Create a Bode Plot Using PGF/TikZ, TikZ Tao

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How to draw a Bode plot? Well, the answer seams easy. If you have a  MATLAB distribution with Control System Toolbox, you can do this using just a single command, for example, 

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bode(tf(4, [2, 1, 0]));

Indeed, MATLAB integrates so many powerful tools that make scientists and engineers’ lives easier. However, this is not the end of our story. Yes, the figure created in MATLAB looks really, really ugly. If you want a publishable quality figure, which includes more colors, more line styles, more elegant annotations and even more, the mathematical equations, you will feel utterly disappointed in the MATLAB’s plotting ability.

So what is the solution?

  • R + Sweave/pgfSweave? Unfortunately, as far as I know, R (and its official package repository) does not provide a bode-plot relevant function. (If anyone knows such a function (or better, a control system package), please leave your comment here. Thanks.)
  • Python + Numpy/Scipy + matplotlib? Yer, this looks like a happy combination. However, you have to learn Python, and, of course, Numpy/Scipy/matplotlib.
  • MATLAB + matlab2pgfplots/matlab2tikz? A clumsy method, and even worse, it does now work for the figure create by bode() function. (In MATLAB 2009b or earlier, the objects generated by the function bode() is quite different from ones generated by the standard plotting command plot(). So you won’t get what you want, if you simply use matlab2pgfplots/matlab2tikz to convert MATLAB figure to PGF/TikZ file. Of course, there are some tricks to do it.)
  • Octave + gnuplot + epslatex/pslatex? OK, it could do the job. But how to put an equation in the upper subfigure (magnitude)? Again need some tricks and more complicate.
  • gnuplot + tikz terminal? This is a solution that satisfies everything. But do you really want to switch between gnuplot and tex all the time when you revise your work? Unless you are an emacs/Vim user, you will find this process is pretty annoying.
  • Can we do everything in TeX?

The answer is yes. Thank Papanicola Robert for his excellent work, the LaTeX package, bodegraph (PGF/TikZ based). Now using a single toolset, in a single editing environment, do a beautiful job. The below is the tex file which draws the bode plots for two control systems.

bodeplot (bodeplot.tex) download
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% Create a Bode plot using Papanicola Robert's package <bodegraph>
% Author: Dazhi Jiang
\documentclass[10pt]{article}

\usepackage{amsmath,amssymb}

\usepackage{tikz}
\usepackage{bodegraph}

\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}

\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}


\begin{document}

% Define the layers to draw the diagram
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\begin{tikzpicture}[>=latex',
    ref lines/.style={thin, blue!60},
    ref points/.style={circle, black, opacity=0.7, fill, minimum size= 3pt, inner sep=0},
    every node/.style={font=\small},
    bode lines/.style={very thick, blue},
    Gclabel/.style={text=blue},
    xscale=12/3]

\begin{scope}[yscale=4/110]
\UnitedB
\semilog{-1}{2}{-50}{60}

% Bode plot (magnitude) for the original system, 4/(s/(1+2s)).
% Asymptotic line
\BodeAmp[ref lines, red!60]{-1:1.35}{\POAmpAsymp{4}{2.0}+\IntAmp{1}}
% Bode plot
\BodeAmp[bode lines, red, name path=Gomagnitude]{-1:1.35}{\POAmp{4}{2.0}+\IntAmp{1}}

% Bode plot (magnitude) for the compensated system, 4(1+s)/(s^2/(1+0.1s)).
% Asymptotic line
\BodeAmp[ref lines]{-1:2}{\APAmpAsymp{4}{0.1}{10}+2*\IntAmp{1}}
% Bode plot
\BodeAmp[bode lines, name path=magnitude]
    {-1:2}{\APAmp{4}{0.1}{10}+2*\IntAmp{1}}

% Reference line, (0dB)
\draw [name path=unitygain, ref lines] (-1,0) -- (2,0);

% Crossover frequency of the original system
\path [name intersections={of=magnitude and unitygain, by=crossover}];
\node (coref) [ref points, label={[blue]below left:$\omega_c$}]
    at (crossover) {};

% Crossover frequency of the compensated system
\path [name intersections={of=Gomagnitude and unitygain, by=Gocrossover}];
\node (Gocoref) [ref points, label={[red]below:$\omega_{co}$}]
    at (Gocrossover) {};

% Labels for the original system (open-loop)
\node [Gclabel, text=red] at (-0.7, 15) {$-20$dB/dec};
\node [Gclabel, text=red] at (0.5, -30) {$-40$dB/dec};
\node (KG) [Gclabel, red!60, text=red, draw]
    at (-0.5, -30) {$KG(s)=\dfrac{4}{s(1+2s)}$};
\draw (KG.east) edge [->, shorten >=1pt, thick, red, bend right=1.5]
    (0.4, -10);

