#!/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 sys as pysys
import numpy as np
import warnings
from control.statefbk import ctrb, obsv, place, place_varga, lqr, gram, acker
from control.matlab import *
from control.exception import slycot_check, ControlDimension
from control.mateqn import care, dare
from control.config import use_numpy_matrix, reset_defaults
class TestStatefbk(unittest.TestCase):
"""Test state feedback functions"""
def setUp(self):
# Use array instead of matrix (and save old value to restore at end)
use_numpy_matrix(False)
# 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.array([[1., 2.], [3., 4.]])
B = np.array([[5.], [7.]])
Wctrue = np.array([[5., 19.], [7., 43.]])
Wc = ctrb(A, B)
np.testing.assert_array_almost_equal(Wc, Wctrue)
self.assertTrue(isinstance(Wc, np.ndarray))
self.assertFalse(isinstance(Wc, np.matrix))
# This test only works in Python 3 due to a conflict with the same
# warning type in other test modules (frd_test.py). See
# https://bugs.python.org/issue4180 for more details
@unittest.skipIf(pysys.version_info < (3, 0), "test requires Python 3+")
def test_ctrb_siso_deprecated(self):
A = np.array([[1., 2.], [3., 4.]])
B = np.array([[5.], [7.]])
# Check that default using np.matrix generates a warning
# TODO: remove this check with matrix type is deprecated
warnings.resetwarnings()
with warnings.catch_warnings(record=True) as w:
use_numpy_matrix(True)
self.assertTrue(issubclass(w[-1].category, UserWarning))
Wc = ctrb(A, B)
self.assertTrue(isinstance(Wc, np.matrix))
self.assertTrue(issubclass(w[-1].category,
PendingDeprecationWarning))
use_numpy_matrix(False)
def testCtrbMIMO(self):
A = np.array([[1., 2.], [3., 4.]])
B = np.array([[5., 6.], [7., 8.]])
Wctrue = np.array([[5., 6., 19., 22.], [7., 8., 43., 50.]])
Wc = ctrb(A, B)
np.testing.assert_array_almost_equal(Wc, Wctrue)
# Make sure default type values are correct
self.assertTrue(isinstance(Wc, np.ndarray))
def testObsvSISO(self):
A = np.array([[1., 2.], [3., 4.]])
C = np.array([[5., 7.]])
Wotrue = np.array([[5., 7.], [26., 38.]])
Wo = obsv(A, C)
np.testing.assert_array_almost_equal(Wo, Wotrue)
# Make sure default type values are correct
self.assertTrue(isinstance(Wo, np.ndarray))
# This test only works in Python 3 due to a conflict with the same
# warning type in other test modules (frd_test.py). See
# https://bugs.python.org/issue4180 for more details
@unittest.skipIf(pysys.version_info < (3, 0), "test requires Python 3+")
def test_obsv_siso_deprecated(self):
A = np.array([[1., 2.], [3., 4.]])
C = np.array([[5., 7.]])
# Check that default type generates a warning
# TODO: remove this check with matrix type is deprecated
with warnings.catch_warnings(record=True) as w:
use_numpy_matrix(True, warn=False) # warnings off
self.assertEqual(len(w), 0)
Wo = obsv(A, C)
self.assertTrue(isinstance(Wo, np.matrix))
use_numpy_matrix(False)
def testObsvMIMO(self):
A = np.array([[1., 2.], [3., 4.]])
C = np.array([[5., 6.], [7., 8.]])
Wotrue = np.array([[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.array([[1.2, -2.3], [3.4, -4.5]])
B = np.array([[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.array([[1., -2.], [3., -4.]])
B = np.array([[5., 6.], [7., 8.]])
C = np.array([[4., 5.], [6., 7.]])
D = np.array([[13., 14.], [15., 16.]])
sys = ss(A, B, C, D)
Wctrue = np.array([[18.5, 24.5], [24.5, 32.5]])
Wc = gram(sys, 'c')
np.testing.assert_array_almost_equal(Wc, Wctrue)
# This test only works in Python 3 due to a conflict with the same
# warning type in other test modules (frd_test.py). See
# https://bugs.python.org/issue4180 for more details
@unittest.skipIf(pysys.version_info < (3, 0) or not slycot_check(),
"test requires Python 3+ and slycot")
def test_gram_wc_deprecated(self):
A = np.array([[1., -2.], [3., -4.]])
B = np.array([[5., 6.], [7., 8.]])
C = np.array([[4., 5.], [6., 7.]])
D = np.array([[13., 14.], [15., 16.]])
sys = ss(A, B, C, D)
# Check that default type generates a warning
# TODO: remove this check with matrix type is deprecated
with warnings.catch_warnings(record=True) as w:
use_numpy_matrix(True)
self.assertTrue(issubclass(w[-1].category, UserWarning))
Wc = gram(sys, 'c')
self.assertTrue(isinstance(Wc, np.ndarray))
use_numpy_matrix(False)
@unittest.skipIf(not slycot_check(), "slycot not installed")
def testGramRc(self):
A = np.array([[1., -2.], [3., -4.]])
B = np.array([[5., 6.], [7., 8.]])
C = np.array([[4., 5.], [6., 7.]])
D = np.array([[13., 14.], [15., 16.]])
sys = ss(A, B, C, D)
Rctrue = np.array([[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.array([[1., -2.], [3., -4.]])
B = np.array([[5., 6.], [7., 8.]])
C = np.array([[4., 5.], [6., 7.]])
D = np.array([[13., 14.], [15., 16.]])
sys = ss(A, B, C, D)
Wotrue = np.array([[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.array([[1., -2.], [3., -4.]])
B = np.array([[5.], [7.]])
C = np.array([[6., 8.]])
D = np.array([[9.]])
sys = ss(A,B,C,D)
Wotrue = np.array([[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.array([[1., -2.], [3., -4.]])
B = np.array([[5., 6.], [7., 8.]])
C = np.array([[4., 5.], [6., 7.]])
D = np.array([[13., 14.], [15., 16.]])
sys = ss(A, B, C, D)
Rotrue = np.array([[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)
@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)
def tearDown(self):
reset_defaults()
if __name__ == '__main__':
unittest.main()
