Lot of works on simscape, IFF and DVF
This commit is contained in:
parent
ee0363ee59
commit
b652aebe59
1
matlab/figs-tikz
Symbolic link
1
matlab/figs-tikz
Symbolic link
@ -0,0 +1 @@
|
||||
../tikz/figs
|
||||
@ -1,229 +1,27 @@
|
||||
<?xml version="1.0" encoding="utf-8"?>
|
||||
<?xml version="1.0" encoding="utf-8"?>
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2020-03-16 lun. 10:52 -->
|
||||
<!-- 2020-06-10 mer. 10:17 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<title>Matlab Computation</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
<meta name="author" content="Dehaeze Thomas" />
|
||||
<style type="text/css">
|
||||
<!--/*--><![CDATA[/*><!--*/
|
||||
.title { text-align: center;
|
||||
margin-bottom: .2em; }
|
||||
.subtitle { text-align: center;
|
||||
font-size: medium;
|
||||
font-weight: bold;
|
||||
margin-top:0; }
|
||||
.todo { font-family: monospace; color: red; }
|
||||
.done { font-family: monospace; color: green; }
|
||||
.priority { font-family: monospace; color: orange; }
|
||||
.tag { background-color: #eee; font-family: monospace;
|
||||
padding: 2px; font-size: 80%; font-weight: normal; }
|
||||
.timestamp { color: #bebebe; }
|
||||
.timestamp-kwd { color: #5f9ea0; }
|
||||
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
||||
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
|
||||
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
|
||||
.underline { text-decoration: underline; }
|
||||
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
|
||||
p.verse { margin-left: 3%; }
|
||||
pre {
|
||||
border: 1px solid #ccc;
|
||||
box-shadow: 3px 3px 3px #eee;
|
||||
padding: 8pt;
|
||||
font-family: monospace;
|
||||
overflow: auto;
|
||||
margin: 1.2em;
|
||||
}
|
||||
pre.src {
|
||||
position: relative;
|
||||
overflow: visible;
|
||||
padding-top: 1.2em;
|
||||
}
|
||||
pre.src:before {
|
||||
display: none;
|
||||
position: absolute;
|
||||
background-color: white;
|
||||
top: -10px;
|
||||
right: 10px;
|
||||
padding: 3px;
|
||||
border: 1px solid black;
|
||||
}
|
||||
pre.src:hover:before { display: inline;}
|
||||
/* Languages per Org manual */
|
||||
pre.src-asymptote:before { content: 'Asymptote'; }
|
||||
pre.src-awk:before { content: 'Awk'; }
|
||||
pre.src-C:before { content: 'C'; }
|
||||
/* pre.src-C++ doesn't work in CSS */
|
||||
pre.src-clojure:before { content: 'Clojure'; }
|
||||
pre.src-css:before { content: 'CSS'; }
|
||||
pre.src-D:before { content: 'D'; }
|
||||
pre.src-ditaa:before { content: 'ditaa'; }
|
||||
pre.src-dot:before { content: 'Graphviz'; }
|
||||
pre.src-calc:before { content: 'Emacs Calc'; }
|
||||
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
|
||||
pre.src-fortran:before { content: 'Fortran'; }
|
||||
pre.src-gnuplot:before { content: 'gnuplot'; }
|
||||
pre.src-haskell:before { content: 'Haskell'; }
|
||||
pre.src-hledger:before { content: 'hledger'; }
|
||||
pre.src-java:before { content: 'Java'; }
|
||||
pre.src-js:before { content: 'Javascript'; }
|
||||
pre.src-latex:before { content: 'LaTeX'; }
|
||||
pre.src-ledger:before { content: 'Ledger'; }
|
||||
pre.src-lisp:before { content: 'Lisp'; }
|
||||
pre.src-lilypond:before { content: 'Lilypond'; }
|
||||
pre.src-lua:before { content: 'Lua'; }
|
||||
pre.src-matlab:before { content: 'MATLAB'; }
|
||||
pre.src-mscgen:before { content: 'Mscgen'; }
|
||||
pre.src-ocaml:before { content: 'Objective Caml'; }
|
||||
pre.src-octave:before { content: 'Octave'; }
|
||||
pre.src-org:before { content: 'Org mode'; }
|
||||
pre.src-oz:before { content: 'OZ'; }
|
||||
pre.src-plantuml:before { content: 'Plantuml'; }
|
||||
pre.src-processing:before { content: 'Processing.js'; }
|
||||
pre.src-python:before { content: 'Python'; }
|
||||
pre.src-R:before { content: 'R'; }
|
||||
pre.src-ruby:before { content: 'Ruby'; }
|
||||
pre.src-sass:before { content: 'Sass'; }
|
||||
pre.src-scheme:before { content: 'Scheme'; }
|
||||
pre.src-screen:before { content: 'Gnu Screen'; }
|
||||
pre.src-sed:before { content: 'Sed'; }
|
||||
pre.src-sh:before { content: 'shell'; }
|
||||
pre.src-sql:before { content: 'SQL'; }
|
||||
pre.src-sqlite:before { content: 'SQLite'; }
|
||||
/* additional languages in org.el's org-babel-load-languages alist */
|
||||
pre.src-forth:before { content: 'Forth'; }
|
||||
pre.src-io:before { content: 'IO'; }
|
||||
pre.src-J:before { content: 'J'; }
|
||||
pre.src-makefile:before { content: 'Makefile'; }
|
||||
pre.src-maxima:before { content: 'Maxima'; }
|
||||
pre.src-perl:before { content: 'Perl'; }
|
||||
pre.src-picolisp:before { content: 'Pico Lisp'; }
|
||||
pre.src-scala:before { content: 'Scala'; }
|
||||
pre.src-shell:before { content: 'Shell Script'; }
|
||||
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
|
||||
/* additional language identifiers per "defun org-babel-execute"
|
||||
in ob-*.el */
|
||||
pre.src-cpp:before { content: 'C++'; }
|
||||
pre.src-abc:before { content: 'ABC'; }
|
||||
pre.src-coq:before { content: 'Coq'; }
|
||||
pre.src-groovy:before { content: 'Groovy'; }
|
||||
/* additional language identifiers from org-babel-shell-names in
|
||||
ob-shell.el: ob-shell is the only babel language using a lambda to put
|
||||
the execution function name together. */
|
||||
pre.src-bash:before { content: 'bash'; }
|
||||
pre.src-csh:before { content: 'csh'; }
|
||||
pre.src-ash:before { content: 'ash'; }
|
||||
pre.src-dash:before { content: 'dash'; }
|
||||
pre.src-ksh:before { content: 'ksh'; }
|
||||
pre.src-mksh:before { content: 'mksh'; }
|
||||
pre.src-posh:before { content: 'posh'; }
|
||||
/* Additional Emacs modes also supported by the LaTeX listings package */
|
||||
pre.src-ada:before { content: 'Ada'; }
|
||||
pre.src-asm:before { content: 'Assembler'; }
|
||||
pre.src-caml:before { content: 'Caml'; }
|
||||
pre.src-delphi:before { content: 'Delphi'; }
|
||||
pre.src-html:before { content: 'HTML'; }
|
||||
pre.src-idl:before { content: 'IDL'; }
|
||||
pre.src-mercury:before { content: 'Mercury'; }
|
||||
pre.src-metapost:before { content: 'MetaPost'; }
|
||||
pre.src-modula-2:before { content: 'Modula-2'; }
|
||||
pre.src-pascal:before { content: 'Pascal'; }
|
||||
pre.src-ps:before { content: 'PostScript'; }
|
||||
pre.src-prolog:before { content: 'Prolog'; }
|
||||
pre.src-simula:before { content: 'Simula'; }
|
||||
pre.src-tcl:before { content: 'tcl'; }
|
||||
pre.src-tex:before { content: 'TeX'; }
|
||||
pre.src-plain-tex:before { content: 'Plain TeX'; }
|
||||
pre.src-verilog:before { content: 'Verilog'; }
|
||||
pre.src-vhdl:before { content: 'VHDL'; }
|
||||
pre.src-xml:before { content: 'XML'; }
|
||||
pre.src-nxml:before { content: 'XML'; }
|
||||
/* add a generic configuration mode; LaTeX export needs an additional
|
||||
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
|
||||
pre.src-conf:before { content: 'Configuration File'; }
|
||||
|
||||
table { border-collapse:collapse; }
|
||||
caption.t-above { caption-side: top; }
|
||||
caption.t-bottom { caption-side: bottom; }
|
||||
td, th { vertical-align:top; }
|
||||
th.org-right { text-align: center; }
