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Thomas Dehaeze
2020-10-05 14:59:04 +02:00
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#+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{mycolor1}{RGB}{79,115,193}
\definecolor{mycolor2}{RGB}{213,91,53}
\definecolor{mycolor3}{RGB}{152,126,49}
#+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
** 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
** 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
** Gain
#+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
** Default line caps
#+begin_src latex
\pgfplotsset{
every axis plot/.append style={line join=round},
every axis plot/.append style={line cap=round},
}
#+end_src
** 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
* 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
** 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
* More Defaults specific to this paper
#+begin_src latex
\tikzset{block/.default={0.8cm}{0.8cm}}
\tikzset{addb/.append style={scale=0.7}}
\tikzset{node distance=0.6}
#+end_src

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\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{mycolor1}{RGB}{79,115,193}
\definecolor{mycolor2}{RGB}{213,91,53}
\definecolor{mycolor3}{RGB}{152,126,49}
\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{
every axis plot/.append style={line join=round},
every axis plot/.append style={line cap=round},
}
\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}
}
\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
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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);
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mark=at position 1.0 with {
\draw[<-] (0, 0) -- (my node);
}
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decorate
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actuator/.default={0.5}{0.2}
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\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}
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\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)
}
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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)
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inertialsensor/.default={0.3}
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\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 (${\i/(1+#3)}*(\tikzlastnode.north east)+{(1+#3-\i)/(1+#3)}*(\tikzlastnode.south east)-0.1*(#1,0)$)
}
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piezo/.default={2}{4}{10}
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\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,
}
}
\tikzset{block/.default={0.8cm}{0.8cm}}
\tikzset{addb/.append style={scale=0.7}}
\tikzset{node distance=0.6}

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\begin{tikzpicture}
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\addplot [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};
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<h1 class="title">Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Tikz Figures</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<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>
</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 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>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
<span class="org-font-latex-sedate">\node</span>[block, above right=0.5 and 0.5 of x](G1){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, below right=0.5 and 0.5 of x](G2){<span class="org-font-latex-math">$G</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.8 of G1](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, right=0.8 of G2](add2){};
<span class="org-font-latex-sedate">\node</span>[block, right=0.8 of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.8 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>};
<span class="org-font-latex-sedate">\node</span>[addb, right=5 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (G1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (G2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G1.east) -- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (G2.east) -- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (add1.north) -- ++(0, 0.8)node[below right](n1){<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-] (add2.north) -- ++(0, 0.8)node[below right](n2){<span class="org-font-latex-math">$n</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H1) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G2.south-|x)+(-0.2, -0.3)$</span>) (<span class="org-font-latex-math">$(n1.north east-|add.east)+(0.2, 0.3)$</span>)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
<span class="org-font-latex-sedate">\node</span>[below left] at (supersensor.north east) {Super Sensor};
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G1.south west)+(-0.3, -0.1)$</span>) (<span class="org-font-latex-math">$(n1.north east)+(0.0, 0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor1.north west) {Sensor 1};
<span class="org-font-latex-sedate">\node</span>[fit={(<span class="org-font-latex-math">$(G2.south west)+(-0.3, -0.1)$</span>) (<span class="org-font-latex-math">$(n2.north east)+(0.0, 0.1)$</span>)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[below right] at (sensor2.north west) {Sensor 2};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</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="orgc3d769f" 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>
</div>
</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 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>}
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
<span class="org-font-latex-sedate">\node</span>[addb, above right=0.8 and 4 of x](add1){};
<span class="org-font-latex-sedate">\node</span>[addb, below right=0.8 and 4 of x](add2){};
<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>};
<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>};
<span class="org-font-latex-sedate">\node</span>[block, left=0.5 of delta1](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=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>};
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
<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>};
<span class="org-font-latex-sedate">\node</span>[addb, right=6 of x](add){};
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (x.center) |- (add2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(add1-|W1.west)+(-0.5, 0)$</span>)node[branch](S1){} |- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(add2-|W2.west)+(-0.5, 0)$</span>)node[branch](S1){} |- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W1.east) -- (delta1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W2.east) -- (delta2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta1.east) -| (add1.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (delta2.east) -| (add2.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add1.east) -- (H1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add2.east) -- (H2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H1.east) -| (add.north);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (H2.east) -| (add.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (add.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(W1.north-|S1)+(-0.2, 0.2)$</span>) (<span class="org-font-latex-math">$(add1.south east)+(0.2, -0.3)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
<span class="org-font-latex-sedate">\node</span>[above right] at (sensor1.south west) {Sensor 1};
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(W2.north-|S1)+(-0.2, 0.2)$</span>) (<span class="org-font-latex-math">$(add2.south east)+(0.2, -0.3)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
