Control package: Difference between revisions
Em3rgent0rdr (talk | contribs) (→PT1 / Low-pass filter step response: script that looks more like the actual displayed plot with two grey dashed lines.) |
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(26 intermediate revisions by 10 users not shown) | |||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Chapter !! Function !! Implemented !! File | ! Chapter !! Function !! Implemented !! File | ||
|- | |- | ||
| rowspan="11" | Basic Models || tf || style="background: green;" | yes || @tf/tf.m | | rowspan="11" | Basic Models || tf || style="background: green;" | yes || @tf/tf.m | ||
|- | |- | ||
| zpk || style="background: green;" | yes || zpk.m | | zpk || style="background: green;" | yes || zpk.m | ||
|- | |- | ||
| ss || style="background: green;" | yes || @ss/ss.m | | ss || style="background: green;" | yes || @ss/ss.m | ||
|- | |- | ||
| frd || style="background: green;" | yes || @frd/frd.m | | frd || style="background: green;" | yes || @frd/frd.m | ||
|- | |- | ||
| pid || style="background: | | pid || style="background: green;" | yes || pid.m | ||
|- | |- | ||
| pidstd || style="background: | | pidstd || style="background: green;" | yes || pidstd.m | ||
|- | |- | ||
| pid2 || style="background: red;" | no | | pid2 || style="background: red;" | no || | ||
|- | |- | ||
| dss || style="background: green;" | yes || @lti/dss.m | | dss || style="background: green;" | yes || @lti/dss.m | ||
|- | |- | ||
| drss || style="background: red;" | no | | drss || style="background: red;" | no || | ||
|- | |- | ||
| filt || style="background: green;" | yes || filt.m | | filt || style="background: green;" | yes || filt.m | ||
|- | |- | ||
| rss || style="background: red;" | no | | rss || style="background: red;" | no || | ||
|- | |- | ||
| rowspan="24" | Tunable Models || ltiblock.gain || style="background: red;" | no | | rowspan="24" | Tunable Models || ltiblock.gain || style="background: red;" | no || | ||
|- | |- | ||
| ltiblock.pid || style="background: red;" | no | | ltiblock.pid || style="background: red;" | no || | ||
|- | |- | ||
| ltiblock.pid2 || style="background: red;" | no | | ltiblock.pid2 || style="background: red;" | no || | ||
|- | |- | ||
| ltiblock.ss || style="background: red;" | no | | ltiblock.ss || style="background: red;" | no || | ||
|- | |- | ||
| ltiblock.tf || style="background: red;" | no | | ltiblock.tf || style="background: red;" | no || | ||
|- | |- | ||
| realp || style="background: red;" | no | | realp || style="background: red;" | no || | ||
|- | |- | ||
| AnalysisPoint || style="background: red;" | no | | AnalysisPoint || style="background: red;" | no || | ||
|- | |- | ||
| genss || style="background: red;" | no | | genss || style="background: red;" | no || | ||
|- | |- | ||
| genfrd || style="background: red;" | no | | genfrd || style="background: red;" | no || | ||
|- | |- | ||
| genmat || style="background: red;" | no | | genmat || style="background: red;" | no || | ||
|- | |- | ||
| getLoopTransfer || style="background: red;" | no | | getLoopTransfer || style="background: red;" | no || | ||
|- | |- | ||
| getIOTransfer || style="background: red;" | no | | getIOTransfer || style="background: red;" | no || | ||
|- | |- | ||
| getSensitivity || style="background: red;" | no | | getSensitivity || style="background: red;" | no || | ||
|- | |- | ||
| getCompSensitivity || style="background: red;" | no | | getCompSensitivity || style="background: red;" | no || | ||
|- | |- | ||
| getPoints || style="background: red;" | no | | getPoints || style="background: red;" | no || | ||
|- | |- | ||
| replaceBlock || style="background: red;" | no | | replaceBlock || style="background: red;" | no || | ||
|- | |- | ||
| getValue || style="background: red;" | no | | getValue || style="background: red;" | no || | ||
|- | |- | ||
| setValue || style="background: red;" | no | | setValue || style="background: red;" | no || | ||
|- | |- | ||
| getBlockValue || style="background: red;" | no | | getBlockValue || style="background: red;" | no || | ||
|- | |- | ||