|
||||
th.org-left { text-align: center; }
|
||||
th.org-center { text-align: center; }
|
||||
td.org-right { text-align: right; }
|
||||
td.org-left { text-align: left; }
|
||||
td.org-center { text-align: center; }
|
||||
dt { font-weight: bold; }
|
||||
.footpara { display: inline; }
|
||||
.footdef { margin-bottom: 1em; }
|
||||
.figure { padding: 1em; }
|
||||
.figure p { text-align: center; }
|
||||
.equation-container {
|
||||
display: table;
|
||||
text-align: center;
|
||||
width: 100%;
|
||||
}
|
||||
.equation {
|
||||
vertical-align: middle;
|
||||
}
|
||||
.equation-label {
|
||||
display: table-cell;
|
||||
text-align: right;
|
||||
vertical-align: middle;
|
||||
}
|
||||
.inlinetask {
|
||||
padding: 10px;
|
||||
border: 2px solid gray;
|
||||
margin: 10px;
|
||||
background: #ffffcc;
|
||||
}
|
||||
#org-div-home-and-up
|
||||
{ text-align: right; font-size: 70%; white-space: nowrap; }
|
||||
textarea { overflow-x: auto; }
|
||||
.linenr { font-size: smaller }
|
||||
.code-highlighted { background-color: #ffff00; }
|
||||
.org-info-js_info-navigation { border-style: none; }
|
||||
#org-info-js_console-label
|
||||
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
|
||||
.org-info-js_search-highlight
|
||||
{ background-color: #ffff00; color: #000000; font-weight: bold; }
|
||||
.org-svg { width: 90%; }
|
||||
/*]]>*/-->
|
||||
</style>
|
||||
<meta name="author" content="Thomas Dehaeze" />
|
||||
<link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
|
||||
<link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
||||
<script src="../js/jquery.min.js"></script>
|
||||
<script src="../js/bootstrap.min.js"></script>
|
||||
<script src="../js/jquery.stickytableheaders.min.js"></script>
|
||||
<script src="../js/readtheorg.js"></script>
|
||||
<script type="text/javascript">
|
||||
// @license magnet:?xt=urn:btih:1f739d935676111cfff4b4693e3816e664797050&dn=gpl-3.0.txt GPL-v3-or-Later
|
||||
<!--/*--><![CDATA[/*><!--*/
|
||||
function CodeHighlightOn(elem, id)
|
||||
{
|
||||
var target = document.getElementById(id);
|
||||
if(null != target) {
|
||||
elem.cacheClassElem = elem.className;
|
||||
elem.cacheClassTarget = target.className;
|
||||
target.className = "code-highlighted";
|
||||
elem.className = "code-highlighted";
|
||||
}
|
||||
}
|
||||
function CodeHighlightOff(elem, id)
|
||||
{
|
||||
var target = document.getElementById(id);
|
||||
if(elem.cacheClassElem)
|
||||
elem.className = elem.cacheClassElem;
|
||||
if(elem.cacheClassTarget)
|
||||
target.className = elem.cacheClassTarget;
|
||||
}
|
||||
/*]]>*///-->
|
||||
// @license-end
|
||||
</script>
|
||||
<script>MathJax = {
|
||||
tex: {
|
||||
tags: 'ams',
|
||||
macros: {bm: ["\\boldsymbol{#1}",1],}
|
||||
}
|
||||
};
|
||||
</script>
|
||||
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
</head>
|
||||
<body>
|
||||
<div id="org-div-home-and-up">
|
||||
@ -232,11 +30,599 @@
|
||||
<a accesskey="H" href="../index.html"> HOME </a>
|
||||
</div><div id="content">
|
||||
<h1 class="title">Matlab Computation</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#org2941be5">1. System Description and Analysis</a>
|
||||
<ul>
|
||||
<li><a href="#org4222b45">1.1. System description</a></li>
|
||||
<li><a href="#org80f8141">1.2. Equations</a></li>
|
||||
<li><a href="#orgbb90994">1.3. Numerical Values</a></li>
|
||||
<li><a href="#org3d04be0">1.4. Campbell Diagram</a></li>
|
||||
<li><a href="#org8144360">1.5. Simscape Model</a></li>
|
||||
<li><a href="#orga371e09">1.6. Comparison with the model</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org912df6c">2. Integral Force Feedback</a>
|
||||
<ul>
|
||||
<li><a href="#orge201c80">2.1. Numerical Values</a></li>
|
||||
<li><a href="#orgbc26950">2.2. Equations</a></li>
|
||||
<li><a href="#org92d4b18">2.3. Poles and Zeros</a></li>
|
||||
<li><a href="#orgbb768e3">2.4. Simscape Model</a></li>
|
||||
<li><a href="#orgdf8d677">2.5. IFF Plant</a></li>
|
||||
<li><a href="#org3f264f4">2.6. Loop Gain</a></li>
|
||||
<li><a href="#org7c25fbe">2.7. Root Locus</a></li>
|
||||
<li><a href="#org82271cf">2.8. Modified IFF</a>
|
||||
<ul>
|
||||
<li><a href="#org60bb927">2.8.1. Control Law</a></li>
|
||||
<li><a href="#org6850379">2.8.2. Loop Gain</a></li>
|
||||
<li><a href="#org7314eea">2.8.3. Root Locus</a></li>
|
||||
<li><a href="#orgb4641d2">2.8.4. Optimal Gain</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgbdc5c77">3. Direct Velocity Feedback</a>
|
||||
<ul>
|
||||
<li><a href="#org3f7448e">3.1. Equations</a></li>
|
||||
<li><a href="#org84263dc">3.2. Numerical Values</a></li>
|
||||
<li><a href="#orgbdad8de">3.3. Simscape Model</a></li>
|
||||
<li><a href="#orge253615">3.4. DVF Plant</a></li>
|
||||
<li><a href="#orgd61ece4">3.5. Loop Gain</a></li>
|
||||
<li><a href="#orgce2b090">3.6. Root Locus</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Notations:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>\(k\): Actuator’s Stiffness [N/m]</li>
|
||||
<li>\(c\): Actuator’s Damping [N/(m/s)]</li>
|
||||
<li>\(m\): Payload’s mass [kg]</li>
|
||||
<li>\(\omega_0 = \sqrt{\frac{k}{m}}\): Resonance of the (non-rotating) mass-spring system [rad/s]</li>
|
||||
<li>\(\Omega = \dot{\theta}\): rotation speed [rad/s]</li>
|
||||
</ul>
|
||||
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
|
||||
<colgroup>
|
||||
<col class="org-left" />
|
||||
|
||||
<col class="org-left" />
|
||||
|
||||
<col class="org-left" />
|
||||
|
||||
<col class="org-left" />
|
||||
</colgroup>
|
||||
<thead>
|
||||
<tr>
|
||||
<th scope="col" class="org-left"> </th>
|
||||
<th scope="col" class="org-left">Mathematical Notation</th>
|
||||
<th scope="col" class="org-left">Matlab</th>
|
||||
<th scope="col" class="org-left">Unit</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-left">Actuator Stiffness</td>
|
||||
<td class="org-left">\(k\)</td>
|
||||
<td class="org-left"><code>k</code></td>
|
||||
<td class="org-left">N/m</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Actuator Damping</td>
|
||||
<td class="org-left">\(c\)</td>
|
||||
<td class="org-left"><code>c</code></td>
|
||||
<td class="org-left">N/(m/s)</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<div id="outline-container-org2941be5" class="outline-2">
|
||||
<h2 id="org2941be5"><span class="section-number-2">1</span> System Description and Analysis</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
<a id="org72741bf"></a>
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4222b45" class="outline-3">
|
||||
<h3 id="org4222b45"><span class="section-number-3">1.1</span> System description</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
The system consists of one 2 degree of freedom translation stage on top of a spindle (figure <a href="#org3ee83a5">1</a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<a href="figs/rotating_xy_platform.pdf">figs/rotating_xy_platform.pdf</a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The control inputs are the forces applied by the actuators of the translation stage (\(F_u\) and \(F_v\)).
