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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-10-05 lun. 14:58 -->
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<!-- 2020-11-12 jeu. 10:44 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Thomas Dehaeze" />
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<link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
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<link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
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<script src="js/jquery.min.js"></script>
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<script src="js/bootstrap.min.js"></script>
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<script src="js/jquery.stickytableheaders.min.js"></script>
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<script src="js/readtheorg.js"></script>
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<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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tex: {
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tags: 'ams',
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<body>
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<div id="content">
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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|
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis
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<br />
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<span class="subtitle">Dehaeze Thomas, Verma Mohit and Collette Christophe</span>
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@ -41,18 +41,18 @@ This method is shown to be easily applicable for the synthesis of complex comple
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</p>
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</blockquote>
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<div id="outline-container-orgf99c99d" class="outline-2">
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<h2 id="orgf99c99d">Paper (<a href="paper/paper.pdf">link</a>)</h2>
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<div class="outline-text-2" id="text-orgf99c99d">
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<div id="outline-container-org51c6c0b" class="outline-2">
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<h2 id="org51c6c0b">Paper (<a href="paper/paper.pdf">link</a>)</h2>
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||||
<div class="outline-text-2" id="text-org51c6c0b">
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<p>
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The paper has been created <a href="https://orgmode.org/">Org Mode</a> (generating <a href="https://www.latex-project.org/">LaTeX</a> code) under <a href="https://www.gnu.org/software/emacs/">Emacs</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-orga085973" class="outline-2">
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<h2 id="orga085973">Tikz Figures (<a href="tikz/index.html">link</a>)</h2>
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||||
<div class="outline-text-2" id="text-orga085973">
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||||
<div id="outline-container-org6820ca5" class="outline-2">
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||||
<h2 id="org6820ca5">Tikz Figures (<a href="tikz/index.html">link</a>)</h2>
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||||
<div class="outline-text-2" id="text-org6820ca5">
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||||
<p>
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||||
All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>.
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||||
</p>
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@ -1,14 +1,15 @@
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#+TITLE: Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis
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:DRAWER:
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#+SUBTITLE: Dehaeze Thomas, Verma Mohit and Collette Christophe
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#+OPTIONS: toc:nil
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#+OPTIONS: html-postamble:nil
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
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#+HTML_HEAD: <script src="js/jquery.min.js"></script>
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#+HTML_HEAD: <script src="js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script src="js/readtheorg.js"></script>
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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:END:
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#+begin_quote
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@ -43,17 +44,8 @@ All the figures for the paper have been generated using [[https://sourceforge.ne
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||||
:END:
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||||
To cite this paper use the following bibtex code.
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||||
#+begin_src bibtex
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||||
@inproceedings{dehaeze19_compl_filter_shapin_using_synth,
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author = {Dehaeze, Thomas and Vermat, Mohit and Collette Christophe},
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||||
title = {Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis},
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booktitle = {7th International Conference on Control, Mechatronics and Automation (ICCMA)},
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year = {2019},
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language = {english},
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||||
doi = {10.1109/ICCMA46720.2019.8988642},
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||||
}
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||||
#+end_src
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||||
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||||
You can also use the formatted citation below.
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||||
#+begin_quote
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||||
Dehaeze T., Vermat M., and Collette C., "Complementary Filters Shaping Using ℋ∞ Synthesis," 2019 7th International Conference on Control, Mechatronics and Automation (ICCMA), Delft, Netherlands, 2019, pp. 459-464.
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#+end_quote
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<!-- 2020-11-12 jeu. 10:44 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Matlab Computation</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Thomas Dehaeze" />
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@ -34,29 +30,29 @@
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<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgcd571e1">1. H-Infinity synthesis of complementary filters</a>
|
||||
<li><a href="#org8213c74">1. H-Infinity synthesis of complementary filters</a>
|
||||
<ul>
|
||||
<li><a href="#orgea65f42">1.1. Synthesis Architecture</a></li>
|
||||
<li><a href="#org8a8a446">1.2. Design of Weighting Function</a></li>
|
||||
<li><a href="#orgfe22503">1.3. H-Infinity Synthesis</a></li>
|
||||
<li><a href="#orgf9471db">1.4. Obtained Complementary Filters</a></li>
|
||||
<li><a href="#org106a9c7">1.1. Synthesis Architecture</a></li>
|
||||
<li><a href="#org986f54a">1.2. Design of Weighting Function</a></li>
|
||||
<li><a href="#orge3bcbcd">1.3. H-Infinity Synthesis</a></li>
|
||||
<li><a href="#org93a0167">1.4. Obtained Complementary Filters</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org0e59118">2. Generating 3 complementary filters</a>
|
||||
<li><a href="#org2f5413b">2. Generating 3 complementary filters</a>
|
||||
<ul>
|
||||
<li><a href="#orgfbd127e">2.1. Theory</a></li>
|
||||
<li><a href="#orgb689a85">2.2. Weights</a></li>
|
||||
<li><a href="#org24d1ff1">2.3. H-Infinity Synthesis</a></li>
|
||||
<li><a href="#orgef81b1e">2.4. Obtained Complementary Filters</a></li>
|
||||
<li><a href="#org180c831">2.1. Theory</a></li>
|
||||
<li><a href="#orgb4c7909">2.2. Weights</a></li>
|
||||
<li><a href="#org5a36c59">2.3. H-Infinity Synthesis</a></li>
|
||||
<li><a href="#orgf8d8907">2.4. Obtained Complementary Filters</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org2c0b99c">3. Implement complementary filters for LIGO</a>
|
||||
<li><a href="#org1236499">3. Implement complementary filters for LIGO</a>
|
||||
<ul>
|
||||
<li><a href="#org6ea0071">3.1. Specifications</a></li>
|
||||
<li><a href="#org8f811fb">3.2. FIR Filter</a></li>
|
||||
<li><a href="#org9a34a27">3.3. Weights</a></li>
|
||||
<li><a href="#orgc9f5d68">3.4. H-Infinity Synthesis</a></li>
|
||||
<li><a href="#orgd83a581">3.5. Compare FIR and H-Infinity Filters</a></li>
|
||||
<li><a href="#org2d8dbcc">3.1. Specifications</a></li>
|
||||
<li><a href="#orga974b40">3.2. FIR Filter</a></li>
|
||||
<li><a href="#org33657ff">3.3. Weights</a></li>
|
||||
<li><a href="#orgb74a3c5">3.4. H-Infinity Synthesis</a></li>
|
||||
<li><a href="#org8b29f2c">3.5. Compare FIR and H-Infinity Filters</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
@ -81,25 +77,25 @@ To achieve this, the sensors included in the filter should complement one anothe
|
||||
This document is divided into several sections:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>in section <a href="#org954a80e">1</a>, the \(\mathcal{H}_\infty\) synthesis is used for generating two complementary filters</li>
|
||||
<li>in section <a href="#orga319f0c">2</a>, a method using the \(\mathcal{H}_\infty\) synthesis is proposed to shape three of more complementary filters</li>
|
||||
<li>in section <a href="#orgb69dc24">3</a>, the \(\mathcal{H}_\infty\) synthesis is used and compared with FIR complementary filters used for LIGO</li>
|
||||
<li>in section <a href="#org181592e">1</a>, the \(\mathcal{H}_\infty\) synthesis is used for generating two complementary filters</li>
|
||||
<li>in section <a href="#org670207e">2</a>, a method using the \(\mathcal{H}_\infty\) synthesis is proposed to shape three of more complementary filters</li>
|
||||
<li>in section <a href="#org3725bd2">3</a>, the \(\mathcal{H}_\infty\) synthesis is used and compared with FIR complementary filters used for LIGO</li>
|
||||
</ul>
|
||||
|
||||
<div class="note" id="org3c0f990">
|
||||
<div class="note" id="orgf9dc18e">
|
||||
<p>
|
||||
Add the Matlab code use to obtain the results presented in the paper are accessible <a href="matlab.zip">here</a> and presented below.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcd571e1" class="outline-2">
|
||||
<h2 id="orgcd571e1"><span class="section-number-2">1</span> H-Infinity synthesis of complementary filters</h2>
|
||||
<div id="outline-container-org8213c74" class="outline-2">
|
||||
<h2 id="org8213c74"><span class="section-number-2">1</span> H-Infinity synthesis of complementary filters</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
<a id="org954a80e"></a>
|
||||
<a id="org181592e"></a>
|
||||
</p>
|
||||
<div class="note" id="orgca3b1ba">
|
||||
<div class="note" id="orgfba238b">
|
||||
<p>
|
||||
The Matlab file corresponding to this section is accessible <a href="matlab/h_inf_synthesis_complementary_filters.m">here</a>.
|
||||
</p>
|
||||
@ -107,8 +103,8 @@ The Matlab file corresponding to this section is accessible <a href="matlab/h_in
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgea65f42" class="outline-3">
|
||||
<h3 id="orgea65f42"><span class="section-number-3">1.1</span> Synthesis Architecture</h3>
|
||||
<div id="outline-container-org106a9c7" class="outline-3">
|
||||
<h3 id="org106a9c7"><span class="section-number-3">1.1</span> Synthesis Architecture</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
We here synthesize two complementary filters using the \(\mathcal{H}_\infty\) synthesis.
