Initial Commit

.gitignore

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+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+.*.lb
+
+## Intermediate documents:
+*.dvi
+*.xdv
+*-converted-to.*
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+## Generated if empty string is given at "Please type another file name for output:"
+.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex(busy)
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
+
+## Build tool directories for auxiliary files
+# latexrun
+latex.out/
+
+## Auxiliary and intermediate files from other packages:
+# algorithms
+*.alg
+*.loa
+
+# achemso
+acs-*.bib
+
+# amsthm
+*.thm
+
+# beamer
+*.nav
+*.pre
+*.snm
+*.vrb
+
+# changes
+*.soc
+
+# comment
+*.cut
+
+# cprotect
+*.cpt
+
+# elsarticle (documentclass of Elsevier journals)
+*.spl
+
+# endnotes
+*.ent
+
+# fixme
+*.lox
+
+# feynmf/feynmp
+*.mf
+*.mp
+*.t[1-9]
+*.t[1-9][0-9]
+*.tfm
+
+#(r)(e)ledmac/(r)(e)ledpar
+*.end
+*.?end
+*.[1-9]
+*.[1-9][0-9]
+*.[1-9][0-9][0-9]
+*.[1-9]R
+*.[1-9][0-9]R
+*.[1-9][0-9][0-9]R
+*.eledsec[1-9]
+*.eledsec[1-9]R
+*.eledsec[1-9][0-9]
+*.eledsec[1-9][0-9]R
+*.eledsec[1-9][0-9][0-9]
+*.eledsec[1-9][0-9][0-9]R
+
+# glossaries
+*.acn
+*.acr
+*.glg
+*.glo
+*.gls
+*.glsdefs
+
+# gnuplottex
+*-gnuplottex-*
+
+# gregoriotex
+*.gaux
+*.gtex
+
+# htlatex
+*.4ct
+*.4tc
+*.idv
+*.lg
+*.trc
+*.xref
+
+# hyperref
+*.brf
+
+# knitr
+*-concordance.tex
+# TODO Comment the next line if you want to keep your tikz graphics files
+*.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# makeidx
+*.idx
+*.ilg
+*.ind
+*.ist
+
+# minitoc
+*.maf
+*.mlf
+*.mlt
+*.mtc[0-9]*
+*.slf[0-9]*
+*.slt[0-9]*
+*.stc[0-9]*
+
+# minted
+_minted*
+*.pyg
+
+# morewrites
+*.mw
+
+# nomencl
+*.nlg
+*.nlo
+*.nls
+
+# pax
+*.pax
+
+# pdfpcnotes
+*.pdfpc
+
+# sagetex
+*.sagetex.sage
+*.sagetex.py
+*.sagetex.scmd
+
+# scrwfile
+*.wrt
+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
+# pdfcomment
+*.upa
+*.upb
+
+# pythontex
+*.pytxcode
+pythontex-files-*/
+
+# tcolorbox
+*.listing
+
+# thmtools
+*.loe
+
+# TikZ & PGF
+*.dpth
+*.md5
+*.auxlock
+
+# todonotes
+*.tdo
+
+# vhistory
+*.hst
+*.ver
+
+# easy-todo
+*.lod
+
+# xcolor
+*.xcp
+
+# xmpincl
+*.xmpi
+
+# xindy
+*.xdy
+
+# xypic precompiled matrices
+*.xyc
+
+# endfloat
+*.ttt
+*.fff
+
+# Latexian
+TSWLatexianTemp*
+
+## Editors:
+# WinEdt
+*.bak
+*.sav
+
+# Texpad
+.texpadtmp
+
+# LyX
+*.lyx~
+
+# Kile
+*.backup
+
+# KBibTeX
+*~[0-9]*
+
+# auto folder when using emacs and auctex
+./auto/*
+*.el
+
+# expex forward references with \gathertags
+*-tags.tex
+
+# standalone packages
+*.sta

Makefile

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+.PHONY: all paper help html publish watch clean cp-figs
+
+SHELL := /bin/bash
+PAPERDIR=paper
+MATLABDIR=matlab
+TIKZDIR=tikz
+
+PAPERNAME=paper
+
+all: paper html publish
+
+paper: cp-figs tangle tex pdf clean
+
+help:
+	@echo "Usage: make <command>"
+	@echo "  all     - Cp-figs tex pdf html publish"
+	@echo "  paper   - Compile the org file to a pdf"
+	@echo "  html    - Export all the org files to html"
+	@echo "  publish - Commit everything and push to repository"
+	@echo "  tex     - Export to paper in org format to tex"
+	@echo "  tangle  - Tangle everything that is in the org paper and tikz file"
+	@echo "  pdf     - Compile the tex file to pdf"
+	@echo "  watch   - Watch the tex file for changes and compile"
+	@echo "  clean   - Clean the paper directory"
+	@echo "  cp-figs - Copy all the necessary figures from tikz and matlab folder to paper folder"
+
+html:
+	for f in *.org;              do emacsclient -e "(progn (find-file \"$$f\") (org-html-export-to-html))"; done
+	for f in $(TIKZDIR)/*.org;    do emacsclient -e "(progn (find-file \"$$f\") (org-html-export-to-html))"; done
+	for f in $(MATLABDIR)/*.org; do emacsclient -e "(progn (find-file \"$$f\") (org-html-export-to-html))"; done
+
+publish:
+	git add . && git commit -m "Update - $$(date +%F)" && git push origin master
+
+tex: $(PAPERDIR)/$(PAPERNAME).org
+	emacsclient -e '(progn (find-file "$(PAPERDIR)/$(PAPERNAME).org") (org-latex-export-to-latex))'
+
+tangle: $(PAPERDIR)/$(PAPERNAME).org
+	emacsclient -e '(progn (find-file "$(PAPERDIR)/$(PAPERNAME).org") (org-babel-tangle))'
+	emacsclient -e '(progn (find-file "$(TIKZDIR)/index.org") (org-babel-tangle))'
+
+pdf: $(PAPERDIR)/$(PAPERNAME).tex
+	latexmk -cd -quiet -bibtex $(PREVIEW_CONTINUOUSLY) -f -pdf -pdflatex="xelatex -synctex=1 -interaction nonstopmode" -use-make $(PAPERDIR)/$(PAPERNAME).tex
+
+# Set the PREVIEW_CONTINUOUSLY variable to -pvc to switch latexmk into the preview continuously mode
+watch: PREVIEW_CONTINUOUSLY=-pvc
+watch: pdf
+
+watch-org: $(PAPERDIR)/$(PAPERNAME).org
+	echo $(PAPERDIR)/$(PAPERNAME).org | entr -s 'make tangle tex pdf'
+
+clean:
+	latexmk -cd -c -bibtex $(PAPERDIR)/$(PAPERNAME).tex
+
+cp-figs:
+	bash scripts/cp-figs.sh

css/htmlize.css

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index.html

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+<?xml version="1.0" encoding="utf-8"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
+"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
+<head>
+<!-- 2019-08-14 mer. 12:07 -->
+<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
+<meta name="viewport" content="width=device-width, initial-scale=1" />
+<title>Optimal and Robust Complementary Filters for Sensor Fusion</title>
+<meta name="generator" content="Org mode" />
+<meta name="author" content="Thomas Dehaeze" />
+<style type="text/css">
+ <!--/*--><![CDATA[/*><!--*/
+  .title  { text-align: center;
+             margin-bottom: .2em; }
+  .subtitle { text-align: center;
+              font-size: medium;
+              font-weight: bold;
+              margin-top:0; }
+  .todo   { font-family: monospace; color: red; }
+  .done   { font-family: monospace; color: green; }
+  .priority { font-family: monospace; color: orange; }
+  .tag    { background-color: #eee; font-family: monospace;
+            padding: 2px; font-size: 80%; font-weight: normal; }
+  .timestamp { color: #bebebe; }
+  .timestamp-kwd { color: #5f9ea0; }
+  .org-right  { margin-left: auto; margin-right: 0px;  text-align: right; }
+  .org-left   { margin-left: 0px;  margin-right: auto; text-align: left; }
+  .org-center { margin-left: auto; margin-right: auto; text-align: center; }
+  .underline { text-decoration: underline; }
+  #postamble p, #preamble p { font-size: 90%; margin: .2em; }
+  p.verse { margin-left: 3%; }
+  pre {
+    border: 1px solid #ccc;
+    box-shadow: 3px 3px 3px #eee;
+    padding: 8pt;
+    font-family: monospace;
+    overflow: auto;
+    margin: 1.2em;
+  }
+  pre.src {
+    position: relative;
+    overflow: visible;
+    padding-top: 1.2em;
+  }
+  pre.src:before {
+    display: none;
+    position: absolute;
+    background-color: white;
+    top: -10px;
+    right: 10px;
+    padding: 3px;
+    border: 1px solid black;
+  }
+  pre.src:hover:before { display: inline;}
+  /* Languages per Org manual */
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+  pre.src-C:before { content: 'C'; }
+  /* pre.src-C++ doesn't work in CSS */
+  pre.src-clojure:before { content: 'Clojure'; }
+  pre.src-css:before { content: 'CSS'; }
+  pre.src-D:before { content: 'D'; }
+  pre.src-ditaa:before { content: 'ditaa'; }
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+  pre.src-fortran:before { content: 'Fortran'; }
+  pre.src-gnuplot:before { content: 'gnuplot'; }
+  pre.src-haskell:before { content: 'Haskell'; }
+  pre.src-hledger:before { content: 'hledger'; }
+  pre.src-java:before { content: 'Java'; }
+  pre.src-js:before { content: 'Javascript'; }
+  pre.src-latex:before { content: 'LaTeX'; }
+  pre.src-ledger:before { content: 'Ledger'; }
+  pre.src-lisp:before { content: 'Lisp'; }
+  pre.src-lilypond:before { content: 'Lilypond'; }
+  pre.src-lua:before { content: 'Lua'; }
+  pre.src-matlab:before { content: 'MATLAB'; }
+  pre.src-mscgen:before { content: 'Mscgen'; }
+  pre.src-ocaml:before { content: 'Objective Caml'; }
+  pre.src-octave:before { content: 'Octave'; }
+  pre.src-org:before { content: 'Org mode'; }
+  pre.src-oz:before { content: 'OZ'; }
+  pre.src-plantuml:before { content: 'Plantuml'; }
+  pre.src-processing:before { content: 'Processing.js'; }
+  pre.src-python:before { content: 'Python'; }
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+</head>
+<body>
+<div id="content">
+<h1 class="title">Optimal and Robust Complementary Filters for Sensor Fusion</h1>
+<div id="table-of-contents">
+<h2>Table of Contents</h2>
+<div id="text-table-of-contents">
+<ul>
+<li><a href="#org724c9ac">1. Paper</a></li>
+<li><a href="#org76ab49b">2. Computation - Matlab</a></li>
+<li><a href="#org3ec9997">3. Figures</a></li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org724c9ac" class="outline-2">
+<h2 id="org724c9ac"><span class="section-number-2">1</span> Paper</h2>
+<div class="outline-text-2" id="text-1">
+<p>
+The current version of the paper is accessible <a href="paper/paper.pdf">here</a>.
+</p>
+</div>
+</div>
+
+<div id="outline-container-org76ab49b" class="outline-2">
+<h2 id="org76ab49b"><span class="section-number-2">2</span> Computation - Matlab</h2>
+<div class="outline-text-2" id="text-2">
+<p>
+The Matlab computation files that permits to obtain all the paper results are accessible <a href="matlab/index.html">here</a>.
+</p>
+</div>
+</div>
+
+<div id="outline-container-org3ec9997" class="outline-2">
+<h2 id="org3ec9997"><span class="section-number-2">3</span> Figures</h2>
+<div class="outline-text-2" id="text-3">
+<p>
+The figures are generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>. The code to generate the figures inside the paper are accessible <a href="tikz/index.html">here</a>.
+</p>
+</div>
+</div>
+</div>
+<div id="postamble" class="status">
+<p class="author">Author: Thomas Dehaeze</p>
+<p class="date">Created: 2019-08-14 mer. 12:07</p>
+<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
+</div>
+</body>
+</html>

index.org

@@ -0,0 +1,19 @@
+#+TITLE: Optimal and Robust Complementary Filters for Sensor Fusion
+:DRAWER:
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
+
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+#+HTML_HEAD: <script src="js/jquery.stickytableheaders.min.js"></script>
+#+HTML_HEAD: <script src="js/readtheorg.js"></script>
+:END:
+
+* Paper
+The current version of the paper is accessible [[file:paper/paper.pdf][here]].
+
+* Computation - Matlab
+The Matlab computation files that permits to obtain all the paper results are accessible [[file:matlab/index.org][here]].
+
+* Figures
+The figures are generated using [[https://sourceforge.net/projects/pgf/][TikZ]]. The code to generate the figures inside the paper are accessible [[file:tikz/index.org][here]].

