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#!/usr/bin/env python
#
# slycot_convert_test.py - test SLICOT-based conversions
# RMM, 30 Mar 2011 (based on TestSlycot from v0.4a)
from __future__ import print_function
import unittest
import numpy as np
from control import matlab
from control.exception import slycot_check
@unittest.skipIf(not slycot_check(), "slycot not installed")
class TestSlycot(unittest.TestCase):
"""TestSlycot compares transfer function and state space conversions for
various numbers of inputs,outputs and states.
1. Usually passes for SISO systems of any state dim, occasonally,
there will be a dimension mismatch if the original randomly
generated ss system is not minimal because td04ad returns a
minimal system.
2. For small systems with many inputs, n<<m, the tests fail
because td04ad returns a minimal ss system which has fewer
states than the original system. It is typical for systems
with many more inputs than states to have extraneous states.
3. For systems with larger dimensions, n~>5 and with 2 or more
outputs the conversion to statespace (td04ad) intermittently
results in an equivalent realization of higher order than the
original tf order. We think this has to do with minimu
realization tolerances in the Fortran. The algorithm doesn't
recognize that two denominators are identical and so it
creates a system with nearly duplicate eigenvalues and
double the state dimension. This should not be a problem in
the python-control usage because the common_den() method finds
repeated roots within a tolerance that we specify.
Matlab: Matlab seems to force its statespace system output to
have order less than or equal to the order of denominators provided,
avoiding the problem of very large state dimension we describe in 3.
It does however, still have similar problems with pole/zero
cancellation such as we encounter in 2, where a statespace system
may have fewer states than the original order of transfer function.
"""
def setUp(self):
"""Define some test parameters."""
self.numTests = 5
self.maxStates = 10
self.maxI = 1
self.maxO = 1
def testTF(self, verbose=False):
""" Directly tests the functions tb04ad and td04ad through direct
comparison of transfer function coefficients.
Similar to convert_test, but tests at a lower level.
"""
from slycot import tb04ad, td04ad
for states in range(1, self.maxStates):
for inputs in range(1, self.maxI+1):
for outputs in range(1, self.maxO+1):
for testNum in range(self.numTests):
ssOriginal = matlab.rss(states, outputs, inputs)
if (verbose):
print('====== Original SS ==========')
print(ssOriginal)
print('states=', states)
print('inputs=', inputs)
print('outputs=', outputs)
tfOriginal_Actrb, tfOriginal_Bctrb, tfOriginal_Cctrb,\
tfOrigingal_nctrb, tfOriginal_index,\
tfOriginal_dcoeff, tfOriginal_ucoeff =\
tb04ad(states, inputs, outputs,
ssOriginal.A, ssOriginal.B,
ssOriginal.C, ssOriginal.D, tol1=0.0)
ssTransformed_nr, ssTransformed_A, ssTransformed_B,\
ssTransformed_C, ssTransformed_D\
= td04ad('R', inputs, outputs, tfOriginal_index,
tfOriginal_dcoeff, tfOriginal_ucoeff,
tol=0.0)
tfTransformed_Actrb, tfTransformed_Bctrb,\
tfTransformed_Cctrb, tfTransformed_nctrb,\
tfTransformed_index, tfTransformed_dcoeff,\
tfTransformed_ucoeff = tb04ad(
ssTransformed_nr, inputs, outputs,
ssTransformed_A, ssTransformed_B,
ssTransformed_C, ssTransformed_D, tol1=0.0)
# print('size(Trans_A)=',ssTransformed_A.shape)
if (verbose):
print('===== Transformed SS ==========')
print(matlab.ss(ssTransformed_A, ssTransformed_B,
ssTransformed_C, ssTransformed_D))
# print('Trans_nr=',ssTransformed_nr
# print('tfOrig_index=',tfOriginal_index)
# print('tfOrig_ucoeff=',tfOriginal_ucoeff)
# print('tfOrig_dcoeff=',tfOriginal_dcoeff)
# print('tfTrans_index=',tfTransformed_index)
# print('tfTrans_ucoeff=',tfTransformed_ucoeff)
# print('tfTrans_dcoeff=',tfTransformed_dcoeff)
# Compare the TF directly, must match
# numerators
# TODO test failing!
# np.testing.assert_array_almost_equal(
# tfOriginal_ucoeff, tfTransformed_ucoeff, decimal=3)
# denominators
# np.testing.assert_array_almost_equal(
# tfOriginal_dcoeff, tfTransformed_dcoeff, decimal=3)
def testFreqResp(self):
"""Compare the bode reponses of the SS systems and TF systems to the original SS
They generally are different realizations but have same freq resp.