<span class="org-font-latex-sedate">\node</span>[above right] at (sensor2.south west) {Sensor 2};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</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="orgde2b8c0" 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>
</div>
</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 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>}
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[shift={(4, 0)}]
<span class="org-comment">% Uncertainty Circle</span>
<span class="org-font-latex-sedate">\node</span>[draw, circle, fill=black!20!white, minimum size=3.6cm] (c) at (0, 0) {};
<span class="org-font-latex-sedate">\path</span>[draw, dotted] (0, 0) circle [radius=1.0];
<span class="org-font-latex-sedate">\path</span>[draw, dashed] (135:1.0) circle [radius=0.8];
<span class="org-comment">% Center of Circle</span>
<span class="org-font-latex-sedate">\node</span>[below] at (0, 0){<span class="org-font-latex-math">$1$</span>};
<span class="org-font-latex-sedate">\draw</span>[&lt;-&gt;, dashed] (0, 0) node[branch]{} -- coordinate[midway](r1) ++(45:1.0);
<span class="org-font-latex-sedate">\draw</span>[&lt;-&gt;, dashed] (135:1.0)node[branch]{} -- coordinate[midway](r2) ++(90:0.8);
<span class="org-font-latex-sedate">\node</span>[] (l1) at (2, 1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">|$</span>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;, dashed, out=-90, in=0] (l1.south) to (r1);
<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>};
<span class="org-font-latex-sedate">\draw</span>[-&gt;, dashed, out=-90, in=0] (l2.south) to (r2);
<span class="org-font-latex-sedate">\draw</span>[&lt;-&gt;, 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">\draw</span>[-&gt;, 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>[-&gt;] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (0, -1.8) -- (0, 2.0) 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>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orgf3182a4" 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>
</div>
</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 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>}
<span class="org-font-latex-sedate">\node</span>[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P(s)$</span>};
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.75!(P.north west) + (-0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.35!(P.north west) + (-0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(P.south east)!0.75!(P.north east) + ( 0.7, 0)$</span>);
<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>[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">\draw</span>[-&gt;] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (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>[-&gt;] (inputu-|sub) node[branch]{} -- (sub.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (sub.east) -- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<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>[-&gt;] (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>[-&gt;] (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"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="org3cb8226" 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>
</div>
</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 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>}
<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">3.5cm</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=1.0<span class="org-font-latex-sedate">\fheight</span>,
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xtick={0.1,1,10, 100},
xminorticks=true,
ymode=log,
ymin=0.0005,
ymax=20,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xlabel={Frequency [Hz]},
xminorgrids,
yminorgrids,
]
<span class="org-font-latex-sedate">\addplot</span> [color=black, line width=1.5pt, forget plot]
table [x=freqs, y=ampl, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matweight_formula.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=black, dashed, line width=1.5pt]
table[row sep=crcr]{<span class="org-comment">%</span>
1 10<span class="org-font-latex-warning">\\</span>
100 10<span class="org-font-latex-warning">\\</span>
};
<span class="org-font-latex-sedate">\addplot</span> [color=black, dashed, line width=1.5pt]
table[row sep=crcr]{<span class="org-comment">%</span>
0.1 0.001<span class="org-font-latex-warning">\\</span>
3 0.001<span class="org-font-latex-warning">\\</span>
};
<span class="org-font-latex-sedate">\addplot</span> [color=black, line width=1.5pt]
table[row sep=crcr]{<span class="org-comment">%</span>
0.1 1<span class="org-font-latex-warning">\\</span>
100 1<span class="org-font-latex-warning">\\</span>
};
<span class="org-font-latex-sedate">\addplot</span> [color=black, dashed, line width=1.5pt]
table[row sep=crcr]{<span class="org-comment">%</span>
10 2<span class="org-font-latex-warning">\\</span>
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>[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){};
<span class="org-font-latex-sedate">\draw</span>[dashed, line cap=round] (7, 2) -- (20, 2) node[right]{<span class="org-font-latex-math">$G_c$</span>};
<span class="org-font-latex-sedate">\draw</span>[dashed, line cap=round] (10, 2) -- (10, 1) node[below]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\omega</span></span><span class="org-font-latex-math">_c$</span>};
<span class="org-font-latex-sedate">\node</span>[right] at (3, 0.1) {<span class="org-font-latex-math">$+n$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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="orga3a1174" 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>
</div>
</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 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>}
<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">6cm</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=0.5<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>)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=1000,
xtick={0.1, 1, 10, 100, 1000},
xticklabels={{}},
xminorticks=true,
ymode=log,
ymin=0.0005,
ymax=20,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xminorgrids,
yminorgrids,
]
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt, forget plot]
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt, forget plot]
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_weights.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_weights.csv};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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=0.45<span class="org-font-latex-sedate">\fheight</span>,
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=1000,
xtick={0.1, 1, 10, 100, 1000},
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-200,
ymax=200,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
legend style={at={(1,1.1)}, outer sep=2pt , anchor=north east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}},
]
<span class="org-font-latex-sedate">\addlegendimage</span>{color=mycolor1, dashed, line width=1.5pt}
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$W_1^{-1}$</span>};
<span class="org-font-latex-sedate">\addlegendimage</span>{color=mycolor2, dashed, line width=1.5pt}
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$W_2^{-1}$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_1$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_2$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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="org49f0f1e" 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>
</div>
</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 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>}
<span class="org-font-latex-sedate">\node</span>[block={5.0cm}{3.5cm}, fill=black!20!white, dashed] (P) {};