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matlab/ref.bib

@@ -0,0 +1,171 @@
+@article{collette15_sensor_fusion_method_high_perfor,
+  author = {C. Collette and F. Matichard},
+  title = {Sensor Fusion Methods for High Performance Active Vibration Isolation Systems},
+  journal = {Journal of Sound and Vibration},
+  volume = {342},
+  number = {nil},
+  pages = {1-21},
+  year = {2015},
+  doi = {10.1016/j.jsv.2015.01.006},
+  url = {https://doi.org/10.1016/j.jsv.2015.01.006},
+  keywords = {},
+}
+
+
+@phdthesis{hua05_low_ligo,
+  author =       {Hua, Wensheng},
+  school =       {stanford university},
+  title =        {Low frequency vibration isolation and alignment system for
+                  advanced LIGO},
+  year =         2005,
+}
+
+
+@inproceedings{hua04_polyp_fir_compl_filter_contr_system,
+  author = {Wensheng Hua and Dan B. Debra and Corwin T. Hardham and Brian T. Lantz and Joseph A. Giaime},
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+}
+
+
+@article{matichard15_seism_isolat_advan_ligo,
+  author = {Matichard, F and Lantz, B and Mittleman, R and Mason, K and Kissel, J and Abbott, B and Biscans, S and McIver, J and Abbott, R and Abbott, S and others},
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+  publisher = {IOP Publishing},
+}
+
+
+@article{min15_compl_filter_desig_angle_estim,
+  author = {Min, Hyung Gi and Jeung, Eun Tae},
+  title = {Complementary Filter Design for Angle Estimation Using Mems Accelerometer and Gyroscope},
+  journal = {Department of Control and Instrumentation, Changwon National University, Changwon, Korea},
+  pages = {641--773},
+  year = {2015},
+}
+
+
+@article{corke04_inert_visual_sensin_system_small_auton_helic,
+  author = {Peter Corke},
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+}
+
+
+@inproceedings{jensen13_basic_uas,
+  author =       {Austin Jensen and Cal Coopmans and YangQuan Chen},
+  title =        {Basics and guidelines of complementary filters for small UAS
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+                  (ICUAS)},
+  year =         2013,
+  pages =        {nil},
+  doi =          {10.1109/icuas.2013.6564726},
+  url =          {https://doi.org/10.1109/icuas.2013.6564726},
+  month =        5,
+}
+
+
+@inproceedings{pascoal99_navig_system_desig_using_time,
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+}
+
+
+@article{zimmermann92_high_bandw_orien_measur_contr,
+  author = {M. Zimmermann and W. Sulzer},
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+  url = {https://doi.org/10.1016/b978-0-08-041276-4.50093-5},
+  publisher = {Elsevier},
+  series = {Robot Control 1991},
+}
+
+
+@inproceedings{baerveldt97_low_cost_low_weigh_attit,
+  author = {A.-J. Baerveldt and R. Klang},
+  title = {A Low-Cost and Low-Weight Attitude Estimation System for an Autonomous Helicopter},
+  booktitle = {Proceedings of IEEE International Conference on Intelligent Engineering Systems},
+  year = {1997},
+  pages = {nil},
+  doi = {10.1109/ines.1997.632450},
+  url = {https://doi.org/10.1109/ines.1997.632450},
+  month = {-},
+}
+
+
+@article{shaw90_bandw_enhan_posit_measur_using_measur_accel,
+  author =       {F.R. Shaw and K. Srinivasan},
+  title =        {Bandwidth Enhancement of Position Measurements Using Measured
+                  Acceleration},
+  journal =      {Mechanical Systems and Signal Processing},
+  volume =       4,
+  number =       1,
+  pages =        {23-38},
+  year =         1990,
+  doi =          {10.1016/0888-3270(90)90038-m},
+  url =          {https://doi.org/10.1016/0888-3270(90)90038-m},
+}
+
+
+@article{brown72_integ_navig_system_kalman_filter,
+  author =       {R. G. Brown},
+  title =        {Integrated Navigation Systems and Kalman Filtering: a
+                  Perspective},
+  journal =      {Navigation},
+  volume =       19,
+  number =       4,
+  pages =        {355-362},
+  year =         1972,
+  doi =          {10.1002/j.2161-4296.1972.tb01706.x},
+  url =          {https://doi.org/10.1002/j.2161-4296.1972.tb01706.x},
+}
+
+
+@article{matichard15_seism_isolat_advan_ligo,
+  author =       {Matichard, F and Lantz, B and Mittleman, R and Mason, K and
+                  Kissel, J and Abbott, B and Biscans, S and McIver, J and
+                  Abbott, R and Abbott, S and others},
+  title =        {Seismic Isolation of Advanced Ligo: Review of Strategy,
+                  Instrumentation and Performance},
+  journal =      {Classical and Quantum Gravity},
+  volume =       32,
+  number =       18,
+  pages =        185003,
+  year =         2015,
+  publisher =    {IOP Publishing},
+}
+
+
+@article{mahony08_nonlin_compl_filter_special_orthog_group,
+  author =       {Robert Mahony and Tarek Hamel and Jean-Michel Pflimlin},
+  title =        {Nonlinear Complementary Filters on the Special Orthogonal
+                  Group},
+  journal =      {IEEE Transactions on Automatic Control},
+  volume =       53,
+  number =       5,
+  pages =        {1203-1218},
+  year =         2008,
+  doi =          {10.1109/tac.2008.923738},
+  url =          {https://doi.org/10.1109/tac.2008.923738},
+}

paper/config.tex

@@ -0,0 +1,28 @@
+% H Infini
+\newcommand{\hinf}{\mathcal{H}_\infty}
+
+% H 2
+\newcommand{\htwo}{\mathcal{H}_2}
+
+% Omega
+\newcommand{\w}{\omega}
+
+% H-Infinity Norm
+\newcommand{\hnorm}[1]{\left\|#1\right\|_{\infty}}
+
+% H-2 Norm
+\newcommand{\normtwo}[1]{\left\|#1\right\|_{2}}
+
+% Norm
+\newcommand{\norm}[1]{\left\|#1\right\|}
+
+% Absolute value
+\newcommand{\abs}[1]{\left\lvert #1 \right\lvert}
+
+% Minimum Subscript
+\newcommand{\smin}{_{\text{min}}}
+
+% Maximum Subscript
+\newcommand{\smax}{_{\text{max}}}
+
+\newcommand*\colvec[1]{\begin{bmatrix}#1\end{bmatrix}}

