, B, C, D)
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Wotrue = np.matrix("257.5 -94.5; -94.5 56.5")
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Wo = gram(sys,'o')
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramWo2(self):
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A = np.matrix("1. -2.; 3. -4.")
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B = np.matrix("5.; 7.")
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C = np.matrix("6. 8.")
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D = np.matrix("9.")
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sys = ss(A,B,C,D)
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Wotrue = np.matrix("198. -72.; -72. 44.")
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Wo = gram(sys,'o')
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np.testing.assert_array_almost_equal(Wo, Wotrue)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testGramRo(self):
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A = np.matrix("1. -2.; 3. -4.")
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B = np.matrix("5. 6.; 7. 8.")
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C = np.matrix("4. 5.; 6. 7.")
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D = np.matrix("13. 14.; 15. 16.")
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sys = ss(A, B, C, D)
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Rotrue = np.matrix("16.04680654 -5.8890222; 0. 4.67112593")
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Ro = gram(sys,'of')
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np.testing.assert_array_almost_equal(Ro, Rotrue)
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def testGramsys(self):
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num =[1.]
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den = [1., 1., 1.]
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sys = tf(num,den)
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self.assertRaises(ValueError, gram, sys, 'o')
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self.assertRaises(ValueError, gram, sys, 'c')
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def testAcker(self):
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for states in range(1, self.maxStates):
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for i in range(self.maxTries):
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# start with a random SS system and transform to TF then
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# back to SS, check that the matrices are the same.
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sys = rss(states, 1, 1)
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if (self.debug):
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print(sys)
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# Make sure the system is not degenerate
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Cmat = ctrb(sys.A, sys.B)
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if np.linalg.matrix_rank(Cmat) != states:
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if (self.debug):
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print(" skipping (not reachable or ill conditioned)")
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continue
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# Place the poles at random locations
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des = rss(states, 1, 1);
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poles = pole(des)
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# Now place the poles using acker
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K = acker(sys.A, sys.B, poles)
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new = ss(sys.A - sys.B * K, sys.B, sys.C, sys.D)
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placed = pole(new)
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# Debugging code
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# diff = np.sort(poles) - np.sort(placed)
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# if not all(diff < 0.001):
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# print("Found a problem:")
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# print(sys)
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# print("desired = ", poles)
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np.testing.assert_array_almost_equal(np.sort(poles),
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np.sort(placed), decimal=4)
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def testPlace(self):
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# Matrices shamelessly stolen from scipy example code.
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A = np.array([[1.380, -0.2077, 6.715, -5.676],
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[-0.5814, -4.290, 0, 0.6750],
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[1.067, 4.273, -6.654, 5.893],
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[0.0480, 4.273, 1.343, -2.104]])
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B = np.array([[0, 5.679],
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[1.136, 1.136],
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[0, 0,],
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[-3.146, 0]])
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P = np.array([-0.5+1j, -0.5-1j, -5.0566, -8.6659])
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K = place(A, B, P)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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# Test that the dimension checks work.
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np.testing.assert_raises(ControlDimension, place, A[1:, :], B, P)
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np.testing.assert_raises(ControlDimension, place, A, B[1:, :], P)
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# Check that we get an error if we ask for too many poles in the same
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# location. Here, rank(B) = 2, so lets place three at the same spot.
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P_repeated = np.array([-0.5, -0.5, -0.5, -8.6659])
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np.testing.assert_raises(ValueError, place, A, B, P_repeated)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_continuous(self):
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"""
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Check that we can place eigenvalues for dtime=False
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"""
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5.], [7.]])
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P = np.array([-2., -2.])
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K = place_varga(A, B, P)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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# Test that the dimension checks work.
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np.testing.assert_raises(ControlDimension, place, A[1:, :], B, P)
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np.testing.assert_raises(ControlDimension, place, A, B[1:, :], P)
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# Regression test against bug #177
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# https://github.com/python-control/python-control/issues/177
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A = np.array([[0, 1], [100, 0]])
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B = np.array([[0], [1]])
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P = np.array([-20 + 10*1j, -20 - 10*1j])
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K = place_varga(A, B, P)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_continuous_partial_eigs(self):
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"""
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Check that we are able to use the alpha parameter to only place
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a subset of the eigenvalues, for the continous time case.
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"""
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# A matrix has eigenvalues at s=-1, and s=-2. Choose alpha = -1.5
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# and check that eigenvalue at s=-2 stays put.
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A = np.array([[1., -2.], [3., -4.]])