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P(s)$</span>};
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.8!(P.north west) + (-0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.4!(P.north west) + (-0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(P.south east)!0.8!(P.north east) + (0.7, 0)$</span>);
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(P.south east)!0.55!(P.north east) + (0.7, 0)$</span>);
<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>[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">\draw</span>[-&gt;] (inputw) node[above right](w){<span class="org-font-latex-math">$w$</span>} -- (sub2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W3-|sub1)node[branch]{} -- (sub1.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (W2-|sub2)node[branch]{} -- (sub2.south);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(sub2.west)+(-0.5, 0)$</span>) node[branch]{} |- (outputv) |- (H.east);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(H.south west)!0.7!(H.north west)$</span>) -| (inputu|-W2) -- (W2.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (<span class="org-font-latex-math">$(H.south west)!0.3!(H.north west)$</span>) -| (<span class="org-font-latex-math">$(inputu|-W3)+(0.4, 0)$</span>) -- (W3.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (sub2.east) -- (sub1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (sub1.east) -- (W1.west);
<span class="org-font-latex-sedate">\draw</span>[-&gt;] (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>[-&gt;] (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>[-&gt;] (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">\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">
<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>
</div>
</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 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>}
<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">6cm</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=0.55<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>)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xticklabels={{}},
xminorticks=true,
ymode=log,
ymin=0.0005,
ymax=20,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xminorgrids,
yminorgrids,
legend columns=2,
legend style={
/tikz/column 2/.style={
column sep=5pt,
},
at={(1,0)}, outer sep=2pt , anchor=south east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}
},
]
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt]
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">${W_1}^{-1}$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_1$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt]
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">${W_2}^{-1}$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_2$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor3, dashed, line width=1.5pt]
table [x=freqs, y=W3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">${W_3}^{-1}$</span>};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor3, line width=1.5pt]
table [x=freqs, y=H3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_3$</span>};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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=0.4<span class="org-font-latex-sedate">\fheight</span>,
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-240,
ymax=240,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
]
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor3, line width=1.5pt]
table [x=freqs, y=H3p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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="org044b17c" 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>
</div>
</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 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">\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=1.0<span class="org-font-latex-sedate">\fheight</span>,
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
scale only axis,
separate axis lines,
every outer x axis line/.append style={black},
every x tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}},
every x tick/.append style={black},
xmode=log,
xmin=0.001,
xmax=1,
xminorticks=true,
xlabel={Frequency [Hz]},
every outer y axis line/.append style={black},
every y tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}},
every y tick/.append style={black},
ymode=log,
ymin=0.005,
ymax=20,
yminorticks=true,
ylabel={Magnitude},
axis background/.style={fill=white},
xmajorgrids,
xminorgrids,
ymajorgrids,
yminorgrids,
legend style={at={(0,1)}, outer sep=2pt, anchor=north west, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}}
]
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
table [x=freqs, y=wHm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$|w_H|^{-1}$</span>}
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
table [x=freqs, y=wLm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$|w_L|^{-1}$</span>}
<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>
0.008 0.008<span class="org-font-latex-warning">\\</span>
};
<span class="org-font-latex-sedate">\addlegendentry</span>{Specifications}
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt, forget plot]
table[row sep=crcr]{<span class="org-comment">%</span>
0.008 0.008<span class="org-font-latex-warning">\\</span>
0.04 1<span class="org-font-latex-warning">\\</span>
};
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt, forget plot]
table[row sep=crcr]{<span class="org-comment">%</span>
0.04 3<span class="org-font-latex-warning">\\</span>
0.1 3<span class="org-font-latex-warning">\\</span>
};
<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>
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>}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orgb9647cd" 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>
</div>
</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 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">\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>)},
scale only axis,
xmode=log,
xmin=0.001,
xmax=1,
xtick={0.001,0.01,0.1,1},
xticklabels={{}},
xminorticks=true,
ymode=log,
ymin=0.002,
ymax=5,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xminorgrids,
yminorgrids,
legend style={at={(1,0)}, outer sep=2pt, anchor=south east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}}
]
<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">\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">\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}
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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=0.3<span class="org-font-latex-sedate">\fheight</span>,
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
scale only axis,
xmode=log,
xmin=0.001,
xmax=1,
xtick={0.001, 0.01, 0.1, 1},
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-180,
ymax=180,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
]
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt, forget plot]
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt, forget plot]
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</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="orgc99b299" 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>
</div>
</div>
</div>
</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>
</div>
</body>
</html>

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#+TITLE: Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis - Tikz Figures
:DRAWER:
#+HTML_LINK_HOME: ../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>
#+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
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :noweb yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
Configuration file is accessible [[file:config.org][here]].