paper/paper.org

@@ -0,0 +1,275 @@
+#+TITLE: Optimal and Robust Complementary Filters for Sensor Fusion
+:DRAWER:
+#+LATEX_CLASS: ieeeconf
+#+LATEX_CLASS_OPTIONS: [9pt, technote, a4paper]
+#+OPTIONS: toc:nil
+#+STARTUP: overview
+
+#+DATE: {{{time(%Y-%m-%d)}}}
+#+AUTHOR: @@latex:\IEEEauthorblockN{Dehaeze Thomas\IEEEauthorrefmark{*} and Collette Christophe} \\@@
+#+AUTHOR: @@latex:\IEEEauthorblockA{Precision Mechatronics Laboratory, ULB\\ Brussels, Belgium\\ Email: \IEEEauthorrefmark{*}dehaeze.thomas@gmail.com}@@
+
+#+LATEX_HEADER: \usepackage{amsmath,amssymb,amsfonts, cases}
+#+LATEX_HEADER: \usepackage{algorithmic, graphicx, textcomp}
+#+LATEX_HEADER: \usepackage{xcolor, import, hyperref}
+#+LATEX_HEADER: \usepackage[USenglish]{babel}
+#+LATEX_HEADER: \setcounter{footnote}{1}
+#+LATEX_HEADER: \input{config.tex}
+
+\bibliographystyle{IEEEtran}
+:END:
+
+* LaTeX Config                                                     :noexport:
+#+begin_src latex :tangle config.tex
+  % H Infini
+  \newcommand{\hinf}{\mathcal{H}_\infty}
+
+  % H 2
+  \newcommand{\htwo}{\mathcal{H}_2}
+
+  % Omega
+  \newcommand{\w}{\omega}
+
+  % H-Infinity Norm
+  \newcommand{\hnorm}[1]{\left\|#1\right\|_{\infty}}
+
+  % H-2 Norm
+  \newcommand{\normtwo}[1]{\left\|#1\right\|_{2}}
+
+  % Norm
+  \newcommand{\norm}[1]{\left\|#1\right\|}
+
+  % Absolute value
+  \newcommand{\abs}[1]{\left\lvert #1 \right\lvert}
+
+  % Minimum Subscript
+  \newcommand{\smin}{_{\text{min}}}
+
+  % Maximum Subscript
+  \newcommand{\smax}{_{\text{max}}}
+
+  \newcommand*\colvec[1]{\begin{bmatrix}#1\end{bmatrix}}
+#+end_src
+
+* Build                                                            :noexport:
+#+BEGIN_SRC emacs-lisp :results none
+  (add-to-list 'org-latex-classes
+               '("ieeeconf"
+                 "\\documentclass{ieeeconf}"
+                 ("\\section{%s}" . "\\section*{%s}")
+                 ("\\subsection{%s}" . "\\subsection*{%s}")
+                 ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
+                 ("\\paragraph{%s}" . "\\paragraph*{%s}")
+                 ("\\subparagraph{%s}" . "\\subparagraph*{%s}"))
+               )
+#+END_SRC
+
+* Abstract                                                           :ignore:
+#+begin_abstract
+  Abstract text to be done
+#+end_abstract
+
+#+begin_IEEEkeywords
+  complementary filters, h-infinity, feedback control
+#+end_IEEEkeywords
+
+* Introduction
+  <<sec:introduction>>
+The basic idea of a complementary filter involves taking two or more sensors, filtering out unreliable frequencies for each sensor and combining the filtered outputs to get a better estimate throughout the entire bandwidth of the system.
+To achieve this, the sensors included in the filter should complement one another by performing better over specific parts of the system bandwidth.
+
+** Establish the importance of the research topic                    :ignore:
+# What are Complementary Filters
+A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies, (i.e.) its magnitude is one and its phase is zero.
+
+# Why Design of Complementary Filter is important
+The proper design of this particular kind of filter is of primary importance in a wide range of applications.
+
+** Descriptions of the applications of complementary filtering       :ignore:
+Often, multiple sensors with different noise or dynamical properties are used to measure the same physical quantity.
+In such case, complementary filters can be used to merge the sensors and forms a "super sensor" that has gives a better estimate of the physical quantity over a wider bandwidth.
+This is called sensor blending or sensor fusion.
+
+# List of all the applications
+
+# Increasing Sensor Bandwidth
+This is widely used for the attitude estimation of unmanned aerial vehicles using various kind of sensors (accelerometers, gyroscopes, vision sensors, inclinometer) cite:zimmermann92_high_bandw_orien_measur_contr,corke04_inert_visual_sensin_system_small_auton_helic,min15_compl_filter_desig_angle_estim.
+
+cite:shaw90_bandw_enhan_posit_measur_using_measur_accel Fast position measurement of flexible structure
+
+# Merging of different sensor types
+cite:matichard15_seism_isolat_advan_ligo (relative displacement measurement at low frequencies with inertial at high frequencies)
+
+# Reducing sensor noise
+cite:hua04_polyp_fir_compl_filter_contr_system
+
+# Improving the control robustness
+cite:collette15_sensor_fusion_method_high_perfor
+
+** Current research focus of the field / Literature review           :ignore:
+# Discuss the different approach to complementary filter design
+The design methods for such filters goes from simple analytical formulas
+
+# Analytical Formulas with limited number of parameter that let the designer choose the parameter value
+# First Order
+cite:corke04_inert_visual_sensin_system_small_auton_helic
+
+# Second Order
+cite:min15_compl_filter_desig_angle_estim
+cite:jensen13_basic_uas
+
+# Third Order and Higher orders
+cite:shaw90_bandw_enhan_posit_measur_using_measur_accel
+cite:zimmermann92_high_bandw_orien_measur_contr
+cite:matichard15_seism_isolat_advan_ligo
+cite:collette15_sensor_fusion_method_high_perfor
+
+# FIR Filters
+cite:hua05_low_ligo
+cite:hua04_polyp_fir_compl_filter_contr_system
+cite:matichard15_seism_isolat_advan_ligo
+
+# Non-linear methods
+cite:mahony08_nonlin_compl_filter_special_orthog_group
+
+# Time Varying
+cite:pascoal99_navig_system_desig_using_time
+
+# Alternate Formulation
+cite:jensen13_basic_uas (feedback system, P, PI, classical control theory for filter design)
+cite:brown72_integ_navig_system_kalman_filter
+
+# LMI / convex Optimization
+cite:pascoal99_navig_system_desig_using_time
+
+# Least Square method for finding the optimal filter coefficients
+cite:min15_compl_filter_desig_angle_estim
+
+** Describe a gap in the research                                    :ignore:
+# There is a need to design optimal complementary filters
+Although
+
+** Describe the paper itself / the problem which is addressed        :ignore:
+In this paper, we propose
+
+** Introduce Each part of the paper                                  :ignore:
+The body of the paper consists of five parts followed by a conclusion.
+
+* H-Infinity synthesis of complementary filters
+  <<sec:hinf_filters>>
+First order complementary filters are easy to synthesize. For instance, one can use the following filters
+\begin{equation}
+H_H(s) = \frac{s/\w_0}{1 + s/\w_0}; \quad H_L(s) = \frac{1}{1 + s/\w_0}
+\end{equation}
+with $\w_0$ is the tuning parameter corresponding to the crossover frequency of the filters.
+
+However, the manual design of higher order complementary filters is far more complex and we have to use an automatic synthesis technique.
+
+
+As shown in Sec. ref:sec:trans_perf, most of the performance requirements can be expressed as upper bounds on the magnitude of the complementary filters.
+
+Thus, the $\mathcal{H}_\infty$ framework seems adapted and we here propose a technique to synthesis complementary filters while specifying uppers bounds on their magnitudes.
+
+** $\hinf$ problem formulation
+   <<sec:hinf_conf>>
+In this section, we formulate the $\hinf$ problem for the synthesis of complementary filters.
+
+The synthesis objective is to shape an high pass filter $H_H$ and a low pass filter $H_L$ while ensuring their complementary property ($H_H + H_L = 1$).
+
+To do so, we define two weighting functions $w_L$ and $w_H$ that will respectively used to shape $H_L$ and $H_H$.
+
+The synthesis problem is then
+\begin{subnumcases}{\text{Find } H_L, H_H \text{ such that}}
+  H_L \text{ and } H_H \text{ are stable} \label{eq:hinf_cond_stability}\\
+  H_L + H_H = 1 \label{eq:hinf_cond_complementarity} \\
+  |w_L H_L| \le 1 \quad \forall\omega \label{eq:hinf_cond_hl} \\
+  |w_H H_H| \le 1 \quad \forall\omega \label{eq:hinf_cond_hh}
+\end{subnumcases}
+
+
+To express this synthesis problem into an $\hinf$ synthesis problem, we define the following generalized plant $P$ (also shown on Fig. ref:fig:sf_hinf_filters_plant_b):
+#+NAME: eq:generalized_plant
+\begin{equation}
+  \colvec{w\\u} = P \colvec{z_H \\ z_L \\ v}; \quad P = \begin{bmatrix} w_H & -w_H \\ 0 & w_L \\ 1 & 0 \end{bmatrix}
+\end{equation}
+
+#+name: fig:sf_hinf_filters_plant_b
+#+caption: Generalized plant for the synthesis of the complementary filters
+#+attr_latex: :float t :scale 1
+file:./figs/sf_hinf_filters_plant_b.pdf
+
+The $\hinf$ synthesis objective is then to design a stable filter $H_L$ (Fig. ref:fig:sf_hinf_filters_b) such that the $\mathcal{H}_\infty$ norm of the transfer function from $w$ to $[z_H, \ z_L]$ is less than $1$:
+\begin{equation}
+  \hnorm{\begin{matrix} (1 - H_L) w_H \\ H_L w_L \end{matrix}} \le 1
+\end{equation}
+Which is equivalent to
+#+NAME: eq:hinf_problem
+\begin{equation}
+  \hnorm{\begin{matrix} H_H w_H \\ H_L w_L \end{matrix}} < 1 \text{ by choosing } H_H = 1 - H_L
+\end{equation}
+
+#+name: fig:sf_hinf_filters_b
+#+caption: $\hinf\text{-synthesis}$ of complementary filters
+#+attr_latex: :float t :scale 1
+file:./figs/sf_hinf_filters_b.pdf
+
+Performance conditions eqref:eq:hinf_cond_hl and eqref:eq:hinf_cond_hl are satisfied by eqref:eq:hinf_problem.
+Complementary condition eqref:eq:hinf_cond_complementarity is satisfied by design: $H_H = 1 - H_L$ and thus $H_L + H_H = 1$.
+The stability condition eqref:eq:hinf_cond_stability is guaranteed by the $H_\infty$ synthesis (*reference*).
+
+
+Using this synthesis method, we are then able to shape at the same time the high pass and low pass filters while ensuring their complementary.
+
+** Control requirements as $\mathcal{H}_\infty$ norm of complementary filters
+As presented in Sec. ref:sec:trans_perf, almost all the requirements can be specified with upper bounds on the complementary filters.
+However, robust performance condition eqref:eq:robust_perf_a is not.
+
+With the $\mathcal{H}_\infty$ synthesis the condition eqref:eq:hinf_problem only ensure
+\begin{align*}
+  \hnorm{\begin{matrix} H_H w_H \\ H_L w_L \end{matrix}} \le 1 &\Leftrightarrow \max_\omega \sqrt{|w_L H_L|^2 + |w_H H_H|^2} \le 1\\
+                                                             &\Rightarrow |w_L H_L| + |w_H H_H| \le \sqrt{2} \quad \forall\omega
+\end{align*}
+
+And thus we have almost robust stability.
+
+** Choice of the weighting functions
+   <<sec:hinf_weighting_func>>
+We here give some advice on the choice of the weighting functions used for the synthesis of the complementary filters.
+
+The shape should be such that the performance requirements are met as explain in Sec. ref:sec:trans_perf.
+
+However, one should be careful when designing the complementary filters, and should only use stable and minimum phase transfer functions.
+The order of the weights should stay reasonably small as this will increase the complexity of the optimization problem.
+
+One should not forget the fundamental limitations of feedback control such that $S + T = 1$.
+Similarly, we here have that $H_L + H_H = 1$ which implies that $H_L$ and $H_H$ cannot be made small at the same time.
+
+** Trade-off between performance and robustness
+
+** Analytical formula of complementary filters
+  <<sec:analytical_complementary_filters>>
+To simplify the synthesis, one can use already synthesized filters
+
+\begin{align}
+  H_L(s) = \frac{1}{1 + \frac{s}{\omega_0}}\\
+  H_H(s) = \frac{\frac{s}{\omega_0}}{1 + \frac{s}{\omega_0}}
+\end{align}
+
+\begin{align}
+  H_L(s) &= \frac{(1+\alpha) (\frac{s}{\omega_0})+1}{\left((\frac{s}{\omega_0})+1\right) \left((\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1\right)}\\
+  H_H(s) &= \frac{(\frac{s}{\omega_0})^2 \left((\frac{s}{\omega_0})+1+\alpha\right)}{\left((\frac{s}{\omega_0})+1\right) \left((\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1\right)}
+\end{align}
+
+\begin{align}
+  H_L(s) &= \frac{\left(1+(\alpha+1)(\beta+1)\right) (\frac{s}{\omega_0})^2 + (1+\alpha+\beta)(\frac{s}{\omega_0}) + 1}{\left(\frac{s}{\omega_0} + 1\right) \left( (\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1 \right) \left( (\frac{s}{\omega_0})^2 + \beta (\frac{s}{\omega_0}) + 1 \right)}\\
+  H_H(s) &= \frac{(\frac{s}{\omega_0})^3 \left( (\frac{s}{\omega_0})^2 + (1+\alpha+\beta) (\frac{s}{\omega_0}) + (1+(\alpha+1)(\beta+1)) \right)}{\left(\frac{s}{\omega_0} + 1\right) \left( (\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1 \right) \left( (\frac{s}{\omega_0})^2 + \beta (\frac{s}{\omega_0}) + 1 \right)}
+\end{align}
+
+* Discussion
+* Conclusion
+  <<sec:conclusion>>
+
+* Acknowledgment
+
+* Bibliography                                                       :ignore:
+\bibliography{ref}