|
||||
@ -116,18 +112,18 @@ The goal is to specify upper bounds on the norms of the two complementary filter
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In order to do so, we use the generalized plant shown on figure <a href="#org46317e2">1</a> where \(W_1(s)\) and \(W_2(s)\) are weighting transfer functions that will be used to shape \(H_1(s)\) and \(H_2(s)\) respectively.
|
||||
In order to do so, we use the generalized plant shown on figure <a href="#orgb57e788">1</a> where \(W_1(s)\) and \(W_2(s)\) are weighting transfer functions that will be used to shape \(H_1(s)\) and \(H_2(s)\) respectively.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org46317e2" class="figure">
|
||||
<div id="orgb57e788" class="figure">
|
||||
<p><img src="figs-tikz/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>\(\mathcal{H}_\infty\) synthesis of the complementary filters</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The \(\mathcal{H}_\infty\) synthesis applied on this generalized plant will give a transfer function \(H_2\) (figure <a href="#org46317e2">1</a>) such that the \(\mathcal{H}_\infty\) norm of the transfer function from \(w\) to \([z_1,\ z_2]\) is less than one:
|
||||
The \(\mathcal{H}_\infty\) synthesis applied on this generalized plant will give a transfer function \(H_2\) (figure <a href="#orgb57e788">1</a>) such that the \(\mathcal{H}_\infty\) norm of the transfer function from \(w\) to \([z_1,\ z_2]\) is less than one:
|
||||
\[ \left\| \begin{array}{c} (1 - H_2(s)) W_1(s) \\ H_2(s) W_2(s) \end{array} \right\|_\infty < 1 \]
|
||||
</p>
|
||||
|
||||
@ -147,8 +143,8 @@ We then see that \(W_1(s)\) and \(W_2(s)\) can be used to shape both \(H_1(s)\)
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8a8a446" class="outline-3">
|
||||
<h3 id="org8a8a446"><span class="section-number-3">1.2</span> Design of Weighting Function</h3>
|
||||
<div id="outline-container-org986f54a" class="outline-3">
|
||||
<h3 id="org986f54a"><span class="section-number-3">1.2</span> Design of Weighting Function</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<p>
|
||||
A formula is proposed to help the design of the weighting functions:
|
||||
@ -172,11 +168,11 @@ The parameters permits to specify:
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
The general shape of a weighting function generated using the formula is shown in figure <a href="#org4ee6999">2</a>.
|
||||
The general shape of a weighting function generated using the formula is shown in figure <a href="#org5840815">2</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org4ee6999" class="figure">
|
||||
<div id="org5840815" class="figure">
|
||||
<p><img src="figs-tikz/weight_formula.png" alt="weight_formula.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Amplitude of the proposed formula for the weighting functions</p>
|
||||
@ -192,7 +188,7 @@ W2 = (((1<span class="org-type">/</span>w0)<span class="org-type">*</span>sqrt((
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org79474f8" class="figure">
|
||||
<div id="org518a313" class="figure">
|
||||
<p><img src="figs/weights_W1_W2.png" alt="weights_W1_W2.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Weights on the complementary filters \(W_1\) and \(W_2\) and the associated performance weights</p>
|
||||
@ -200,8 +196,8 @@ W2 = (((1<span class="org-type">/</span>w0)<span class="org-type">*</span>sqrt((
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfe22503" class="outline-3">
|
||||
<h3 id="orgfe22503"><span class="section-number-3">1.3</span> H-Infinity Synthesis</h3>
|
||||
<div id="outline-container-orge3bcbcd" class="outline-3">
|
||||
<h3 id="orge3bcbcd"><span class="section-number-3">1.3</span> H-Infinity Synthesis</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
We define the generalized plant \(P\) on matlab.
|
||||
@ -221,7 +217,7 @@ And we do the \(\mathcal{H}_\infty\) synthesis using the <code>hinfsyn</code> co
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example" id="org9fcd456">
|
||||
<pre class="example" id="org819e288">
|
||||
[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
|
||||
Resetting value of Gamma min based on D_11, D_12, D_21 terms
|
||||
|
||||
@ -255,7 +251,7 @@ Test bounds: 0.1000 < gamma <= 1050.0000
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
We then define the high pass filter \(H_1 = 1 - H_2\). The bode plot of both \(H_1\) and \(H_2\) is shown on figure <a href="#orgbc23afe">4</a>.
|
||||
We then define the high pass filter \(H_1 = 1 - H_2\). The bode plot of both \(H_1\) and \(H_2\) is shown on figure <a href="#orgf63dab4">4</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -265,15 +261,15 @@ We then define the high pass filter \(H_1 = 1 - H_2\). The bode plot of both \(H
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf9471db" class="outline-3">
|
||||
<h3 id="orgf9471db"><span class="section-number-3">1.4</span> Obtained Complementary Filters</h3>
|
||||
<div id="outline-container-org93a0167" class="outline-3">
|
||||
<h3 id="org93a0167"><span class="section-number-3">1.4</span> Obtained Complementary Filters</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<p>
|
||||
The obtained complementary filters are shown on figure <a href="#orgbc23afe">4</a>.
|
||||
The obtained complementary filters are shown on figure <a href="#orgf63dab4">4</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgbc23afe" class="figure">
|
||||
<div id="orgf63dab4" class="figure">
|
||||
<p><img src="figs/hinf_filters_results.png" alt="hinf_filters_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Obtained complementary filters using \(\mathcal{H}_\infty\) synthesis</p>
|
||||
@ -282,13 +278,13 @@ The obtained complementary filters are shown on figure <a href="#orgbc23afe">4</
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0e59118" class="outline-2">
|
||||
<h2 id="org0e59118"><span class="section-number-2">2</span> Generating 3 complementary filters</h2>
|
||||
<div id="outline-container-org2f5413b" class="outline-2">
|
||||
<h2 id="org2f5413b"><span class="section-number-2">2</span> Generating 3 complementary filters</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="orga319f0c"></a>
|
||||
<a id="org670207e"></a>
|
||||
</p>
|
||||
<div class="note" id="org2ba2674">
|
||||
<div class="note" id="org9dc9516">
|
||||
<p>
|
||||
The Matlab file corresponding to this section is accessible <a href="matlab/three_comp_filters.m">here</a>.
|
||||
</p>
|
||||
@ -296,8 +292,8 @@ The Matlab file corresponding to this section is accessible <a href="matlab/thre
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfbd127e" class="outline-3">
|
||||
<h3 id="orgfbd127e"><span class="section-number-3">2.1</span> Theory</h3>
|
||||
<div id="outline-container-org180c831" class="outline-3">
|
||||
<h3 id="org180c831"><span class="section-number-3">2.1</span> Theory</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
We want:
|
||||
@ -310,11 +306,11 @@ We want:
|
||||
\end{align*}
|
||||
|
||||
<p>
|
||||
For that, we use the \(\mathcal{H}_\infty\) synthesis with the architecture shown on figure <a href="#org353bdb6">5</a>.
|
||||
For that, we use the \(\mathcal{H}_\infty\) synthesis with the architecture shown on figure <a href="#orga622494">5</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org353bdb6" class="figure">
|
||||
<div id="orga622494" class="figure">
|
||||
<p><img src="figs-tikz/comp_filter_three_hinf.png" alt="comp_filter_three_hinf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Generalized architecture for generating 3 complementary filters</p>
|
||||
@ -335,8 +331,8 @@ And thus if we choose \(H_1 = 1 - H_2 - H_3\) we have solved the problem.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb689a85" class="outline-3">
|
||||
<h3 id="orgb689a85"><span class="section-number-3">2.2</span> Weights</h3>
|
||||
<div id="outline-container-orgb4c7909" class="outline-3">
|
||||
<h3 id="orgb4c7909"><span class="section-number-3">2.2</span> Weights</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
First we define the weights.
|
||||
@ -353,7 +349,7 @@ W3 = (((1<span class="org-type">/</span>w0)<span class="org-type">*</span>sqrt((
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org743463d" class="figure">
|
||||
<div id="org9526a8b" class="figure">
|
||||
<p><img src="figs/three_weighting_functions.png" alt="three_weighting_functions.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Three weighting functions used for the \(\mathcal{H}_\infty\) synthesis of the complementary filters</p>
|
||||
@ -361,8 +357,8 @@ W3 = (((1<span class="org-type">/</span>w0)<span class="org-type">*</span>sqrt((
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org24d1ff1" class="outline-3">
|
||||
<h3 id="org24d1ff1"><span class="section-number-3">2.3</span> H-Infinity Synthesis</h3>
|
||||
<div id="outline-container-org5a36c59" class="outline-3">
|
||||
<h3 id="org5a36c59"><span class="section-number-3">2.3</span> H-Infinity Synthesis</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
Then we create the generalized plant <code>P</code>.
|
||||
@ -383,7 +379,7 @@ And we do the \(\mathcal{H}_\infty\) synthesis.