* Fig 1: Sensor Fusion Architecture
#+begin_src latex :file fusion_super_sensor.pdf :tangle figs/fusion_super_sensor.tex
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[block, above right=0.5 and 0.5 of x](G1){$G_1(s)$};
\node[block, below right=0.5 and 0.5 of x](G2){$G_2(s)$};
\node[addb, right=0.8 of G1](add1){};
\node[addb, right=0.8 of G2](add2){};
\node[block, right=0.8 of add1](H1){$H_1(s)$};
\node[block, right=0.8 of add2](H2){$H_2(s)$};
\node[addb, right=5 of x](add){};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[->] (x.center) |- (G1.west);
\draw[->] (x.center) |- (G2.west);
\draw[->] (G1.east) -- (add1.west);
\draw[->] (G2.east) -- (add2.west);
\draw[<-] (add1.north) -- ++(0, 0.8)node[below right](n1){$n_1$};
\draw[<-] (add2.north) -- ++(0, 0.8)node[below right](n2){$n_2$};
\draw[->] (add1.east) -- (H1.west);
\draw[->] (add2.east) -- (H2.west);
\draw[->] (H1) -| (add.north);
\draw[->] (H2) -| (add.south);
\draw[->] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[fit={($(G2.south-|x)+(-0.2, -0.3)$) ($(n1.north east-|add.east)+(0.2, 0.3)$)}, fill=black!10!white, draw, dashed, inner sep=0pt] (supersensor) {};
\node[below left] at (supersensor.north east) {Super Sensor};
\node[fit={($(G1.south west)+(-0.3, -0.1)$) ($(n1.north east)+(0.0, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor1) {};
\node[below right] at (sensor1.north west) {Sensor 1};
\node[fit={($(G2.south west)+(-0.3, -0.1)$) ($(n2.north east)+(0.0, 0.1)$)}, fill=black!20!white, draw, dashed, inner sep=0pt] (sensor2) {};
\node[below right] at (sensor2.north west) {Sensor 2};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:fusion_super_sensor
#+caption: Sensor Fusion Architecture ([[./figs/fusion_super_sensor.png][png]], [[./figs/fusion_super_sensor.pdf][pdf]], [[./figs/fusion_super_sensor.tex][tex]]).
#+RESULTS:
[[file:figs/fusion_super_sensor.png]]
* Fig 2: Sensor fusion architecture with sensor dynamics uncertainty
#+begin_src latex :file sensor_fusion_dynamic_uncertainty.pdf :tangle figs/sensor_fusion_dynamic_uncertainty.tex
\begin{tikzpicture}
\node[branch] (x) at (0, 0);
\node[addb, above right=0.8 and 4 of x](add1){};
\node[addb, below right=0.8 and 4 of x](add2){};
\node[block, above left=0.2 and 0.1 of add1](delta1){$\Delta_1(s)$};
\node[block, above left=0.2 and 0.1 of add2](delta2){$\Delta_2(s)$};
\node[block, left=0.5 of delta1](W1){$w_1(s)$};
\node[block, left=0.5 of delta2](W2){$w_2(s)$};
\node[block, right=0.5 of add1](H1){$H_1(s)$};
\node[block, right=0.5 of add2](H2){$H_2(s)$};
\node[addb, right=6 of x](add){};
\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
\draw[->] (x.center) |- (add1.west);
\draw[->] (x.center) |- (add2.west);
\draw[->] ($(add1-|W1.west)+(-0.5, 0)$)node[branch](S1){} |- (W1.west);
\draw[->] ($(add2-|W2.west)+(-0.5, 0)$)node[branch](S1){} |- (W2.west);
\draw[->] (W1.east) -- (delta1.west);
\draw[->] (W2.east) -- (delta2.west);
\draw[->] (delta1.east) -| (add1.north);
\draw[->] (delta2.east) -| (add2.north);
\draw[->] (add1.east) -- (H1.west);
\draw[->] (add2.east) -- (H2.west);
\draw[->] (H1.east) -| (add.north);
\draw[->] (H2.east) -| (add.south);
\draw[->] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
\begin{scope}[on background layer]
\node[block, fit={($(W1.north-|S1)+(-0.2, 0.2)$) ($(add1.south east)+(0.2, -0.3)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
\node[above right] at (sensor1.south west) {Sensor 1};
\node[block, fit={($(W2.north-|S1)+(-0.2, 0.2)$) ($(add2.south east)+(0.2, -0.3)$)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
\node[above right] at (sensor2.south west) {Sensor 2};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:sensor_fusion_dynamic_uncertainty
#+caption: Sensor fusion architecture with sensor dynamics uncertainty ([[./figs/sensor_fusion_dynamic_uncertainty.png][png]], [[./figs/sensor_fusion_dynamic_uncertainty.pdf][pdf]], [[./figs/sensor_fusion_dynamic_uncertainty.tex][tex]]).