|
||||
As the translation stage is rotating around the Z axis due to the spindle, the forces are applied along \(u\) and \(v\).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The measurement is either the \(x-y\) displacement of the object located on top of the translation stage or the \(u-v\) displacement of the sample with respect to a fixed reference frame.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org80f8141" class="outline-3">
|
||||
<h3 id="org80f8141"><span class="section-number-3">1.2</span> Equations</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<p>
|
||||
Based on the Figure <a href="#org3ee83a5">1</a>.
|
||||
</p>
|
||||
|
||||
\begin{equation}
|
||||
\begin{bmatrix} d_u \\ d_v \end{bmatrix} =
|
||||
\frac{\frac{1}{k}}{\left( \frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \right)^2 + \left( 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \right)^2}
|
||||
\begin{bmatrix}
|
||||
\frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} & 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \\
|
||||
-2 \frac{\Omega}{\omega_0}\frac{s}{\omega_0} & \frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \\
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
\end{equation}
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbb90994" class="outline-3">
|
||||
<h3 id="orgbb90994"><span class="section-number-3">1.3</span> Numerical Values</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">k = 2;
|
||||
m = 1;
|
||||
c = 0.05;
|
||||
xi = c/(2*sqrt(k*m));
|
||||
|
||||
w0 = sqrt(k/m);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3d04be0" class="outline-3">
|
||||
<h3 id="org3d04be0"><span class="section-number-3">1.4</span> Campbell Diagram</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<p>
|
||||
Compute the poles
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">wrs = linspace(0, 2, 51); % [rad/s]
|
||||
|
||||
polesvc = zeros(4, length(wrs));
|
||||
|
||||
for i = 1:length(wrs)
|
||||
wr = wrs(i);
|
||||
polei = pole(1/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wrs(i)^2)/(w0^2))^2 + (2*wrs(i)*s/(w0^2))^2));
|
||||
[~, i_sort] = sort(imag(polei));
|
||||
polesvc(:, i) = polei(i_sort);
|
||||
end
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8144360" class="outline-3">
|
||||
<h3 id="org8144360"><span class="section-number-3">1.5</span> Simscape Model</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">open('rotating_frame.slx');
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">k = 2;
|
||||
m = 1;
|
||||
c = 0.05;
|
||||
xi = c/(2*sqrt(k*m));
|
||||
|
||||
w0 = sqrt(k/m);
|
||||
wr = 0.1;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">%% Name of the Simulink File
|
||||
mdl = 'rotating_frame';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fu'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Fv'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Tuv'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Tuv'], 2, 'openoutput'); io_i = io_i + 1;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">G = linearize(mdl, io, 0);
|
||||
|
||||
%% Input/Output definition
|
||||
G.InputName = {'Fu', 'Fv'};
|
||||
G.OutputName = {'du', 'dv'};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga371e09" class="outline-3">
|
||||
<h3 id="orga371e09"><span class="section-number-3">1.6</span> Comparison with the model</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ga = (1/k)/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2))^2 + (2*wr*s/(w0^2))^2) * ...
|
||||
[(s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2), 2*wr*s/(w0^2) ; ...
|
||||
-2*wr*s/(w0^2), (s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2)];
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">figure; bode(G, 'k-', Ga, 'r--')
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org912df6c" class="outline-2">
|
||||
<h2 id="org912df6c"><span class="section-number-2">2</span> Integral Force Feedback</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
</div>
|
||||
<div id="outline-container-orge201c80" class="outline-3">
|
||||
<h3 id="orge201c80"><span class="section-number-3">2.1</span> Numerical Values</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">k = 1;
|
||||
m = 1;
|
||||
xi = 0.01;
|
||||
c = 2*xi*sqrt(k*m);
|
||||
w0 = sqrt(k/m);
|
||||
wr = 0.1*w0;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbc26950" class="outline-3">
|
||||
<h3 id="orgbc26950"><span class="section-number-3">2.2</span> Equations</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
The sensed forces are equal to:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\begin{bmatrix} F_{um} \\ F_{vm} \end{bmatrix} =
|
||||
\begin{bmatrix}
|
||||
1 & 0 \\
|
||||
0 & 1
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix} - (c s + k)
|
||||
\begin{bmatrix} d_u \\ d_v \end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
<div class="important">
|
||||
\begin{equation}
|
||||
\begin{bmatrix} F_{um} \\ F_{vm} \end{bmatrix} =
|
||||
\frac{1}{\left( \frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \right)^2 + \left( 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \right)^2}
|
||||
\begin{bmatrix}
|
||||
(\frac{s^2}{{\omega_0}^2} - \frac{\Omega^2}{{\omega_0}^2}) (\frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2}) + (2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0})^2 & - (2 \xi \frac{s}{\omega_0} + 1) 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \\
|
||||
(2 \xi \frac{s}{\omega_0} + 1) 2 \frac{\Omega}{\omega_0}\frac{s}{\omega_0} & (\frac{s^2}{{\omega_0}^2} - \frac{\Omega^2}{{\omega_0}^2}) (\frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2}) + (2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0})^2 \\
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Giffa = 1/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2))^2 + (2*wr*s/(w0^2))^2) * ...
|
||||
[(s^2/w0^2 - wr^2/w0^2)*((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2)) + (2*wr*s/(w0^2))^2, - (2*xi*s/w0 + 1)*2*wr*s/(w0^2) ; ...