| setBlockValue || style="background: red;" | no | | setBlockValue || style="background: red;" | no || | ||
|- | |- | ||
| showBlockValue || style="background: red;" | no | | showBlockValue || style="background: red;" | no || | ||
|- | |- | ||
| showTunable || style="background: red;" | no | | showTunable || style="background: red;" | no || | ||
|- | |- | ||
| nblocks || style="background: red;" | no | | nblocks || style="background: red;" | no || | ||
|- | |- | ||
| getLFTModel || style="background: red;" | no | | getLFTModel || style="background: red;" | no || | ||
|- | |- | ||
| rowspan="9" | Model with Time Delays || pade || style="background: red;" | no | | rowspan="9" | Model with Time Delays || pade || style="background: red;" | no || | ||
|- | |- | ||
| absorbDelay || style="background: red;" | no | | absorbDelay || style="background: red;" | no || | ||
|- | |- | ||
| thiran || style="background: green;" | yes || thiran.m | | thiran || style="background: green;" | yes || thiran.m | ||
|- | |- | ||
| hasdelay || style="background: red;" | no | | hasdelay || style="background: red;" | no || | ||
|- | |- | ||
| hasInternalDelay || style="background: red;" | no | | hasInternalDelay || style="background: red;" | no || | ||
|- | |- | ||
| totaldelay || style="background: red;" | no | | totaldelay || style="background: red;" | no || | ||
|- | |- | ||
| delayss || style="background: red;" | no | | delayss || style="background: red;" | no || | ||
|- | |- | ||
| setDelayModel || style="background: red;" | no | | setDelayModel || style="background: red;" | no || | ||
|- | |- | ||
| getDelayModel || style="background: red;" | no | | getDelayModel || style="background: red;" | no || | ||
|- | |- | ||
| rowspan="26" | Model Attributes || get || style="background: green;" | yes || @iddata/get.m | | rowspan="26" | Model Attributes || get || style="background: green;" | yes || @iddata/get.m | ||
|- | |- | ||
| set || style="background: green;" | yes || @iddata/set.m | | set || style="background: green;" | yes || @iddata/set.m | ||
|- | |- | ||
| tfdata || style="background: green;" | yes || @lti/tfdata.m | | tfdata || style="background: green;" | yes || @lti/tfdata.m | ||
|- | |- | ||
| zpkdata || style="background: green;" | yes || @lti/zpkdata.m | | zpkdata || style="background: green;" | yes || @lti/zpkdata.m | ||
|- | |- | ||
| ssdata || style="background: green;" | yes || @lti/ssdata.m | | ssdata || style="background: green;" | yes || @lti/ssdata.m | ||
|- | |- | ||
| frdata || style="background: green;" | yes || @lti/frdata.m | | frdata || style="background: green;" | yes || @lti/frdata.m | ||
|- | |- | ||
| piddata || style="background: red;" | no | | piddata || style="background: red;" | no || | ||
|- | |- | ||
| pidstddata || style="background: red;" | no | | pidstddata || style="background: red;" | no || | ||
|- | |- | ||
| piddata2 || style="background: red;" | no | | piddata2 || style="background: red;" | no || | ||
|- | |- | ||
| pidstddata2 || style="background: red;" | no | | pidstddata2 || style="background: red;" | no || | ||
|- | |- | ||
| dssdata || style="background: green;" | yes || @lti/dssdata.m | | dssdata || style="background: green;" | yes || @lti/dssdata.m | ||
|- | |- | ||
| chgFreqUnit || style="background: red;" | no | | chgFreqUnit || style="background: red;" | no || | ||
|- | |- | ||
| chgTimeUnit || style="background: red;" | no | | chgTimeUnit || style="background: red;" | no || | ||
|- | |- | ||
| isct || style="background: green;" | yes || @lti/isct.m | | isct || style="background: green;" | yes || @lti/isct.m | ||
|- | |- | ||
| isdt || style="background: green;" | yes || @lti/isdt.m | | isdt || style="background: green;" | yes || @lti/isdt.m | ||
|- | |- | ||
| isempty || style="background: green;" | yes || built-in function | | isempty || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| isfinite || style="background: green;" | yes || built-in function | | isfinite || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| isParametric || style="background: red;" | no | | isParametric || style="background: red;" | no || | ||
