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Commitb6b92d0

Browse files
authored
Merge branch 'master' into rlocus_zoom
2 parentsc65c100 +4286329 commitb6b92d0

39 files changed

+1421
-824
lines changed

‎.travis.yml

Lines changed: 5 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -28,10 +28,9 @@ env:
2828
before_install:
2929
# Install gfortran for testing slycot; use apt-get instead of conda in
3030
# order to include the proper CXXABI dependency (updated in GCC 4.9)
31-
# Also need to include liblapack here, to make sure paths are right
3231
-if [[ "$SLYCOT" != "" ]]; then
3332
sudo apt-get update -qq;
34-
sudo apt-get install gfortran liblapack-dev;
33+
sudo apt-get install gfortran;
3534
fi
3635
# Install display manager to allow testing of plotting functions
3736
-export DISPLAY=:99.0
@@ -51,6 +50,10 @@ before_install:
5150
-conda info -a
5251
-conda create -q -n test-environment python="$TRAVIS_PYTHON_VERSION" pip coverage
5352
-source activate test-environment
53+
# Install openblas if slycot is being used
54+
-if [[ "$SLYCOT" != "" ]]; then
55+
conda install openblas;
56+
fi
5457
# Make sure to look in the right place for python libraries (for slycot)
5558
-export LIBRARY_PATH="$HOME/miniconda/envs/test-environment/lib"
5659
# coveralls not in conda repos => install via pip instead

‎README.rst

Lines changed: 10 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -24,7 +24,7 @@ Features
2424
Links
2525
=====
2626

27-
- Project home page: http://python-control.sourceforge.net
27+
- Project home page: http://python-control.org
2828
- Source code repository: https://github.com/python-control/python-control
2929
- Documentation: http://python-control.readthedocs.org/
3030
- Issue tracker: https://github.com/python-control/python-control/issues
@@ -46,7 +46,7 @@ https://github.com/python-control/Slycot
4646
Installation
4747
============
4848

49-
The package may be installed using pip or distutils.
49+
The package may be installed using pip, conda, or distutils.
5050

5151
Pip
5252
---
@@ -56,6 +56,14 @@ To install using pip::
5656
pip install slycot # optional
5757
pip install control
5858

59+
conda-forge
60+
-----------
61+
62+
Binaries are available from conda-forge for selected platforms (Linux and
63+
MacOS). Install using
64+
65+
conda install -c conda-forge control
66+
5967
Distutils
6068
---------
6169

‎control/bdalg.py

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -62,12 +62,12 @@
6262
__all__= ['series','parallel','negate','feedback','append','connect']
6363

6464
defseries(sys1,*sysn):
65-
"""Return the series connection (... * sys3 *) sys2 * sys1
65+
"""Return the series connection (...\* sys3\*) sys2\* sys1
6666
6767
Parameters
6868
----------
6969
sys1: scalar, StateSpace, TransferFunction, or FRD
70-
*sysn: other scalars, StateSpaces, TransferFunctions, or FRDs
70+
sysn: other scalars, StateSpaces, TransferFunctions, or FRDs
7171
7272
Returns
7373
-------

‎control/canonical.py

Lines changed: 75 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -6,8 +6,8 @@
66
from .statespimportStateSpace
77
from .statefbkimportctrb,obsv
88

9-
fromnumpyimportzeros,shape,poly
10-
fromnumpy.linalgimportsolve,matrix_rank
9+
fromnumpyimportzeros,shape,poly,iscomplex,hstack
10+
fromnumpy.linalgimportsolve,matrix_rank,eig
1111

1212
__all__= ['canonical_form','reachable_form','observable_form']
1313

@@ -22,7 +22,7 @@ def canonical_form(xsys, form='reachable'):
2222
Canonical form for transformation. Chosen from:
2323
* 'reachable' - reachable canonical form
2424
* 'observable' - observable canonical form
25-
* 'modal' - modal canonical form [not implemented]
25+
* 'modal' - modal canonical form
2626
2727
Returns
2828
-------
@@ -37,6 +37,8 @@ def canonical_form(xsys, form='reachable'):
3737
returnreachable_form(xsys)
3838
elifform=='observable':
3939
returnobservable_form(xsys)
40+
elifform=='modal':
41+
returnmodal_form(xsys)
4042
else:
4143
raiseControlNotImplemented(
4244
"Canonical form '%s' not yet implemented"%form)
@@ -133,9 +135,78 @@ def observable_form(xsys):
133135
Wrz=obsv(zsys.A,zsys.C)
134136