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example" id="org4dc4918">
|
||||
<pre class="example" id="orgd289daa">
|
||||
[H, ~, gamma, ~] = hinfsyn(P, 1, 2,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
|
||||
Resetting value of Gamma min based on D_11, D_12, D_21 terms
|
||||
|
||||
@ -418,8 +414,8 @@ Test bounds: 0.1000 < gamma <= 1050.0000
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgef81b1e" class="outline-3">
|
||||
<h3 id="orgef81b1e"><span class="section-number-3">2.4</span> Obtained Complementary Filters</h3>
|
||||
<div id="outline-container-orgf8d8907" class="outline-3">
|
||||
<h3 id="orgf8d8907"><span class="section-number-3">2.4</span> Obtained Complementary Filters</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<p>
|
||||
The obtained filters are:
|
||||
@ -432,7 +428,7 @@ H1 = 1 <span class="org-type">-</span> H2 <span class="org-type">-</span> H3;
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7b51da2" class="figure">
|
||||
<div id="orgf8995ee" class="figure">
|
||||
<p><img src="figs/three_complementary_filters_results.png" alt="three_complementary_filters_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>The three complementary filters obtained after \(\mathcal{H}_\infty\) synthesis</p>
|
||||
@ -441,13 +437,13 @@ H1 = 1 <span class="org-type">-</span> H2 <span class="org-type">-</span> H3;
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2c0b99c" class="outline-2">
|
||||
<h2 id="org2c0b99c"><span class="section-number-2">3</span> Implement complementary filters for LIGO</h2>
|
||||
<div id="outline-container-org1236499" class="outline-2">
|
||||
<h2 id="org1236499"><span class="section-number-2">3</span> Implement complementary filters for LIGO</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="orgb69dc24"></a>
|
||||
<a id="org3725bd2"></a>
|
||||
</p>
|
||||
<div class="note" id="orgce8d730">
|
||||
<div class="note" id="orgef062eb">
|
||||
<p>
|
||||
The Matlab file corresponding to this section is accessible <a href="matlab/comp_filters_ligo.m">here</a>.
|
||||
</p>
|
||||
@ -463,8 +459,8 @@ The FIR complementary filters designed in (<a href="#citeproc_bib_item_1">Hua 20
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6ea0071" class="outline-3">
|
||||
<h3 id="org6ea0071"><span class="section-number-3">3.1</span> Specifications</h3>
|
||||
<div id="outline-container-org2d8dbcc" class="outline-3">
|
||||
<h3 id="org2d8dbcc"><span class="section-number-3">3.1</span> Specifications</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
The specifications for the filters are:
|
||||
@ -477,11 +473,11 @@ The specifications for the filters are:
|
||||
</ol>
|
||||
|
||||
<p>
|
||||
The specifications are translated in upper bounds of the complementary filters are shown on figure <a href="#orgcfe60ed">8</a>.
|
||||
The specifications are translated in upper bounds of the complementary filters are shown on figure <a href="#orge86890c">8</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgcfe60ed" class="figure">
|
||||
<div id="orge86890c" class="figure">
|
||||
<p><img src="figs/ligo_specifications.png" alt="ligo_specifications.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Specification for the LIGO complementary filters</p>
|
||||
@ -489,8 +485,8 @@ The specifications are translated in upper bounds of the complementary filters a
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8f811fb" class="outline-3">
|
||||
<h3 id="org8f811fb"><span class="section-number-3">3.2</span> FIR Filter</h3>
|
||||
<div id="outline-container-orga974b40" class="outline-3">
|
||||
<h3 id="orga974b40"><span class="section-number-3">3.2</span> FIR Filter</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
We here try to implement the FIR complementary filter synthesis as explained in (<a href="#citeproc_bib_item_1">Hua 2005</a>).
|
||||
@ -571,7 +567,7 @@ h = y(2<span class="org-type">:</span>end);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example" id="orgd562951">
|
||||
<pre class="example" id="orgbf29758">
|
||||
cvx_begin
|
||||
variable y(n+1,1)
|
||||
% t
|
||||
@ -648,7 +644,7 @@ h = y(2:end);
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
Finally, we compute the filter response over the frequency vector defined and the result is shown on figure <a href="#org0d25e01">9</a> which is very close to the filters obtain in (<a href="#citeproc_bib_item_1">Hua 2005</a>).
|
||||
Finally, we compute the filter response over the frequency vector defined and the result is shown on figure <a href="#org6095ba3">9</a> which is very close to the filters obtain in (<a href="#citeproc_bib_item_1">Hua 2005</a>).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -658,16 +654,16 @@ H = [exp(<span class="org-type">-</span><span class="org-constant">j</span><span
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0d25e01" class="figure">
|
||||
<div id="org6095ba3" class="figure">
|
||||
<p><img src="figs/fir_filter_ligo.png" alt="fir_filter_ligo.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>FIR Complementary filters obtain after convex optimization (<a href="./figs/fir_filter_ligo.png">png</a>, <a href="./figs/fir_filter_ligo.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 9: </span>FIR Complementary filters obtain after convex optimization</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9a34a27" class="outline-3">
|
||||
<h3 id="org9a34a27"><span class="section-number-3">3.3</span> Weights</h3>
|
||||
<div id="outline-container-org33657ff" class="outline-3">
|
||||
<h3 id="org33657ff"><span class="section-number-3">3.3</span> Weights</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
We design weights that will be used for the \(\mathcal{H}_\infty\) synthesis of the complementary filters.
|
||||
@ -681,11 +677,11 @@ Here are the requirements on the filters:
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
The bode plot of the weights is shown on figure <a href="#orge27ef5e">10</a>.
|
||||
The bode plot of the weights is shown on figure <a href="#org9b70f72">10</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orge27ef5e" class="figure">
|
||||
<div id="org9b70f72" class="figure">
|
||||
<p><img src="figs/ligo_weights.png" alt="ligo_weights.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Weights for the \(\mathcal{H}_\infty\) synthesis</p>
|
||||
@ -693,11 +689,11 @@ The bode plot of the weights is shown on figure <a href="#orge27ef5e">10</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc9f5d68" class="outline-3">
|
||||
<h3 id="orgc9f5d68"><span class="section-number-3">3.4</span> H-Infinity Synthesis</h3>
|
||||
<div id="outline-container-orgb74a3c5" class="outline-3">
|
||||
<h3 id="orgb74a3c5"><span class="section-number-3">3.4</span> H-Infinity Synthesis</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
We define the generalized plant as shown on figure <a href="#org46317e2">1</a>.
|
||||
We define the generalized plant as shown on figure <a href="#orgb57e788">1</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">P = [0 wL;
|
||||
@ -714,7 +710,7 @@ And we do the \(\mathcal{H}_\infty\) synthesis using the <code>hinfsyn</code> co
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example" id="org51b2320">
|
||||
<pre class="example" id="orgc616ee9">
|
||||
[Hl, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
|
||||
Resetting value of Gamma min based on D_11, D_12, D_21 terms
|
||||
|
||||
@ -749,18 +745,18 @@ The high pass filter is defined as \(H_H = 1 - H_L\).
|
||||
The size of the filters is shown below.
|
||||
</p>
|
||||
|
||||
<pre class="example" id="orgede384d">
|
||||
<pre class="example" id="org2166bb4">
|
||||
size(Hh), size(Hl)
|
||||
State-space model with 1 outputs, 1 inputs, and 27 states.
|
||||
State-space model with 1 outputs, 1 inputs, and 27 states.
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
The bode plot of the obtained filters as shown on figure <a href="#org941eede">11</a>.
|
||||
The bode plot of the obtained filters as shown on figure <a href="#org637c959">11</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org941eede" class="figure">
|
||||
<div id="org637c959" class="figure">
|
||||
<p><img src="figs/hinf_synthesis_ligo_results.png" alt="hinf_synthesis_ligo_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Obtained complementary filters using the \(\mathcal{H}_\infty\) synthesis</p>
|
||||
@ -768,15 +764,15 @@ The bode plot of the obtained filters as shown on figure <a href="#org941eede">1
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd83a581" class="outline-3">
|
||||
<h3 id="orgd83a581"><span class="section-number-3">3.5</span> Compare FIR and H-Infinity Filters</h3>
|
||||
<div id="outline-container-org8b29f2c" class="outline-3">
|
||||
<h3 id="org8b29f2c"><span class="section-number-3">3.5</span> Compare FIR and H-Infinity Filters</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<p>
|
||||
Let’s now compare the FIR filters designed in (<a href="#citeproc_bib_item_1">Hua 2005</a>) and the one obtained with the \(\mathcal{H}_\infty\) synthesis on figure <a href="#org4f70e8a">12</a>.