|
||||
(2*xi*s/w0 + 1)*2*wr*s/(w0^2), (s^2/w0^2 - wr^2/w0^2)*((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2))+ (2*wr*s/(w0^2))^2];
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org92d4b18" class="outline-3">
|
||||
<h3 id="org92d4b18"><span class="section-number-3">2.3</span> Poles and Zeros</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">syms wr w0 xi positive
|
||||
assumealso(w0 > wr)
|
||||
syms x
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">z = (x^2/w0^2 - wr^2/w0^2)*((x^2)/(w0^2) + 1 - (wr^2)/(w0^2)) + (2*wr*x/(w0^2))^2 == 0
|
||||
p = ((x^2)/(w0^2) + 1 - (wr^2)/(w0^2))^2 + (2*wr*x/(w0^2))^2 == 0
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">solve(p, x)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">solve(z, x)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The zeros are the roots of:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\left( \frac{s^2}{{\omega_0}^2} - \frac{\Omega^2}{{\omega_0}^2} \right) \left( \frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \right) + \left( 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \right)^2 = 0
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
Poles (without damping)
|
||||
</p>
|
||||
\begin{equation}
|
||||
\left(\begin{array}{c} -w_{0}\,1{}\mathrm{i}-\mathrm{wr}\,1{}\mathrm{i}\\ -w_{0}\,1{}\mathrm{i}+\mathrm{wr}\,1{}\mathrm{i}\\ w_{0}\,1{}\mathrm{i}-\mathrm{wr}\,1{}\mathrm{i}\\ w_{0}\,1{}\mathrm{i}+\mathrm{wr}\,1{}\mathrm{i} \end{array}\right)
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
Zeros (without damping)
|
||||
</p>
|
||||
\begin{equation}
|
||||
\left(\begin{array}{c} -\sqrt{-\frac{w_{0}\,\sqrt{{w_{0}}^2+8\,{\mathrm{wr}}^2}}{2}-\frac{{w_{0}}^2}{2}-{\mathrm{wr}}^2}\\ -\sqrt{\frac{w_{0}\,\sqrt{{w_{0}}^2+8\,{\mathrm{wr}}^2}}{2}-\frac{{w_{0}}^2}{2}-{\mathrm{wr}}^2}\\ \sqrt{-\frac{w_{0}\,\sqrt{{w_{0}}^2+8\,{\mathrm{wr}}^2}}{2}-\frac{{w_{0}}^2}{2}-{\mathrm{wr}}^2}\\ \sqrt{\frac{w_{0}\,\sqrt{{w_{0}}^2+8\,{\mathrm{wr}}^2}}{2}-\frac{{w_{0}}^2}{2}-{\mathrm{wr}}^2} \end{array}\right)
|
||||
\end{equation}
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbb768e3" class="outline-3">
|
||||
<h3 id="orgbb768e3"><span class="section-number-3">2.4</span> Simscape Model</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">%% Name of the Simulink File
|
||||
mdl = 'rotating_frame';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fu'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Fv'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Tuv'], 5, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Tuv'], 6, 'openoutput'); io_i = io_i + 1;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Giff = linearize(mdl, io, 0);
|
||||
|
||||
%% Input/Output definition
|
||||
Giff.InputName = {'Fu', 'Fv'};
|
||||
Giff.OutputName = {'Fmu', 'Fmv'};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">figure; bode(Giff, Giffa)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdf8d677" class="outline-3">
|
||||
<h3 id="orgdf8d677"><span class="section-number-3">2.5</span> IFF Plant</h3>
|
||||
</div>
|
||||
<div id="outline-container-org3f264f4" class="outline-3">
|
||||
<h3 id="org3f264f4"><span class="section-number-3">2.6</span> Loop Gain</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<p>
|
||||
Let’s take \(\Omega = \frac{\omega_0}{10}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">ws = 0.1*w0;
|
||||
G_iff = 1/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (ws^2)/(w0^2))^2 + (2*ws*s/(w0^2))^2) * ...
|
||||
[(s^2/w0^2 - ws^2/w0^2)*((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (ws^2)/(w0^2)) + (2*ws*s/(w0^2))^2, - (2*xi*s/w0 + 1)*2*ws*s/(w0^2) ; ...
|
||||
(2*xi*s/w0 + 1)*2*ws*s/(w0^2), (s^2/w0^2 - ws^2/w0^2)*((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (ws^2)/(w0^2))+ (2*ws*s/(w0^2))^2];
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7c25fbe" class="outline-3">
|
||||
<h3 id="org7c25fbe"><span class="section-number-3">2.7</span> Root Locus</h3>
|
||||
</div>
|
||||
<div id="outline-container-org82271cf" class="outline-3">
|
||||
<h3 id="org82271cf"><span class="section-number-3">2.8</span> Modified IFF</h3>
|
||||
<div class="outline-text-3" id="text-2-8">
|
||||
</div>
|
||||
<div id="outline-container-org60bb927" class="outline-4">
|
||||
<h4 id="org60bb927"><span class="section-number-4">2.8.1</span> Control Law</h4>
|
||||
<div class="outline-text-4" id="text-2-8-1">
|
||||
<p>
|
||||
Let’s take the integral feedback controller as a low pass filter (pseudo integrator):
|
||||
</p>
|
||||
\begin{equation}
|
||||
K_{\text{IFF}} = \begin{bmatrix}
|
||||
g\frac{\omega_i}{\omega_i + s} & 0 \\
|
||||
0 & g\frac{\omega_i}{\omega_i + s}
|
||||
\end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">xi = 0.005;
|
||||
w0 = 1;
|
||||
ws = 0.1*w0;
|
||||
|
||||
G_iff = 1/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (ws^2)/(w0^2))^2 + (2*ws*s/(w0^2))^2) * ...
|
||||
[(s^2/w0^2 - ws^2/w0^2)*((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (ws^2)/(w0^2)) + (2*ws*s/(w0^2))^2, - (2*xi*s/w0 + 1)*2*ws*s/(w0^2) ; ...
|
||||
(2*xi*s/w0 + 1)*2*ws*s/(w0^2), (s^2/w0^2 - ws^2/w0^2)*((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (ws^2)/(w0^2))+ (2*ws*s/(w0^2))^2];
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">g = 100;
|
||||
wi = ws;
|
||||
|
||||
K_iff = (g/(1+s/wi))*eye(2);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6850379" class="outline-4">
|
||||
<h4 id="org6850379"><span class="section-number-4">2.8.2</span> Loop Gain</h4>
|
||||
</div>
|
||||
<div id="outline-container-org7314eea" class="outline-4">
|
||||
<h4 id="org7314eea"><span class="section-number-4">2.8.3</span> Root Locus</h4>
|
||||
</div>
|
||||
<div id="outline-container-orgb4641d2" class="outline-4">
|
||||
<h4 id="orgb4641d2"><span class="section-number-4">2.8.4</span> Optimal Gain</h4>
|
||||
<div class="outline-text-4" id="text-2-8-4">
|
||||
<p>
|
||||
The DC gain for Giff is (for \(\Omega < \omega_0\)):
|
||||
</p>
|
||||
\begin{equation}
|
||||
G_{\text{IFF}}(\omega = 0) = \frac{1}{1 - \frac{{\omega_0}^2}{\Omega^2}} \begin{bmatrix}
|
||||
1 & 0 \\
|
||||
0 & 1
|
||||
\end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
The maximum gain where is system is still stable is
|
||||
</p>
|
||||
\begin{equation}
|
||||
g_\text{max} = \frac{{\omega_0}^2}{\Omega^2} - 1
|
||||
\end{equation}
|
||||
|
||||
|
||||
<p>
|
||||
Let’s find the gain that maximize the simultaneous damping of the two modes.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">K_opt = (opt_gain/(1+s/wi))*eye(2);
|
||||
|
||||
G_cl = feedback(G_iff, K_opt);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbdc5c77" class="outline-2">
|
||||
<h2 id="orgbdc5c77"><span class="section-number-2">3</span> Direct Velocity Feedback</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
</div>
|
||||
<div id="outline-container-org3f7448e" class="outline-3">
|
||||
<h3 id="org3f7448e"><span class="section-number-3">3.1</span> Equations</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
The sensed relative velocity are equal to:
|
||||
</p>
|
||||
|
||||
<div class="important">
|
||||
\begin{equation}
|
||||
\begin{bmatrix} \dot{d}_u \\ \dot{d}_v \end{bmatrix} =
|
||||
\frac{s \frac{1}{k}}{\left( \frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \right)^2 + \left( 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \right)^2}
|
||||
\begin{bmatrix}
|
||||
\frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} & 2 \frac{\Omega}{\omega_0} \frac{s}{\omega_0} \\
|
||||
-2 \frac{\Omega}{\omega_0}\frac{s}{\omega_0} & \frac{s^2}{{\omega_0}^2} + 2 \xi \frac{s}{\omega_0} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \\
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org84263dc" class="outline-3">
|
||||
<h3 id="org84263dc"><span class="section-number-3">3.2</span> Numerical Values</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">k = 1;
|
||||
m = 1;
|
||||
c = 0.05;
|
||||
xi = c/(2*sqrt(k*m));
|
||||
|
||||
w0 = sqrt(k/m);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ga = (s/k)/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2))^2 + (2*wr*s/(w0^2))^2) * ...