|- | |- | ||
| isproper || style="background: red;" | no | | isproper || style="background: red;" | no || | ||
|- | |- | ||
| isreal || style="background: green;" | yes || built-in function | | isreal || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| isiso || style="background: red;" | no | | isiso || style="background: red;" | no || | ||
|- | |- | ||
| isstable || style="background: green;" | yes || @lti/isstable.m | | isstable || style="background: green;" | yes || @lti/isstable.m | ||
|- | |- | ||
| isstatic || style="background: red;" | no | | isstatic || style="background: red;" | no || | ||
|- | |- | ||
| order || style="background: red;" | no | | order || style="background: red;" | no || | ||
|- | |- | ||
| ndims || style="background: green;" | yes || built-in function | | ndims || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| size || style="background: green;" | yes || built-in function | | size || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| rowspan="5" | Model Arrays || stack || style="background: red;" | no | | rowspan="5" | Model Arrays || stack || style="background: red;" | no || | ||
|- | |- | ||
| nmodels || style="background: red;" | no | | nmodels || style="background: red;" | no || | ||
|- | |- | ||
| permute || style="background: green;" | yes || built-in function | | permute || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| reshape || style="background: green;" | yes || built-in function | | reshape || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| repsys || style="background: green;" | yes || repsys.m | | repsys || style="background: green;" | yes || repsys.m | ||
|- | |- | ||
|} | |} | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Function !! Implemented !! File | ! Function !! Implemented !! File | ||
|- | |- | ||
| feedback || style="background: green;" | yes || @lti/feedback.m | | feedback || style="background: green;" | yes || @lti/feedback.m | ||
|- | |- | ||
| connect || style="background: green;" | yes || @lti/connect.m | | connect || style="background: green;" | yes || @lti/connect.m | ||
|- | |- | ||
| sumblk || style="background: green;" | yes || sumblk.m | | sumblk || style="background: green;" | yes || sumblk.m | ||
|- | |- | ||
| series || style="background: | | series || style="background: green;" | yes || @lti/series.m | ||
|- | |- | ||
| parallel || style="background: | | parallel || style="background: green;" | yes || @lti/parallel.m | ||
|- | |- | ||
| append || style="background: green;" | yes || append.m | | append || style="background: green;" | yes || append.m | ||
|- | |- | ||
| blkdiag || style="background: green;" | yes || @lti/blkdiag.m | | blkdiag || style="background: green;" | yes || @lti/blkdiag.m | ||
|- | |- | ||
| imp2exp || style="background: red;" | no | | imp2exp || style="background: red;" | no || | ||
|- | |- | ||
| inv || style="background: green;" | yes || built-in function | | inv || style="background: green;" | yes || built-in function | ||
|- | |- | ||
| lft || style="background: red;" | no | | lft || style="background: red;" | no || | ||
|- | |- | ||
| connectOptions || style="background: red;" | no | | connectOptions || style="background: red;" | no || | ||
|- | |- | ||
|} | |} | ||
Line 317: | Line 317: | ||
| getPeakGain || style="background: red;" | no || || || || || | | getPeakGain || style="background: red;" | no || || || || || | ||
|- | |- | ||
| rowspan=" | | rowspan="11" | Stability Analysis || pole || style="background: green;" | yes || @lti/pole.m || || || || | ||
|- | |- | ||
| zero || style="background: green;" | yes || @lti/zero.m || || || || | | zero || style="background: green;" | yes || @lti/zero.m || || || || | ||
|- | |- | ||
| damp || style="background: | | damp || style="background: green;" | yes || damp.m || || || || | ||
|- | |- | ||
| dsort || style="background: | | dsort || style="background: green;" | yes || dsort.m || || || || | ||
|- | |- | ||
| esort || style="background: | | esort || style="background: green;" | yes || esort.m || || || || | ||
|- | |- | ||