|
||||
Let’s now compare the FIR filters designed in (<a href="#citeproc_bib_item_1">Hua 2005</a>) and the one obtained with the \(\mathcal{H}_\infty\) synthesis on figure <a href="#orgf4bf8ca">12</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org4f70e8a" class="figure">
|
||||
<div id="orgf4bf8ca" class="figure">
|
||||
<p><img src="figs/comp_fir_ligo_hinf.png" alt="comp_fir_ligo_hinf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Comparison between the FIR filters developped for LIGO and the \(\mathcal{H}_\infty\) complementary filters</p>
|
||||
@ -796,7 +792,7 @@ Let’s now compare the FIR filters designed in (<a href="#citeproc_bib_item
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
||||
<p class="date">Created: 2020-10-26 lun. 18:59</p>
|
||||
<p class="date">Created: 2020-11-12 jeu. 10:44</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -1,18 +1,14 @@
|
||||
#+TITLE: Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis - Matlab Computation
|
||||
:DRAWER:
|
||||
#+HTML_LINK_HOME: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||||
|
||||
#+LATEX_CLASS: cleanreport
|
||||
#+LATEX_CLASS_OPTIONS: [tocnp, secbreak, minted]
|
||||
|
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<a accesskey="H" href="../index.html"> HOME </a>
|
||||
</div><div id="content">
|
||||
<h1 class="title">LaTeX Configuration for Tikz Figures</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#org1dd6f76">1. Packages</a></li>
|
||||
<li><a href="#orgb097669">2. Tikz related packages</a></li>
|
||||
<li><a href="#orgef8c9ec">3. Tikz Libraries</a></li>
|
||||
<li><a href="#org8ca068a">4. PGF Plot libraries and config</a></li>
|
||||
<li><a href="#org4eb0de4">5. Setup size of figures</a></li>
|
||||
<li><a href="#orga3a90aa">6. Setup Arrows style</a></li>
|
||||
<li><a href="#orge17acf4">7. Colors</a></li>
|
||||
<li><a href="#orgee5bb97">8. Control</a>
|
||||
<li><a href="#orgeb233fa">1. Packages</a></li>
|
||||
<li><a href="#org8c39360">2. Tikz related packages</a></li>
|
||||
<li><a href="#org983cb7d">3. Tikz Libraries</a></li>
|
||||
<li><a href="#org1148426">4. PGF Plot libraries and config</a></li>
|
||||
<li><a href="#org35d7300">5. Setup size of figures</a></li>
|
||||
<li><a href="#orgede76fe">6. Setup Arrows style</a></li>
|
||||
<li><a href="#org96b5d69">7. Colors</a></li>
|
||||
<li><a href="#orga318f09">8. Control</a>
|
||||
<ul>
|
||||
<li><a href="#orgea8451a">8.1. Blocks</a></li>
|
||||
<li><a href="#org7ce8263">8.2. Branches</a></li>
|
||||
<li><a href="#org28a7366">8.3. Hand Writen Style</a></li>
|
||||
<li><a href="#org71f1934">8.4. DAC</a></li>
|
||||
<li><a href="#org3701401">8.5. ADC</a></li>
|
||||
<li><a href="#orgb647158">8.6. Gain</a></li>
|
||||
<li><a href="#orgf9c3aa6">8.7. Add / Substract / Divide / Multiply block</a></li>
|
||||
<li><a href="#org5f8db63">8.1. Blocks</a></li>
|
||||
<li><a href="#org6e2b7de">8.2. Branches</a></li>
|
||||
<li><a href="#orgd36d746">8.3. Hand Writen Style</a></li>
|
||||
<li><a href="#org2640267">8.4. DAC</a></li>
|
||||
<li><a href="#orga191a8b">8.5. ADC</a></li>
|
||||
<li><a href="#orged7cf36">8.6. Gain</a></li>
|
||||
<li><a href="#org38d8e7d">8.7. Add / Substract / Divide / Multiply block</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org29efc5d">9. Plots</a>
|
||||
<li><a href="#org7aad8c7">9. Plots</a>
|
||||
<ul>
|
||||
<li><a href="#org9add0aa">9.1. Default line caps</a></li>
|
||||
<li><a href="#orge810969">9.2. Grid</a></li>
|
||||
<li><a href="#org1e383fb">9.3. Lines</a></li>
|
||||
<li><a href="#org5ebbe78">9.4. Ticks</a></li>
|
||||
<li><a href="#org999fa62">9.5. Size</a></li>
|
||||
<li><a href="#org85d084a">9.6. Label</a></li>
|
||||
<li><a href="#org29946e8">9.7. Legend</a></li>
|
||||
<li><a href="#org9e10fa4">9.1. Default line caps</a></li>
|
||||
<li><a href="#org7d05724">9.2. Grid</a></li>
|
||||
<li><a href="#org494eb40">9.3. Lines</a></li>
|
||||
<li><a href="#org2fb301b">9.4. Ticks</a></li>
|
||||
<li><a href="#orgdf46af2">9.5. Size</a></li>
|
||||
<li><a href="#orgb5d9397">9.6. Label</a></li>
|
||||
<li><a href="#org95997d3">9.7. Legend</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org407f0ee">10. Mechanical</a>
|
||||
<li><a href="#org8620c5d">10. Mechanical</a>
|
||||
<ul>
|
||||
<li><a href="#orgffe197b">10.1. Spring</a></li>
|
||||
<li><a href="#org1f14fa9">10.2. Coil</a></li>
|
||||
<li><a href="#org1622011">10.3. Damper</a></li>
|
||||
<li><a href="#org5b48f92">10.4. Actuator</a></li>
|
||||
<li><a href="#orgf654c5a">10.5. Ground</a></li>
|
||||
<li><a href="#org6be18b5">10.6. Force Sensor</a></li>
|
||||
<li><a href="#org3655499">10.7. Inertial Sensor</a></li>
|
||||
<li><a href="#org2072839">10.8. Cross</a></li>
|
||||
<li><a href="#org551a108">10.9. Piezoelectric actuator</a></li>
|
||||
<li><a href="#org9769616">10.10. Voice coil</a></li>
|
||||
<li><a href="#org4fad7e8">10.1. Spring</a></li>
|
||||
<li><a href="#orgda1e1f4">10.2. Coil</a></li>
|
||||
<li><a href="#org2d2c2fe">10.3. Damper</a></li>
|
||||
<li><a href="#orgbd3233c">10.4. Actuator</a></li>
|
||||
<li><a href="#orgd0c4527">10.5. Ground</a></li>
|
||||
<li><a href="#org4c41ca9">10.6. Force Sensor</a></li>
|
||||
<li><a href="#org4699edc">10.7. Inertial Sensor</a></li>
|
||||
<li><a href="#orgfc14769">10.8. Cross</a></li>
|
||||
<li><a href="#org7593ed1">10.9. Piezoelectric actuator</a></li>
|
||||
<li><a href="#orgebe134c">10.10. Voice coil</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgd9f02f9">11. Optics</a></li>
|
||||
<li><a href="#orgb27c58d">12. Misc</a></li>
|
||||
<li><a href="#org17bab25">13. More Defaults specific to this paper</a></li>
|
||||
<li><a href="#orgd1f3c70">11. Optics</a></li>
|
||||
<li><a href="#orgbd5a2ff">12. Misc</a></li>
|
||||
<li><a href="#org27f9f50">13. More Defaults specific to this paper</a></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1dd6f76" class="outline-2">
|
||||
<h2 id="org1dd6f76"><span class="section-number-2">1</span> Packages</h2>
|
||||
<div id="outline-container-orgeb233fa" class="outline-2">
|
||||
<h2 id="orgeb233fa"><span class="section-number-2">1</span> Packages</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>[<span class="org-variable-name">utf8</span>]{<span class="org-function-name">inputenc</span>}
|
||||
@ -350,8 +119,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb097669" class="outline-2">
|
||||
<h2 id="orgb097669"><span class="section-number-2">2</span> Tikz related packages</h2>
|
||||
<div id="outline-container-org8c39360" class="outline-2">
|
||||
<h2 id="org8c39360"><span class="section-number-2">2</span> Tikz related packages</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">tikz</span>} <span class="org-comment">% Tikz</span>
|
||||
@ -365,8 +134,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgef8c9ec" class="outline-2">
|
||||
<h2 id="orgef8c9ec"><span class="section-number-2">3</span> Tikz Libraries</h2>
|
||||
<div id="outline-container-org983cb7d" class="outline-2">
|
||||
<h2 id="org983cb7d"><span class="section-number-2">3</span> Tikz Libraries</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\usetikzlibrary</span>{arrows} <span class="org-comment">% Arrow tip library</span>
|
||||
@ -393,8 +162,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8ca068a" class="outline-2">
|
||||
<h2 id="org8ca068a"><span class="section-number-2">4</span> PGF Plot libraries and config</h2>
|
||||
<div id="outline-container-org1148426" class="outline-2">
|
||||
<h2 id="org1148426"><span class="section-number-2">4</span> PGF Plot libraries and config</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\usepgfplotslibrary</span>{patchplots}
|
||||
@ -407,8 +176,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4eb0de4" class="outline-2">
|
||||
<h2 id="org4eb0de4"><span class="section-number-2">5</span> Setup size of figures</h2>
|
||||
<div id="outline-container-org35d7300" class="outline-2">
|
||||
