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#!/usr/bin/env python
#
# modelsimp_test.py - test model reduction functions
# RMM, 30 Mar 2011 (based on TestModelSimp from v0.4a)
import unittest
import numpy as np
import warnings
import control
from control.modelsimp import *
from control.matlab import *
from control.exception import slycot_check, ControlMIMONotImplemented
class TestModelsimp(unittest.TestCase):
def setUp(self):
# Use array instead of matrix (and save old value to restore at end)
control.use_numpy_matrix(False)
@unittest.skipIf(not slycot_check(), "slycot not installed")
def testHSVD(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)
hsv = hsvd(sys)
hsvtrue = np.array([24.42686, 0.5731395]) # from MATLAB
np.testing.assert_array_almost_equal(hsv, hsvtrue)
# Make sure default type values are correct
self.assertTrue(isinstance(hsv, np.ndarray))
self.assertFalse(isinstance(hsv, np.matrix))
# Check that using numpy.matrix does *not* affect answer
with warnings.catch_warnings(record=True) as w:
control.use_numpy_matrix(True)
self.assertTrue(issubclass(w[-1].category, UserWarning))
# Redefine the system (using np.matrix for storage)
sys = ss(A, B, C, D)
# Compute the Hankel singular value decomposition
hsv = hsvd(sys)
# Make sure that return type is correct
self.assertTrue(isinstance(hsv, np.ndarray))
self.assertFalse(isinstance(hsv, np.matrix))
# Go back to using the normal np.array representation
control.use_numpy_matrix(False)
def testMarkovSignature(self):
U = np.array([[1., 1., 1., 1., 1.]])
Y = U
m = 3
H = markov(Y, U, m, transpose=False)
Htrue = np.array([[1., 0., 0.]])
np.testing.assert_array_almost_equal( H, Htrue )
# Make sure that transposed data also works
H = markov(np.transpose(Y), np.transpose(U), m, transpose=True)
np.testing.assert_array_almost_equal( H, np.transpose(Htrue) )
# Default (in v0.8.4 and below) should be transpose=True (w/ warning)
import warnings
warnings.simplefilter('always', UserWarning) # don't supress
with warnings.catch_warnings(record=True) as w:
# Set up warnings filter to only show warnings in control module
warnings.filterwarnings("ignore")
warnings.filterwarnings("always", module="control")
# Generate Markov parameters without any arguments
H = markov(np.transpose(Y), np.transpose(U), m)
np.testing.assert_array_almost_equal( H, np.transpose(Htrue) )
# Make sure we got a warning
self.assertEqual(len(w), 1)
self.assertIn("assumed to be in rows", str(w[-1].message))
self.assertIn("change in a future release", str(w[-1].message))
# Test example from docstring
T = np.linspace(0, 10, 100)
U = np.ones((1, 100))
T, Y, _ = control.forced_response(
control.tf([1], [1, 0.5], True), T, U)
H = markov(Y, U, 3, transpose=False)
# Test example from issue #395
inp = np.array([1, 2])
outp = np.array([2, 4])
mrk = markov(outp, inp, 1, transpose=False)
# Make sure MIMO generates an error
U = np.ones((2, 100)) # 2 inputs (Y unchanged, with 1 output)
np.testing.assert_raises(ControlMIMONotImplemented, markov, Y, U, m)
# Make sure markov() returns the right answer
def testMarkovResults(self):
#
# Test over a range of parameters
#
# k = order of the system
# m = number of Markov parameters
# n = size of the data vector
#
# Values should match exactly for n = m, otherewise you get a
# close match but errors due to the assumption that C A^k B =
# 0 for k > m-2 (see modelsimp.py).
#
for k, m, n in \
((2, 2, 2), (2, 5, 5), (5, 2, 2), (5, 5, 5), (5, 10, 10)):
# Generate stable continuous time system
Hc = control.rss(k, 1, 1)
# Choose sampling time based on fastest time constant / 10
w, _ = np.linalg.eig(Hc.A)
Ts = np.min(-np.real(w)) / 10.
# Convert to a discrete time system via sampling
Hd = control.c2d(Hc, Ts, 'zoh')
# Compute the Markov parameters from state space
Mtrue = np.hstack([Hd.D] + [np.dot(
Hd.C, np.dot(np.linalg.matrix_power(Hd.A, i),
Hd.B)) for i in range(m-1)])
# Generate input/output data
T = np.array(range(n)) * Ts
U = np.cos(T) + np.sin(T/np.pi)
_, Y, _ = control.forced_response(Hd, T, U, squeeze=True)
Mcomp = markov(Y, U, m, transpose=False)
# Compare to results from markov()
np.testing.assert_array_almost_equal(Mtrue, Mcomp)
def testModredMatchDC(self):
#balanced realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = np.array(
[[-1.958, -1.194, 1.824, -1.464],
[-1.194, -0.8344, 2.563, -1.351],
[-1.824, -2.563, -1.124, 2.704],
[-1.464, -1.351, -2.704, -11.08]])
B = np.array([[-0.9057], [-0.4068], [-0.3263], [-0.3474]])
C = np.array([[-0.9057, -0.4068, 0.3263, -0.3474]])
D = np.array([[0.]])