paper/paper.tex

@@ -0,0 +1,229 @@
+% Created 2019-08-12 lun. 16:02
+% Intended LaTeX compiler: pdflatex
+\documentclass[9pt, technote, a4paper]{ieeeconf}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{grffile}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{textcomp}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\usepackage[most]{tcolorbox}
+\usepackage{siunitx}
+\usepackage{amsmath,amssymb,amsfonts, cases}
+\usepackage{algorithmic, graphicx, textcomp}
+\usepackage{xcolor, import, hyperref}
+\usepackage[USenglish, english]{babel}
+\setcounter{footnote}{1}
+\input{config.tex}
+\author{\IEEEauthorblockN{Dehaeze Thomas\IEEEauthorrefmark{*} and Collette Christophe} \\ \IEEEauthorblockA{Precision Mechatronics Laboratory, ULB\\ Brussels, Belgium\\ Email: \IEEEauthorrefmark{*}dehaeze.thomas@gmail.com}}
+\date{2019-08-12}
+\title{On the Design of Complementary Filters for Control}
+\hypersetup{
+ pdfauthor={\IEEEauthorblockN{Dehaeze Thomas\IEEEauthorrefmark{*} and Collette Christophe} \\ \IEEEauthorblockA{Precision Mechatronics Laboratory, ULB\\ Brussels, Belgium\\ Email: \IEEEauthorrefmark{*}dehaeze.thomas@gmail.com}},
+ pdftitle={On the Design of Complementary Filters for Control},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 26.2 (Org mode 9.2.5)},
+ pdflang={English}}
+\begin{document}
+
+\maketitle
+\bibliographystyle{IEEEtran}
+
+\begin{abstract}
+Abstract text to be done
+\end{abstract}
+
+\begin{IEEEkeywords}
+complementary filters, h-infinity, feedback control
+\end{IEEEkeywords}
+
+\section{Introduction}
+\label{sec:orgb15ebed}
+  \label{sec:introduction}
+The basic idea of a complementary filter involves taking two or more sensors, filtering out unreliable frequencies for each sensor and combining the filtered outputs to get a better estimate throughout the entire bandwidth of the system.
+To achieve this, the sensors included in the filter should complement one another by performing better over specific parts of the system bandwidth.
+A set of filters is said to be complementary if the sum of their transfer functions is equal to one at all frequencies, (i.e.) its magnitude is one and its phase is zero.
+
+The proper design of this particular kind of filter is of primary importance in a wide range of applications.
+Often, multiple sensors with different noise or dynamical properties are used to measure the same physical quantity.
+In such case, complementary filters can be used to merge the sensors and forms a "super sensor" that has gives a better estimate of the physical quantity over a wider bandwidth.
+This is called sensor blending or sensor fusion.
+
+This is widely used for the attitude estimation of unmanned aerial vehicles using various kind of sensors (accelerometers, gyroscopes, vision sensors, inclinometer) \cite{zimmermann92_high_bandw_orien_measur_contr,corke04_inert_visual_sensin_system_small_auton_helic,min15_compl_filter_desig_angle_estim}.
+
+\cite{shaw90_bandw_enhan_posit_measur_using_measur_accel} Fast position measurement of flexible structure
+
+\cite{matichard15_seism_isolat_advan_ligo} (relative displacement measurement at low frequencies with inertial at high frequencies)
+
+\cite{hua04_polyp_fir_compl_filter_contr_system}
+
+\cite{collette15_sensor_fusion_method_high_perfor}
+The design methods for such filters goes from simple analytical formulas
+
+\cite{corke04_inert_visual_sensin_system_small_auton_helic}
+
+\cite{min15_compl_filter_desig_angle_estim}
+\cite{jensen13_basic_uas}
+
+\cite{shaw90_bandw_enhan_posit_measur_using_measur_accel}
+\cite{zimmermann92_high_bandw_orien_measur_contr}
+\cite{matichard15_seism_isolat_advan_ligo}
+\cite{collette15_sensor_fusion_method_high_perfor}
+
+\cite{hua05_low_ligo}
+\cite{hua04_polyp_fir_compl_filter_contr_system}
+\cite{matichard15_seism_isolat_advan_ligo}
+
+\cite{mahony08_nonlin_compl_filter_special_orthog_group}
+
+\cite{pascoal99_navig_system_desig_using_time}
+
+\cite{jensen13_basic_uas} (feedback system, P, PI, classical control theory for filter design)
+\cite{brown72_integ_navig_system_kalman_filter}
+
+\cite{pascoal99_navig_system_desig_using_time}
+
+\cite{min15_compl_filter_desig_angle_estim}
+Although
+In this paper, we propose
+The body of the paper consists of five parts followed by a conclusion.
+
+\section{H-Infinity synthesis of complementary filters}
+\label{sec:org303afb5}
+  \label{sec:hinf_filters}
+First order complementary filters are easy to synthesize. For instance, one can use the following filters
+\begin{equation}
+H_H(s) = \frac{s/\w_0}{1 + s/\w_0}; \quad H_L(s) = \frac{1}{1 + s/\w_0}
+\end{equation}
+with \(\w_0\) is the tuning parameter corresponding to the crossover frequency of the filters.
+
+However, the manual design of higher order complementary filters is far more complex and we have to use an automatic synthesis technique.
+
+
+As shown in Sec. \ref{sec:trans_perf}, most of the performance requirements can be expressed as upper bounds on the magnitude of the complementary filters.
+
+Thus, the \(\mathcal{H}_\infty\) framework seems adapted and we here propose a technique to synthesis complementary filters while specifying uppers bounds on their magnitudes.
+
+\subsection{\(\hinf\) problem formulation}
+\label{sec:org9dcb2b1}
+   \label{sec:hinf_conf}
+In this section, we formulate the \(\hinf\) problem for the synthesis of complementary filters.
+
+The synthesis objective is to shape an high pass filter \(H_H\) and a low pass filter \(H_L\) while ensuring their complementary property (\(H_H + H_L = 1\)).
+
+To do so, we define two weighting functions \(w_L\) and \(w_H\) that will respectively used to shape \(H_L\) and \(H_H\).
+
+The synthesis problem is then
+\begin{subnumcases}{\text{Find } H_L, H_H \text{ such that}}
+  H_L \text{ and } H_H \text{ are stable} \label{eq:hinf_cond_stability}\\
+  H_L + H_H = 1 \label{eq:hinf_cond_complementarity} \\
+  |w_L H_L| \le 1 \quad \forall\omega \label{eq:hinf_cond_hl} \\
+  |w_H H_H| \le 1 \quad \forall\omega \label{eq:hinf_cond_hh}
+\end{subnumcases}
+
+
+To express this synthesis problem into an \(\hinf\) synthesis problem, we define the following generalized plant \(P\) (also shown on Fig. \ref{fig:sf_hinf_filters_plant_b}):
+\begin{equation}
+\label{eq:generalized_plant}
+  \colvec{w\\u} = P \colvec{z_H \\ z_L \\ v}; \quad P = \begin{bmatrix} w_H & -w_H \\ 0 & w_L \\ 1 & 0 \end{bmatrix}
+\end{equation}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{./figs/sf_hinf_filters_plant_b.pdf}
+\caption{\label{fig:sf_hinf_filters_plant_b}
+Generalized plant for the synthesis of the complementary filters}
+\end{figure}
+
+The \(\hinf\) synthesis objective is then to design a stable filter \(H_L\) (Fig. \ref{fig:sf_hinf_filters_b}) such that the \(\mathcal{H}_\infty\) norm of the transfer function from \(w\) to \([z_H, \ z_L]\) is less than \(1\):
+\begin{equation}
+  \hnorm{\begin{matrix} (1 - H_L) w_H \\ H_L w_L \end{matrix}} \le 1
+\end{equation}
+Which is equivalent to
+\begin{equation}
+\label{eq:hinf_problem}
+  \hnorm{\begin{matrix} H_H w_H \\ H_L w_L \end{matrix}} < 1 \text{ by choosing } H_H = 1 - H_L
+\end{equation}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1]{./figs/sf_hinf_filters_b.pdf}
+\caption{\label{fig:sf_hinf_filters_b}
+\(\hinf\text{-synthesis}\) of complementary filters}
+\end{figure}
+
+Performance conditions \eqref{eq:hinf_cond_hl} and \eqref{eq:hinf_cond_hl} are satisfied by \eqref{eq:hinf_problem}.
+Complementary condition \eqref{eq:hinf_cond_complementarity} is satisfied by design: \(H_H = 1 - H_L\) and thus \(H_L + H_H = 1\).
+The stability condition \eqref{eq:hinf_cond_stability} is guaranteed by the \(H_\infty\) synthesis (\textbf{reference}).
+
+
+Using this synthesis method, we are then able to shape at the same time the high pass and low pass filters while ensuring their complementary.
+
+\subsection{Control requirements as \(\mathcal{H}_\infty\) norm of complementary filters}
+\label{sec:orgb7d25ea}
+As presented in Sec. \ref{sec:trans_perf}, almost all the requirements can be specified with upper bounds on the complementary filters.
+However, robust performance condition \eqref{eq:robust_perf_a} is not.
+
+With the \(\mathcal{H}_\infty\) synthesis the condition \eqref{eq:hinf_problem} only ensure
+\begin{align*}
+  \hnorm{\begin{matrix} H_H w_H \\ H_L w_L \end{matrix}} \le 1 &\Leftrightarrow \max_\omega \sqrt{|w_L H_L|^2 + |w_H H_H|^2} \le 1\\
+                                                             &\Rightarrow |w_L H_L| + |w_H H_H| \le \sqrt{2} \quad \forall\omega
+\end{align*}
+
+And thus we have almost robust stability.
+
+\subsection{Choice of the weighting functions}
+\label{sec:org2d7aa5b}
+   \label{sec:hinf_weighting_func}
+We here give some advice on the choice of the weighting functions used for the synthesis of the complementary filters.
+
+The shape should be such that the performance requirements are met as explain in Sec. \ref{sec:trans_perf}.
+
+However, one should be careful when designing the complementary filters, and should only use stable and minimum phase transfer functions.
+The order of the weights should stay reasonably small as this will increase the complexity of the optimization problem.
+
+One should not forget the fundamental limitations of feedback control such that \(S + T = 1\).
+Similarly, we here have that \(H_L + H_H = 1\) which implies that \(H_L\) and \(H_H\) cannot be made small at the same time.
+
+\subsection{Trade-off between performance and robustness}
+\label{sec:org7af3efe}
+
+\subsection{Analytical formula of complementary filters}
+\label{sec:org477b4a4}
+  \label{sec:analytical_complementary_filters}
+To simplify the synthesis, one can use already synthesized filters
+
+\begin{align}
+  H_L(s) = \frac{1}{1 + \frac{s}{\omega_0}}\\
+  H_H(s) = \frac{\frac{s}{\omega_0}}{1 + \frac{s}{\omega_0}}
+\end{align}
+
+\begin{align}
+  H_L(s) &= \frac{(1+\alpha) (\frac{s}{\omega_0})+1}{\left((\frac{s}{\omega_0})+1\right) \left((\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1\right)}\\
+  H_H(s) &= \frac{(\frac{s}{\omega_0})^2 \left((\frac{s}{\omega_0})+1+\alpha\right)}{\left((\frac{s}{\omega_0})+1\right) \left((\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1\right)}
+\end{align}
+
+\begin{align}
+  H_L(s) &= \frac{\left(1+(\alpha+1)(\beta+1)\right) (\frac{s}{\omega_0})^2 + (1+\alpha+\beta)(\frac{s}{\omega_0}) + 1}{\left(\frac{s}{\omega_0} + 1\right) \left( (\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1 \right) \left( (\frac{s}{\omega_0})^2 + \beta (\frac{s}{\omega_0}) + 1 \right)}\\
+  H_H(s) &= \frac{(\frac{s}{\omega_0})^3 \left( (\frac{s}{\omega_0})^2 + (1+\alpha+\beta) (\frac{s}{\omega_0}) + (1+(\alpha+1)(\beta+1)) \right)}{\left(\frac{s}{\omega_0} + 1\right) \left( (\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1 \right) \left( (\frac{s}{\omega_0})^2 + \beta (\frac{s}{\omega_0}) + 1 \right)}
+\end{align}
+
+\section{Discussion}
+\label{sec:org4fb9d01}
+\section{Conclusion}
+\label{sec:orgecd9d50}
+\label{sec:conclusion}
+
+\section{Acknowledgment}
+\label{sec:org5cf5157}
+
+\bibliography{ref}
+\end{document}