| tzero || style="background: red;" | no || || || || || | | tzero || style="background: red;" | no || || || || || | ||
|- | |||
| pzmap || style="background: green;" | yes || pzmap.m || || || || | |||
|- | |- | ||
| pzplot || style="background: red;" | no || || || || || | | pzplot || style="background: red;" | no || || || || || | ||
Line 373: | Line 375: | ||
| pidtuneOptions || style="background: red;" | no || || || || || | | pidtuneOptions || style="background: red;" | no || || || || || | ||
|- | |- | ||
| rowspan=" | | rowspan="5" | SISO Feedback Loops || rlocus || style="background: green;" | yes || rlocus.m || || || || | ||
|- | |||
| sgrid || style="background: red;" | no || || || || || | |||
|- | |- | ||
| rlocusplot || style="background: red;" | no || || || || || | | rlocusplot || style="background: red;" | no || || || || || | ||
Line 405: | Line 409: | ||
| norm || style="background: green;" | yes || @lti/norm.m || || || || | | norm || style="background: green;" | yes || @lti/norm.m || || || || | ||
|- | |- | ||
| rowspan=" | | rowspan="4" | Pole Placement || estim || style="background: green;" | yes || estim.m || || || || | ||
|- | |- | ||
| place || style="background: green;" | yes || place.m || || || || | | place || style="background: green;" | yes || place.m || || || || | ||
|- | |- | ||
| reg || style="background: red;" | no || || | | acker || style="background: green;" | yes || acker.m || || || || | ||
|- | |||
| reg || style="background: red;" | no || || || || | |||
|- | |- | ||
|} | |} | ||
Line 434: | Line 440: | ||
|- | |- | ||
| gdare || style="background: red;" | no || || || || || | | gdare || style="background: red;" | no || || || || || | ||
|- | |||
| icare || style="background: red;" | no || || || || || | |||
|- | |||
| idare || style="background: red;" | no || || || || || | |||
|- | |- | ||
| ctrb || style="background: green;" | yes || ctrb.m || || || || | | ctrb || style="background: green;" | yes || ctrb.m || || || || | ||
Line 461: | Line 471: | ||
#add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1 | #add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1 | ||
hold on | hold on | ||
plot ([0 T1], [0 1], " | plot ([0 T1], [0 1], "--", 'color', [.75 .75 .75]) | ||
plot ([T1 T1], [0 1], " | plot ([T1 T1], [0 1], "--", 'color', [.75 .75 .75]) | ||
hold off | hold off | ||
</syntaxhighlight>}} | </syntaxhighlight>}} | ||
Line 503: | Line 512: | ||
ymajorgrids, | ymajorgrids, | ||
enlarge x limits=false, | enlarge x limits=false, | ||
xmode=log, | |||
] | ] | ||
\nextgroupplot[ | \nextgroupplot[ | ||
title={Bode Diagram of $P$}, | title={Bode Diagram of $P$}, | ||
ylabel={Magnitude / \si{\decibel}}, | ylabel={Magnitude / \si{\decibel}}, | ||
] | ] | ||
\addplot[blue,line width=1pt] table[x index=0,y index=1]{\datatable}; | \addplot[blue,line width=1pt] table[x index=0,y index=1]{\datatable}; | ||
\nextgroupplot[ | \nextgroupplot[ | ||
xlabel={Frequency / \si{\radian\per\second}}, | xlabel={Frequency / \si{\radian\per\second}}, | ||
ylabel={Phase / \si{\degree}}, | ylabel={Phase / \si{\degree}}, | ||
Line 528: | Line 536: | ||
=== Inverted Pendulum === | === Inverted Pendulum === | ||
==== Model ==== | |||
A nonlinear model of the inverted pendulum can be derived by | A nonlinear model of the inverted pendulum can be derived by | ||
Line 584: | Line 594: | ||
</math> | </math> | ||
==== Transfer functions ==== | |||
By dividing the state variables by the input one obtains the transfer functions | |||
<math> | <math> | ||
Line 639: | Line 651: | ||
</syntaxhighlight>}} | </syntaxhighlight>}} | ||
one obtains the | one obtains the bode diagrams of the two transfer functions. | ||
<div><ul> | |||
<li style="display: inline-block;"> [[File:bode_g1.png|frame|Bode diagram of the cart movement transfer function.]] </li> | |||
<li style="display: inline-block;"> [[File:bode_g2.png|frame|Bode diagram of the pendulums rotation transfer function.]] </li> | |||
</ul></div> | |||
[[Category:Octave | [[Category:Octave Forge]] |
Latest revision as of 05:49, 28 August 2023
The control package is part of the Octave Forge project.
