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Commitf5bca43

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additional updates based on@roryyorke review feedback
1 parent1965eb3 commitf5bca43

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3 files changed

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-38
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3 files changed

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‎control/descfcn.py

Lines changed: 23 additions & 26 deletions
Original file line numberDiff line numberDiff line change
@@ -21,7 +21,7 @@
2121
from .freqplotimportnyquist_plot
2222

2323
__all__= ['describing_function','describing_function_plot',
24-
'DescribingFunctionNonlinearity','backlash_nonlinearity',
24+
'DescribingFunctionNonlinearity','friction_backlash_nonlinearity',
2525
'relay_hysteresis_nonlinearity','saturation_nonlinearity']
2626

2727
# Class for nonlinearities with a built-in describing function
@@ -95,7 +95,7 @@ def describing_function(
9595
use the :class:`~control.DescribingFunctionNonlinearity` class,
9696
which provides this functionality.
9797
98-
A :float orarray_like
98+
A : array_like
9999
The amplitude(s) at which the describing function should be calculated.
100100
101101
zero_check : bool, optional
@@ -112,25 +112,19 @@ def describing_function(
112112
113113
Returns
114114
-------
115-
df : complex or array of complex
116-
The (complex) value of the describing function at the given amplitude.
117-
If the `A` parameter is an array of amplitudes, then an array of
118-
corresponding describing function values is returned.
115+
df : array of complex
116+
The (complex) value of the describing function at the given amplitudes.
119117
120118
Raises
121119
------
122120
TypeError
123-
If A < 0 or if A = 0 and the function F(0) is non-zero.
121+
If A[i] < 0 or if A[i] = 0 and the function F(0) is non-zero.
124122
125123
"""
126124
# If there is an analytical solution, trying using that first
127125
iftry_methodandhasattr(F,'describing_function'):
128126
try:
129-
# Go through all of the amplitudes we were given
130-
df= []
131-
forainnp.atleast_1d(A):
132-
df.append(F.describing_function(a))
133-
returnnp.array(df).reshape(np.shape(A))
127+
returnnp.vectorize(F.describing_function,otypes=[complex])(A)
134128
exceptNotImplementedError:
135129
# Drop through and do the numerical computation
136130
pass
@@ -170,17 +164,20 @@ def describing_function(
170164
# See if this is a static nonlinearity (assume not, just in case)
171165
ifnothasattr(F,'_isstatic')ornotF._isstatic():
172166
# Initialize any internal state by going through an initial cycle
173-
[F(x)forxinnp.atleast_1d(A).min()*sin_theta]
167+
forxinnp.atleast_1d(A).min()*sin_theta:
168+
F(x)# ignore the result
174169

175170
# Go through all of the amplitudes we were given
176-
df= []
177-
forainnp.atleast_1d(A):
171+
retdf=np.empty(np.shape(A),dtype=complex)
172+
df=retdf# Access to the return array
173+
df.shape= (-1, )# as a 1D array
174+
fori,ainenumerate(np.atleast_1d(A)):
178175
# Make sure we got a valid argument
179176
ifa==0:
180177
# Check to make sure the function has zero output with zero input
181178
ifzero_checkandnp.squeeze(F(0.))!=0:
182179
raiseValueError("function must evaluate to zero at zero")
183-
df.append(1.)
180+
df[i]=1.
184181
continue
185182
elifa<0:
186183
raiseValueError("cannot evaluate describing function for A < 0")
@@ -195,10 +192,10 @@ def describing_function(
195192
df_real= (F_eval @sin_theta)*scale# = M_1 \cos\phi / a
196193
df_imag= (F_eval @cos_theta)*scale# = M_1 \sin\phi / a
197194

198-
df.append(df_real+1j*df_imag)
195+
df[i]=df_real+1j*df_imag
199196

200197
# Return the values in the same shape as they were requested
201-
returnnp.array(df).reshape(np.shape(A))
198+
returnretdf
202199

203200

204201
defdescribing_function_plot(
@@ -437,16 +434,16 @@ def describing_function(self, A):
437434
returndf_real+1j*df_imag
438435

439436

440-
#Backlash nonlinearity (#48 in Gelb and Vander Velde, 1968)
441-
classbacklash_nonlinearity(DescribingFunctionNonlinearity):
437+
#Friction-dominated backlash nonlinearity (#48 in Gelb and Vander Velde, 1968)
438+
classfriction_backlash_nonlinearity(DescribingFunctionNonlinearity):
442439
"""Backlash nonlinearity for use in describing function analysis
443440
444-
This class creates a nonlinear function representing abacklash
445-
nonlinearity ,including the describing function for the nonlinearity. The
446-
following call creates a nonlinear function suitable for describing
447-
function analysis:
441+
This class creates a nonlinear function representing afriction-dominated
442+
backlashnonlinearity ,including the describing function for the
443+
nonlinearity. Thefollowing call creates a nonlinear function suitable
444+
for describingfunction analysis:
448445
449-
F =backlash_nonlinearity(b)
446+
F =friction_backlash_nonlinearity(b)
450447
451448
This function maintains an internal state representing the 'center' of a
452449
mechanism with backlash. If the new input is within `b/2` of the current
@@ -457,7 +454,7 @@ class backlash_nonlinearity(DescribingFunctionNonlinearity):
457454