sys = ss(A,B,C,D)
rsys = modred(sys,[2, 3],'matchdc')
Artrue = np.array([[-4.431, -4.552], [-4.552, -5.361]])
Brtrue = np.array([[-1.362], [-1.031]])
Crtrue = np.array([[-1.362, -1.031]])
Drtrue = np.array([[-0.08384]])
np.testing.assert_array_almost_equal(rsys.A, Artrue,decimal=3)
np.testing.assert_array_almost_equal(rsys.B, Brtrue,decimal=3)
np.testing.assert_array_almost_equal(rsys.C, Crtrue,decimal=3)
np.testing.assert_array_almost_equal(rsys.D, Drtrue,decimal=2)
def testModredUnstable(self):
# Check if an error is thrown when an unstable system is given
A = np.array(
[[4.5418, 3.3999, 5.0342, 4.3808],
[0.3890, 0.3599, 0.4195, 0.1760],
[-4.2117, -3.2395, -4.6760, -4.2180],
[0.0052, 0.0429, 0.0155, 0.2743]])
B = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
C = np.array([[1.0, 2.0, 3.0, 4.0], [1.0, 2.0, 3.0, 4.0]])
D = np.array([[0.0, 0.0], [0.0, 0.0]])
sys = ss(A,B,C,D)
np.testing.assert_raises(ValueError, modred, sys, [2, 3])
def testModredTruncate(self):
#balanced realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = np.array(
[[-1.958, -1.194, 1.824, -1.464],
[-1.194, -0.8344, 2.563, -1.351],
[-1.824, -2.563, -1.124, 2.704],
[-1.464, -1.351, -2.704, -11.08]])
B = np.array([[-0.9057], [-0.4068], [-0.3263], [-0.3474]])
C = np.array([[-0.9057, -0.4068, 0.3263, -0.3474]])
D = np.array([[0.]])
sys = ss(A,B,C,D)
rsys = modred(sys,[2, 3],'truncate')
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[-0.9057], [-0.4068]])
Crtrue = np.array([[-0.9057, -0.4068]])
Drtrue = np.array([[0.]])
np.testing.assert_array_almost_equal(rsys.A, Artrue)
np.testing.assert_array_almost_equal(rsys.B, Brtrue)
np.testing.assert_array_almost_equal(rsys.C, Crtrue)
np.testing.assert_array_almost_equal(rsys.D, Drtrue)
@unittest.skipIf(not slycot_check(), "slycot not installed")
def testBalredTruncate(self):
#controlable canonical realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = np.array(
[[-15., -7.5, -6.25, -1.875],
[8., 0., 0., 0.],
[0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = np.array([[2.], [0.], [0.], [0.]])
C = np.array([[0.5, 0.6875, 0.7031, 0.5]])
D = np.array([[0.]])
sys = ss(A,B,C,D)
orders = 2
rsys = balred(sys,orders,method='truncate')
Artrue = np.array([[-1.958, -1.194], [-1.194, -0.8344]])
Brtrue = np.array([[0.9057], [0.4068]])
Crtrue = np.array([[0.9057, 0.4068]])
Drtrue = np.array([[0.]])
np.testing.assert_array_almost_equal(rsys.A, Artrue,decimal=2)
np.testing.assert_array_almost_equal(rsys.B, Brtrue,decimal=4)
np.testing.assert_array_almost_equal(rsys.C, Crtrue,decimal=4)
np.testing.assert_array_almost_equal(rsys.D, Drtrue,decimal=4)
@unittest.skipIf(not slycot_check(), "slycot not installed")
def testBalredMatchDC(self):
#controlable canonical realization computed in matlab for the transfer function:
# num = [1 11 45 32], den = [1 15 60 200 60]
A = np.array(
[[-15., -7.5, -6.25, -1.875],
[8., 0., 0., 0.],
[0., 4., 0., 0.],
[0., 0., 1., 0.]])
B = np.array([[2.], [0.], [0.], [0.]])
C = np.array([[0.5, 0.6875, 0.7031, 0.5]])
D = np.array([[0.]])
sys = ss(A,B,C,D)
orders = 2
rsys = balred(sys,orders,method='matchdc')
Artrue = np.array(
[[-4.43094773, -4.55232904],
[-4.55232904, -5.36195206]])
Brtrue = np.array([[1.36235673], [1.03114388]])
Crtrue = np.array([[1.36235673, 1.03114388]])
Drtrue = np.array([[-0.08383902]])
np.testing.assert_array_almost_equal(rsys.A, Artrue,decimal=2)
np.testing.assert_array_almost_equal(rsys.B, Brtrue,decimal=4)
np.testing.assert_array_almost_equal(rsys.C, Crtrue,decimal=4)
np.testing.assert_array_almost_equal(rsys.D, Drtrue,decimal=4)
def tearDown(self):
# Reset configuration variables to their original settings
control.config.reset_defaults()
if __name__ == '__main__':
unittest.main()