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Line 469: − Try also <code style="font-size:14px; border:solid lightgray 1px; padding: 2px">bode(P)</code> (a first order low-pass filter has -3db magnitude at f=1/T1).+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
→PT1 / Low-pass filter step response
=== 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:14px">
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
[[File:Pt1.png|600px]]
[[File:Pt1.png|600px]]
==== Bode Diagram for TikZ/PGFplots ====
We use the same system as before but we draw now with the <code style="font-size:14px; border:solid lightgray 1px; padding: 2px">bode(P)</code> a bode diagram.
The output is then written to a .csv file.
<!-- {{SyntaxHighlight| -->
{{Code|Creating a transfer function and plotting its response|<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 transfer function and plotting its response|<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,
]
\nextgroupplot[
title={Bode Diagram of $P$},
xmode=log,
ylabel={Magnitude / \si{\decibel}},
]
\addplot[blue,line width=2pt] table[x index=0,y index=1]{\datatable};
\nextgroupplot[
xmode=log,
xlabel={Frequency / \si{\radian\per\second}},
ylabel={Phase / \si{\degree}},
]
\addplot[red,line width=2pt] 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]]
Try also (a first order low-pass filter has -3db magnitude at f=1/T1).
=== Inverted Pendulum ===
=== Inverted Pendulum ===