#+RESULTS:
[[file:figs/sensor_fusion_dynamic_uncertainty.png]]
* Fig 3: Uncertainty set of the super sensor dynamics
#+begin_src latex :file uncertainty_set_super_sensor.pdf :tangle figs/uncertainty_set_super_sensor.tex :exports both
\begin{tikzpicture}
\begin{scope}[shift={(4, 0)}]
% Uncertainty Circle
\node[draw, circle, fill=black!20!white, minimum size=3.6cm] (c) at (0, 0) {};
\path[draw, dotted] (0, 0) circle [radius=1.0];
\path[draw, dashed] (135:1.0) circle [radius=0.8];
% Center of Circle
\node[below] at (0, 0){$1$};
\draw[<->, dashed] (0, 0) node[branch]{} -- coordinate[midway](r1) ++(45:1.0);
\draw[<->, dashed] (135:1.0)node[branch]{} -- coordinate[midway](r2) ++(90:0.8);
\node[] (l1) at (2, 1.5) {$|w_1 H_1|$};
\draw[->, dashed, out=-90, in=0] (l1.south) to (r1);
\node[] (l2) at (-2.5, 1.5) {$|w_2 H_2|$};
\draw[->, dashed, out=0, in=-180] (l2.east) to (r2);
\draw[<->, dashed] (0, 0) -- coordinate[near end](r3) ++(200:1.8);
\node[] (l3) at (-2.5, -1.5) {$|w_1 H_1| + |w_2 H_2|$};
\draw[->, dashed, out=90, in=-90] (l3.north) to (r3);
\end{scope}
% Real and Imaginary Axis
\draw[->] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
\draw[->] (0, -1.7) -- (0, 1.7) node[below left]{Im};
\draw[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=2);
\draw[dashed] (1, 0) arc (0:28:1) node[midway, right]{$\Delta \phi$};
\end{tikzpicture}
#+end_src
#+name: fig:uncertainty_set_super_sensor
#+caption: 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) ([[./figs/uncertainty_set_super_sensor.png][png]], [[./figs/uncertainty_set_super_sensor.pdf][pdf]], [[./figs/uncertainty_set_super_sensor.tex][tex]]).
#+RESULTS:
[[file:figs/uncertainty_set_super_sensor.png]]
* Fig 4: Architecture used for $\mathcal{H}_\infty$ synthesis of complementary filters
#+begin_src latex :file h_infinity_robust_fusion.pdf :tangle figs/h_infinity_robust_fusion.tex :exports both
\begin{tikzpicture}
\node[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
\coordinate[] (inputw) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.35!(P.north west) + (-0.7, 0)$);
\coordinate[] (output1) at ($(P.south east)!0.75!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.35!(P.north east) + ( 0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( 0.7, 0)$);
\node[block, left=1.4 of output1] (W1){$W_1(s)$};
\node[block, left=1.4 of output2] (W2){$W_2(s)$};
\node[addb={+}{}{}{}{-}, left=of W1] (sub) {};
\node[block, below=0.3 of P] (H2) {$H_2(s)$};
\draw[->] (inputw) node[above right]{$w$} -- (sub.west);
\draw[->] (H2.west) -| ($(inputu)+(0.35, 0)$) node[above]{$u$} -- (W2.west);
\draw[->] (inputu-|sub) node[branch]{} -- (sub.south);
\draw[->] (sub.east) -- (W1.west);
\draw[->] ($(sub.west)+(-0.6, 0)$) node[branch]{} |- ($(outputv)+(-0.35, 0)$) node[above]{$v$} |- (H2.east);
\draw[->] (W1.east) -- (output1)node[above left]{$z_1$};
\draw[->] (W2.east) -- (output2)node[above left]{$z_2$};
\end{tikzpicture}
#+end_src
#+name: fig:h_infinity_robust_fusion
#+caption: Architecture used for $\mathcal{H}_\infty$ synthesis of complementary filters ([[./figs/h_infinity_robust_fusion.png][png]], [[./figs/h_infinity_robust_fusion.pdf][pdf]], [[./figs/h_infinity_robust_fusion.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_robust_fusion.png]]
* Fig 5: Magnitude of a weighting function generated using the proposed formula
#+begin_src matlab :exports none :results none
s = zpk('s');
freqs = logspace(-1, 2, 500);
n = 2;
w0 = 2*pi*10;
G0 = 1e-3;
G1 = 10;
Gc = 2;
W = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
T = table(freqs', ...
abs(squeeze(freqresp(W, freqs, 'Hz'))), ...