Currently this test may only be applied to SISO systems.
"""
from slycot import tb04ad, td04ad
for states in range(1, self.maxStates):
for testNum in range(self.numTests):
for inputs in range(1, 1):
for outputs in range(1, 1):
ssOriginal = matlab.rss(states, outputs, inputs)
tfOriginal_Actrb, tfOriginal_Bctrb, tfOriginal_Cctrb,\
tfOrigingal_nctrb, tfOriginal_index,\
tfOriginal_dcoeff, tfOriginal_ucoeff = tb04ad(
states, inputs, outputs, ssOriginal.A,
ssOriginal.B, ssOriginal.C, ssOriginal.D,
tol1=0.0)
ssTransformed_nr, ssTransformed_A, ssTransformed_B,\
ssTransformed_C, ssTransformed_D\
= td04ad('R', inputs, outputs, tfOriginal_index,
tfOriginal_dcoeff, tfOriginal_ucoeff,
tol=0.0)
tfTransformed_Actrb, tfTransformed_Bctrb,\
tfTransformed_Cctrb, tfTransformed_nctrb,\
tfTransformed_index, tfTransformed_dcoeff,\
tfTransformed_ucoeff = tb04ad(
ssTransformed_nr, inputs, outputs,
ssTransformed_A, ssTransformed_B,
ssTransformed_C, ssTransformed_D,
tol1=0.0)
numTransformed = np.array(tfTransformed_ucoeff)
denTransformed = np.array(tfTransformed_dcoeff)
numOriginal = np.array(tfOriginal_ucoeff)
denOriginal = np.array(tfOriginal_dcoeff)
ssTransformed = matlab.ss(ssTransformed_A,
ssTransformed_B,
ssTransformed_C,
ssTransformed_D)
for inputNum in range(inputs):
for outputNum in range(outputs):
[ssOriginalMag, ssOriginalPhase, freq] =\
matlab.bode(ssOriginal, Plot=False)
[tfOriginalMag, tfOriginalPhase, freq] =\
matlab.bode(matlab.tf(
numOriginal[outputNum][inputNum],
denOriginal[outputNum]), Plot=False)
[ssTransformedMag, ssTransformedPhase, freq] =\
matlab.bode(ssTransformed,
freq, Plot=False)
[tfTransformedMag, tfTransformedPhase, freq] =\
matlab.bode(matlab.tf(
numTransformed[outputNum][inputNum],
denTransformed[outputNum]),
freq, Plot=False)
# print('numOrig=',
# numOriginal[outputNum][inputNum])
# print('denOrig=',
# denOriginal[outputNum])
# print('numTrans=',
# numTransformed[outputNum][inputNum])
# print('denTrans=',
# denTransformed[outputNum])
np.testing.assert_array_almost_equal(
ssOriginalMag, tfOriginalMag, decimal=3)
np.testing.assert_array_almost_equal(
ssOriginalPhase, tfOriginalPhase,
decimal=3)
np.testing.assert_array_almost_equal(
ssOriginalMag, ssTransformedMag, decimal=3)
np.testing.assert_array_almost_equal(
ssOriginalPhase, ssTransformedPhase,
decimal=3)
np.testing.assert_array_almost_equal(
tfOriginalMag, tfTransformedMag, decimal=3)
np.testing.assert_array_almost_equal(
tfOriginalPhase, tfTransformedPhase,
decimal=2)
# These are here for once the above is made into a unittest.
def suite():
return unittest.TestLoader().loadTestsFromTestCase(TestSlycot)
if __name__ == '__main__':
unittest.main()