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