'VariableNames', {'freqs', 'ampl'});
writetable(T, '../matlab/mat/weight_formula.csv');
#+end_src
#+begin_src latex :file weight_formula.pdf :tangle figs/weight_formula.tex :exports both
\setlength\fwidth{6.5cm}
\setlength\fheight{3.5cm}
\begin{tikzpicture}
\begin{axis}[%
width=1.0\fwidth,
height=1.0\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xtick={0.1,1,10, 100},
xminorticks=true,
ymode=log,
ymin=0.0005,
ymax=20,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xlabel={Frequency [Hz]},
xminorgrids,
yminorgrids,
]
\addplot [color=black, line width=1.5pt, forget plot]
table [x=freqs, y=ampl, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matweight_formula.csv};
\addplot [color=black, dashed, line width=1.5pt]
table[row sep=crcr]{%
1 10\\
100 10\\
};
\addplot [color=black, dashed, line width=1.5pt]
table[row sep=crcr]{%
0.1 0.001\\
3 0.001\\
};
\addplot [color=black, line width=1.5pt]
table[row sep=crcr]{%
0.1 1\\
100 1\\
};
\addplot [color=black, dashed, line width=1.5pt]
table[row sep=crcr]{%
10 2\\
10 1\\
};
\node[below] at (2, 10) {$G_\infty$};
\node[above] at (2, 0.001) {$G_0$};
\node[branch] at (10, 2){};
\draw[dashed, line cap=round] (7, 2) -- (20, 2) node[right]{$G_c$};
\draw[dashed, line cap=round] (10, 2) -- (10, 1) node[below]{$\omega_c$};
\node[right] at (3, 0.1) {$+n$};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:weight_formula
#+caption: Magnitude of a weighting function generated using the proposed formula ([[./figs/weight_formula.png][png]], [[./figs/weight_formula.pdf][pdf]], [[./figs/weight_formula.tex][tex]]).
#+RESULTS:
[[file:figs/weight_formula.png]]
* Fig 6: Frequency response of the weighting functions and complementary filters obtained using $\mathcal{H}_\infty$ synthesis
#+begin_src latex :file hinf_synthesis_results.pdf :tangle figs/hinf_synthesis_results.tex :exports both
\setlength\fwidth{6.5cm}
\setlength\fheight{6cm}
\begin{tikzpicture}
\begin{axis}[%
width=1.0\fwidth,
height=0.5\fheight,
at={(0.0\fwidth, 0.47\fheight)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=1000,
xtick={0.1, 1, 10, 100, 1000},
xticklabels={{}},
xminorticks=true,
ymode=log,
ymin=0.0005,
ymax=20,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xminorgrids,
yminorgrids,
]
\addplot [color=mycolor1, line width=1.5pt, forget plot]
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
\addplot [color=mycolor2, line width=1.5pt, forget plot]
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
\addplot [color=mycolor1, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_weights.csv};
\addplot [color=mycolor2, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_weights.csv};
\end{axis}
\begin{axis}[%
width=1.0\fwidth,
height=0.45\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=1000,
xtick={0.1, 1, 10, 100, 1000},
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-200,
ymax=200,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
legend style={at={(1,1.1)}, outer sep=2pt , anchor=north east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}},
]
\addlegendimage{color=mycolor1, dashed, line width=1.5pt}
\addlegendentry{$W_1^{-1}$};
\addlegendimage{color=mycolor2, dashed, line width=1.5pt}
\addlegendentry{$W_2^{-1}$};
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
\addlegendentry{$H_1$};
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
\addlegendentry{$H_2$};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:hinf_synthesis_results
#+caption: Frequency response of the weighting functions and complementary filters obtained using $\mathcal{H}_\infty$ synthesis ([[./figs/hinf_synthesis_results.png][png]], [[./figs/hinf_synthesis_results.pdf][pdf]], [[./figs/hinf_synthesis_results.tex][tex]]).