458455
def__init__(self,b):
459456
# Create the describing function nonlinearity object
460-
super(backlash_nonlinearity,self).__init__()
457+
super(friction_backlash_nonlinearity,self).__init__()
461458

462459
self.b=b# backlash distance
463460
self.center=0# current center position

‎control/tests/descfcn_test.py

Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -12,8 +12,8 @@
1212
importnumpyasnp
1313
importcontrolasct
1414
importmath
15-
fromcontrol.descfcnimportsaturation_nonlinearity,backlash_nonlinearity,\
16-
relay_hysteresis_nonlinearity
15+
fromcontrol.descfcnimportsaturation_nonlinearity, \
16+
friction_backlash_nonlinearity,relay_hysteresis_nonlinearity
1717

1818

1919
# Static function via a class
@@ -84,15 +84,15 @@ def test_saturation_describing_function(satsys):
8484
df_anal= [satfcn.describing_function(a)forainamprange]
8585

8686
# Compute describing function for a static function
87-
df_fcn=[ct.describing_function(saturation,a)forainamprange]
87+
df_fcn=ct.describing_function(saturation,amprange)
8888
np.testing.assert_almost_equal(df_fcn,df_anal,decimal=3)
8989

9090
# Compute describing function for a describing function nonlinearity
91-
df_fcn=[ct.describing_function(satfcn,a)forainamprange]
91+
df_fcn=ct.describing_function(satfcn,amprange)
9292
np.testing.assert_almost_equal(df_fcn,df_anal,decimal=3)
9393

9494
# Compute describing function for a static I/O system
95-
df_sys=[ct.describing_function(satsys,a)forainamprange]
95+
df_sys=ct.describing_function(satsys,amprange)
9696
np.testing.assert_almost_equal(df_sys,df_anal,decimal=3)
9797

9898
# Compute describing function on an array of values
@@ -109,13 +109,13 @@ class my_saturation(ct.DescribingFunctionNonlinearity):
109109
def__call__(self,x):
110110
returnsaturation(x)
111111
satfcn_nometh=my_saturation()
112-
df_nometh=[ct.describing_function(satfcn_nometh,a)forainamprange]
112+
df_nometh=ct.describing_function(satfcn_nometh,amprange)
113113
np.testing.assert_almost_equal(df_nometh,df_anal,decimal=3)
114114

115115

116116
@pytest.mark.parametrize("fcn, amin, amax", [
117117
[saturation_nonlinearity(1),0,10],
118-
[backlash_nonlinearity(2),1,10],
118+
[friction_backlash_nonlinearity(2),1,10],
119119
[relay_hysteresis_nonlinearity(1,1),3,10],
120120
])
121121
deftest_describing_function(fcn,amin,amax):
@@ -161,7 +161,7 @@ def test_describing_function_plot():
161161
# Multiple intersections
162162
H_multiple=H_simple*ct.tf(*ct.pade(5,4))*4
163163
omega=np.logspace(-1,3,50)
164-
F_backlash=ct.descfcn.backlash_nonlinearity(1)
164+
F_backlash=ct.descfcn.friction_backlash_nonlinearity(1)
165165
amp=np.linspace(0.6,5,50)
166166
xsects=ct.describing_function_plot(H_multiple,F_backlash,amp,omega)
167167
fora,winxsects:

‎examples/describing_functions.ipynb

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -97,7 +97,7 @@
9797
"metadata": {},
9898
"source": [
9999
"### Backlash nonlinearity\n",
100-
"A backlash nonlinearity can be obtained using the `ct.backlash_nonlinearity` function. This function takes as is argument the size of the backlash region."
100+
"Afriction-dominatedbacklash nonlinearity can be obtained using the `ct.friction_backlash_nonlinearity` function. This function takes as is argument the size of the backlash region."
101101
]
102102
},
103103
{
@@ -119,13 +119,13 @@
119119
}
120120
],
121121
"source": [
122-
"backlash = ct.backlash_nonlinearity(0.5)\n",
122+
"backlash = ct.friction_backlash_nonlinearity(0.5)\n",
123123
"theta = np.linspace(0, 2*np.pi, 50)\n",
124124
"x = np.sin(theta)\n",
125125
"plt.plot(x, [backlash(z) for z in x])\n",
126126
"plt.xlabel(\"Input, x\")\n",
127127
"plt.ylabel(\"Output, y = backlash(x)\")\n",
128-
"plt.title(\"Input/output map for a backlash nonlinearity\");"
128+
"plt.title(\"Input/output map for afriction-dominatedbacklash nonlinearity\");"
129129
]
130130
},
131131
{
@@ -365,7 +365,7 @@
365365
"omega = np.logspace(-3, 3, 500)\n",
366366
"\n",
367367
"# Nonlinearity\n",
368-
"F_backlash = ct.backlash_nonlinearity(1)\n",
368+
"F_backlash = ct.friction_backlash_nonlinearity(1)\n",
369369
"amp = np.linspace(0.6, 5, 50)\n",
370370
"\n",
371371
"# Describing function plot\n",

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