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#+TITLE: LaTeX Configuration for Tikz Figures
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:DRAWER:
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_HEAD: <script src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <script src="../js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script src="../js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script src="../js/readtheorg.js"></script>
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#+PROPERTY: header-args:latex+ :tangle config.tex
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#+PROPERTY: header-args:latex+ :exports code
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:END:
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* Packages
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#+begin_src latex
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage[french, english]{babel} % Last language is main language
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\usepackage{lmodern} % Latin Modern Font
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\usepackage{gensymb} % Generic symbols for both text and math mode
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\usepackage{standalone} % Used to generate standalone Tikz
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\usepackage{amsmath} % Main math Package
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\usepackage{mathtools} % Extension package to amsmath
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\usepackage{amsthm} % Typesetting theorems (AMS style)
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\usepackage{amsfonts} % More fonts from the AMS
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\usepackage{textcomp} % provide many text symbols
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\usepackage{steinmetz} % For phase symbol
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\usepackage{xstring} % Utils to manipulate strings
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\usepackage{etoolbox} % Add basic if/then
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\usepackage{esvect} % Beautyfull vectors
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\usepackage{graphicx} % Enhanced support for graphics
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\usepackage{grffile} % Used by matlab2tikz
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\usepackage{microtype} % typographic tuning
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\usepackage{setspace} % for line spacing, e.g. \onehalfspacing
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\usepackage{tabularx} % table features
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\usepackage{enumitem} % for simple list modifications
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\usepackage{booktabs} % better table support
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\usepackage{stackengine} %
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\usepackage[load-configurations=abbreviations]{siunitx} % SI units
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\sisetup{
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locale = US,
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detect-all,
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range-phrase=--,
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range-units=single
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}
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#+end_src
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* Tikz related packages
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#+begin_src latex
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\usepackage{tikz} % Tikz
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\usepackage{tikzscale} % Used to scale Tikz graphics
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\usepackage{adjustbox} % Used to proper positioning of tikz pictures
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\usepackage{circuitikz} % Draw electronic circuits
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\usepackage{pgfpages} % Needed to use notes
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\usepackage{pgfplots} % Used to plot functions
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#+end_src
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* Tikz Libraries
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#+begin_src latex
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\usetikzlibrary{arrows} % Arrow tip library
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\usetikzlibrary{arrows.meta} % Add some arrows
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\usetikzlibrary{calc} % The library allows advanced Coordinate Calculations
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\usetikzlibrary{intersections} % calculate intersections of paths
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\usetikzlibrary{matrix} %
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\usetikzlibrary{patterns} %
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\usetikzlibrary{shapes} % Defines circle and rectangle
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\usetikzlibrary{shapes.geometric} % Use for the shape diamond and isosceles triangle
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\usetikzlibrary{snakes} % snake=coil and snake=zigzag using segment amplitude=10pt
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\usetikzlibrary{positioning} % Additional options for placing nodes
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\usetikzlibrary{3d} % Plot 3D shapes
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\usetikzlibrary{spy} % Creating a magnified area
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\usetikzlibrary{decorations.text} % Used to make text follows a curve
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\usetikzlibrary{decorations.pathmorphing} % deformation of a path
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\usetikzlibrary{decorations.markings} % Used for spring and damper
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\usetikzlibrary{babel} % A tiny library that make the interaction with the babel package easier
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\usetikzlibrary{plotmarks} % This library defines a number of plot marks
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\usetikzlibrary{fit} % Used to make rectangle as nodes by specifying two points
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\usetikzlibrary{backgrounds} % Used to put things under others
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#+end_src
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* PGF Plot libraries and config
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#+begin_src latex
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\usepgfplotslibrary{patchplots}
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\usepgfplotslibrary{groupplots}
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\pgfplotsset{compat=newest}
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\pgfplotsset{plot coordinates/math parser=false}
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#+end_src
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* Setup size of figures
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#+begin_src latex
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\newlength{\fheight}
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\newlength{\fwidth}
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\setlength{\fwidth}{85mm}
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\setlength{\fheight}{112mm}
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#+end_src
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* Setup Arrows style
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#+begin_src latex
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\tikzset{>=Stealth}
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% Setup default Linewidth
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\tikzset{every path/.style={line width=1pt}}
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#+end_src
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* Colors
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#+begin_src latex
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\usepackage{xcolor}% Color extension
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\definecolor{mycolor1}{RGB}{79,115,193}
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\definecolor{mycolor2}{RGB}{213,91,53}
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\definecolor{mycolor3}{RGB}{152,126,49}
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#+end_src
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* Control
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** Blocks
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#+begin_src latex
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\tikzset{%
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block/.style n args={2}{%
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draw,
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fill=white,
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minimum width = #1,
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minimum height = #2,
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},
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block/.default={1.2cm}{1.0cm}
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}
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#+end_src
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** Branches
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#+begin_src latex
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\tikzstyle{branch}=[fill,shape=circle,minimum size=4pt,inner sep=0pt]
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\tikzstyle{->top}=[-{Stealth[color=black, scale=0.8]}, draw=white, double=black, double distance=1pt, line width=1pt]
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\tikzstyle{<-top}=[{stealth[color=black, scale=0.8]}-, draw=white, double=black, double distance=1pt, line width=1pt]
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#+end_src
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** Hand Writen Style
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Usefull for schematic plots
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#+begin_src latex
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\tikzstyle{handwriten}=[decorate,decoration={random steps,amplitude=0.1pt,segment length=0.8pt}]
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#+end_src
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** DAC
