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Latest revision Your text
Line 7: Line 7:
 
{| class="wikitable"  
 
{| class="wikitable"  
 
|-
 
|-
! Chapter !! Function !! Implemented !! File
+
! Chapter !! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
 
|-
 
|-
| 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: red;"  | no  ||
+
|                                pid    || style="background: red;"  | no  ||            || || || ||
 
|-
 
|-
|                                pidstd || style="background: red;"  | no  ||
+
|                                pidstd || style="background: red;"  | no  ||            || || || ||
 
|-
 
|-
|                                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         || || || ||
 
|-
 
|-
 
|}
 
|}
Line 165: Line 165:
 
{| class="wikitable"  
 
{| class="wikitable"  
 
|-
 
|-
! Function !! Implemented !! File
+
! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
 
|-
 
|-
| 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: green;" | yes || @lti/series.m
+
| series || style="background: red;" | no ||  ||  || || ||
 
|-
 
|-
| parallel || style="background: green;" | yes || @lti/parallel.m
+
| parallel || style="background: red;" | no ||  ||  || || ||
 
|-
 
|-
| 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="11" | Stability Analysis || pole || style="background: green;" | yes || @lti/pole.m ||  || || ||
+
| rowspan="10" | 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: green;" | yes || damp.m ||  || || ||
+
| damp || style="background: red;" | no || ||  || || ||
 
|-
 
|-
| dsort || style="background: green;" | yes || dsort.m ||  || || ||
+
| dsort || style="background: red;" | no || ||  || || ||
 
|-
 
|-
| esort || style="background: green;" | yes || esort.m ||  || || ||
+
| esort || style="background: red;" | no || ||  || || ||
 
|-
 
|-
 
| 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 375: Line 373:
 
| pidtuneOptions || style="background: red;" | no ||  ||  || || ||
 
| pidtuneOptions || style="background: red;" | no ||  ||  || || ||
 
|-
 
|-
| rowspan="5" | SISO Feedback Loops || rlocus || style="background: green;" | yes || rlocus.m ||  || || ||
+
| rowspan="4" | 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 455: Line 451:
 
== Examples ==
 
== Examples ==
  
=== PT1 / Low-pass filter step response ===
+
=== PT1/low-pass filter step response ===
 
 
 
<!-- {{SyntaxHighlight| -->
 
<!-- {{SyntaxHighlight| -->
{{Code|Creating a transfer function and plotting its response|<syntaxhighlight lang="octave" style="font-size:14px">
+
{{Code|Creating a transfer function and plotting its response|<syntaxhighlight lang="octave" style="font-size:13px">
  T1 = 0.4;             # time constant
+
  T1=0.4;               # time constant
  P = tf([1], [T1 1])# create transfer function model
+
  P=tf([1], [T1 1])     # create transfer function model
  step(P, 2)            # plot step response
+
  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
 
  #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], "g")
+
  plot ([0 T1], [0 1],"g")
  plot ([T1 T1], [0 1], "k")
+
  plot ([T1 T1], [0 1],"k")
  plot ([0 T1], [1-1/e 1-1/e], "m")
+
  plot ([0 T1], [1-1/e 1-1/e],"m")
 
  hold off
 
  hold off
 
</syntaxhighlight>}}
 
</syntaxhighlight>}}
Line 473: Line 468:
 
[[File:Pt1.png|600px]]
 
[[File:Pt1.png|600px]]
  
==== Bode Diagram with TikZ/PGFplots ====
+
Try also bode(P)!  
 
+
(a first order low-pass filter has -3db magnitude at f=1/T1)
We use the same system as before but we draw now with <code style="font-size:14px; border:solid lightgray 1px; padding: 2px">bode(P)</code> a bode diagram.
 
The output is written to a .csv file.
 
 
 
<!-- {{SyntaxHighlight| -->
 
{{Code|Creating a transfer function and calculating its bode diagram|<syntaxhighlight lang="octave" style="font-size:14px">
 
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]);
 
</syntaxhighlight>}}
 
 
 
We can then invoke LaTeX with the following .tex file
 
 
 
<!-- {{SyntaxHighlight| -->
 
{{Code|Creating a bode diagram with pgfplots|<syntaxhighlight lang="latex" style="font-size:14px">
 
\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}
 
</syntaxhighlight>}}
 
 
 
to generate a beautiful bode diagram
 
 
 
[[File:bode_p.png]]
 
 
 
It can be seen that a first order low-pass filter has <math display="inline">-3\,dB</math> magnitude at <math display="inline">f=1/T_1=2.5\,rad/s</math>.
 
  
 
=== 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 568: Line 507:
 
|}
 
|}
  
[[File:inverted_pendulum_new.png|frame|Schematic drawing of the inverted pendulum.]]
+
[[File:inverted_pendulum_new.png]]
  
 
Linearization around the point <math display="inline">\theta=\pi</math> and substitution of <math display="inline">\theta'=\theta-\pi</math> (from here on in the analysis, <math display="inline">\theta'</math> will be written as <math display="inline">\theta</math>, but it should be noted that <math display="inline">\theta</math> now
 
Linearization around the point <math display="inline">\theta=\pi</math> and substitution of <math display="inline">\theta'=\theta-\pi</math> (from here on in the analysis, <math display="inline">\theta'</math> will be written as <math display="inline">\theta</math>, but it should be noted that <math display="inline">\theta</math> now
Line 589: Line 528:
 
</math>
 
</math>
  
==== Transfer functions ====
+
and by dividing the state variables by the input one obtains the transfer functions
 
 
By dividing the state variables by the input one obtains the transfer functions
 
  
 
<math>
 
<math>
Line 624: Line 561:
 
<!-- {{SyntaxHighlight| -->
 
<!-- {{SyntaxHighlight| -->
 
{{Code|Creating the transfer functions for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
 
{{Code|Creating the transfer functions for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
m = 0.15;
+
m = 0.15;
l = 0.314;
+
l = 0.314;
M = 1.3;
+
M = 1.3;
I = 0;
+
I = 7.38e-5;
g = 9.80665;
+
g = 9.80665;
b = 20;
+
b = 20;
c = 20;
+
c = 0;
 
+
G1 = tf([m*l^2+I b -m*g*l],
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]);
        [(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],
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]);
        [(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]);
 
 
</syntaxhighlight>}}
 
</syntaxhighlight>}}
  
and by invoking the <code style="font-size:14px; border:solid lightgray 1px; padding: 2px">bode</code> command
+
and by invoking the <code style="font-size:14px; border:solid darkgray 1px">bode</code> command
  
 
<!-- {{SyntaxHighlight| -->
 
<!-- {{SyntaxHighlight| -->
 
{{Code|Creating Bode plots for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
 
{{Code|Creating Bode plots for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
bode(G1);
+
bode(G1);
bode(G2);
+
bode(G2);
 
</syntaxhighlight>}}
 
</syntaxhighlight>}}
  
one obtains the bode diagrams of the two transfer functions.
+
One obtains the Bode plots of the two transfer functions.
 +
 
 +
==References==
 +
<references />
  
<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 Forge]]
+
[[Category:Octave-Forge]]

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