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B = np.array([[5.], [7.]])
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P = np.array([-3.])
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P_expected = np.array([-2.0, -3.0])
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alpha = -1.5
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K = place_varga(A, B, P, alpha=alpha)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P_expected.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P_expected, P_placed)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_discrete(self):
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"""
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Check that we can place poles using dtime=True (discrete time)
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"""
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A = np.array([[1., 0], [0, 0.5]])
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B = np.array([[5.], [7.]])
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P = np.array([0.5, 0.5])
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K = place_varga(A, B, P, dtime=True)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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# No guarantee of the ordering, so sort them
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P.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P, P_placed)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def testPlace_varga_discrete_partial_eigs(self):
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""""
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Check that we can only assign a single eigenvalue in the discrete
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time case.
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"""
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# A matrix has eigenvalues at 1.0 and 0.5. Set alpha = 0.51, and
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# check that the eigenvalue at 0.5 is not moved.
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A = np.array([[1., 0], [0, 0.5]])
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B = np.array([[5.], [7.]])
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P = np.array([0.2, 0.6])
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P_expected = np.array([0.5, 0.6])
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alpha = 0.51
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K = place_varga(A, B, P, dtime=True, alpha=alpha)
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P_placed = np.linalg.eigvals(A - B.dot(K))
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P_expected.sort()
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P_placed.sort()
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np.testing.assert_array_almost_equal(P_expected, P_placed)
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def check_LQR(self, K, S, poles, Q, R):
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S_expected = np.array(np.sqrt(Q * R))
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K_expected = S_expected / R
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poles_expected = np.array([-K_expected])
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np.testing.assert_array_almost_equal(S, S_expected)
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np.testing.assert_array_almost_equal(K, K_expected)
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np.testing.assert_array_almost_equal(poles, poles_expected)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_LQR_integrator(self):
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A, B, Q, R = 0., 1., 10., 2.
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K, S, poles = lqr(A, B, Q, R)
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self.check_LQR(K, S, poles, Q, R)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_LQR_3args(self):
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sys = ss(0., 1., 1., 0.)
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Q, R = 10., 2.
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K, S, poles = lqr(sys, Q, R)
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self.check_LQR(K, S, poles, Q, R)
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def check_LQE(self, L, P, poles, G, QN, RN):
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P_expected = np.array(np.sqrt(G*QN*G * RN))
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L_expected = P_expected / RN
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poles_expected = np.array([-L_expected], ndmin=2)
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np.testing.assert_array_almost_equal(P, P_expected)
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np.testing.assert_array_almost_equal(L, L_expected)
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np.testing.assert_array_almost_equal(poles, poles_expected)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_LQE(self):
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A, G, C, QN, RN = 0., .1, 1., 10., 2.
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L, P, poles = lqe(A, G, C, QN, RN)
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self.check_LQE(L, P, poles, G, QN, RN)
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@unittest.skipIf(not slycot_check(), "slycot not installed")
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def test_care(self):
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#unit test for stabilizing and anti-stabilizing feedbacks
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#continuous-time
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A = np.diag([1,-1])
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B = np.identity(2)
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||
|
|
Q = np.identity(2)
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||
|
|
R = np.identity(2)
|
||
|
|
S = 0 * B
|
||
|
|
E = np.identity(2)
|
||
|
|
X, L , G = care(A, B, Q, R, S, E, stabilizing=True)
|
||
|
|
assert np.all(np.real(L) < 0)
|
||
|
|
X, L , G = care(A, B, Q, R, S, E, stabilizing=False)
|
||
|
|
assert np.all(np.real(L) > 0)
|
||
|
|
|
||
|
|
@unittest.skipIf(not slycot_check(), "slycot not installed")
|
||
|
|
def test_dare(self):
|
||
|
|
#discrete-time
|
||
|
|
A = np.diag([0.5,2])
|
||
|
|
B = np.identity(2)
|
||
|
|
Q = np.identity(2)
|
||
|
|
R = np.identity(2)
|
||
|
|
S = 0 * B
|
||
|
|
E = np.identity(2)
|
||
|
|
X, L , G = dare(A, B, Q, R, S, E, stabilizing=True)
|
||
|
|
assert np.all(np.abs(L) < 1)
|
||
|
|
X, L , G = dare(A, B, Q, R, S, E, stabilizing=False)
|
||
|
|
assert np.all(np.abs(L) > 1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_suite():
|
||
|
|
return unittest.TestLoader().loadTestsFromTestCase(TestStatefbk)
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
unittest.main()
|