|
||||
[(s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2), 2*wr*s/(w0^2) ; ...
|
||||
-2*wr*s/(w0^2), (s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2)];
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbdad8de" class="outline-3">
|
||||
<h3 id="orgbdad8de"><span class="section-number-3">3.3</span> Simscape Model</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">%% Name of the Simulink File
|
||||
mdl = 'rotating_frame';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fu'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Fv'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Tuv'], 3, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Tuv'], 4, 'openoutput'); io_i = io_i + 1;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">G = linearize(mdl, io, 0);
|
||||
|
||||
%% Input/Output definition
|
||||
G.InputName = {'Fu', 'Fv'};
|
||||
G.OutputName = {'Vu', 'Vv'};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge253615" class="outline-3">
|
||||
<h3 id="orge253615"><span class="section-number-3">3.4</span> DVF Plant</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">figure; bode(G, Ga)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd61ece4" class="outline-3">
|
||||
<h3 id="orgd61ece4"><span class="section-number-3">3.5</span> Loop Gain</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<p>
|
||||
Let’s take \(\Omega = \frac{\omega_0}{10}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">ws = 0.1*w0;
|
||||
G_dvf = (s/k)/(((s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2))^2 + (2*wr*s/(w0^2))^2) * ...
|
||||
[(s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2), 2*wr*s/(w0^2) ; ...
|
||||
-2*wr*s/(w0^2), (s^2)/(w0^2) + 2*xi*s/w0 + 1 - (wr^2)/(w0^2)];
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgce2b090" class="outline-3">
|
||||
<h3 id="orgce2b090"><span class="section-number-3">3.6</span> Root Locus</h3>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-03-16 lun. 10:52</p>
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
||||
<p class="date">Created: 2020-06-10 mer. 10:17</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
1545
matlab/index.org
1545
matlab/index.org
File diff suppressed because it is too large
Load Diff
BIN
matlab/matlab/rotating_frame.slx
Normal file
BIN
matlab/matlab/rotating_frame.slx
Normal file
Binary file not shown.
BIN
matlab/rotating_frame.slxc
Normal file
BIN
matlab/rotating_frame.slxc
Normal file
Binary file not shown.
BIN
matlab/slprj/sim/varcache/rotating_frame/checksumOfCache.mat
Normal file
BIN
matlab/slprj/sim/varcache/rotating_frame/checksumOfCache.mat
Normal file
Binary file not shown.
@ -0,0 +1,6 @@
|
||||
<?xml version="1.0" encoding="UTF-8"?>
|
||||
<MF0 version="1.1" packageUris="http://schema.mathworks.com/mf0/SlCache/19700101">
|
||||
<slcache.FileAttributes type="slcache.FileAttributes" uuid="15bc2eb6-a155-4074-be73-5774ec44e8b6">
|
||||
<checksum>VGJCKM9/+mTYcitIBBt14A==</checksum>
|
||||
</slcache.FileAttributes>
|
||||
</MF0>
|
||||
BIN
matlab/slprj/sim/varcache/rotating_frame/varInfo.mat
Normal file
BIN
matlab/slprj/sim/varcache/rotating_frame/varInfo.mat
Normal file
Binary file not shown.
@ -3,13 +3,13 @@
|
||||
(lambda ()
|
||||
(TeX-add-to-alist 'LaTeX-provided-package-options
|
||||
'(("inputenc" "utf8") ("fontenc" "T1") ("ulem" "normalem") ("tcolorbox" "most") ("babel" "USenglish" "english")))
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "href")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperref")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperimage")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperbaseurl")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "nolinkurl")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "url")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "path")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "url")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "nolinkurl")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperbaseurl")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperimage")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperref")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-braces-local "href")
|
||||
(add-to-list 'LaTeX-verbatim-macros-with-delims-local "path")
|
||||
(TeX-run-style-hooks
|
||||
"latex2e"
|
||||
@ -42,13 +42,20 @@
|
||||
"import"
|
||||
"babel")
|
||||
(LaTeX-add-labels
|
||||
"sec:org8c48899"
|
||||
"sec:org335669b"
|
||||
"sec:introduction"
|
||||
"sec:org60f23e3"
|
||||
"sec:org8b756e7"
|
||||
"sec:theory"
|
||||
"sec:orgd677659"
|
||||
"sec:orgbf4a596"
|
||||
"fig:rotating_xy_platform"
|
||||
"sec:orgaa8880a"
|
||||
"eq:energy_inertial_frame"
|
||||
"eq:lagrangian_inertial_frame"
|
||||
"sec:org754b644"
|
||||
"sec:org9cbf82a"
|
||||
"sec:org8d24de3"
|
||||
"sec:conclusion"
|
||||
"sec:orgf333899")
|
||||
"sec:orgb252937")
|
||||
(LaTeX-add-bibliographies
|
||||
"ref"))
|
||||
:latex)
|
||||
|
||||
134
paper/paper.org
134
paper/paper.org
@ -58,11 +58,145 @@
|
||||
* Theory
|
||||
<<sec:theory>>
|
||||
|
||||
** Rotating Positioning Stage
|
||||
|
||||
# Description of the system
|
||||
|
||||
- $k$: Actuator's Stiffness [N/m]
|
||||
- $m$: Payload's mass [kg]
|
||||
- $\omega_0 = \sqrt{\frac{k}{m}}$: Resonance of the (non-rotating) mass-spring system [rad/s]
|
||||
- $\omega_r = \dot{\theta}$: rotation speed [rad/s]
|
||||
|
||||
|
||||
#+name: fig:rotating_xy_platform
|
||||
#+caption: Figure caption
|
||||
#+attr_latex: :scale 1
|
||||
[[file:figs/rotating_xy_platform.pdf]]
|
||||
|
||||
|
||||
** Equation of Motion
|
||||
|
||||
Let's express the kinetic energy $T$ and the potential energy $V$ of the mass $m$ (neglecting the rotational energy):
|
||||
#+name: eq:energy_inertial_frame
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
T & = \frac{1}{2} m \left( \dot{x}^2 + \dot{y}^2 \right) \\
|
||||
R & = \frac{1}{2} c \left( \dot{x}^2 + \dot{y}^2 \right) \\
|
||||
V & = \frac{1}{2} k \left( x^2 + y^2 \right)
|
||||
\end{align}
|
||||
\end{subequations}
|
||||
|
||||
The Lagrangian is the kinetic energy minus the potential energy:
|
||||
#+name: eq:lagrangian_inertial_frame
|
||||
\begin{equation}
|
||||
L = T-V = \frac{1}{2} m \left( \dot{x}^2 + \dot{y}^2 \right) - \frac{1}{2} k \left( x^2 + y^2 \right)
|
||||
\end{equation}
|
||||
|
||||
The external forces applied to the mass are:
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
F_{\text{ext}, x} &= F_u \cos{\theta} - F_v \sin{\theta}\\
|
||||
F_{\text{ext}, y} &= F_u \sin{\theta} + F_v \cos{\theta}
|
||||
\end{align}
|
||||
\end{subequations}
|
||||
|
||||
|
||||
From the Lagrange's equations of the second kind eqref:eq:lagrange_second_kind, the equation of motion eqref:eq:eom_mixed is obtained.