paper/ref.bib

@@ -0,0 +1,171 @@
+@article{collette15_sensor_fusion_method_high_perfor,
+  author = {C. Collette and F. Matichard},
+  title = {Sensor Fusion Methods for High Performance Active Vibration Isolation Systems},
+  journal = {Journal of Sound and Vibration},
+  volume = {342},
+  number = {nil},
+  pages = {1-21},
+  year = {2015},
+  doi = {10.1016/j.jsv.2015.01.006},
+  url = {https://doi.org/10.1016/j.jsv.2015.01.006},
+  keywords = {},
+}
+
+
+@phdthesis{hua05_low_ligo,
+  author =       {Hua, Wensheng},
+  school =       {stanford university},
+  title =        {Low frequency vibration isolation and alignment system for
+                  advanced LIGO},
+  year =         2005,
+}
+
+
+@inproceedings{hua04_polyp_fir_compl_filter_contr_system,
+  author = {Wensheng Hua and Dan B. Debra and Corwin T. Hardham and Brian T. Lantz and Joseph A. Giaime},
+  title = {Polyphase FIR Complementary Filters for Control Systems},
+  booktitle = {Proceedings of ASPE Spring Topical Meeting on Control of Precision Systems},
+  year = {2004},
+  pages = {109--114},
+}
+
+
+@article{matichard15_seism_isolat_advan_ligo,
+  author = {Matichard, F and Lantz, B and Mittleman, R and Mason, K and Kissel, J and Abbott, B and Biscans, S and McIver, J and Abbott, R and Abbott, S and others},
+  title = {Seismic Isolation of Advanced Ligo: Review of Strategy, Instrumentation and Performance},
+  journal = {Classical and Quantum Gravity},
+  volume = {32},
+  number = {18},
+  pages = {185003},
+  year = {2015},
+  publisher = {IOP Publishing},
+}
+
+
+@article{min15_compl_filter_desig_angle_estim,
+  author = {Min, Hyung Gi and Jeung, Eun Tae},
+  title = {Complementary Filter Design for Angle Estimation Using Mems Accelerometer and Gyroscope},
+  journal = {Department of Control and Instrumentation, Changwon National University, Changwon, Korea},
+  pages = {641--773},
+  year = {2015},
+}
+
+
+@article{corke04_inert_visual_sensin_system_small_auton_helic,
+  author = {Peter Corke},
+  title = {An Inertial and Visual Sensing System for a Small Autonomous Helicopter},
+  journal = {Journal of Robotic Systems},
+  volume = {21},
+  number = {2},
+  pages = {43-51},
+  year = {2004},
+  doi = {10.1002/rob.10127},
+  url = {https://doi.org/10.1002/rob.10127},
+}
+
+
+@inproceedings{jensen13_basic_uas,
+  author =       {Austin Jensen and Cal Coopmans and YangQuan Chen},
+  title =        {Basics and guidelines of complementary filters for small UAS
+                  navigation},
+  booktitle =    {2013 International Conference on Unmanned Aircraft Systems
+                  (ICUAS)},
+  year =         2013,
+  pages =        {nil},
+  doi =          {10.1109/icuas.2013.6564726},
+  url =          {https://doi.org/10.1109/icuas.2013.6564726},
+  month =        5,
+}
+
+
+@inproceedings{pascoal99_navig_system_desig_using_time,
+  author = {A. Pascoal and I. Kaminer and P. Oliveira},
+  title = {Navigation System Design Using Time-Varying Complementary Filters},
+  booktitle = {Guidance, Navigation, and Control Conference and Exhibit},
+  year = {1999},
+  pages = {nil},
+  doi = {10.2514/6.1999-4290},
+  url = {https://doi.org/10.2514/6.1999-4290},
+}
+
+
+@article{zimmermann92_high_bandw_orien_measur_contr,
+  author = {M. Zimmermann and W. Sulzer},
+  title = {High Bandwidth Orientation Measurement and Control Based on Complementary Filtering},
+  journal = {Robot Control 1991},
+  pages = {525-530},
+  year = {1992},
+  doi = {10.1016/b978-0-08-041276-4.50093-5},
+  url = {https://doi.org/10.1016/b978-0-08-041276-4.50093-5},
+  publisher = {Elsevier},
+  series = {Robot Control 1991},
+}
+
+
+@inproceedings{baerveldt97_low_cost_low_weigh_attit,
+  author = {A.-J. Baerveldt and R. Klang},
+  title = {A Low-Cost and Low-Weight Attitude Estimation System for an Autonomous Helicopter},
+  booktitle = {Proceedings of IEEE International Conference on Intelligent Engineering Systems},
+  year = {1997},
+  pages = {nil},
+  doi = {10.1109/ines.1997.632450},
+  url = {https://doi.org/10.1109/ines.1997.632450},
+  month = {-},
+}
+
+
+@article{shaw90_bandw_enhan_posit_measur_using_measur_accel,
+  author =       {F.R. Shaw and K. Srinivasan},
+  title =        {Bandwidth Enhancement of Position Measurements Using Measured
+                  Acceleration},
+  journal =      {Mechanical Systems and Signal Processing},
+  volume =       4,
+  number =       1,
+  pages =        {23-38},
+  year =         1990,
+  doi =          {10.1016/0888-3270(90)90038-m},
+  url =          {https://doi.org/10.1016/0888-3270(90)90038-m},
+}
+
+
+@article{brown72_integ_navig_system_kalman_filter,
+  author =       {R. G. Brown},
+  title =        {Integrated Navigation Systems and Kalman Filtering: a
+                  Perspective},
+  journal =      {Navigation},
+  volume =       19,
+  number =       4,
+  pages =        {355-362},
+  year =         1972,
+  doi =          {10.1002/j.2161-4296.1972.tb01706.x},
+  url =          {https://doi.org/10.1002/j.2161-4296.1972.tb01706.x},
+}
+
+
+@article{matichard15_seism_isolat_advan_ligo,
+  author =       {Matichard, F and Lantz, B and Mittleman, R and Mason, K and
+                  Kissel, J and Abbott, B and Biscans, S and McIver, J and
+                  Abbott, R and Abbott, S and others},
+  title =        {Seismic Isolation of Advanced Ligo: Review of Strategy,
+                  Instrumentation and Performance},
+  journal =      {Classical and Quantum Gravity},
+  volume =       32,
+  number =       18,
+  pages =        185003,
+  year =         2015,
+  publisher =    {IOP Publishing},
+}
+
+
+@article{mahony08_nonlin_compl_filter_special_orthog_group,
+  author =       {Robert Mahony and Tarek Hamel and Jean-Michel Pflimlin},
+  title =        {Nonlinear Complementary Filters on the Special Orthogonal
+                  Group},
+  journal =      {IEEE Transactions on Automatic Control},
+  volume =       53,
+  number =       5,
+  pages =        {1203-1218},
+  year =         2008,
+  doi =          {10.1109/tac.2008.923738},
+  url =          {https://doi.org/10.1109/tac.2008.923738},
+}