Function listEdit
Linear System RepresentationEdit
Chapter | Function | Implemented | File |
---|---|---|---|
Basic Models | tf | yes | @tf/tf.m |
zpk | yes | zpk.m | |
ss | yes | @ss/ss.m | |
frd | yes | @frd/frd.m | |
pid | yes | pid.m | |
pidstd | yes | pidstd.m | |
pid2 | no | ||
dss | yes | @lti/dss.m | |
drss | no | ||
filt | yes | filt.m | |
rss | no | ||
Tunable Models | ltiblock.gain | no | |
ltiblock.pid | no | ||
ltiblock.pid2 | no | ||
ltiblock.ss | no | ||
ltiblock.tf | no | ||
realp | no | ||
AnalysisPoint | no | ||
genss | no | ||
genfrd | no | ||
genmat | no | ||
getLoopTransfer | no | ||
getIOTransfer | no | ||
getSensitivity | no | ||
getCompSensitivity | no | ||
getPoints | no | ||
replaceBlock | no | ||
getValue | no | ||
setValue | no | ||
getBlockValue | no | ||
setBlockValue | no | ||
showBlockValue | no | ||
showTunable | no | ||
nblocks | no | ||
getLFTModel | no | ||
Model with Time Delays | pade | no | |
absorbDelay | no | ||
thiran | yes | thiran.m | |
hasdelay | no | ||
hasInternalDelay | no | ||
totaldelay | no | ||
delayss | no | ||
setDelayModel | no | ||
getDelayModel | no | ||
Model Attributes | get | yes | @iddata/get.m |
set | yes | @iddata/set.m | |
tfdata | yes | @lti/tfdata.m | |
zpkdata | yes | @lti/zpkdata.m | |
ssdata | yes | @lti/ssdata.m | |
frdata | yes | @lti/frdata.m | |
piddata | no | ||
pidstddata | no | ||
piddata2 | no | ||
pidstddata2 | no | ||
dssdata | yes | @lti/dssdata.m | |
chgFreqUnit | no | ||
chgTimeUnit | no | ||
isct | yes | @lti/isct.m | |
isdt | yes | @lti/isdt.m | |
isempty | yes | built-in function | |
isfinite | yes | built-in function | |
isParametric | no | ||
isproper | no | ||
isreal | yes | built-in function | |
isiso | no | ||
isstable | yes | @lti/isstable.m | |
isstatic | no | ||
order | no | ||
ndims | yes | built-in function | |
size | yes | built-in function | |
Model Arrays | stack | no | |
nmodels | no | ||
permute | yes | built-in function | |
reshape | yes | built-in function | |
repsys | yes | repsys.m |
Model InterconnectionEdit
Function | Implemented | File |
---|---|---|
feedback | yes | @lti/feedback.m |
connect | yes | @lti/connect.m |
sumblk | yes | sumblk.m |
series | yes | @lti/series.m |
parallel | yes | @lti/parallel.m |
append | yes | append.m |
blkdiag | yes | @lti/blkdiag.m |
imp2exp | no | |
inv | yes | built-in function |
lft | no | |
connectOptions | no |
Model TransformationEdit
Chapter | Function | Implemented | File | Number of Tests | Status | SLICOT functions | Priority (0-2) |
---|---|---|---|---|---|---|---|
Model Type Conversion | pidstd2 | no | |||||
make1DOF | no | ||||||
make2DOF | no | ||||||
getComponents | no | ||||||
Continuous-Discrete Conversion | c2d | yes | @lti/c2d.m | ||||
d2c | yes | @lti/d2c.m | |||||
d2d | yes | @lti/d2d.m | |||||
upsample | no | ||||||
c2dOptions | no | ||||||
d2cOptions | no | ||||||
d2dOptions | no | ||||||
Model Simplification | hsvd | yes | hsvd.m | ||||
hsvplot | no | ||||||
sminreal | yes | @lti/sminreal.m | |||||
balred | no | ||||||
minreal | yes | @lti/minreal.m | |||||
balreal | no | ||||||
modred | no | ||||||