|
||||
|
||||
#+name: eq:lagrange_second_kind
|
||||
\begin{equation}
|
||||
\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}_j} \right) = \frac{\partial L}{\partial q_j}
|
||||
\end{equation}
|
||||
|
||||
#+name: eq:eom_mixed
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
m\ddot{x} + kx = F_u \cos{\theta} - F_v \sin{\theta}\\
|
||||
m\ddot{y} + ky = F_u \sin{\theta} + F_v \cos{\theta}
|
||||
\end{align}
|
||||
\end{subequations}
|
||||
|
||||
Performing the change coordinates from $(x, y)$ to $(d_x, d_y, \theta)$:
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
x & = d_u \cos{\theta} - d_v \sin{\theta}\\
|
||||
y & = d_u \sin{\theta} + d_v \cos{\theta}
|
||||
\end{align}
|
||||
\end{subequations}
|
||||
|
||||
Gives
|
||||
#+name: eq:oem_coupled
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
m \ddot{d_u} + (k - m\dot{\theta}^2) d_u &= F_u + 2 m\dot{d_v}\dot{\theta} + m d_v\ddot{\theta} \label{eq:du_coupled} \\
|
||||
m \ddot{d_v} + (k \underbrace{-\ m\dot{\theta}^2}_{\text{Centrif.}}) d_v &= F_v \underbrace{-\ 2 m\dot{d_u}\dot{\theta}}_{\text{Coriolis}} \underbrace{-\ m d_u\ddot{\theta}}_{\text{Euler}} \label{eq:dv_coupled}
|
||||
\end{align}
|
||||
\end{subequations}
|
||||
|
||||
We obtain two differential equations that are coupled through:
|
||||
- *Euler forces*: $m d_v \ddot{\theta}$
|
||||
- *Coriolis forces*: $2 m \dot{d_v} \dot{\theta}$
|
||||
|
||||
Without the coupling terms, each equation is the equation of a one degree of freedom mass-spring system with mass $m$ and stiffness $k- m\dot{\theta}^2$.
|
||||
Thus, the term $- m\dot{\theta}^2$ acts like a negative stiffness (due to *centrifugal forces*).
|
||||
|
||||
** Constant Rotating Speed
|
||||
To simplify, let's consider a constant rotating speed $\dot{\theta} = \omega_r$ and thus $\ddot{\theta} = 0$.
|
||||
|
||||
#+NAME: eq:coupledplant
|
||||
\begin{equation}
|
||||
\begin{bmatrix} d_u \\ d_v \end{bmatrix} =
|
||||
\frac{1}{(m s^2 + (k - m{\omega_0}^2))^2 + (2 m {\omega_0} s)^2}
|
||||
\begin{bmatrix}
|
||||
ms^2 + (k-m{\omega_0}^2) & 2 m \omega_0 s \\
|
||||
-2 m \omega_0 s & ms^2 + (k-m{\omega_0}^2) \\
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
#+NAME: eq:coupled_plant
|
||||
\begin{equation}
|
||||
\begin{bmatrix} d_u \\ d_v \end{bmatrix} =
|
||||
\frac{\frac{1}{k}}{\left( \frac{s^2}{{\omega_0}^2} + (1 - \frac{{\omega_r}^2}{{\omega_0}^2}) \right)^2 + \left( 2 \frac{{\omega_r} s}{{\omega_0}^2} \right)^2}
|
||||
\begin{bmatrix}
|
||||
\frac{s^2}{{\omega_0}^2} + 1 - \frac{{\omega_r}^2}{{\omega_0}^2} & 2 \frac{\omega_r s}{{\omega_0}^2} \\
|
||||
-2 \frac{\omega_r s}{{\omega_0}^2} & \frac{s^2}{{\omega_0}^2} + 1 - \frac{{\omega_r}^2}{{\omega_0}^2} \\
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
When the rotation speed is null, the coupling terms are equal to zero and the diagonal terms corresponds to one degree of freedom mass spring system.
|
||||
#+NAME: eq:coupled_plant_no_rot
|
||||
\begin{equation}
|
||||
\begin{bmatrix} d_u \\ d_v \end{bmatrix} =
|
||||
\frac{\frac{1}{k}}{\frac{s^2}{{\omega_0}^2} + 1}
|
||||
\begin{bmatrix}
|
||||
1 & 0 \\
|
||||
0 & 1
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
\end{equation}
|
||||
|
||||
# Campbell Diagram
|
||||
|
||||
When the rotation speed in not null, the resonance frequency is duplicated into two pairs of complex conjugate poles.
|
||||
As the rotation speed increases, one of the two resonant frequency goes to lower frequencies as the other one goes to higher frequencies (Figure [[fig:campbell_diagram]]).
|
||||
|
||||
#+name: fig:campbell_diagram
|
||||
#+caption: Campbell Diagram
|
||||
[[file:figs/campbell_diagram.pdf]]
|
||||
|
||||
# Bode Plots for different ratio wr/w0
|
||||
|
||||
The magnitude of the coupling terms are increasing with the rotation speed.
|
||||
|
||||
|
||||
** Integral Force Feedback
|
||||
|
||||
|
||||
** Direct Velocity Feedback
|
||||
|
||||
|
||||
* Conclusion
|
||||
<<sec:conclusion>>
|
||||
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
% Created 2020-06-08 lun. 11:15
|
||||
% Created 2020-06-08 lun. 11:40
|
||||
% Intended LaTeX compiler: pdflatex
|
||||
\documentclass{ISMA_USD2020}
|
||||
\usepackage[utf8]{inputenc}
|
||||
@ -49,27 +49,56 @@
|
||||
}
|
||||
|
||||
\section{Introduction}
|
||||
\label{sec:orgd787473}
|
||||
\label{sec:org335669b}
|
||||
\label{sec:introduction}
|
||||
|
||||
|
||||
\section{Theory}
|
||||
\label{sec:org808f338}
|
||||
\label{sec:org8b756e7}
|
||||
\label{sec:theory}
|
||||
|
||||
\subsection{Rotating Positioning Stage}
|
||||
\label{sec:orgbf4a596}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/rotating_xy_platform.pdf}
|
||||
\caption{\label{fig:figure_name}Figure caption}
|
||||
\caption{\label{fig:rotating_xy_platform}Figure caption}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Equation of Motion}
|
||||
\label{sec:orgaa8880a}
|
||||
|
||||
Let's express the kinetic energy \(T\) and the potential energy \(V\) of the mass \(m\):
|
||||
\begin{align}
|
||||
\label{eq:energy_inertial_frame}
|
||||
T & = \frac{1}{2} m \left( \dot{x}^2 + \dot{y}^2 \right) \\
|
||||
V & = \frac{1}{2} k \left( x^2 + y^2 \right)
|
||||
\end{align}
|
||||
|
||||
The Lagrangian is the kinetic energy minus the potential energy.
|
||||
\begin{equation}
|
||||
\label{eq:lagrangian_inertial_frame}
|
||||
L = T-V = \frac{1}{2} m \left( \dot{x}^2 + \dot{y}^2 \right) - \frac{1}{2} k \left( x^2 + y^2 \right)
|
||||
\end{equation}
|
||||
|
||||
|
||||
\subsection{Integral Force Feedback}
|
||||
\label{sec:org754b644}
|
||||
|
||||
|
||||
\subsection{Direct Velocity Feedback}
|
||||
\label{sec:org9cbf82a}
|
||||
|
||||
|
||||
\section{Conclusion}
|
||||
\label{sec:orgab2ddd2}
|
||||
\label{sec:org8d24de3}
|
||||
\label{sec:conclusion}
|
||||
|
||||
|
||||
\section{Acknowledgment}
|
||||
\label{sec:orga63f041}
|
||||
\label{sec:orgb252937}
|
||||
|
||||
|
||||
\bibliography{ref}
|
||||
|
||||
Binary file not shown.