135137
# Transformation from one form to another
136-
Tzx=inv(Wrz)*Wrx
138+
Tzx=solve(Wrz,Wrx)# matrix left division, Tzx = inv(Wrz) * Wrx
139+
140+
ifmatrix_rank(Tzx)!=xsys.states:
141+
raiseValueError("Transformation matrix singular to working precision.")
137142

138143
# Finally, compute the output matrix
139144
zsys.B=Tzx*xsys.B
140145

141146
returnzsys,Tzx
147+
148+
defmodal_form(xsys):
149+
"""Convert a system into modal canonical form
150+
151+
Parameters
152+
----------
153+
xsys : StateSpace object
154+
System to be transformed, with state `x`
155+
156+
Returns
157+
-------
158+
zsys : StateSpace object
159+
System in modal canonical form, with state `z`
160+
T : matrix
161+
Coordinate transformation: z = T * x
162+
"""
163+
# Check to make sure we have a SISO system
164+
ifnotissiso(xsys):
165+
raiseControlNotImplemented(
166+
"Canonical forms for MIMO systems not yet supported")
167+
168+
# Create a new system, starting with a copy of the old one
169+
zsys=StateSpace(xsys)
170+
171+
# Calculate eigenvalues and matrix of eigenvectors Tzx,
172+
eigval,eigvec=eig(xsys.A)
173+
174+
# Eigenvalues and according eigenvectors are not sorted,
175+
# thus modal transformation is ambiguous
176+
# Sorting eigenvalues and respective vectors by largest to smallest eigenvalue
177+
idx=eigval.argsort()[::-1]
178+
eigval=eigval[idx]
179+
eigvec=eigvec[:,idx]
180+
181+
# If all eigenvalues are real, the matrix of eigenvectors is Tzx directly
182+
ifnotiscomplex(eigval).any():
183+
Tzx=eigvec
184+
else:
185+
# A is an arbitrary semisimple matrix
186+
187+
# Keep track of complex conjugates (need only one)
188+
lst_conjugates= []
189+
Tzx=None
190+
forval,vecinzip(eigval,eigvec.T):
191+
ifiscomplex(val):
192+
ifvalnotinlst_conjugates:
193+
lst_conjugates.append(val.conjugate())
194+
ifTzxisnotNone:
195+
Tzx=hstack((Tzx,hstack((vec.real.T,vec.imag.T))))
196+
else:
197+
Tzx=hstack((vec.real.T,vec.imag.T))
198+
else:
199+
# if conjugate has already been seen, skip this eigenvalue
200+
lst_conjugates.remove(val)
201+
else:
202+
ifTzxisnotNone:
203+
Tzx=hstack((Tzx,vec.real.T))
204+
else:
205+
Tzx=vec.real.T
206+
207+
# Generate the system matrices for the desired canonical form
208+
zsys.A=solve(Tzx,xsys.A).dot(Tzx)
209+
zsys.B=solve(Tzx,xsys.B)
210+
zsys.C=xsys.C.dot(Tzx)
211+
212+
returnzsys,Tzx

‎control/config.py

Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -18,6 +18,8 @@
1818
defuse_matlab_defaults():
1919
"""
2020
Use MATLAB compatible configuration settings
21+
22+
The following conventions are used:
2123
* Bode plots plot gain in dB, phase in degrees, frequency in Hertz
2224
"""
2325
# Bode plot defaults
@@ -28,7 +30,9 @@ def use_matlab_defaults():
2830
# Set defaults to match FBS (Astrom and Murray)
2931
defuse_fbs_defaults():
3032
"""
31-
Use `Astrom and Murray <http://fbsbook.org>`_ compatible settings
33+
Use `Feedback Systems <http://fbsbook.org>`_ (FBS) compatible settings
34+
35+
The following conventions are used:
3236
* Bode plots plot gain in powers of ten, phase in degrees,
3337
frequency in Hertz
3438
"""