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#+begin_src latex
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\tikzset{%
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DAC/.style={%
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draw,
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signal,
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}
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}
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#+end_src
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** ADC
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#+begin_src latex
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\tikzset{%
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ADC/.style={%
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draw,
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signal,
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signal to = west,
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}
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}
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#+end_src
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** Gain
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#+begin_src latex
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\tikzset{%
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gain right/.style={%
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draw,
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regular polygon,
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regular polygon sides = 3,
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inner sep = 2pt,
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shape border rotate=-90
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},
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gain left/.style={%
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draw,
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regular polygon,
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regular polygon sides = 3,
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inner sep = 2pt,
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shape border rotate=90
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},
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gain top/.style={%
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draw,
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regular polygon,
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regular polygon sides = 3,
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inner sep = 2pt,
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shape border rotate=0
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},
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gain bottom/.style={%
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draw,
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regular polygon,
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regular polygon sides = 3,
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inner sep = 2pt,
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shape border rotate=180
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},
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}
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#+end_src
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** Add / Substract / Divide / Multiply block
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#+begin_src latex
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\tikzset{% Add block with Circled operations
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addc/.style n args={5}{%
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draw,
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fill=white,
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circle,
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outer sep = 0pt,
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inner sep = 0pt,
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minimum size = 2em,
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execute at begin node={\LARGE $#1$},
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append after command={\pgfextra{\let\mainnode=\tikzlastnode}
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\ifx#2\empty\else
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node[draw, circle, outer sep=6pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
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\fi
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\ifx#3\empty\else
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node[draw, circle, outer sep=6pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
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\fi
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\ifx#4\empty\else
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node[draw, circle, outer sep=6pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
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\fi
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\ifx#5\empty\else
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node[draw, circle, outer sep=6pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
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\fi
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}
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},
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addc/.default={+}{}{}{}{},
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}
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#+end_src
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#+begin_src latex
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\tikzset{% Add Block
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addb/.style n args={5}{%
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draw,
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fill=white,
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circle,
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outer sep = 0pt,
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inner sep = 0pt,
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minimum size = 2em,
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execute at begin node={\LARGE $#1$},
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append after command={\pgfextra{\let\mainnode=\tikzlastnode}
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\ifx#2\empty\else
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node[outer sep=2pt, inner sep=0pt, above left] at (\mainnode.west) {$#2$}%
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\fi
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\ifx#3\empty\else
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node[outer sep=2pt, inner sep=0pt, above right] at (\mainnode.north) {$#3$}%
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\fi
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\ifx#4\empty\else
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node[outer sep=2pt, inner sep=0pt, below right] at (\mainnode.east) {$#4$}%
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\fi
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\ifx#5\empty\else
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node[outer sep=2pt, inner sep=0pt, below left] at (\mainnode.south) {$#5$}%
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\fi
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}
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},
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addb/.default={+}{}{}{}{},
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}
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#+end_src
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* Plots
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** Default line caps
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#+begin_src latex
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\pgfplotsset{
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every axis plot/.append style={line join=round},
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every axis plot/.append style={line cap=round},
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}
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#+end_src
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** Grid
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#+begin_src latex
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\pgfplotsset{grid style={black}}
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\pgfplotsset{major grid style={black!30!white}}
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\pgfplotsset{minor grid style={black!10!white}}
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\pgfplotsset{xmajorgrids}
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\pgfplotsset{ymajorgrids}
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#+end_src
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** Lines
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#+begin_src latex
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\pgfplotsset{separate axis lines=false} % draw axis as rectangle and not as 4 lines
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\pgfplotsset{every outer x axis line/.append style={black}}
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\pgfplotsset{every outer y axis line/.append style={black}}
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\pgfplotsset{axis background/.style={fill=white}}
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\pgfplotsset{axis x line*=bottom} % solid line on the bottom with thin on the top
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\pgfplotsset{axis y line*=left} % solid line on the left with thin on the right
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#+end_src
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** Ticks
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#+begin_src latex
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\pgfplotsset{every y tick label/.append style={font=\color{black}}}
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\pgfplotsset{every y tick/.append style={black}}
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\pgfplotsset{every x tick label/.append style={font=\color{black}}}
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\pgfplotsset{every x tick/.append style={black}}
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#+end_src
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** Size
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If =scale only axis=false= (the default), pgfplots will try to produce the desired width including labels, titles and ticks.