tikz/config.org

@@ -0,0 +1,690 @@
+#+TITLE: LaTeX Configuration for Tikz Figures
+:DRAWER:
+#+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>
+
+#+PROPERTY: header-args:latex+ :tangle config.tex
+#+PROPERTY: header-args:latex+ :exports code
+:END:
+
+* Packages
+#+begin_src latex
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+
+\usepackage[french, english]{babel} % Last language is main language
+
+\usepackage{lmodern} % Latin Modern Font
+\usepackage{gensymb} % Generic symbols for both text and math mode
+
+\usepackage{standalone} % Used to generate standalone Tikz
+
+\usepackage{amsmath}   % Main math Package
+\usepackage{mathtools} % Extension package to amsmath
+\usepackage{amsthm}    % Typesetting theorems (AMS style)
+\usepackage{amsfonts}  % More fonts from the AMS
+\usepackage{textcomp}  % provide many text symbols
+\usepackage{steinmetz} % For phase symbol
+
+\usepackage{xstring}  % Utils to manipulate strings
+\usepackage{etoolbox} % Add basic if/then
+\usepackage{esvect}   % Beautyfull vectors
+\usepackage{graphicx} % Enhanced support for graphics
+\usepackage{grffile}  % Used by matlab2tikz
+
+\usepackage{microtype} % typographic tuning
+\usepackage{setspace}  % for line spacing, e.g. \onehalfspacing
+\usepackage{tabularx}  % table features
+\usepackage{enumitem}  % for simple list modifications
+\usepackage{booktabs}  % better table support
+
+\usepackage{stackengine} %
+
+\usepackage[load-configurations=abbreviations]{siunitx} % SI units
+\sisetup{
+    locale = US,
+    detect-all,
+    range-phrase=--,
+    range-units=single
+}
+#+end_src
+
+* Tikz related packages
+#+begin_src latex
+  \usepackage{tikz}       % Tikz
+  \usepackage{tikzscale}  % Used to scale Tikz graphics
+  \usepackage{adjustbox}  % Used to proper positioning of tikz pictures
+  \usepackage{circuitikz} % Draw electronic circuits
+  \usepackage{pgfpages}   % Needed to use notes
+  \usepackage{pgfplots}   % Used to plot functions
+#+end_src
+
+* Tikz Libraries
+#+begin_src latex
+  \usetikzlibrary{arrows}                   % Arrow tip library
+  \usetikzlibrary{arrows.meta}              % Add some arrows
+  \usetikzlibrary{calc}                     % The library allows advanced Coordinate Calculations
+  \usetikzlibrary{intersections}            % calculate intersections of paths
+  \usetikzlibrary{matrix}                   %
+  \usetikzlibrary{patterns}                 %
+  \usetikzlibrary{shapes}                   % Defines circle and rectangle
+  \usetikzlibrary{shapes.geometric}         % Use for the shape diamond and isosceles triangle
+  \usetikzlibrary{snakes}                   % snake=coil and snake=zigzag using segment amplitude=10pt
+  \usetikzlibrary{positioning}              % Additional options for placing nodes
+  \usetikzlibrary{3d}                       % Plot 3D shapes
+  \usetikzlibrary{spy}                      % Creating a magnified area
+  \usetikzlibrary{decorations.text}         % Used to make text follows a curve
+  \usetikzlibrary{decorations.pathmorphing} % deformation of a path
+  \usetikzlibrary{decorations.markings}     % Used for spring and damper
+  \usetikzlibrary{babel}                    % A tiny library that make the interaction with the babel package easier
+  \usetikzlibrary{plotmarks}                % This library defines a number of plot marks
+  \usetikzlibrary{fit}                      % Used to make rectangle as nodes by specifying two points
+  \usetikzlibrary{backgrounds}              % Used to put things under others
+#+end_src
+
+* PGF Plot libraries and config
+#+begin_src latex
+  \usepgfplotslibrary{patchplots}
+  \usepgfplotslibrary{groupplots}
+
+  \pgfplotsset{compat=newest}
+  \pgfplotsset{plot coordinates/math parser=false}
+#+end_src
+
+* Setup size of figures
+#+begin_src latex
+  \newlength{\fheight}
+  \newlength{\fwidth}
+
+  \setlength{\fwidth}{85mm}
+  \setlength{\fheight}{112mm}
+#+end_src
+
+* Setup Arrows style
+#+begin_src latex
+  \tikzset{>=Stealth}
+  % Setup default Linewidth
+  \tikzset{every path/.style={line width=1pt}}
+#+end_src
+
+* Colors
+#+begin_src latex
+  \usepackage{xcolor}% Color extension
+
+  \definecolor{colorblack}{rgb}{0, 0, 0}
+  \definecolor{colorblue}{rgb}{0, 0.4470, 0.7410}
+  \definecolor{colorred}{rgb}{0.8500, 0.3250, 0.0980}
+  \definecolor{coloryellow}{rgb}{0.9290, 0.6940, 0.1250}
+  \definecolor{colorpurple}{rgb}{0.4940, 0.1840, 0.5560}
+  \definecolor{colorgreen}{rgb}{0.4660, 0.6740, 0.1880}
+  \definecolor{colorcyan}{rgb}{0.3010, 0.7450, 0.9330}
+  \definecolor{colorbordeau}{rgb}{0.6350, 0.0780, 0.1840}
+
+  % Main color
+  \definecolor{maincolor}{RGB}{89, 9, 38}
+  \definecolor{secondcolor}{RGB}{20, 9, 89}
+#+end_src
+
+* Control
+** Blocks
+#+begin_src latex
+  \tikzset{%
+    block/.style n args={2}{%
+      draw,
+      fill=white,
+      minimum width  = #1,
+      minimum height = #2,
+    },
+    block/.default={1.2cm}{1.0cm}
+  }
+#+end_src
+
+** TODO Branches
+#+begin_src latex
+  \tikzstyle{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
+  \tikzstyle{->top}=[-{Stealth[color=black, scale=0.8]}, draw=white, double=black, double distance=1pt, line width=1pt]
+  \tikzstyle{<-top}=[{stealth[color=black, scale=0.8]}-, draw=white, double=black, double distance=1pt, line width=1pt]
+#+end_src
+
+** TODO Hand Writen Style
+Usefull for schematic plots
+#+begin_src latex
+  \tikzstyle{handwriten}=[decorate,decoration={random steps,amplitude=0.1pt,segment length=0.8pt}]
+#+end_src
+
+** DAC
+#+begin_src latex
+  \tikzset{%
+    DAC/.style={%
+      draw,
+      signal,
+    }
+  }
+#+end_src
+
+** ADC
+#+begin_src latex
+  \tikzset{%
+    ADC/.style={%
+      draw,
+      signal,
+      signal to = west,
+    }
+  }
+#+end_src
+
+** TODO Gain
+Maybe use =isosceles= instead of regular polygon?
+#+begin_src latex
+  \tikzset{%
+    gain right/.style={%
+      draw,
+      regular polygon,
+      regular polygon sides = 3,
+      inner sep = 2pt,
+      shape border rotate=-90
+    },
+    gain left/.style={%
+      draw,
+      regular polygon,
+      regular polygon sides = 3,
+      inner sep = 2pt,
+      shape border rotate=90
+    },
+    gain top/.style={%
+      draw,
+      regular polygon,
+      regular polygon sides = 3,
+      inner sep = 2pt,
+      shape border rotate=0
+    },
+    gain bottom/.style={%
+      draw,
+      regular polygon,
+      regular polygon sides = 3,
+      inner sep = 2pt,
+      shape border rotate=180
+    },
+  }
+#+end_src
+
+** Add / Substract / Divide / Multiply block
+#+begin_src latex
+  \tikzset{% Add block with Circled operations
+    addc/.style n args={5}{%
+      draw,
+      fill=white,
+      circle,
+      outer sep = 0pt,
+      inner sep = 0pt,
+      minimum size = 2em,
+      execute at begin node={\LARGE $#1$},
+      append after command={\pgfextra{\let\mainnode=\tikzlastnode}
+        \ifx#2\empty\else
+        node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
+        \fi
+        \ifx#3\empty\else
+        node[draw, circle, outer sep=6pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
+        \fi
+        \ifx#4\empty\else
+        node[draw, circle, outer sep=6pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
+        \fi
+        \ifx#5\empty\else
+        node[draw, circle, outer sep=6pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
+        \fi
+        }
+    },
+    addc/.default={+}{}{}{}{},
+  }
+#+end_src
+
+#+begin_src latex
+  \tikzset{% Add Block
+    addb/.style n args={5}{%
+      draw,
+      fill=white,
+      circle,
+      outer sep = 0pt,
+      inner sep = 0pt,
+      minimum size = 2em,
+      execute at begin node={\LARGE $#1$},
+      append after command={\pgfextra{\let\mainnode=\tikzlastnode}
+        \ifx#2\empty\else
+        node[outer sep=2pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
+        \fi
+        \ifx#3\empty\else
+        node[outer sep=2pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
+        \fi
+        \ifx#4\empty\else
+        node[outer sep=2pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
+        \fi
+        \ifx#5\empty\else
+        node[outer sep=2pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
+        \fi
+        }
+    },
+    addb/.default={+}{}{}{}{},
+  }
+#+end_src
+
+* Plots
+** Grid
+#+begin_src latex
+  \pgfplotsset{grid style={black}}
+  \pgfplotsset{major grid style={black!30!white}}
+  \pgfplotsset{minor grid style={black!10!white}}
+  \pgfplotsset{xmajorgrids}
+  \pgfplotsset{ymajorgrids}
+#+end_src
+
+** Lines
+#+begin_src latex
+  \pgfplotsset{separate axis lines=false} % draw axis as rectangle and not as 4 lines
+  \pgfplotsset{every outer x axis line/.append style={black}}
+  \pgfplotsset{every outer y axis line/.append style={black}}
+  \pgfplotsset{axis background/.style={fill=white}}
+  \pgfplotsset{axis x line*=bottom} % solid line on the bottom with thin on the top
+  \pgfplotsset{axis y line*=left} % solid line on the left with thin on the right
+#+end_src
+
+** Ticks
+#+begin_src latex
+  \pgfplotsset{every y tick label/.append style={font=\color{black}}}
+  \pgfplotsset{every y tick/.append style={black}}
+  \pgfplotsset{every x tick label/.append style={font=\color{black}}}
+  \pgfplotsset{every x tick/.append style={black}}
+#+end_src
+
+** Size
+If =scale only axis=false= (the default), pgfplots will try to produce the desired width including labels, titles and ticks.
+#+begin_src latex
+  \pgfplotsset{scale only axis=true}
+#+end_src
+
+** Label
+Used to align all of ylabel of one figure.
+#+begin_src latex
+  \pgfplotsset{ylabel absolute}
+#+end_src
+
+** Legend
+#+begin_src latex
+  % https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834
+
+  % argument #1: any options
+  \newenvironment{customlegend}[1][]{%
+    \begingroup
+    % inits/clears the lists (which might be populated from previous