<h2 id="org35d7300"><span class="section-number-2">5</span> Setup size of figures</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\newlength</span></span>{<span class="org-font-latex-sedate"><span class="org-function-name">\fheight</span></span>}
|
||||
@ -421,8 +190,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga3a90aa" class="outline-2">
|
||||
<h2 id="orga3a90aa"><span class="section-number-2">6</span> Setup Arrows style</h2>
|
||||
<div id="outline-container-orgede76fe" class="outline-2">
|
||||
<h2 id="orgede76fe"><span class="section-number-2">6</span> Setup Arrows style</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{>=Stealth}
|
||||
@ -433,8 +202,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge17acf4" class="outline-2">
|
||||
<h2 id="orge17acf4"><span class="section-number-2">7</span> Colors</h2>
|
||||
<div id="outline-container-org96b5d69" class="outline-2">
|
||||
<h2 id="org96b5d69"><span class="section-number-2">7</span> Colors</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\usepackage</span></span>{<span class="org-function-name">xcolor</span>}<span class="org-comment">% Color extension</span>
|
||||
@ -447,12 +216,12 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgee5bb97" class="outline-2">
|
||||
<h2 id="orgee5bb97"><span class="section-number-2">8</span> Control</h2>
|
||||
<div id="outline-container-orga318f09" class="outline-2">
|
||||
<h2 id="orga318f09"><span class="section-number-2">8</span> Control</h2>
|
||||
<div class="outline-text-2" id="text-8">
|
||||
</div>
|
||||
<div id="outline-container-orgea8451a" class="outline-3">
|
||||
<h3 id="orgea8451a"><span class="section-number-3">8.1</span> Blocks</h3>
|
||||
<div id="outline-container-org5f8db63" class="outline-3">
|
||||
<h3 id="org5f8db63"><span class="section-number-3">8.1</span> Blocks</h3>
|
||||
<div class="outline-text-3" id="text-8-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -469,8 +238,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7ce8263" class="outline-3">
|
||||
<h3 id="org7ce8263"><span class="section-number-3">8.2</span> Branches</h3>
|
||||
<div id="outline-container-org6e2b7de" class="outline-3">
|
||||
<h3 id="org6e2b7de"><span class="section-number-3">8.2</span> Branches</h3>
|
||||
<div class="outline-text-3" id="text-8-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzstyle</span>{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
|
||||
@ -481,8 +250,8 @@ for the JavaScript code in this tag.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org28a7366" class="outline-3">
|
||||
<h3 id="org28a7366"><span class="section-number-3">8.3</span> Hand Writen Style</h3>
|
||||
<div id="outline-container-orgd36d746" class="outline-3">
|
||||
<h3 id="orgd36d746"><span class="section-number-3">8.3</span> Hand Writen Style</h3>
|
||||
<div class="outline-text-3" id="text-8-3">
|
||||
<p>
|
||||
Usefull for schematic plots
|
||||
@ -494,8 +263,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org71f1934" class="outline-3">
|
||||
<h3 id="org71f1934"><span class="section-number-3">8.4</span> DAC</h3>
|
||||
<div id="outline-container-org2640267" class="outline-3">
|
||||
<h3 id="org2640267"><span class="section-number-3">8.4</span> DAC</h3>
|
||||
<div class="outline-text-3" id="text-8-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -509,8 +278,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3701401" class="outline-3">
|
||||
<h3 id="org3701401"><span class="section-number-3">8.5</span> ADC</h3>
|
||||
<div id="outline-container-orga191a8b" class="outline-3">
|
||||
<h3 id="orga191a8b"><span class="section-number-3">8.5</span> ADC</h3>
|
||||
<div class="outline-text-3" id="text-8-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -525,8 +294,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb647158" class="outline-3">
|
||||
<h3 id="orgb647158"><span class="section-number-3">8.6</span> Gain</h3>
|
||||
<div id="outline-container-orged7cf36" class="outline-3">
|
||||
<h3 id="orged7cf36"><span class="section-number-3">8.6</span> Gain</h3>
|
||||
<div class="outline-text-3" id="text-8-6">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -564,8 +333,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf9c3aa6" class="outline-3">
|
||||
<h3 id="orgf9c3aa6"><span class="section-number-3">8.7</span> Add / Substract / Divide / Multiply block</h3>
|
||||
<div id="outline-container-org38d8e7d" class="outline-3">
|
||||
<h3 id="org38d8e7d"><span class="section-number-3">8.7</span> Add / Substract / Divide / Multiply block</h3>
|
||||
<div class="outline-text-3" id="text-8-7">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">% Add block with Circled operations</span>
|
||||
@ -630,12 +399,12 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org29efc5d" class="outline-2">
|
||||
<h2 id="org29efc5d"><span class="section-number-2">9</span> Plots</h2>
|
||||
<div id="outline-container-org7aad8c7" class="outline-2">
|
||||
<h2 id="org7aad8c7"><span class="section-number-2">9</span> Plots</h2>
|
||||
<div class="outline-text-2" id="text-9">
|
||||
</div>
|
||||
<div id="outline-container-org9add0aa" class="outline-3">
|
||||
<h3 id="org9add0aa"><span class="section-number-3">9.1</span> Default line caps</h3>
|
||||
<div id="outline-container-org9e10fa4" class="outline-3">
|
||||
<h3 id="org9e10fa4"><span class="section-number-3">9.1</span> Default line caps</h3>
|
||||
<div class="outline-text-3" id="text-9-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{
|
||||
@ -647,8 +416,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge810969" class="outline-3">
|
||||
<h3 id="orge810969"><span class="section-number-3">9.2</span> Grid</h3>
|
||||
<div id="outline-container-org7d05724" class="outline-3">
|
||||
<h3 id="org7d05724"><span class="section-number-3">9.2</span> Grid</h3>
|
||||
<div class="outline-text-3" id="text-9-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{grid style={black}}
|
||||
@ -661,8 +430,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1e383fb" class="outline-3">
|
||||
<h3 id="org1e383fb"><span class="section-number-3">9.3</span> Lines</h3>
|
||||
<div id="outline-container-org494eb40" class="outline-3">
|
||||
<h3 id="org494eb40"><span class="section-number-3">9.3</span> Lines</h3>
|
||||
<div class="outline-text-3" id="text-9-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{separate axis lines=false} <span class="org-comment">% draw axis as rectangle and not as 4 lines</span>
|
||||
@ -676,8 +445,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5ebbe78" class="outline-3">
|
||||
<h3 id="org5ebbe78"><span class="section-number-3">9.4</span> Ticks</h3>
|
||||
<div id="outline-container-org2fb301b" class="outline-3">
|
||||
<h3 id="org2fb301b"><span class="section-number-3">9.4</span> Ticks</h3>
|
||||
<div class="outline-text-3" id="text-9-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\pgfplotsset</span>{every y tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}}}
|
||||
@ -689,8 +458,8 @@ Usefull for schematic plots
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org999fa62" class="outline-3">
|
||||
<h3 id="org999fa62"><span class="section-number-3">9.5</span> Size</h3>
|
||||
<div id="outline-container-orgdf46af2" class="outline-3">
|
||||
<h3 id="orgdf46af2"><span class="section-number-3">9.5</span> Size</h3>
|
||||
<div class="outline-text-3" id="text-9-5">
|
||||
<p>
|
||||
If <code>scale only axis=false</code> (the default), pgfplots will try to produce the desired width including labels, titles and ticks.
|
||||
@ -702,8 +471,8 @@ If <code>scale only axis=false</code> (the default), pgfplots will try to produc
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org85d084a" class="outline-3">
|
||||
<h3 id="org85d084a"><span class="section-number-3">9.6</span> Label</h3>
|
||||
<div id="outline-container-orgb5d9397" class="outline-3">
|
||||
<h3 id="orgb5d9397"><span class="section-number-3">9.6</span> Label</h3>
|
||||
<div class="outline-text-3" id="text-9-6">
|
||||
<p>
|
||||
Used to align all of ylabel of one figure.