#+RESULTS:
[[file:figs/hinf_synthesis_results.png]]
* Fig 7: Architecture for $\mathcal{H}_\infty$ synthesis of three complementary filters
#+begin_src latex :file comp_filter_three_hinf.pdf :tangle figs/comp_filter_three_hinf.tex
\begin{tikzpicture}
\node[block={5.0cm}{3.5cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
\coordinate[] (inputw) at ($(P.south west)!0.8!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.4!(P.north west) + (-0.7, 0)$);
\coordinate[] (output1) at ($(P.south east)!0.8!(P.north east) + (0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.55!(P.north east) + (0.7, 0)$);
\coordinate[] (output3) at ($(P.south east)!0.3!(P.north east) + (0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + (0.7, 0)$);
\node[block, left=1.4 of output1] (W1){$W_1(s)$};
\node[block, left=1.4 of output2] (W2){$W_2(s)$};
\node[block, left=1.4 of output3] (W3){$W_3(s)$};
\node[addb={+}{}{}{}{-}, left=of W1] (sub1) {};
\node[addb={+}{}{}{}{-}, left=of sub1] (sub2) {};
\node[block, below=0.3 of P] (H) {$\begin{bmatrix}H_2(s) \\ H_3(s)\end{bmatrix}$};
\draw[->] (inputw) node[above right](w){$w$} -- (sub2.west);
\draw[->] (W3-|sub1)node[branch]{} -- (sub1.south);
\draw[->] (W2-|sub2)node[branch]{} -- (sub2.south);
\draw[->] ($(sub2.west)+(-0.5, 0)$) node[branch]{} |- (outputv) |- (H.east);
\draw[->] ($(H.south west)!0.7!(H.north west)$) -| (inputu|-W2) -- (W2.west);
\draw[->] ($(H.south west)!0.3!(H.north west)$) -| ($(inputu|-W3)+(0.4, 0)$) -- (W3.west);
\draw[->] (sub2.east) -- (sub1.west);
\draw[->] (sub1.east) -- (W1.west);
\draw[->] (W1.east) -- (output1)node[above left](z){$z_1$};
\draw[->] (W2.east) -- (output2)node[above left]{$z_2$};
\draw[->] (W3.east) -- (output3)node[above left]{$z_3$};
\node[above] at (W2-|w){$u_1$};
\node[above] at (W3-|w){$u_2$};
\node[above] at (outputv-|z){$v$};
\end{tikzpicture}
#+end_src
#+name: fig:comp_filter_three_hinf
#+caption: Architecture for $\mathcal{H}_\infty$ synthesis of three complementary filters ([[./figs/comp_filter_three_hinf.png][png]], [[./figs/comp_filter_three_hinf.pdf][pdf]], [[./figs/comp_filter_three_hinf.tex][tex]]).
#+RESULTS:
[[file:figs/comp_filter_three_hinf.png]]
* Fig 8: Frequency response of the weighting functions and three complementary filters obtained using $\mathcal{H}_\infty$ synthesis
#+begin_src latex :file hinf_three_synthesis_results.pdf :tangle figs/hinf_three_synthesis_results.tex :exports both
\setlength\fwidth{6.5cm}
\setlength\fheight{6cm}
\begin{tikzpicture}
\begin{axis}[%
width=1.0\fwidth,
height=0.55\fheight,
at={(0.0\fwidth, 0.42\fheight)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xticklabels={{}},
xminorticks=true,
ymode=log,
ymin=0.0005,
ymax=20,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xminorgrids,
yminorgrids,
legend columns=2,
legend style={
/tikz/column 2/.style={
column sep=5pt,
},
at={(1,0)}, outer sep=2pt , anchor=south east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}
},
]
\addplot [color=mycolor1, dashed, line width=1.5pt]
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
\addlegendentry{${W_1}^{-1}$};
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addlegendentry{$H_1$};
\addplot [color=mycolor2, dashed, line width=1.5pt]
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
\addlegendentry{${W_2}^{-1}$};
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addlegendentry{$H_2$};
\addplot [color=mycolor3, dashed, line width=1.5pt]
table [x=freqs, y=W3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
\addlegendentry{${W_3}^{-1}$};
\addplot [color=mycolor3, line width=1.5pt]
table [x=freqs, y=H3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addlegendentry{$H_3$};
\end{axis}
\begin{axis}[%
width=1.0\fwidth,
height=0.4\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
xmode=log,
xmin=0.1,
xmax=100,
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-240,
ymax=240,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
]
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\addplot [color=mycolor3, line width=1.5pt]
table [x=freqs, y=H3p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:hinf_three_synthesis_results
#+caption: Frequency response of the weighting functions and three complementary filters obtained using $\mathcal{H}_\infty$ synthesis ([[./figs/hinf_three_synthesis_results.png][png]], [[./figs/hinf_three_synthesis_results.pdf][pdf]], [[./figs/hinf_three_synthesis_results.tex][tex]]).