balredOptions | no | ||||||
hsvdOptions | no | ||||||
State-Coordinate Transformation | canon | no | |||||
prescale | yes | @lti/prescale.m | |||||
ss2ss | no | ||||||
xperm | yes | @lti/xperm.m | |||||
Modal Decomposition | modsep | no | |||||
stabsep | no | ||||||
freqsep | no | ||||||
stabsepOptions | no | ||||||
freqsepOptions | no |
Linear AnalysisEdit
Chapter | Function | Implemented | File | Number of Tests | Status | SLICOT functions | Priority (0-2) |
---|---|---|---|---|---|---|---|
Time-Domain Analysis | linearSystemAnalyzer | no | |||||
impulseplot | no | ||||||
initialplot | no | ||||||
lsimplot | no | ||||||
stepplot | no | ||||||
covar | yes | covar.m | |||||
impulse | yes | impulse.m | |||||
initial | yes | initial.m | |||||
lsim | yes | lsim.m | |||||
step | yes | step.m | |||||
lsiminfo | no | ||||||
stepinfo | no | ||||||
stepDataOptions | no | ||||||
Frequency-Domain Analysis | bodeplot | no | |||||
nicholsplot | no | ||||||
nyquistplot | no | ||||||
sigmaplot | no | ||||||
bode | yes | bode.m | |||||
nichols | yes | nichols.m | |||||
nyquist | yes | nyquist.m | |||||
sigma | yes | sigma.m | |||||
evalfr | no | ||||||
freqresp | yes | @lti/freqresp.m | |||||
bandwidth | yes | built-in function | |||||
dcgain | yes | @lti/dcgain.m | |||||
getGainCrossover | no | ||||||
getPeakGain | no | ||||||
Stability Analysis | pole | yes | @lti/pole.m | ||||
zero | yes | @lti/zero.m | |||||
damp | yes | damp.m | |||||
dsort | yes | dsort.m | |||||
esort | yes | esort.m | |||||
tzero | no | ||||||
pzmap | yes | pzmap.m | |||||
pzplot | no | ||||||
iopzplot | no | ||||||
allmargin | no | ||||||
margin | yes | margin.m | |||||
Plot Customization | bodeoptions | no | |||||
hsvoptions | no | ||||||
nicholsoptions | no | ||||||
nyquistoptions | no | ||||||
pzoptions | no | ||||||
sigmaoptions | no | ||||||
timeoptions | no | ||||||
setoptions | no | ||||||
getoptions | no | ||||||
ctrlpref | no | ||||||
updateSystem | no |
Control DesignEdit
Chapter | Function | Implemented | File | Number of Tests | Status | SLICOT functions | Priority (0-2) |
---|---|---|---|---|---|---|---|
PID Controller Tuning | pidTuner | no | |||||
pidtune | no | ||||||
pidtuneOptions | no | ||||||
SISO Feedback Loops | rlocus | yes | rlocus.m | ||||
sgrid | no | ||||||
rlocusplot | no | ||||||
controlSystemDesigner | no | ||||||
sisoinit | no | ||||||
Linear-Quadratic-Gaussian Control | lqr | yes | lqr.m | ||||
lqry | no | ||||||
lqi | no | ||||||
dlqr | yes | dlqr.m | |||||
lqrd | no | ||||||
kalman | yes | kalman.m | |||||
kalmd | no | ||||||
lqg | no | ||||||
lqgreg | no | ||||||
lqgtrack | no | ||||||
augstate | no | ||||||
norm | yes | @lti/norm.m | |||||
Pole Placement | estim | yes | estim.m | ||||
place | yes | place.m | |||||
acker | yes | acker.m | |||||
reg | no |
Matrix ComputationsEdit
Function | Implemented | File | Number of Tests | Status | SLICOT functions | Priority (0-2) |
---|---|---|---|---|---|---|
lyap | yes | lyap.m | ||||
lyapchol | yes | lyapchol.m | ||||
dlyap | yes | dlyap.m | ||||
dlyapchol | yes | dlyapchol.m | ||||
care | yes | care.m | ||||
dare | yes | dare.m | ||||