Binary file not shown.
|
Before Width: | Height: | Size: 69 KiB After Width: | Height: | Size: 71 KiB |
@ -131,6 +131,9 @@
|
||||
<symbol overflow="visible" id="glyph6-2">
|
||||
<path style="stroke:none;" d="M 2.875 -2.484375 C 2.875 -3.265625 2.765625 -4.46875 2.21875 -5.578125 C 1.625 -6.8125 0.765625 -7.453125 0.671875 -7.453125 C 0.609375 -7.453125 0.5625 -7.40625 0.5625 -7.359375 C 0.5625 -7.328125 0.5625 -7.296875 0.75 -7.125 C 1.734375 -6.140625 2.296875 -4.5625 2.296875 -2.484375 C 2.296875 -0.78125 1.921875 0.96875 0.703125 2.21875 C 0.5625 2.328125 0.5625 2.359375 0.5625 2.390625 C 0.5625 2.4375 0.609375 2.484375 0.671875 2.484375 C 0.765625 2.484375 1.65625 1.8125 2.25 0.546875 C 2.75 -0.546875 2.875 -1.65625 2.875 -2.484375 Z M 2.875 -2.484375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph6-3">
|
||||
<path style="stroke:none;" d="M 6.734375 -1.609375 L 6.484375 -1.609375 C 6.421875 -1.34375 6.390625 -1.125 6.296875 -0.890625 C 6.25 -0.71875 6.21875 -0.640625 5.640625 -0.640625 L 4.84375 -0.640625 C 4.984375 -1.203125 5.28125 -1.671875 5.734375 -2.328125 C 6.203125 -3.046875 6.609375 -3.734375 6.609375 -4.515625 C 6.609375 -5.890625 5.265625 -7 3.59375 -7 C 1.875 -7 0.5625 -5.875 0.5625 -4.515625 C 0.5625 -3.734375 0.96875 -3.046875 1.4375 -2.328125 C 1.875 -1.671875 2.1875 -1.203125 2.3125 -0.640625 L 1.515625 -0.640625 C 0.9375 -0.640625 0.921875 -0.71875 0.859375 -0.875 C 0.78125 -1.109375 0.734375 -1.359375 0.6875 -1.609375 L 0.4375 -1.609375 L 0.765625 0 L 2.359375 0 C 2.578125 0 2.609375 0 2.609375 -0.203125 C 2.609375 -0.90625 2.296875 -1.78125 2.0625 -2.421875 C 1.859375 -2.984375 1.578125 -3.78125 1.578125 -4.515625 C 1.578125 -6.109375 2.671875 -6.78125 3.578125 -6.78125 C 4.53125 -6.78125 5.578125 -6.078125 5.578125 -4.515625 C 5.578125 -3.78125 5.3125 -3.015625 5.03125 -2.203125 C 4.875 -1.78125 4.5625 -0.890625 4.5625 -0.203125 C 4.5625 0 4.59375 0 4.8125 0 L 6.40625 0 Z M 6.734375 -1.609375 "/>
|
||||
</symbol>
|
||||
</g>
|
||||
<clipPath id="clip1">
|
||||
<path d="M 6 0.0585938 L 247.367188 0.0585938 L 247.367188 242 L 6 242 Z M 6 0.0585938 "/>
|
||||
@ -350,5 +353,10 @@
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph6-2" x="125.690727" y="116.547764"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.21357 -0.00146372 C 99.21357 21.773194 92.04549 42.909035 78.896826 60.157103 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.053653 -0.00146221 L 1.609367 1.684941 L 3.088612 0.000405489 L 1.608324 -1.681639 Z M 6.053653 -0.00146221 " transform="matrix(-0.621003,-0.779531,-0.779531,0.621003,213.750386,56.325385)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph6-3" x="215.304364" y="83.663151"/>
|
||||
</g>
|
||||
</g>
|
||||
</svg>
|
||||
|
||||
|
Before Width: | Height: | Size: 63 KiB After Width: | Height: | Size: 65 KiB |
BIN
tikz/figs/rotating_xy_platform_springs.pdf
Normal file
BIN
tikz/figs/rotating_xy_platform_springs.pdf
Normal file
Binary file not shown.
BIN
tikz/figs/rotating_xy_platform_springs.png
Normal file
BIN
tikz/figs/rotating_xy_platform_springs.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 68 KiB |
293
tikz/figs/rotating_xy_platform_springs.svg
Normal file
293
tikz/figs/rotating_xy_platform_springs.svg
Normal file
@ -0,0 +1,293 @@
|
||||
<?xml version="1.0" encoding="UTF-8"?>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="248.182pt" height="246.302pt" viewBox="0 0 248.182 246.302" version="1.2">
|
||||
<defs>
|
||||
<g>
|
||||
<symbol overflow="visible" id="glyph0-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-1">
|
||||
<path style="stroke:none;" d="M 5.75 -3.5625 C 5.734375 -3.609375 5.6875 -3.703125 5.5625 -3.640625 C 5.46875 -3.59375 5.5 -3.53125 5.515625 -3.453125 C 5.71875 -2.9375 5.5625 -2.640625 5.3125 -2.515625 C 5.046875 -2.390625 4.890625 -2.5 4.75 -2.625 C 4.59375 -2.75 4.28125 -3.265625 4.0625 -3.625 C 3.75 -4.09375 3.421875 -4.609375 2.40625 -4.46875 C 3.078125 -5.03125 3.46875 -5.8125 3.171875 -6.453125 C 2.8125 -7.25 1.515625 -7.4375 0.328125 -6.890625 L -2.25 -5.6875 L -2.140625 -5.4375 L -1.953125 -5.515625 C -1.328125 -5.8125 -1.28125 -5.734375 -1.140625 -5.421875 L 0.84375 -1.171875 C 0.984375 -0.875 1.015625 -0.78125 0.390625 -0.484375 L 0.203125 -0.40625 L 0.328125 -0.15625 C 0.6875 -0.359375 1.09375 -0.546875 1.484375 -0.734375 C 1.875 -0.90625 2.28125 -1.09375 2.671875 -1.25 L 2.546875 -1.5 L 2.375 -1.40625 C 1.75 -1.125 1.703125 -1.203125 1.5625 -1.5 L 0.625 -3.515625 L 1.59375 -3.984375 C 2.171875 -4.25 2.578125 -4.046875 2.625 -4.046875 C 3.015625 -3.875 3.0625 -3.734375 3.328125 -3.171875 C 3.59375 -2.625 3.75 -2.265625 4.265625 -2.140625 C 4.796875 -2.015625 5.28125 -2.234375 5.375 -2.28125 C 6.046875 -2.59375 5.84375 -3.375 5.75 -3.5625 Z M 2.34375 -6.0625 C 2.671875 -5.375 2.5625 -4.671875 1.46875 -4.15625 L 0.53125 -3.71875 L -0.4375 -5.796875 C -0.546875 -6.015625 -0.5625 -6.109375 -0.421875 -6.203125 C -0.375 -6.265625 -0.125 -6.375 0.046875 -6.453125 C 0.765625 -6.78125 1.78125 -7.265625 2.34375 -6.0625 Z M 2.34375 -6.0625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-2">
|
||||