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#+begin_src latex
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\pgfplotsset{scale only axis=true}
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#+end_src
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** Label
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Used to align all of ylabel of one figure.
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#+begin_src latex
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\pgfplotsset{ylabel absolute}
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#+end_src
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** Legend
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#+begin_src latex
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% https://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834
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% argument #1: any options
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\newenvironment{customlegend}[1][]{%
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\begingroup
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% inits/clears the lists (which might be populated from previous
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% axes):
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\csname pgfplots@init@cleared@structures\endcsname
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\pgfplotsset{#1}%
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}{%
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% draws the legend:
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\csname pgfplots@createlegend\endcsname
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\endgroup
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}%
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% makes \addlegendimage available (typically only available within an
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% axis environment):
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\def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}
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% definition to insert numbers
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% \pgfkeys{/pgfplots/number in legend/.style={%
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% /pgfplots/legend image code/.code={%
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% \node at (0.125,-0.0225){#1}; % <= changed x value
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% },%
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||||
% },
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% }
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\pgfplotsset{
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every legend to name picture/.style={west}
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}
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||||
#+end_src
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||||
* Mechanical
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||||
** Spring
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||||
#+begin_src latex
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||||
\tikzset{%
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spring/.style={%
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||||
thick,
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||||
decoration={
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||||
zigzag,
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pre length = #1cm,
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post length = #1cm,
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||||
segment length = 6
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||||
},
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||||
decorate
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||||
},
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||||
spring/.default={0.2}
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||||
}
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||||
#+end_src
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||||
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** Coil
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#+begin_src latex
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\tikzset{%
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coil/.style n args={2}{%
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||||
thick,
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||||
decoration={
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||||
coil,
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||||
pre length = #1cm,
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||||
post length = #2cm,
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||||
segment length = 4
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||||
},
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||||
decorate
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||||
},
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||||
coil/.default={0.3}{0.3}
|
||||
}
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||||
#+end_src
|
||||
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||||
** Damper
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||||
#+begin_src latex
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||||
\tikzset{%
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||||
damper/.style n args={2}{%
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||||
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
|
||||
+513
@@ -0,0 +1,513 @@
|
||||
\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
|
||||
},
|
||||
damper/.default={12}{3}
|
||||
}
|
||||
|
||||
\tikzset{%
|
||||
actuator/.style n args={2}{%
|
||||
thick,
|
||||
draw=none,
|
||||
decoration={
|
||||
markings,
|
||||
mark connection node=my node,
|
||||
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% ======================
|
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% Parameters
|
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% ======================
|
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\def\voicecoilw{#1} % Total Width
|
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|
||||
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|
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|
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|
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|
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|
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|
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\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)}]
|
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% ======================
|
||||
% Magnet
|
||||
% ======================
|
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\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);
|
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|
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|
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|
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% Top conductive Magnet
|
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|
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\end{scope}
|
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% ======================
|
||||
|
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% ======================
|
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% Coil
|
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% ======================
|
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|
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|
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\draw[] (-\coilwidth, 0.5*\magneth) -- ++(0, 0.7*\magneth);
|
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% Point on the coil
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|
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{
|
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|
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|
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|