‎control/frdata.py

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -452,8 +452,8 @@ def _convertToFRD(sys, omega, inputs=1, outputs=1):
452452
scalar, then the number of inputs and outputs can be specified
453453
manually, as in:
454454
455-
>>>sys = _convertToFRD(3.) # Assumes inputs = outputs = 1
456-
>>>sys = _convertToFRD(1., inputs=3, outputs=2)
455+
>>>frd = _convertToFRD(3., omega) # Assumes inputs = outputs = 1
456+
>>>frd = _convertToFRD(1., omegs, inputs=3, outputs=2)
457457
458458
In the latter example, sys's matrix transfer function is [[1., 1., 1.]
459459
[1., 1., 1.]].

‎control/freqplot.py

Lines changed: 60 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -47,6 +47,7 @@
4747
importmath
4848
from .ctrlutilimportunwrap
4949
from .bdalgimportfeedback
50+
from .marginsimportstability_margins
5051

5152
__all__= ['bode_plot','nyquist_plot','gangof4_plot',
5253
'bode','nyquist','gangof4']
@@ -60,17 +61,18 @@
6061

6162
# Bode plot
6263
defbode_plot(syslist,omega=None,dB=None,Hz=None,deg=None,
63-
Plot=True,omega_limits=None,omega_num=None,*args,**kwargs):
64-
"""Bode plot for a system
64+
Plot=True,omega_limits=None,omega_num=None,margins=None,*args,**kwargs):
65+
"""
66+
Bode plot for a system
6567
6668
Plots a Bode plot for the system over a (optional) frequency range.
6769
6870
Parameters
6971
----------
7072
syslist : linsys
7173
List of linear input/output systems (single system is OK)
72-
omega :freq_range
73-
Range of frequencies in rad/sec
74+
omega :list
75+
List of frequencies in rad/sec to be used for frequency response
7476
dB : boolean
7577
If True, plot result in dB
7678
Hz : boolean
@@ -84,7 +86,9 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
8486
If Hz=True the limits are in Hz otherwise in rad/s.
8587
omega_num: int
8688
number of samples
87-
*args, **kwargs:
89+
margins : boolean
90+
if True, plot gain and phase margin
91+
\*args, \**kwargs:
8892
Additional options to matplotlib (color, linestyle, etc)
8993
9094
Returns
@@ -105,7 +109,7 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
105109
2. If a discrete time model is given, the frequency response is plotted
106110
along the upper branch of the unit circle, using the mapping z = exp(j
107111
\omega dt) where omega ranges from 0 to pi/dt and dt is the discrete
108-
time base. If not timebase is specified (dt = True), dt is set to 1.
112+
timebase. If not timebase is specified (dt = True), dt is set to 1.
109113
110114
Examples
111115
--------
@@ -208,7 +212,7 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
208212
color=pltline[0].get_color())
209213

210214
# Add a grid to the plot + labeling
211-
ax_mag.grid(True,which='both')
215+
ax_mag.grid(FalseifmarginselseTrue,which='both')
212216
ax_mag.set_ylabel("Magnitude (dB)"ifdBelse"Magnitude")
213217

214218
# Phase plot
@@ -218,6 +222,50 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
218222
phase_plot=phase
219223
ax_phase.semilogx(omega_plot,phase_plot,*args,**kwargs)
220224