gcare | no | |||||
gdare | no | |||||
icare | no | |||||
idare | no | |||||
ctrb | yes | ctrb.m | ||||
obsv | yes | obsv.m | ||||
ctrbf | yes | ctrbf.m | ||||
obsvf | yes | obsvf.m | ||||
gram | yes | gram.m | ||||
bdschur | no |
ExamplesEdit
PT1 / Low-pass filter step responseEdit
Code: Creating a transfer function and plotting its response |
T1 = 0.4; # time constant
P = tf([1], [T1 1]); # create transfer function model
step(P, 2) # plot step response
#add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1
hold on
plot ([0 T1], [0 1], "--", 'color', [.75 .75 .75])
plot ([T1 T1], [0 1], "--", 'color', [.75 .75 .75])
hold off
|
Bode Diagram with TikZ/PGFplotsEdit
We use the same system as before but we draw now with bode(P)
a bode diagram.
The output is written to a .csv file.
Code: Creating a transfer function and calculating its bode diagram |
T1 = 0.4; # time constant
P = tf([1], [T1 1]);
[mag, pha, w] = bode(P);
csvwrite("dat/bode_p.csv", [w', 20*log10(mag), pha]);
|
We can then invoke LaTeX with the following .tex file
Code: Creating a bode diagram with pgfplots |
\documentclass[tikz]{standalone}
\usepackage{pgfplotstable}
\usepackage{siunitx}
\usetikzlibrary{pgfplots.groupplots}
\begin{document}
\pgfplotstableread[col sep=comma]{\detokenize{/path/to/csv/file/dat/bode_p.csv}}\datatable
\begin{tikzpicture}
\begin{groupplot}[
group style={rows=2},
width=0.8\textwidth,
height=0.4\textwidth,
xmajorgrids,
ymajorgrids,
enlarge x limits=false,
xmode=log,
]
\nextgroupplot[
title={Bode Diagram of $P$},
ylabel={Magnitude / \si{\decibel}},
]
\addplot[blue,line width=1pt] table[x index=0,y index=1]{\datatable};
\nextgroupplot[
xlabel={Frequency / \si{\radian\per\second}},
ylabel={Phase / \si{\degree}},
]
\addplot[red,line width=1pt] table[x index=0,y index=2]{\datatable};
\end{groupplot}
\end{tikzpicture}
\end{document}
|
to generate a beautiful bode diagram
It can be seen that a first order low-pass filter has magnitude at .
Inverted PendulumEdit
ModelEdit
A nonlinear model of the inverted pendulum can be derived by
where the variables are defined as
Name | Definition |
---|---|
Mass of the cart | |
Mass of the pendulum | |
Translational damping coefficient | |
Length of the pendulum | |
Inertia of the pendulum | |
Rotational damping coefficient |
Linearization around the point and substitution of (from here on in the analysis, will be written as , but it should be noted that now measures from a new reference) leads to
This can be expressed in the frequency domain like
Transfer functionsEdit
By dividing the state variables by the input one obtains the transfer functions
with
This can be expressed in Octave
Code: Creating the transfer functions for the inverted pendulum |
m = 0.15;
l = 0.314;
M = 1.3;
I = 0;
g = 9.80665;
b = 20;
c = 20;
G1 = tf([m*l^2+I b -m*g*l],
[(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c 0]);
G2 = tf([-m*l],
[(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c]);
|
and by invoking the bode
command
Code: Creating Bode plots for the inverted pendulum |
bode(G1);
bode(G2);
|
one obtains the bode diagrams of the two transfer functions.