|
||||
@ -715,8 +484,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org29946e8" class="outline-3">
|
||||
<h3 id="org29946e8"><span class="section-number-3">9.7</span> Legend</h3>
|
||||
<div id="outline-container-org95997d3" class="outline-3">
|
||||
<h3 id="org95997d3"><span class="section-number-3">9.7</span> Legend</h3>
|
||||
<div class="outline-text-3" id="text-9-7">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-comment-delimiter">% </span><span class="org-comment">https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834</span>
|
||||
@ -754,12 +523,12 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org407f0ee" class="outline-2">
|
||||
<h2 id="org407f0ee"><span class="section-number-2">10</span> Mechanical</h2>
|
||||
<div id="outline-container-org8620c5d" class="outline-2">
|
||||
<h2 id="org8620c5d"><span class="section-number-2">10</span> Mechanical</h2>
|
||||
<div class="outline-text-2" id="text-10">
|
||||
</div>
|
||||
<div id="outline-container-orgffe197b" class="outline-3">
|
||||
<h3 id="orgffe197b"><span class="section-number-3">10.1</span> Spring</h3>
|
||||
<div id="outline-container-org4fad7e8" class="outline-3">
|
||||
<h3 id="org4fad7e8"><span class="section-number-3">10.1</span> Spring</h3>
|
||||
<div class="outline-text-3" id="text-10-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -780,8 +549,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1f14fa9" class="outline-3">
|
||||
<h3 id="org1f14fa9"><span class="section-number-3">10.2</span> Coil</h3>
|
||||
<div id="outline-container-orgda1e1f4" class="outline-3">
|
||||
<h3 id="orgda1e1f4"><span class="section-number-3">10.2</span> Coil</h3>
|
||||
<div class="outline-text-3" id="text-10-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -802,8 +571,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1622011" class="outline-3">
|
||||
<h3 id="org1622011"><span class="section-number-3">10.3</span> Damper</h3>
|
||||
<div id="outline-container-org2d2c2fe" class="outline-3">
|
||||
<h3 id="org2d2c2fe"><span class="section-number-3">10.3</span> Damper</h3>
|
||||
<div class="outline-text-3" id="text-10-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -830,8 +599,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5b48f92" class="outline-3">
|
||||
<h3 id="org5b48f92"><span class="section-number-3">10.4</span> Actuator</h3>
|
||||
<div id="outline-container-orgbd3233c" class="outline-3">
|
||||
<h3 id="orgbd3233c"><span class="section-number-3">10.4</span> Actuator</h3>
|
||||
<div class="outline-text-3" id="text-10-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -861,8 +630,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf654c5a" class="outline-3">
|
||||
<h3 id="orgf654c5a"><span class="section-number-3">10.5</span> Ground</h3>
|
||||
<div id="outline-container-orgd0c4527" class="outline-3">
|
||||
<h3 id="orgd0c4527"><span class="section-number-3">10.5</span> Ground</h3>
|
||||
<div class="outline-text-3" id="text-10-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -884,8 +653,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6be18b5" class="outline-3">
|
||||
<h3 id="org6be18b5"><span class="section-number-3">10.6</span> Force Sensor</h3>
|
||||
<div id="outline-container-org4c41ca9" class="outline-3">
|
||||
<h3 id="org4c41ca9"><span class="section-number-3">10.6</span> Force Sensor</h3>
|
||||
<div class="outline-text-3" id="text-10-6">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -914,8 +683,8 @@ Used to align all of ylabel of one figure.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3655499" class="outline-3">
|
||||
<h3 id="org3655499"><span class="section-number-3">10.7</span> Inertial Sensor</h3>
|
||||
<div id="outline-container-org4699edc" class="outline-3">
|
||||
<h3 id="org4699edc"><span class="section-number-3">10.7</span> Inertial Sensor</h3>
|
||||
<div class="outline-text-3" id="text-10-7">
|
||||
<div class="org-src-container">
|
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<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
|
||||
@ -943,8 +712,8 @@ Used to align all of ylabel of one figure.
|
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</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2072839" class="outline-3">
|
||||
<h3 id="org2072839"><span class="section-number-3">10.8</span> Cross</h3>
|
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|
||||
<h3 id="orgfc14769"><span class="section-number-3">10.8</span> Cross</h3>
|
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|
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|
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@ -957,8 +726,8 @@ Used to align all of ylabel of one figure.
|
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|
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|
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|
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|
||||
<div id="outline-container-org7593ed1" class="outline-3">
|
||||
<h3 id="org7593ed1"><span class="section-number-3">10.9</span> Piezoelectric actuator</h3>
|
||||
<div class="outline-text-3" id="text-10-9">
|
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|
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|
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@ -986,8 +755,8 @@ Used to align all of ylabel of one figure.
|
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|
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|
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|
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<div id="outline-container-org9769616" class="outline-3">
|
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|
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<div id="outline-container-orgebe134c" class="outline-3">
|
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<h3 id="orgebe134c"><span class="section-number-3">10.10</span> Voice coil</h3>
|
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<div class="outline-text-3" id="text-10-10">
|
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|
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@ -1058,8 +827,8 @@ Used to align all of ylabel of one figure.
|
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|
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|
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|
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<div id="outline-container-orgd9f02f9" class="outline-2">
|
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<h2 id="orgd9f02f9"><span class="section-number-2">11</span> Optics</h2>
|
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<div id="outline-container-orgd1f3c70" class="outline-2">
|
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<h2 id="orgd1f3c70"><span class="section-number-2">11</span> Optics</h2>
|
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<div class="outline-text-2" id="text-11">
|
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<div class="org-src-container">
|
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<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
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@ -1087,8 +856,8 @@ Used to align all of ylabel of one figure.
|
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</div>
|
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|
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<div id="outline-container-orgb27c58d" class="outline-2">
|
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<h2 id="orgb27c58d"><span class="section-number-2">12</span> Misc</h2>
|
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<div id="outline-container-orgbd5a2ff" class="outline-2">
|
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<h2 id="orgbd5a2ff"><span class="section-number-2">12</span> Misc</h2>
|
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<div class="outline-text-2" id="text-12">
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|
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<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{<span class="org-comment">%</span>
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@ -1105,8 +874,8 @@ Used to align all of ylabel of one figure.
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|
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<div id="outline-container-org17bab25" class="outline-2">
|
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<h2 id="org17bab25"><span class="section-number-2">13</span> More Defaults specific to this paper</h2>
|
||||
<div id="outline-container-org27f9f50" class="outline-2">
|
||||
<h2 id="org27f9f50"><span class="section-number-2">13</span> More Defaults specific to this paper</h2>
|
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<div class="outline-text-2" id="text-13">
|
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<div class="org-src-container">
|
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<pre class="src src-latex"><span class="org-font-latex-sedate">\tikzset</span>{block/.default={0.8cm}{0.8cm}}
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@ -1119,8 +888,7 @@ Used to align all of ylabel of one figure.
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|
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<div id="postamble" class="status">
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
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<p class="date">Created: 2019-11-05 mar. 17:27</p>
|
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
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<p class="date">Created: 2020-11-12 jeu. 10:44</p>
|
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|
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|
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@ -1,11 +1,10 @@
|
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#+TITLE: LaTeX Configuration for Tikz Figures
|
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:DRAWER:
|
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|
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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442
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442
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@ -3,270 +3,21 @@
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/*]]>*/-->
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@licstart The following is the entire license notice for the
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Copyright (C) 2012-2019 Free Software Foundation, Inc.
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|
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may distribute non-source (e.g., minimized or compacted) forms of
|
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that code without the copy of the GNU GPL normally required by
|
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section 4, provided you include this license notice and a URL
|
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through which recipients can access the Corresponding Source.
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@ -279,36 +30,35 @@ for the JavaScript code in this tag.
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<h2>Table of Contents</h2>
|
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<div id="text-table-of-contents">
|
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<ul>
|
||||
<li><a href="#orge7053aa">1. Fig 1: Sensor Fusion Architecture</a></li>
|
||||
<li><a href="#org39b5d0c">2. Fig 2: Sensor fusion architecture with sensor dynamics uncertainty</a></li>
|
||||
<li><a href="#orgfc9382d">3. Fig 3: Uncertainty set of the super sensor dynamics</a></li>
|
||||
<li><a href="#orgb356b70">4. Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</a></li>
|
||||
<li><a href="#orgdeaeaf4">5. Fig 5: Magnitude of a weighting function generated using the proposed formula</a></li>
|
||||
<li><a href="#org8ce545c">6. Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</a></li>
|
||||
<li><a href="#orgac21d24">7. Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters</a></li>
|
||||
<li><a href="#org9688457">8. Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</a></li>
|
||||
<li><a href="#org8d6867c">9. Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis</a></li>
|
||||
<li><a href="#orgb6ae2f5">10. Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)</a></li>
|
||||
<li><a href="#org9059d4e">1. Fig 1: Sensor Fusion Architecture</a></li>
|
||||
<li><a href="#orgf8987c9">2. Fig 2: Sensor fusion architecture with sensor dynamics uncertainty</a></li>
|
||||
<li><a href="#org1801a90">3. Fig 3: Uncertainty set of the super sensor dynamics</a></li>
|
||||
<li><a href="#org355bde0">4. Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</a></li>
|
||||
<li><a href="#org879ecb3">5. Fig 5: Magnitude of a weighting function generated using the proposed formula</a></li>
|
||||
<li><a href="#org2b1f7ae">6. Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</a></li>
|
||||
<li><a href="#org84a7e33">7. Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters</a></li>
|
||||
<li><a href="#org20bfce3">8. Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</a></li>
|
||||
<li><a href="#orgb08c277">9. Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis</a></li>
|
||||
<li><a href="#org74b4762">10. Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)</a></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Configuration file is accessible <a href="config.html">here</a>.
