-
Notifications
You must be signed in to change notification settings - Fork 458
Expand file tree
/
Copy pathslycot_convert_test.py
More file actions
213 lines (185 loc) · 8.93 KB
/
Copy pathslycot_convert_test.py
File metadata and controls
213 lines (185 loc) · 8.93 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
"""slycot_convert_test.py - test SLICOT-based conversions
RMM, 30 Mar 2011 (based on TestSlycot from v0.4a)
"""
import numpy as np
import pytest
from control import bode, rss, ss, tf
numTests = 5
maxStates = 10
maxI = 1
maxO = 1
@pytest.fixture(scope="module")
def fixedseed():
"""Get consistent test results"""
np.random.seed(0)
@pytest.mark.slycot
@pytest.mark.usefixtures("fixedseed")
class TestSlycot:
"""Test Slycot system conversion
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.
"""
@pytest.fixture
def verbose(self):
"""Set to True and switch off pytest stdout capture to print info"""
return False
@pytest.mark.parametrize("testNum", np.arange(numTests) + 1)
@pytest.mark.parametrize("inputs", np.arange(maxI) + 1)
@pytest.mark.parametrize("outputs", np.arange(maxO) + 1)
@pytest.mark.parametrize("states", np.arange(maxStates) + 1)
def testTF(self, states, outputs, inputs, testNum, verbose):
"""Test transfer function conversion.
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
ssOriginal = 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(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)
@pytest.mark.usefixtures("legacy_plot_signature")
@pytest.mark.parametrize("testNum", np.arange(numTests) + 1)
@pytest.mark.parametrize("inputs", np.arange(1) + 1) # SISO only
@pytest.mark.parametrize("outputs", np.arange(1) + 1) # SISO only
@pytest.mark.parametrize("states", np.arange(maxStates) + 1)
def testFreqResp(self, states, outputs, inputs, testNum, verbose):
"""Compare bode responses.
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
ssOriginal = 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 = ss(ssTransformed_A,
ssTransformed_B,
ssTransformed_C,
ssTransformed_D)
for inputNum in range(inputs):
for outputNum in range(outputs):
[ssOriginalMag, ssOriginalPhase, freq] =\
bode(ssOriginal, plot=False)
[tfOriginalMag, tfOriginalPhase, freq] =\
bode(tf(numOriginal[outputNum][inputNum],
denOriginal[outputNum]),
plot=False)
[ssTransformedMag, ssTransformedPhase, freq] =\
bode(ssTransformed,
freq,
plot=False)
[tfTransformedMag, tfTransformedPhase, freq] =\
bode(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)