225+
# Show the phase and gain margins in the plot
226+
ifmargins:
227+
margin=stability_margins(sys)
228+
gm,pm,Wcg,Wcp=margin[0],margin[1],margin[3],margin[4]
229+
ifpm>=0.:
230+
phase_limit=-180.
231+
else:
232+
phase_limit=180.
233+
234+
ax_mag.axhline(y=0ifdBelse1,color='k',linestyle=':')
235+
ax_phase.axhline(y=phase_limitifdegelsemath.radians(phase_limit),color='k',linestyle=':')
236+
mag_ylim=ax_mag.get_ylim()
237+
phase_ylim=ax_phase.get_ylim()
238+
239+
ifpm!=float('inf')andWcp!=float('nan'):
240+
ifdB:
241+
ax_mag.semilogx([Wcp,Wcp], [0.,-1e5],color='k',linestyle=':')
242+
else:
243+
ax_mag.loglog([Wcp,Wcp], [1.,1e-8],color='k',linestyle=':')
244+
245+
ifdeg:
246+
ax_phase.semilogx([Wcp,Wcp], [1e5,phase_limit+pm],color='k',linestyle=':')
247+
ax_phase.semilogx([Wcp,Wcp], [phase_limit+pm,phase_limit],color='k')
248+
else:
249+
ax_phase.semilogx([Wcp,Wcp], [1e5,math.radians(phase_limit)+math.radians(pm)],color='k',linestyle=':')
250+
ax_phase.semilogx([Wcp,Wcp], [math.radians(phase_limit)+math.radians(pm),math.radians(phase_limit)],color='k')
251+
252+
ifgm!=float('inf')andWcg!=float('nan'):
253+
ifdB:
254+
ax_mag.semilogx([Wcg,Wcg], [-20.*np.log10(gm),-1e5],color='k',linestyle=':')
255+
ax_mag.semilogx([Wcg,Wcg], [0,-20*np.log10(gm)],color='k')
256+
else:
257+
ax_mag.loglog([Wcg,Wcg], [1./gm,1e-8],color='k',linestyle=':')
258+
ax_mag.loglog([Wcg,Wcg], [1.,1./gm],color='k')
259+
260+
ifdeg:
261+
ax_phase.semilogx([Wcg,Wcg], [1e-8,phase_limit],color='k',linestyle=':')
262+
else:
263+
ax_phase.semilogx([Wcg,Wcg], [1e-8,math.radians(phase_limit)],color='k',linestyle=':')
264+
265+
ax_mag.set_ylim(mag_ylim)
266+
ax_phase.set_ylim(phase_ylim)
267+
plt.suptitle('Gm = %.2f %s(at %.2f rad/s), Pm = %.2f %s (at %.2f rad/s)'%(20*np.log10(gm)ifdBelsegm,'dB 'ifdBelse'\b',Wcg,pmifdegelsemath.radians(pm),'deg'ifdegelse'rad',Wcp))
268+
221269
ifnyquistfrq_plot:
222270
ax_phase.axvline(nyquistfrq_plot,color=pltline[0].get_color())
223271

@@ -236,7 +284,7 @@ def genZeroCenteredSeries(val_min, val_max, period):
236284
ylim=ax_phase.get_ylim()
237285
ax_phase.set_yticks(genZeroCenteredSeries(ylim[0],ylim[1],math.pi/4.))
238286
ax_phase.set_yticks(genZeroCenteredSeries(ylim[0],ylim[1],math.pi/12.),minor=True)
239-
ax_phase.grid(True,which='both')
287+
ax_phase.grid(FalseifmarginselseTrue,which='both')
240288
# ax_mag.grid(which='minor', alpha=0.3)
241289
# ax_mag.grid(which='major', alpha=0.9)
242290
# ax_phase.grid(which='minor', alpha=0.3)
@@ -253,7 +301,8 @@ def genZeroCenteredSeries(val_min, val_max, period):
253301
# Nyquist plot
254302
defnyquist_plot(syslist,omega=None,Plot=True,color='b',
255303
labelFreq=0,*args,**kwargs):
256-
"""Nyquist plot for a system
304+
"""
305+
Nyquist plot for a system
257306
258307
Plots a Nyquist plot for the system over a (optional) frequency range.
259308
@@ -267,7 +316,7 @@ def nyquist_plot(syslist, omega=None, Plot=True, color='b',
267316
If True, plot magnitude
268317
labelFreq : int
269318
Label every nth frequency on the plot
270-
*args, **kwargs:
319+
\*args,\**kwargs:
271320
Additional options to matplotlib (color, linestyle, etc)
272321
273322
Returns
@@ -283,6 +332,7 @@ def nyquist_plot(syslist, omega=None, Plot=True, color='b',
283332
--------
284333
>>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
285334
>>> real, imag, freq = nyquist_plot(sys)
335+
286336
"""
287337
# If argument was a singleton, turn it into a list
288338
if (notgetattr(syslist,'__iter__',False)):

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