|
||||
</p>
|
||||
|
||||
<div id="outline-container-orge7053aa" class="outline-2">
|
||||
<h2 id="orge7053aa"><span class="section-number-2">1</span> Fig 1: Sensor Fusion Architecture</h2>
|
||||
<div id="outline-container-org9059d4e" class="outline-2">
|
||||
<h2 id="org9059d4e"><span class="section-number-2">1</span> Fig 1: Sensor Fusion Architecture</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
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<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
|
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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|
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|
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|
||||
@ -316,8 +66,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
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<span class="org-font-latex-sedate">\draw</span>[->] (x.center) |- (G2.west);
|
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|
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|
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|
||||
<span class="org-font-latex-sedate">\draw</span>[<-] (add1.north) -- ++(0, 0.8)node[below right](n1){<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[<-] (add2.north) -- ++(0, 0.8)node[below right](n2){<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
|
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<span class="org-font-latex-sedate">\draw</span>[->] (add1.east) -- (H1.west);
|
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<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (H2.west);
|
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<span class="org-font-latex-sedate">\draw</span>[->] (H1) -| (add.north);
|
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@ -338,7 +88,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
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</div>
|
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|
||||
|
||||
<div id="orgc3d769f" class="figure">
|
||||
<div id="org9c10944" class="figure">
|
||||
<p><img src="figs/fusion_super_sensor.png" alt="fusion_super_sensor.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Sensor Fusion Architecture (<a href="./figs/fusion_super_sensor.png">png</a>, <a href="./figs/fusion_super_sensor.pdf">pdf</a>, <a href="./figs/fusion_super_sensor.tex">tex</a>).</p>
|
||||
@ -346,20 +96,20 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org39b5d0c" class="outline-2">
|
||||
<h2 id="org39b5d0c"><span class="section-number-2">2</span> Fig 2: Sensor fusion architecture with sensor dynamics uncertainty</h2>
|
||||
<div id="outline-container-orgf8987c9" class="outline-2">
|
||||
<h2 id="orgf8987c9"><span class="section-number-2">2</span> Fig 2: Sensor fusion architecture with sensor dynamics uncertainty</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
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<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
|
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<span class="org-font-latex-sedate">\node</span>[addb, above right=0.8 and 4 of x](add1){};
|
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|
||||
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0.1 of add1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
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<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0.1 of add2](delta2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
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|
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<span class="org-font-latex-sedate">\node</span>[block, left=0.5 of delta2](W2){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
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|
||||
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
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|
||||
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|
||||
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|
||||
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2(s)$</span>};
|
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<span class="org-font-latex-sedate">\node</span>[addb, right=6 of x](add){};
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|
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|
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@ -388,7 +138,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgde2b8c0" class="figure">
|
||||
<div id="orgfc65b94" class="figure">
|
||||
<p><img src="figs/sensor_fusion_dynamic_uncertainty.png" alt="sensor_fusion_dynamic_uncertainty.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_dynamic_uncertainty.png">png</a>, <a href="./figs/sensor_fusion_dynamic_uncertainty.pdf">pdf</a>, <a href="./figs/sensor_fusion_dynamic_uncertainty.tex">tex</a>).</p>
|
||||
@ -396,8 +146,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfc9382d" class="outline-2">
|
||||
<h2 id="orgfc9382d"><span class="section-number-2">3</span> Fig 3: Uncertainty set of the super sensor dynamics</h2>
|
||||
<div id="outline-container-org1801a90" class="outline-2">
|
||||
<h2 id="org1801a90"><span class="section-number-2">3</span> Fig 3: Uncertainty set of the super sensor dynamics</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
@ -414,25 +164,20 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (0, 0) node[branch]{} -- coordinate[midway](r1) ++(45:1.0);
|
||||
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (135:1.0)node[branch]{} -- coordinate[midway](r2) ++(90:0.8);
|
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|
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|
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<span class="org-font-latex-sedate">\node</span>[] (l1) at (2, 1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1|$</span>};
|
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|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[] (l2) at (0, 2.0) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">|$</span>};
|
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<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=-90, in=0] (l2.south) to (r2);
|
||||
<span class="org-font-latex-sedate">\node</span>[] (l2) at (-2.5, 1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2|$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=0, in=-180] (l2.east) to (r2);
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (0, 0) -- coordinate[near end](r3) ++(200:1.8);
|
||||
<span class="org-font-latex-sedate">\node</span>[] (l3) at (-2.5, -1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">| + |w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">|$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[] (l3) at (-2.5, -1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1| + |w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2 H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2|$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=90, in=-90] (l3.north) to (r3);
|
||||
|
||||
<span class="org-comment">% % Uncertainty Regions</span>
|
||||
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below left] at (45:1.8) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{</span><span class="org-font-latex-sedate"><span class="org-comment">\text</span></span><span class="org-comment">{ss}}$};</span>
|
||||
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[above left] at (-45:1.0) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{1}$};</span>
|
||||
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below] at ($(135:1.0)+(0, 0.8)$) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{2}$};</span>
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
|
||||
|
||||
<span class="org-comment">% Real and Imaginary Axis</span>
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (0, -1.8) -- (0, 2.0) node[below left]{Im};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (0, -1.7) -- (0, 1.7) node[below left]{Im};
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=2);
|
||||
<span class="org-font-latex-sedate">\draw</span>[dashed] (1, 0) arc (0:28:1) node[midway, right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"> </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\phi</span></span><span class="org-font-latex-math">$</span>};
|
||||
@ -441,7 +186,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgf3182a4" class="figure">
|
||||
<div id="orga1a6d2e" class="figure">
|
||||
<p><img src="figs/uncertainty_set_super_sensor.png" alt="uncertainty_set_super_sensor.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Uncertainty region of the super sensor dynamics in the complex plane (solid circle), of the sensor 1 (dotted circle) and of the sensor 2 (dashed circle) (<a href="./figs/uncertainty_set_super_sensor.png">png</a>, <a href="./figs/uncertainty_set_super_sensor.pdf">pdf</a>, <a href="./figs/uncertainty_set_super_sensor.tex">tex</a>).</p>
|
||||
@ -449,8 +194,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb356b70" class="outline-2">
|
||||
<h2 id="orgb356b70"><span class="section-number-2">4</span> Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</h2>
|
||||
<div id="outline-container-org355bde0" class="outline-2">
|
||||
<h2 id="org355bde0"><span class="section-number-2">4</span> Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
@ -464,25 +209,25 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(P.south east)!0.35!(P.north east) + ( 0.7, 0)$</span>);
|
||||
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.1!(P.north east) + ( 0.7, 0)$</span>);
|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of W1] (sub) {};
|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H2) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H2) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2(s)$</span>};
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (H2.west) -| (<span class="org-font-latex-math">$(inputu)+(0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$u$</span>} -- (W2.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (inputu-|sub) node[branch]{} -- (sub.south);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (sub.east) -- (W1.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(sub.west)+(-0.6, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$v$</span>} |- (H2.east);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org3cb8226" class="figure">
|
||||
<div id="org903a05c" class="figure">
|
||||
<p><img src="figs/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (<a href="./figs/h_infinity_robust_fusion.png">png</a>, <a href="./figs/h_infinity_robust_fusion.pdf">pdf</a>, <a href="./figs/h_infinity_robust_fusion.tex">tex</a>).</p>
|
||||
@ -490,8 +235,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdeaeaf4" class="outline-2">
|
||||
<h2 id="orgdeaeaf4"><span class="section-number-2">5</span> Fig 5: Magnitude of a weighting function generated using the proposed formula</h2>
|
||||
<div id="outline-container-org879ecb3" class="outline-2">
|
||||
<h2 id="org879ecb3"><span class="section-number-2">5</span> Fig 5: Magnitude of a weighting function generated using the proposed formula</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
||||
@ -545,7 +290,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
10 1<span class="org-font-latex-warning">\\</span>
|
||||
};
|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[below] at (2, 10) {<span class="org-font-latex-math">$G_\infty$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[below] at (2, 10) {<span class="org-font-latex-math">$G_</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\infty</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (2, 0.001) {<span class="org-font-latex-math">$G_0$</span>};
|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[branch] at (10, 2){};
|
||||
@ -560,7 +305,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orga3a1174" class="figure">
|
||||
<div id="org1aeddba" class="figure">
|
||||
<p><img src="figs/weight_formula.png" alt="weight_formula.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Magnitude of a weighting function generated using the proposed formula (<a href="./figs/weight_formula.png">png</a>, <a href="./figs/weight_formula.pdf">pdf</a>, <a href="./figs/weight_formula.tex">tex</a>).</p>
|
||||
@ -568,8 +313,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8ce545c" class="outline-2">
|
||||
<h2 id="org8ce545c"><span class="section-number-2">6</span> Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</h2>
|
||||
<div id="outline-container-org2b1f7ae" class="outline-2">
|
||||