+    % axes):
+    \csname pgfplots@init@cleared@structures\endcsname
+    \pgfplotsset{#1}%
+  }{%
+    % draws the legend:
+    \csname pgfplots@createlegend\endcsname
+    \endgroup
+  }%
+
+  % makes \addlegendimage available (typically only available within an
+  % axis environment):
+  \def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}
+
+  % definition to insert numbers
+  % \pgfkeys{/pgfplots/number in legend/.style={%
+  %     /pgfplots/legend image code/.code={%
+  %       \node at (0.125,-0.0225){#1}; % <= changed x value
+  %     },%
+  %   },
+  % }
+  \pgfplotsset{
+    every legend to name picture/.style={west}
+  }
+#+end_src
+
+** Upper and Lower bounds
+#+begin_src latex
+  \tikzstyle{upperbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=60}}]
+  \tikzstyle{lowerbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=-60}}]
+#+end_src
+
+And we add the corresdonding
+#+begin_src latex
+  \pgfplotsset{
+    /pgfplots/upperbound/.style 1 args={
+      legend image code/.code={
+        \draw[##1, upperbound]
+          plot coordinates {
+          (0cm,0cm)
+          (0.6cm,0cm)
+        }
+      }
+    }
+  }
+#+end_src
+
+** Pole
+#+begin_src latex
+  \tikzset{%
+    pole/.style{%
+      color=red,
+      cross out,
+      draw,
+      inner sep=0pt,
+      outer sep=0pt,
+      minimum size=#1pt
+    },
+    pole/.default={4}
+  }
+#+end_src
+
+** Zero
+#+begin_src latex
+  \tikzset{%
+    zero/.style{%
+      color=red,
+      circle,
+      draw,
+      inner sep=0pt,
+      outer sep=0pt,
+      minimum size=#1pt
+    },
+    zero/.default={4}
+  }
+#+end_src
+
+* Mechanical
+** Spring
+#+begin_src latex
+  \tikzset{%
+    spring/.style={%
+      thick,
+      decoration={
+        zigzag,
+        pre length  = #1cm,
+        post length = #1cm,
+        segment length = 6
+      },
+      decorate
+    },
+    spring/.default={0.2}
+  }
+#+end_src
+
+** Coil
+#+begin_src latex
+  \tikzset{%
+    coil/.style n args={2}{%
+      thick,
+      decoration={
+        coil,
+        pre length  = #1cm,
+        post length = #2cm,
+        segment length = 4
+      },
+      decorate
+    },
+    coil/.default={0.3}{0.3}
+  }
+#+end_src
+
+** Damper
+#+begin_src latex
+  \tikzset{%
+    damper/.style n args={2}{%
+      thick,
+      decoration={markings, mark connection node=dmp, mark=at position 0.5 with {
+          \node (dmp) [thick,
+                       inner sep = 0pt,
+                       transform shape,
+                       rotate  =-90,
+                       minimum width  = #1pt,
+                       minimum height = #2pt,
+                       draw=none] {};
+          \draw [thick] ($(dmp.north east)+(0.6*#2pt,0)$) -- (dmp.south east) -- (dmp.south west) -- ($(dmp.north west)+(0.6*#2pt,0)$);
+          \draw [thick] ($(dmp.north)+(0,-0.3*#1pt)$) -- ($(dmp.north)+(0,0.3*#1pt)$);
+        }
+      },
+      decorate
+    },
+    damper/.default={12}{3}
+  }
+#+end_src
+
+** Actuator
+#+begin_src latex
+  \tikzset{%
+    actuator/.style n args={2}{%
+      thick,
+      draw=none,
+      decoration={
+        markings,
+        mark connection node=my node,
+        mark=at position .5 with {
+          \node [draw, inner sep=0pt, minimum width=#1cm, minimum height=#2cm,
+          transform shape, fill=white] (my node) {};
+        },
+        mark=at position .0 with {
+          \draw[<-] (0, 0) -- (my node);
+        },
+        mark=at position 1.0 with {
+          \draw[<-] (0, 0) -- (my node);
+        }
+      },
+      decorate
+    },
+    actuator/.default={0.5}{0.2}
+  }
+#+end_src
+
+** Ground
+#+begin_src latex
+  \tikzset{%
+    ground/.style n args={2}{%
+      fill,
+      pattern = north east lines,
+      draw = none,
+      anchor = north,
+      minimum width  = #1cm,
+      minimum height = #2cm,
+      append after command={
+        (\tikzlastnode.north west) edge (\tikzlastnode.north east)
+      }
+    },
+    ground/.default={2.5}{0.3}
+  }
+#+end_src
+
+** Force Sensor
+#+begin_src latex
+  \tikzset{%
+    forcesensor/.style n args={2}{%
+      rectangle,
+      outer sep=0pt,
+      inner sep=0pt,
+      draw=black,
+      fill=white!60!black,
+      anchor=south,
+      minimum width =#1cm,
+      minimum height=#2cm,
+      append after command={
+        [every edge/.append style={
+          thick,
+          black,
+        }]
+        (\tikzlastnode.north west) edge (\tikzlastnode.south east)
+        (\tikzlastnode.north east) edge (\tikzlastnode.south west)
+      }
+    },
+    forcesensor/.default={2.0}{0.5}
+  }
+#+end_src
+
+** Inertial Sensor
+#+begin_src latex
+  \tikzset{%
+    inertialsensor/.style={%
+      rectangle,
+      outer sep=0pt,
+      inner sep=0pt,
+      draw=black,
+      fill=white!60!black,
+      anchor=south east,
+      minimum size=#1cm,
+      append after command={
+        [every edge/.append style={
+          thick,
+          black,
+        }]
+        (\tikzlastnode.north west) edge (\tikzlastnode.south east)
+        (\tikzlastnode.north east) edge (\tikzlastnode.south west)
+      }
+    },
+    inertialsensor/.default={0.3}
+  }
+#+end_src
+
+** Axis Rotator
+#+begin_src latex
+  \newcommand{\AxisRotator}[1][rotate=0]{%
+    \tikz [x=0.1cm,y=0.30cm,-stealth,#1] \draw (0,0) arc (-150:150:1 and 1);%
+  }
+#+end_src
+
+** Cross
+#+begin_src latex
+  \tikzstyle{cross}=[path picture={
+    \draw[black]
+    (path picture bounding box.south east) -- (path picture bounding box.north west) (path picture bounding box.south west) -- (path picture bounding box.north east);
+  }]
+
+#+end_src
+
+** Piezoelectric actuator
+#+begin_src latex
+  \tikzset{%
+    piezo/.style n args={3}{%
+      draw,
+      rectangle,
+      minimum width  = #1cm,
+      minimum height = #2cm,
+      fill=blue!10!white,
+      anchor=center,
+      append after command={
+        [every edge/.append style={
+          thick,
+          black,
+        }]
+        \foreach \i in {1,...,#3}{
+          (${\i/(1+#3)}*(\tikzlastnode.north west)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south west)+0.1*(#1,0)$) edge (${\i/(1+#3)}*(\tikzlastnode.north east)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south east)-0.1*(#1,0)$)
+        }
+      }
+    },
+    piezo/.default={2}{4}{10}
+  }
+#+end_src
+
+** Voice coil
+#+begin_src latex
+  \def\voicecoil#1#2#3{
+    % ======================
+    % Parameters
+    % ======================
+    \def\voicecoilw{#1} % Total Width
+    \def\voicecoilh{#2} % Total Height
+
+    \def\magnetw{\voicecoilw} % Width of the magnet
+    \def\magneth{\voicecoilh/1.4} % Height of the magnet
+
+    \def\magnetwb{0.15*\magnetw} % Width of the borders of the magnet
+    \def\magnetmw{0.15*\magnetw} % Width of the middle part of the magnet
+    \def\magnetwg{0.5*\magnetw} % Width of the gap of the magnet
+
+    \def\magnethl{\magnetwb} % Height of the low part of the magnet
+    \def\magnetmh{0.15*\magneth} % Height of the middle part of the magnet
+    \def\magnethg{0.2*\magneth} % Height of the gap of the magnet
+    % ======================
+
+    \begin{scope}[shift={(0.5*\voicecoilw, 0.5*\voicecoilh)}, rotate=#3, shift={(0, -0.5*\voicecoilh)}]
+      % ======================
+      % Magnet
+      % ======================
+      \draw[fill=white] (0, 0) -| ++(0.5*\magnetw, \magneth) -| ++(-0.5*\magnetw+0.5*\magnetwg, -\magnethg) -| (0.5*\magnetw-\magnetwb, \magnethl) -| (-0.5*\magnetw+\magnetwb, \magneth-\magnethg) -| (-0.5*\magnetwg, \magneth) -| (-0.5*\magnetw, 0) -- (cycle);
+      \begin{scope}[shift={(0, \magnethl)}]
+        \draw[fill=red]  (-0.5*\magnetmw, 0) rectangle (0.5*\magnetmw, \magnetmh);
+        \draw[fill=blue] (-0.5*\magnetmw, \magnetmh) rectangle (0.5*\magnetmw, 2*\magnetmh);
+        % Top conductive Magnet
+        \draw[fill=white] (-0.5*\magnetmw, 2*\magnetmh) -| (0.5*\magnetmw, -\magnethl+\magneth-\magnethg) -| ++(0.1, \magnethg) -| ++(-0.2-\magnetmw, -\magnethg) -| (-0.5*\magnetmw, \magnetmh);
+      \end{scope}
+      % ======================
+
+      % ======================
+      % Coil
+      % ======================
+      \pgfmathsetmacro{\coilwidth}{0.5*0.5*\magnetmw+0.5*0.1+0.25*\magnetwg}%
+      \draw[] ( \coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
+      \draw[] (-\coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
+      % Point on the coil
+      \foreach \x in {0,1,...,9}
+      {
+        \node[circle,inner sep=0.6pt,fill] at ( \coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
+        \node[circle,inner sep=0.6pt,fill] at (-\coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
+      }
+      \draw[fill=white] (-0.5*\magnetw, 1.2*\magneth) rectangle ++(\magnetw, \magnethg);
+      % ======================
+
+      % ======================
+      % Coordinates
+      % ======================
+      % Force
+      \coordinate[] (vc_force) at (0, \magneth-0.5*\magnethg);
+      % Coil
+      \coordinate[] (vc_coil) at (0, \voicecoilh);
+      % Magnet
+      \coordinate[] (vc_magnet) at (0, 0);
+      % Coil Wires
+      \coordinate[] (vc_wire_one) at ( \coilwidth, 1.2*\magneth);
+      \coordinate[] (vc_wire_two) at (-\coilwidth, 1.2*\magneth);
+      % ======================
+    \end{scope}
+  }
+#+end_src
+
+* Optics
+#+begin_src latex
+  \tikzset{%
+    ->-/.style={
+      decoration={
+        markings,
+        mark = at position #1 with {\arrow{>}
+        }
+      },
+      postaction={decorate}
+    }
+  }
+  \tikzset{%
+    -<-/.style={
+      decoration={
+        markings,
+        mark = at position #1 with {\arrow{<}
+        }
+      },
+      postaction={decorate}
+    }
+  }
+#+end_src
+
+* Misc
+#+begin_src latex
+  \tikzset{%
+    labelc/.style= {%
+      draw,
+      fill=white,
+      shape=circle,
+      inner sep=2pt,
+      outer sep=6pt,
+    }
+  }
+#+end_src