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|
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% ======================
|
||||
|
||||
% ======================
|
||||
% Coordinates
|
||||
% ======================
|
||||
% Force
|
||||
\coordinate[] (vc_force) at (0, \magneth-0.5*\magnethg);
|
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% Coil
|
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|
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% Magnet
|
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|
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% Coil Wires
|
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\coordinate[] (vc_wire_one) at ( \coilwidth, 1.2*\magneth);
|
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\coordinate[] (vc_wire_two) at (-\coilwidth, 1.2*\magneth);
|
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% ======================
|
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|
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After Width: | Height: | Size: 39 KiB |
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\begin{tikzpicture}
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\node[branch] (x) at (0, 0);
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\node[block, above right=0.5 and 0.5 of x](G1){$G_1(s)$};
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\node[block, below right=0.5 and 0.5 of x](G2){$G_2(s)$};
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\node[addb, right=0.8 of G1](add1){};
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\node[addb, right=0.8 of G2](add2){};
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\node[block, right=0.8 of add1](H1){$H_1(s)$};
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\node[block, right=0.8 of add2](H2){$H_2(s)$};
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\node[addb, right=5 of x](add){};
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\draw[] ($(x)+(-0.7, 0)$) node[above right]{$x$} -- (x.center);
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\draw[->] (x.center) |- (G1.west);
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\draw[->] (x.center) |- (G2.west);
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\draw[->] (G1.east) -- (add1.west);
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\draw[->] (G2.east) -- (add2.west);
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\draw[<-] (add1.north) -- ++(0, 0.8)node[below right](n1){$n_1$};
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\draw[<-] (add2.north) -- ++(0, 0.8)node[below right](n2){$n_2$};
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\draw[->] (add1.east) -- (H1.west);
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\draw[->] (add2.east) -- (H2.west);
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\draw[->] (H1) -| (add.north);
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\draw[->] (H2) -| (add.south);
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\draw[->] (add.east) -- ++(0.7, 0) node[above left]{$\hat{x}$};
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\begin{scope}[on background layer]
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\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) {};
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\node[below left] at (supersensor.north east) {Super Sensor};
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\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) {};
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\node[below right] at (sensor1.north west) {Sensor 1};
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\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) {};
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\node[below right] at (sensor2.north west) {Sensor 2};
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\end{scope}
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Tikz Figures</h1>
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<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>
|
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</div>
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</div>
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<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">
|
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<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
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<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
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</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>}
|
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|
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|
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|
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|
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</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">
|
||||
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|
||||
<span class="org-font-latex-sedate">\draw</span>[->, 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>[->, dashed, out=-90, in=0] (l2.south) to (r2);
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (0, 0) -- coordinate[near end](r3) ++(200:1.8);
|
||||
<span class="org-font-latex-sedate">\node</span>[] (l3) at (-2.5, -1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">| + |w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">|$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=90, in=-90] (l3.north) to (r3);
|
||||
|
||||
<span class="org-comment">% % Uncertainty Regions</span>
|
||||
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below left] at (45:1.8) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{</span><span class="org-font-latex-sedate"><span class="org-comment">\text</span></span><span class="org-comment">{ss}}$};</span>
|
||||
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[above left] at (-45:1.0) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{1}$};</span>
|
||||
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below] at ($(135:1.0)+(0, 0.8)$) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{2}$};</span>
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
|
||||
|
||||
<span class="org-comment">% Real and Imaginary Axis</span>
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (0, -1.8) -- (0, 2.0) node[below left]{Im};
|
||||
|
||||
<span class="org-font-latex-sedate">\draw</span>[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>[->] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (H2.west) -| (<span class="org-font-latex-math">$(inputu)+(0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$u$</span>} -- (W2.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (inputu-|sub) node[branch]{} -- (sub.south);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (sub.east) -- (W1.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(sub.west)+(-0.6, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$v$</span>} |- (H2.east);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate"><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>[->] (inputw) node[above right](w){<span class="org-font-latex-math">$w$</span>} -- (sub2.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W3-|sub1)node[branch]{} -- (sub1.south);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2-|sub2)node[branch]{} -- (sub2.south);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (<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>[->] (<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>[->] (<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>[->] (sub2.east) -- (sub1.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (sub1.east) -- (W1.west);
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left](z){<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (W3.east) -- (output3)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (W2-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\node</span>[above] at (W3-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\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>
|
||||
+637
@@ -0,0 +1,637 @@
|
||||
#+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]]
|
||||
Reference in new issue
Block a user