<h2 id="org2b1f7ae"><span class="section-number-2">6</span> Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
||||
@ -579,7 +324,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
||||
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
||||
height=0.5<span class="org-font-latex-sedate">\fheight</span>,
|
||||
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.5<span class="org-font-latex-sedate">\fheight</span>)},
|
||||
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.47<span class="org-font-latex-sedate">\fheight</span>)},
|
||||
scale only axis,
|
||||
xmode=log,
|
||||
xmin=0.1,
|
||||
@ -643,7 +388,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org49f0f1e" class="figure">
|
||||
<div id="orgd2fb3fa" class="figure">
|
||||
<p><img src="figs/hinf_synthesis_results.png" alt="hinf_synthesis_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis (<a href="./figs/hinf_synthesis_results.png">png</a>, <a href="./figs/hinf_synthesis_results.pdf">pdf</a>, <a href="./figs/hinf_synthesis_results.tex">tex</a>).</p>
|
||||
@ -651,8 +396,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgac21d24" class="outline-2">
|
||||
<h2 id="orgac21d24"><span class="section-number-2">7</span> Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters</h2>
|
||||
<div id="outline-container-org84a7e33" class="outline-2">
|
||||
<h2 id="org84a7e33"><span class="section-number-2">7</span> Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
@ -667,13 +412,13 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
<span class="org-font-latex-sedate">\coordinate</span>[] (output3) at (<span class="org-font-latex-math">$(P.south east)!0.3!(P.north east) + (0.7, 0)$</span>);
|
||||
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.1!(P.north east) + (0.7, 0)$</span>);
|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output3] (W3){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output3] (W3){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">3(s)$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of W1] (sub1) {};
|
||||
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of sub1] (sub2) {};
|
||||
|
||||
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-keyword"><span class="org-font-latex-math">\begin</span></span></span><span class="org-font-latex-math">{</span><span class="org-function-name"><span class="org-font-latex-math">bmatrix</span></span><span class="org-font-latex-math">}H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s) \\ H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">(s)</span><span class="org-font-latex-sedate"><span class="org-keyword"><span class="org-font-latex-math">\end</span></span></span><span class="org-font-latex-math">{</span><span class="org-function-name"><span class="org-font-latex-math">bmatrix</span></span><span class="org-font-latex-math">}$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-keyword"><span class="org-font-latex-math">\begin</span></span></span><span class="org-font-latex-math">{</span><span class="org-function-name"><span class="org-font-latex-math">bmatrix</span></span><span class="org-font-latex-math">}H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2(s) \\ H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">3(s)</span><span class="org-font-latex-sedate"><span class="org-keyword"><span class="org-font-latex-math">\end</span></span></span><span class="org-font-latex-math">{</span><span class="org-function-name"><span class="org-font-latex-math">bmatrix</span></span><span class="org-font-latex-math">}$</span>};
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (inputw) node[above right](w){<span class="org-font-latex-math">$w$</span>} -- (sub2.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W3-|sub1)node[branch]{} -- (sub1.south);
|
||||
@ -684,18 +429,18 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (sub2.east) -- (sub1.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (sub1.east) -- (W1.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left](z){<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W3.east) -- (output3)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (W2-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (W3-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left](z){<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W3.east) -- (output3)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">3$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (W2-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">1$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (W3-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">2$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (outputv-|z){<span class="org-font-latex-math">$v$</span>};
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd2b8673" class="figure">
|
||||
<div id="orgb697644" class="figure">
|
||||
<p><img src="figs/comp_filter_three_hinf.png" alt="comp_filter_three_hinf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters (<a href="./figs/comp_filter_three_hinf.png">png</a>, <a href="./figs/comp_filter_three_hinf.pdf">pdf</a>, <a href="./figs/comp_filter_three_hinf.tex">tex</a>).</p>
|
||||
@ -703,8 +448,8 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9688457" class="outline-2">
|
||||
<h2 id="org9688457"><span class="section-number-2">8</span> Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</h2>
|
||||
<div id="outline-container-org20bfce3" class="outline-2">
|
||||
<h2 id="org20bfce3"><span class="section-number-2">8</span> Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</h2>
|
||||
<div class="outline-text-2" id="text-8">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
||||
@ -714,7 +459,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
||||
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
||||
height=0.55<span class="org-font-latex-sedate">\fheight</span>,
|
||||
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.45<span class="org-font-latex-sedate">\fheight</span>)},
|
||||
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.42<span class="org-font-latex-sedate">\fheight</span>)},
|
||||
scale only axis,
|
||||
xmode=log,
|
||||
xmin=0.1,
|
||||
@ -791,7 +536,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org044b17c" class="figure">
|
||||
<div id="orgdaa24c8" class="figure">
|
||||
<p><img src="figs/hinf_three_synthesis_results.png" alt="hinf_three_synthesis_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis (<a href="./figs/hinf_three_synthesis_results.png">png</a>, <a href="./figs/hinf_three_synthesis_results.pdf">pdf</a>, <a href="./figs/hinf_three_synthesis_results.tex">tex</a>).</p>
|
||||
@ -799,12 +544,12 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8d6867c" class="outline-2">
|
||||
<h2 id="org8d6867c"><span class="section-number-2">9</span> Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis</h2>
|
||||
<div id="outline-container-orgb08c277" class="outline-2">
|
||||
<h2 id="orgb08c277"><span class="section-number-2">9</span> Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis</h2>
|
||||
<div class="outline-text-2" id="text-9">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">4cm</span>}
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">3.2cm</span>}
|
||||
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
||||
@ -847,7 +592,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
|
||||
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt]
|
||||
table[row sep=crcr]{<span class="org-comment">%</span>
|
||||
0.0005 0.008<span class="org-font-latex-warning">\\</span>
|
||||
0.0005 0.008<span class="org-font-latex-warning">\\</span>
|
||||
0.008 0.008<span class="org-font-latex-warning">\\</span>
|
||||
};
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{Specifications}
|
||||
@ -864,7 +609,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
};
|
||||
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt]
|
||||
table[row sep=crcr]{<span class="org-comment">%</span>
|
||||
0.1 0.045<span class="org-font-latex-warning">\\</span>
|
||||
0.1 0.045<span class="org-font-latex-warning">\\</span>
|
||||
2 0.045<span class="org-font-latex-warning">\\</span>
|
||||
};
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
||||
@ -873,7 +618,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgb9647cd" class="figure">
|
||||
<div id="org2ba2505" class="figure">
|
||||
<p><img src="figs/ligo_weights.png" alt="ligo_weights.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis (<a href="./figs/ligo_weights.png">png</a>, <a href="./figs/ligo_weights.pdf">pdf</a>, <a href="./figs/ligo_weights.tex">tex</a>).</p>
|
||||
@ -881,18 +626,18 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb6ae2f5" class="outline-2">
|
||||
<h2 id="orgb6ae2f5"><span class="section-number-2">10</span> Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)</h2>
|
||||
<div id="outline-container-org74b4762" class="outline-2">
|
||||
<h2 id="org74b4762"><span class="section-number-2">10</span> Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)</h2>
|
||||
<div class="outline-text-2" id="text-10">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">7cm</span>}
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">6.8cm</span>}
|
||||
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
||||
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
||||
height=0.60<span class="org-font-latex-sedate">\fheight</span>,
|
||||
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.35<span class="org-font-latex-sedate">\fheight</span>)},
|
||||
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.32<span class="org-font-latex-sedate">\fheight</span>)},
|
||||
scale only axis,
|
||||
xmode=log,
|
||||
xmin=0.001,
|
||||
@ -912,13 +657,13 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
]
|
||||
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
|
||||
table [x=freqs, y=Hhm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_H(s)$</span> - <span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}_\infty$</span>}
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_H(s)$</span> - <span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}_</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\infty</span></span><span class="org-font-latex-math">$</span>}
|
||||
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt]
|
||||
table [x=freqs, y=Hhm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_H(s)$</span> - FIR}
|
||||
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
|
||||
table [x=freqs, y=Hlm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_L(s)$</span> - <span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}_\infty$</span>}
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_L(s)$</span> - <span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}_</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\infty</span></span><span class="org-font-latex-math">$</span>}
|
||||
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt]
|
||||
table [x=freqs, y=Hlm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
|
||||
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_L(s)$</span> - FIR}
|
||||
@ -955,7 +700,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgc99b299" class="figure">
|
||||
<div id="org6bce6a7" class="figure">
|
||||
<p><img src="figs/comp_fir_ligo_hinf.png" alt="comp_fir_ligo_hinf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed) (<a href="./figs/comp_fir_ligo_hinf.png">png</a>, <a href="./figs/comp_fir_ligo_hinf.pdf">pdf</a>, <a href="./figs/comp_fir_ligo_hinf.tex">tex</a>).</p>
|
||||
@ -965,8 +710,7 @@ Configuration file is accessible <a href="config.html">here</a>.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
||||
<p class="date">Created: 2019-09-26 jeu. 17:46</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
<p class="date">Created: 2020-11-12 jeu. 10:44</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -1,14 +1,10 @@
|
||||
#+TITLE: Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis - Tikz Figures
|
||||
:DRAWER:
|
||||
#+HTML_LINK_HOME: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
||||
#+HTML_HEAD: <script src="../js/jquery.min.js"></script>
|
||||
#+HTML_HEAD: <script src="../js/bootstrap.min.js"></script>
|
||||
#+HTML_HEAD: <script src="../js/jquery.stickytableheaders.min.js"></script>
|
||||
#+HTML_HEAD: <script src="../js/readtheorg.js"></script>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||||
|
||||
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/tikz/}{config.tex}")
|
||||
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||||
|
||||
Loading…
Reference in New Issue
Block a user