tikz/config.tex

@@ -0,0 +1,556 @@
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+
+\usepackage[french, english]{babel} % Last language is main language
+
+\usepackage{lmodern} % Latin Modern Font
+\usepackage{gensymb} % Generic symbols for both text and math mode
+
+\usepackage{standalone} % Used to generate standalone Tikz
+
+\usepackage{amsmath}   % Main math Package
+\usepackage{mathtools} % Extension package to amsmath
+\usepackage{amsthm}    % Typesetting theorems (AMS style)
+\usepackage{amsfonts}  % More fonts from the AMS
+\usepackage{textcomp}  % provide many text symbols
+\usepackage{steinmetz} % For phase symbol
+
+\usepackage{xstring}  % Utils to manipulate strings
+\usepackage{etoolbox} % Add basic if/then
+\usepackage{esvect}   % Beautyfull vectors
+\usepackage{graphicx} % Enhanced support for graphics
+\usepackage{grffile}  % Used by matlab2tikz
+
+\usepackage{microtype} % typographic tuning
+\usepackage{setspace}  % for line spacing, e.g. \onehalfspacing
+\usepackage{tabularx}  % table features
+\usepackage{enumitem}  % for simple list modifications
+\usepackage{booktabs}  % better table support
+
+\usepackage{stackengine} %
+
+\usepackage[load-configurations=abbreviations]{siunitx} % SI units
+\sisetup{
+    locale = US,
+    detect-all,
+    range-phrase=--,
+    range-units=single
+}
+
+\usepackage{tikz}       % Tikz
+\usepackage{tikzscale}  % Used to scale Tikz graphics
+\usepackage{adjustbox}  % Used to proper positioning of tikz pictures
+\usepackage{circuitikz} % Draw electronic circuits
+\usepackage{pgfpages}   % Needed to use notes
+\usepackage{pgfplots}   % Used to plot functions
+
+\usetikzlibrary{arrows}                   % Arrow tip library
+\usetikzlibrary{arrows.meta}              % Add some arrows
+\usetikzlibrary{calc}                     % The library allows advanced Coordinate Calculations
+\usetikzlibrary{intersections}            % calculate intersections of paths
+\usetikzlibrary{matrix}                   %
+\usetikzlibrary{patterns}                 %
+\usetikzlibrary{shapes}                   % Defines circle and rectangle
+\usetikzlibrary{shapes.geometric}         % Use for the shape diamond and isosceles triangle
+\usetikzlibrary{snakes}                   % snake=coil and snake=zigzag using segment amplitude=10pt
+\usetikzlibrary{positioning}              % Additional options for placing nodes
+\usetikzlibrary{3d}                       % Plot 3D shapes
+\usetikzlibrary{spy}                      % Creating a magnified area
+\usetikzlibrary{decorations.text}         % Used to make text follows a curve
+\usetikzlibrary{decorations.pathmorphing} % deformation of a path
+\usetikzlibrary{decorations.markings}     % Used for spring and damper
+\usetikzlibrary{babel}                    % A tiny library that make the interaction with the babel package easier
+\usetikzlibrary{plotmarks}                % This library defines a number of plot marks
+\usetikzlibrary{fit}                      % Used to make rectangle as nodes by specifying two points
+\usetikzlibrary{backgrounds}              % Used to put things under others
+
+\usepgfplotslibrary{patchplots}
+\usepgfplotslibrary{groupplots}
+
+\pgfplotsset{compat=newest}
+\pgfplotsset{plot coordinates/math parser=false}
+
+\newlength{\fheight}
+\newlength{\fwidth}
+
+\setlength{\fwidth}{85mm}
+\setlength{\fheight}{112mm}
+
+\tikzset{>=Stealth}
+% Setup default Linewidth
+\tikzset{every path/.style={line width=1pt}}
+
+\usepackage{xcolor}% Color extension
+
+\definecolor{colorblack}{rgb}{0, 0, 0}
+\definecolor{colorblue}{rgb}{0, 0.4470, 0.7410}
+\definecolor{colorred}{rgb}{0.8500, 0.3250, 0.0980}
+\definecolor{coloryellow}{rgb}{0.9290, 0.6940, 0.1250}
+\definecolor{colorpurple}{rgb}{0.4940, 0.1840, 0.5560}
+\definecolor{colorgreen}{rgb}{0.4660, 0.6740, 0.1880}
+\definecolor{colorcyan}{rgb}{0.3010, 0.7450, 0.9330}
+\definecolor{colorbordeau}{rgb}{0.6350, 0.0780, 0.1840}
+
+% Main color
+\definecolor{maincolor}{RGB}{89, 9, 38}
+\definecolor{secondcolor}{RGB}{20, 9, 89}
+
+\tikzset{%
+  block/.style n args={2}{%
+    draw,
+    fill=white,
+    minimum width  = #1,
+    minimum height = #2,
+  },
+  block/.default={1.2cm}{1.0cm}
+}
+
+\tikzstyle{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
+\tikzstyle{->top}=[-{Stealth[color=black, scale=0.8]}, draw=white, double=black, double distance=1pt, line width=1pt]
+\tikzstyle{<-top}=[{stealth[color=black, scale=0.8]}-, draw=white, double=black, double distance=1pt, line width=1pt]
+
+\tikzstyle{handwriten}=[decorate,decoration={random steps,amplitude=0.1pt,segment length=0.8pt}]
+
+\tikzset{%
+  DAC/.style={%
+    draw,
+    signal,
+  }
+}
+
+\tikzset{%
+  ADC/.style={%
+    draw,
+    signal,
+    signal to = west,
+  }
+}
+
+\tikzset{%
+  gain right/.style={%
+    draw,
+    regular polygon,
+    regular polygon sides = 3,
+    inner sep = 2pt,
+    shape border rotate=-90
+  },
+  gain left/.style={%
+    draw,
+    regular polygon,
+    regular polygon sides = 3,
+    inner sep = 2pt,
+    shape border rotate=90
+  },
+  gain top/.style={%
+    draw,
+    regular polygon,
+    regular polygon sides = 3,
+    inner sep = 2pt,
+    shape border rotate=0
+  },
+  gain bottom/.style={%
+    draw,
+    regular polygon,
+    regular polygon sides = 3,
+    inner sep = 2pt,
+    shape border rotate=180
+  },
+}
+
+\tikzset{% Add block with Circled operations
+  addc/.style n args={5}{%
+    draw,
+    fill=white,
+    circle,
+    outer sep = 0pt,
+    inner sep = 0pt,
+    minimum size = 2em,
+    execute at begin node={\LARGE $#1$},
+    append after command={\pgfextra{\let\mainnode=\tikzlastnode}
+      \ifx#2\empty\else
+      node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
+      \fi
+      \ifx#3\empty\else
+      node[draw, circle, outer sep=6pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
+      \fi
+      \ifx#4\empty\else
+      node[draw, circle, outer sep=6pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
+      \fi
+      \ifx#5\empty\else
+      node[draw, circle, outer sep=6pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
+      \fi
+      }
+  },
+  addc/.default={+}{}{}{}{},
+}
+
+\tikzset{% Add Block
+  addb/.style n args={5}{%
+    draw,
+    fill=white,
+    circle,
+    outer sep = 0pt,
+    inner sep = 0pt,
+    minimum size = 2em,
+    execute at begin node={\LARGE $#1$},
+    append after command={\pgfextra{\let\mainnode=\tikzlastnode}
+      \ifx#2\empty\else
+      node[outer sep=2pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
+      \fi
+      \ifx#3\empty\else
+      node[outer sep=2pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
+      \fi
+      \ifx#4\empty\else
+      node[outer sep=2pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
+      \fi
+      \ifx#5\empty\else
+      node[outer sep=2pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
+      \fi
+      }
+  },
+  addb/.default={+}{}{}{}{},
+}
+
+\pgfplotsset{grid style={black}}
+\pgfplotsset{major grid style={black!30!white}}
+\pgfplotsset{minor grid style={black!10!white}}
+\pgfplotsset{xmajorgrids}
+\pgfplotsset{ymajorgrids}
+
+\pgfplotsset{separate axis lines=false} % draw axis as rectangle and not as 4 lines
+\pgfplotsset{every outer x axis line/.append style={black}}
+\pgfplotsset{every outer y axis line/.append style={black}}
+\pgfplotsset{axis background/.style={fill=white}}
+\pgfplotsset{axis x line*=bottom} % solid line on the bottom with thin on the top
+\pgfplotsset{axis y line*=left} % solid line on the left with thin on the right
+
+\pgfplotsset{every y tick label/.append style={font=\color{black}}}
+\pgfplotsset{every y tick/.append style={black}}
+\pgfplotsset{every x tick label/.append style={font=\color{black}}}
+\pgfplotsset{every x tick/.append style={black}}
+
+\pgfplotsset{scale only axis=true}
+
+\pgfplotsset{ylabel absolute}
+
+% https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834
+
+% argument #1: any options
+\newenvironment{customlegend}[1][]{%
+  \begingroup
+  % inits/clears the lists (which might be populated from previous
+  % axes):
+  \csname pgfplots@init@cleared@structures\endcsname
+  \pgfplotsset{#1}%
+}{%
+  % draws the legend:
+  \csname pgfplots@createlegend\endcsname
+  \endgroup
+}%
+
+% makes \addlegendimage available (typically only available within an
+% axis environment):
+\def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}
+
+% definition to insert numbers
+% \pgfkeys{/pgfplots/number in legend/.style={%
+%     /pgfplots/legend image code/.code={%
+%       \node at (0.125,-0.0225){#1}; % <= changed x value
+%     },%
+%   },
+% }
+\pgfplotsset{
+  every legend to name picture/.style={west}
+}
+
+\tikzstyle{upperbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=60}}]
+\tikzstyle{lowerbound}=[line cap=round, postaction={decorate,draw,decoration={border, segment length=0.2cm, amplitude=0.3cm, angle=-60}}]
+
+\pgfplotsset{
+  /pgfplots/upperbound/.style 1 args={
+    legend image code/.code={
+      \draw[##1, upperbound]
+        plot coordinates {
+        (0cm,0cm)
+        (0.6cm,0cm)
+      }
+    }
+  }
+}
+
+\tikzset{%
+  pole/.style{%
+    color=red,
+    cross out,
+    draw,
+    inner sep=0pt,
+    outer sep=0pt,
+    minimum size=#1pt
+  },
+  pole/.default={4}
+}
+
+\tikzset{%
+  zero/.style{%
+    color=red,
+    circle,
+    draw,
+    inner sep=0pt,
+    outer sep=0pt,
+    minimum size=#1pt
+  },
+  zero/.default={4}
+}
+
+\tikzset{%
+  spring/.style={%
+    thick,
+    decoration={
+      zigzag,
+      pre length  = #1cm,
+      post length = #1cm,
+      segment length = 6
+    },
+    decorate
+  },
+  spring/.default={0.2}
+}
+
+\tikzset{%
+  coil/.style n args={2}{%
+    thick,
+    decoration={
+      coil,
+      pre length  = #1cm,
+      post length = #2cm,
+      segment length = 4
+    },
+    decorate
+  },
+  coil/.default={0.3}{0.3}
+}
+
+\tikzset{%
+  damper/.style n args={2}{%
+    thick,
+    decoration={markings, mark connection node=dmp, mark=at position 0.5 with {
+        \node (dmp) [thick,
+                     inner sep = 0pt,
+                     transform shape,
+                     rotate  =-90,
+                     minimum width  = #1pt,
+                     minimum height = #2pt,
+                     draw=none] {};
+        \draw [thick] ($(dmp.north east)+(0.6*#2pt,0)$) -- (dmp.south east) -- (dmp.south west) -- ($(dmp.north west)+(0.6*#2pt,0)$);
+        \draw [thick] ($(dmp.north)+(0,-0.3*#1pt)$) -- ($(dmp.north)+(0,0.3*#1pt)$);
+      }
+    },
+    decorate
+  },
+  damper/.default={12}{3}
+}
+
+\tikzset{%
+  actuator/.style n args={2}{%
+    thick,
+    draw=none,
+    decoration={
+      markings,
+      mark connection node=my node,
+      mark=at position .5 with {
+        \node [draw, inner sep=0pt, minimum width=#1cm, minimum height=#2cm,
+        transform shape, fill=white] (my node) {};
+      },
+      mark=at position .0 with {
+        \draw[<-] (0, 0) -- (my node);
+      },
+      mark=at position 1.0 with {
+        \draw[<-] (0, 0) -- (my node);
+      }
+    },
+    decorate
+  },
+  actuator/.default={0.5}{0.2}
+}
+
+\tikzset{%
+  ground/.style n args={2}{%
+    fill,
+    pattern = north east lines,
+    draw = none,
+    anchor = north,
+    minimum width  = #1cm,
+    minimum height = #2cm,
+    append after command={
+      (\tikzlastnode.north west) edge (\tikzlastnode.north east)
+    }
+  },
+  ground/.default={2.5}{0.3}
+}
+
+\tikzset{%
+  forcesensor/.style n args={2}{%
+    rectangle,
+    outer sep=0pt,
+    inner sep=0pt,
+    draw=black,
+    fill=white!60!black,
+    anchor=south,
+    minimum width =#1cm,
+    minimum height=#2cm,
+    append after command={
+      [every edge/.append style={
+        thick,
+        black,
+      }]
+      (\tikzlastnode.north west) edge (\tikzlastnode.south east)
+      (\tikzlastnode.north east) edge (\tikzlastnode.south west)
+    }
+  },
+  forcesensor/.default={2.0}{0.5}
+}
+
+\tikzset{%
+  inertialsensor/.style={%
+    rectangle,
+    outer sep=0pt,
+    inner sep=0pt,
+    draw=black,
+    fill=white!60!black,
+    anchor=south east,
+    minimum size=#1cm,
+    append after command={
+      [every edge/.append style={
+        thick,
+        black,
+      }]
+      (\tikzlastnode.north west) edge (\tikzlastnode.south east)
+      (\tikzlastnode.north east) edge (\tikzlastnode.south west)
+    }
+  },
+  inertialsensor/.default={0.3}
+}
+
+\newcommand{\AxisRotator}[1][rotate=0]{%
+  \tikz [x=0.1cm,y=0.30cm,-stealth,#1] \draw (0,0) arc (-150:150:1 and 1);%
+}
+
+\tikzstyle{cross}=[path picture={
+  \draw[black]
+  (path picture bounding box.south east) -- (path picture bounding box.north west) (path picture bounding box.south west) -- (path picture bounding box.north east);
+}]
+
+\tikzset{%
+  piezo/.style n args={3}{%
+    draw,
+    rectangle,
+    minimum width  = #1cm,
+    minimum height = #2cm,
+    fill=blue!10!white,
+    anchor=center,
+    append after command={
+      [every edge/.append style={
+        thick,
+        black,
+      }]
+      \foreach \i in {1,...,#3}{
+        (${\i/(1+#3)}*(\tikzlastnode.north west)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south west)+0.1*(#1,0)$) edge (${\i/(1+#3)}*(\tikzlastnode.north east)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south east)-0.1*(#1,0)$)
+      }
+    }
+  },
+  piezo/.default={2}{4}{10}
+}
+
+\def\voicecoil#1#2#3{
+  % ======================
+  % Parameters
+  % ======================
+  \def\voicecoilw{#1} % Total Width
+  \def\voicecoilh{#2} % Total Height
+
+  \def\magnetw{\voicecoilw} % Width of the magnet
+  \def\magneth{\voicecoilh/1.4} % Height of the magnet
+
+  \def\magnetwb{0.15*\magnetw} % Width of the borders of the magnet
+  \def\magnetmw{0.15*\magnetw} % Width of the middle part of the magnet
+  \def\magnetwg{0.5*\magnetw} % Width of the gap of the magnet
+
+  \def\magnethl{\magnetwb} % Height of the low part of the magnet
+  \def\magnetmh{0.15*\magneth} % Height of the middle part of the magnet
+  \def\magnethg{0.2*\magneth} % Height of the gap of the magnet
+  % ======================
+
+  \begin{scope}[shift={(0.5*\voicecoilw, 0.5*\voicecoilh)}, rotate=#3, shift={(0, -0.5*\voicecoilh)}]
+    % ======================
+    % Magnet
+    % ======================
+    \draw[fill=white] (0, 0) -| ++(0.5*\magnetw, \magneth) -| ++(-0.5*\magnetw+0.5*\magnetwg, -\magnethg) -| (0.5*\magnetw-\magnetwb, \magnethl) -| (-0.5*\magnetw+\magnetwb, \magneth-\magnethg) -| (-0.5*\magnetwg, \magneth) -| (-0.5*\magnetw, 0) -- (cycle);
+    \begin{scope}[shift={(0, \magnethl)}]
+      \draw[fill=red]  (-0.5*\magnetmw, 0) rectangle (0.5*\magnetmw, \magnetmh);
+      \draw[fill=blue] (-0.5*\magnetmw, \magnetmh) rectangle (0.5*\magnetmw, 2*\magnetmh);
+      % Top conductive Magnet
+      \draw[fill=white] (-0.5*\magnetmw, 2*\magnetmh) -| (0.5*\magnetmw, -\magnethl+\magneth-\magnethg) -| ++(0.1, \magnethg) -| ++(-0.2-\magnetmw, -\magnethg) -| (-0.5*\magnetmw, \magnetmh);
+    \end{scope}
+    % ======================
+
+    % ======================
+    % Coil
+    % ======================
+    \pgfmathsetmacro{\coilwidth}{0.5*0.5*\magnetmw+0.5*0.1+0.25*\magnetwg}%
+    \draw[] ( \coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
+    \draw[] (-\coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
+    % Point on the coil
+    \foreach \x in {0,1,...,9}
+    {
+      \node[circle,inner sep=0.6pt,fill] at ( \coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
+      \node[circle,inner sep=0.6pt,fill] at (-\coilwidth, \x*0.7*\magneth/10+0.5*\magneth);
+    }
+    \draw[fill=white] (-0.5*\magnetw, 1.2*\magneth) rectangle ++(\magnetw, \magnethg);
+    % ======================
+
+    % ======================
+    % Coordinates
+    % ======================
+    % Force
+    \coordinate[] (vc_force) at (0, \magneth-0.5*\magnethg);
+    % Coil
+    \coordinate[] (vc_coil) at (0, \voicecoilh);
+    % Magnet
+    \coordinate[] (vc_magnet) at (0, 0);
+    % Coil Wires
+    \coordinate[] (vc_wire_one) at ( \coilwidth, 1.2*\magneth);
+    \coordinate[] (vc_wire_two) at (-\coilwidth, 1.2*\magneth);
+    % ======================
+  \end{scope}
+}
+
+\tikzset{%
+  ->-/.style={
+    decoration={
+      markings,
+      mark = at position #1 with {\arrow{>}
+      }
+    },
+    postaction={decorate}
+  }
+}
+\tikzset{%
+  -<-/.style={
+    decoration={
+      markings,
+      mark = at position #1 with {\arrow{<}
+      }
+    },
+    postaction={decorate}
+  }
+}
+
+\tikzset{%
+  labelc/.style= {%
+    draw,
+    fill=white,
+    shape=circle,
+    inner sep=2pt,
+    outer sep=6pt,
+  }
+}

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