% Labels for the compensated system (open-loop)
\node [ref points, label={[blue]below left:$\omega_2$}] at (0, 0) {};
\node [ref points, label={[blue]below right:$\omega_3$}] at (1, 0) {};
\node [Gclabel] at (-0.4, 40) {$-40$dB/dec};
\node [Gclabel] at (0.5, 10) {$-20$dB/dec};
\node [Gclabel] at (1.6, -20) {$-40$dB/dec};
\node (KDG) [Gclabel, blue!60, text=blue, draw]
    at (1.4, 40) {$KD(s)G(s)=\dfrac{4(1+s)}{s^2(1+0.1s)}$};
\draw (KDG.west) edge [->, shorten >=1pt, thick, blue, bend right=1.5]
    (0.17, 10);

% Axes label
\node [below=6pt] at (0.5,-50) {Frequency, $\omega$};
\node [rotate=90] at (-1.25,5) {Magnitude, $20\log(|G(\text{j}\omega)|)$};


\end{scope}

\begin{scope}[yshift=-3.5cm,yscale=4/180]
\UniteDegre
\OrdBode{30}
\semilog{-1}{2}{-180}{0}

% Bode plot (phase) for the original system, 4/(s/(1+2s)).
% Asymptotic line
\BodeArg[ref lines, red!60]{-1:2}{\POArgAsymp{4}{2.0}+\IntArg{1}}
% Bode plot
\BodeArg[bode lines, red, name path=Gophase]{-1:2}{\POArg{4}{2}+\IntArg{1}}

% Bode plot (magnitude) for the compensated system, 4(1+s)/(s^2/(1+0.1s)).
% Asymptotic line
\BodeArg[ref lines]{-1:2}{\APArgAsymp{4}{0.1}{10}+2*\IntArg{1}}
% Bode plot
\BodeArg[bode lines, name path=phase]{-1:2}{\APArg{4}{0.1}{10}+2*\IntArg{1}}

% Phase margin of the original system
\path [name path=Gowcref] (Gocrossover) -- ++(0,-330);
\path [name intersections={of=Gophase and Gowcref, by=Gophasemargin}];
\node (Gopmref) [ref points] at (Gophasemargin) {};
\draw [ref lines, red!60, densely dotted] (Gocoref.south) -- (Gopmref.north);
\draw [ref lines, <->, red] let \p1=(Gophasemargin)
    in
        (Gopmref.south) -- node[left, Gclabel, text=red] {$\text{PM}_o$} (\x1,-180);

% Phase margin of the compensated system
\path[name path=wcref] (crossover) -- ++(0,-300);
\path [name intersections={of=phase and wcref, by=phasemargin}];
\node (pmref) [ref points] at (phasemargin) {};
\draw [ref lines, densely dotted] (coref.south) -- (pmref.north);
\draw [ref lines, <->, blue] let \p1=(phasemargin)
    in
        (pmref.south) -- node[left, Gclabel] {PM} (\x1,-180);

% System Labels
\node (KGphase) [Gclabel, red!60, text=red, draw]
    at (-0.5, -40) {$KG(s)=\dfrac{4}{s(1+2s)}$};
\draw[->, shorten >=1pt, thick, red]
    (KGphase.south) .. controls +(down:30) and +(0.1,10) .. (-0.65, -114);

\node (KDGphase) [Gclabel, blue!60, text=blue, draw]
    at (1.4, -40) {$KD(s)G(s)=\dfrac{4(1+s)}{s^2(1+0.1s)}$};
\draw[->, shorten >=1pt, thick, blue]
    (KDGphase.south) .. controls +(down:40) and +(0.1,30) .. (1.1, -146);

% Axes label
\node [below=6pt] at (0.5, -180) {Frequency, $\omega$};
\node [rotate=90] at (-1.25, -90) {Phase, $\angle G(\text{j}\omega)$};
\end{scope}

% Background
\begin{pgfonlayer}{background}
    \path (-1.4cm,2.8cm) node (tl) {};
    \path (2.3cm, -8.4cm) node (br) {};

    \path[fill=brown!20] (tl) rectangle (br);
\end{pgfonlayer}

\end{tikzpicture}

\end{document}

Here is he thumbnail of the plot. You can find the tex and pdf file from my SkyDrive.

The bodeplots of two control systems

Update:
The code has been included in the PGF/TikZ gallery, TeXample.net, see here.