#+RESULTS:
[[file:figs/hinf_three_synthesis_results.png]]
* Fig 9: Specifications and weighting functions magnitude used for $\mathcal{H}_\infty$ synthesis
#+begin_src latex :file ligo_weights.pdf :tangle figs/ligo_weights.tex :exports both
\setlength\fwidth{6.5cm}
\setlength\fheight{3.2cm}
\begin{tikzpicture}
\begin{axis}[%
width=1.0\fwidth,
height=1.0\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
separate axis lines,
every outer x axis line/.append style={black},
every x tick label/.append style={font=\color{black}},
every x tick/.append style={black},
xmode=log,
xmin=0.001,
xmax=1,
xminorticks=true,
xlabel={Frequency [Hz]},
every outer y axis line/.append style={black},
every y tick label/.append style={font=\color{black}},
every y tick/.append style={black},
ymode=log,
ymin=0.005,
ymax=20,
yminorticks=true,
ylabel={Magnitude},
axis background/.style={fill=white},
xmajorgrids,
xminorgrids,
ymajorgrids,
yminorgrids,
legend style={at={(0,1)}, outer sep=2pt, anchor=north west, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}}
]
\addplot [color=mycolor1, line width=1.5pt]
table [x=freqs, y=wHm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
\addlegendentry{$|w_H|^{-1}$}
\addplot [color=mycolor2, line width=1.5pt]
table [x=freqs, y=wLm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
\addlegendentry{$|w_L|^{-1}$}
\addplot [color=black, dotted, line width=1.5pt]
table[row sep=crcr]{%
0.0005 0.008\\
0.008 0.008\\
};
\addlegendentry{Specifications}
\addplot [color=black, dotted, line width=1.5pt, forget plot]
table[row sep=crcr]{%
0.008 0.008\\
0.04 1\\
};
\addplot [color=black, dotted, line width=1.5pt, forget plot]
table[row sep=crcr]{%
0.04 3\\
0.1 3\\
};
\addplot [color=black, dotted, line width=1.5pt]
table[row sep=crcr]{%
0.1 0.045\\
2 0.045\\
};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:ligo_weights
#+caption: Specifications and weighting functions magnitude used for $\mathcal{H}_\infty$ synthesis ([[./figs/ligo_weights.png][png]], [[./figs/ligo_weights.pdf][pdf]], [[./figs/ligo_weights.tex][tex]]).
#+RESULTS:
[[file:figs/ligo_weights.png]]
* Fig 10: Comparison of the FIR filters (solid) with the filters obtained with $\mathcal{H}_\infty$ synthesis (dashed)
#+begin_src latex :file comp_fir_ligo_hinf.pdf :tangle figs/comp_fir_ligo_hinf.tex :exports both
\setlength\fwidth{6.5cm}
\setlength\fheight{6.8cm}
\begin{tikzpicture}
\begin{axis}[%
width=1.0\fwidth,
height=0.60\fheight,
at={(0.0\fwidth, 0.32\fheight)},
scale only axis,
xmode=log,
xmin=0.001,
xmax=1,
xtick={0.001,0.01,0.1,1},
xticklabels={{}},
xminorticks=true,
ymode=log,
ymin=0.002,
ymax=5,
ytick={0.001, 0.01, 0.1, 1, 10},
yminorticks=true,
ylabel={Magnitude},
xminorgrids,
yminorgrids,
legend style={at={(1,0)}, outer sep=2pt, anchor=south east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}}
]
\addplot [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};
\addlegendentry{$H_H(s)$ - $\mathcal{H}_\infty$}
\addplot [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};
\addlegendentry{$H_H(s)$ - FIR}
\addplot [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};
\addlegendentry{$H_L(s)$ - $\mathcal{H}_\infty$}
\addplot [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};
\addlegendentry{$H_L(s)$ - FIR}
\end{axis}
\begin{axis}[%
width=1.0\fwidth,
height=0.3\fheight,
at={(0.0\fwidth, 0.0\fheight)},
scale only axis,
xmode=log,
xmin=0.001,
xmax=1,
xtick={0.001, 0.01, 0.1, 1},
xminorticks=true,
xlabel={Frequency [Hz]},
ymin=-180,
ymax=180,
ytick={-180, -90, 0, 90, 180},
ylabel={Phase [deg]},
xminorgrids,
]
\addplot [color=mycolor1, line width=1.5pt, forget plot]
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
\addplot [color=mycolor1, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
\addplot [color=mycolor2, line width=1.5pt, forget plot]
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
\addplot [color=mycolor2, dashed, line width=1.5pt, forget plot]
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
\end{axis}
\end{tikzpicture}
#+end_src
#+name: fig:comp_fir_ligo_hinf
#+caption: Comparison of the FIR filters (solid) with the filters obtained with $\mathcal{H}_\infty$ synthesis (dashed) ([[./figs/comp_fir_ligo_hinf.png][png]], [[./figs/comp_fir_ligo_hinf.pdf][pdf]], [[./figs/comp_fir_ligo_hinf.tex][tex]]).
#+RESULTS:
[[file:figs/comp_fir_ligo_hinf.png]]