<path style="stroke:none;" d="M 3.109375 -3.5625 C 2.625 -4.625 1.390625 -5.0625 0.390625 -4.59375 C -0.640625 -4.109375 -1.046875 -2.875 -0.578125 -1.84375 C -0.09375 -0.8125 1.125 -0.421875 2.109375 -0.890625 C 3.140625 -1.375 3.578125 -2.546875 3.109375 -3.5625 Z M 2.390625 -3.296875 C 2.53125 -3 2.75 -2.53125 2.703125 -2.078125 C 2.65625 -1.59375 2.359375 -1.265625 2.015625 -1.109375 C 1.609375 -0.921875 1.171875 -0.96875 0.84375 -1.1875 C 0.46875 -1.421875 0.265625 -1.875 0.09375 -2.234375 C -0.046875 -2.53125 -0.25 -3 -0.203125 -3.421875 C -0.15625 -3.9375 0.1875 -4.25 0.46875 -4.390625 C 0.9375 -4.609375 1.375 -4.5 1.6875 -4.296875 C 2.03125 -4.046875 2.234375 -3.640625 2.390625 -3.296875 Z M 2.390625 -3.296875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-3">
|
||||
<path style="stroke:none;" d="M 2.3125 -2.296875 L 2.09375 -2.765625 L 1.859375 -2.65625 L 2.0625 -2.21875 C 2.34375 -1.609375 2.234375 -1.203125 1.9375 -1.078125 C 1.390625 -0.828125 1.0625 -1.53125 0.984375 -1.671875 L -0.0625 -3.9375 L 1.125 -4.484375 L 1.015625 -4.734375 L -0.171875 -4.1875 L -0.875 -5.671875 L -1.09375 -5.5625 C -0.78125 -4.875 -0.6875 -3.90625 -1.453125 -3.515625 L -1.359375 -3.328125 L -0.65625 -3.65625 L 0.390625 -1.40625 C 0.8125 -0.5 1.5625 -0.625 1.984375 -0.828125 C 2.546875 -1.078125 2.578125 -1.71875 2.3125 -2.296875 Z M 2.3125 -2.296875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-4">
|
||||
<path style="stroke:none;" d="M 3.671875 -2.59375 L 3.46875 -3.046875 L 3.25 -2.9375 L 3.453125 -2.484375 C 3.5 -2.40625 3.6875 -2 3.40625 -1.875 C 3.109375 -1.734375 2.921875 -2.125 2.875 -2.25 L 2.203125 -3.671875 C 1.984375 -4.140625 1.859375 -4.40625 1.328125 -4.578125 C 0.90625 -4.703125 0.484375 -4.640625 0.0625 -4.4375 C -0.609375 -4.125 -1.015625 -3.515625 -0.78125 -3.015625 C -0.65625 -2.75 -0.421875 -2.6875 -0.21875 -2.796875 C 0 -2.890625 0.078125 -3.140625 -0.015625 -3.34375 C -0.1875 -3.6875 -0.578125 -3.5625 -0.578125 -3.5625 C -0.4375 -3.875 -0.09375 -4.125 0.140625 -4.234375 C 0.5625 -4.421875 1.171875 -4.328125 1.5 -3.625 L 1.625 -3.359375 C 1.203125 -3.140625 0.609375 -2.8125 0.171875 -2.3125 C -0.28125 -1.75 -0.25 -1.25 -0.109375 -0.921875 C 0.203125 -0.25 1.09375 -0.40625 1.640625 -0.671875 C 2.3125 -0.984375 2.40625 -1.5625 2.421875 -1.828125 C 2.625 -1.515625 2.96875 -1.328125 3.328125 -1.5 C 3.53125 -1.59375 3.984375 -1.953125 3.671875 -2.59375 Z M 2.09375 -2.359375 C 2.453125 -1.578125 1.96875 -1.046875 1.609375 -0.875 C 1.234375 -0.703125 0.75 -0.796875 0.546875 -1.21875 C 0.296875 -1.75 0.484375 -2.53125 1.71875 -3.15625 Z M 2.09375 -2.359375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-5">
|
||||
<path style="stroke:none;" d="M 2.046875 -0.953125 L 1.921875 -1.203125 C 1.40625 -0.96875 1.34375 -0.984375 1.203125 -1.296875 L -0.1875 -4.265625 L -1.296875 -3.65625 L -1.1875 -3.40625 C -0.6875 -3.640625 -0.5625 -3.609375 -0.375 -3.21875 L 0.625 -1.046875 C 0.796875 -0.671875 0.703125 -0.640625 0.171875 -0.390625 L 0.296875 -0.140625 C 0.65625 -0.3125 0.8125 -0.421875 1.171875 -0.578125 C 1.296875 -0.640625 1.640625 -0.796875 2.046875 -0.953125 Z M -0.6875 -5.640625 C -0.796875 -5.875 -1.078125 -5.984375 -1.328125 -5.875 C -1.5625 -5.75 -1.671875 -5.46875 -1.5625 -5.234375 C -1.453125 -4.984375 -1.15625 -4.875 -0.921875 -5 C -0.671875 -5.109375 -0.578125 -5.390625 -0.6875 -5.640625 Z M -0.6875 -5.640625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-6">
|
||||
<path style="stroke:none;" d="M 4.4375 -2.0625 L 4.3125 -2.3125 C 3.890625 -2.125 3.6875 -2.03125 3.578125 -2.28125 L 2.859375 -3.828125 C 2.53125 -4.515625 2.4375 -4.734375 2.0625 -4.921875 C 1.78125 -5.046875 1.421875 -5.015625 1 -4.828125 C 0.25 -4.46875 0.1875 -3.75 0.171875 -3.484375 L 0.15625 -3.484375 L -0.21875 -4.265625 L -1.34375 -3.625 L -1.234375 -3.375 C -0.6875 -3.640625 -0.578125 -3.609375 -0.390625 -3.21875 L 0.609375 -1.046875 C 0.78125 -0.671875 0.703125 -0.640625 0.15625 -0.375 L 0.28125 -0.125 C 0.671875 -0.328125 0.8125 -0.421875 1.1875 -0.59375 C 1.578125 -0.78125 1.703125 -0.8125 2.125 -0.984375 L 2 -1.234375 C 1.46875 -1 1.375 -0.953125 1.203125 -1.328125 L 0.515625 -2.796875 C 0.125 -3.65625 0.53125 -4.375 1.046875 -4.609375 C 1.515625 -4.84375 1.828125 -4.46875 2.0625 -4 L 2.921875 -2.125 C 3.09375 -1.75 2.984375 -1.703125 2.453125 -1.453125 L 2.578125 -1.203125 C 2.953125 -1.390625 3.09375 -1.484375 3.5 -1.671875 C 3.875 -1.84375 4 -1.890625 4.4375 -2.0625 Z M 4.4375 -2.0625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-7">
|
||||
<path style="stroke:none;" d="M 2.5 -5.140625 C 2.4375 -5.28125 2.21875 -5.5 1.90625 -5.359375 C 1.671875 -5.25 1.328125 -4.984375 1.1875 -4.546875 C 0.875 -4.640625 0.515625 -4.59375 0.171875 -4.4375 C -0.59375 -4.078125 -0.90625 -3.265625 -0.609375 -2.625 C -0.421875 -2.21875 -0.046875 -2.03125 0.140625 -1.96875 C 0.125 -1.9375 0.03125 -1.5625 0.203125 -1.1875 C 0.34375 -0.90625 0.59375 -0.671875 0.90625 -0.640625 C 0.53125 -0.296875 0.359375 0.140625 0.53125 0.53125 C 0.796875 1.09375 1.8125 1.1875 2.84375 0.703125 C 3.859375 0.234375 4.5 -0.578125 4.203125 -1.21875 C 4.046875 -1.546875 3.734375 -1.828125 3.34375 -1.890625 C 2.765625 -1.953125 2.296875 -1.734375 1.515625 -1.375 C 1.359375 -1.296875 1.109375 -1.1875 1.015625 -1.15625 C 0.765625 -1.09375 0.5 -1.25 0.375 -1.515625 C 0.328125 -1.640625 0.3125 -1.78125 0.34375 -1.90625 C 0.609375 -1.875 0.90625 -1.890625 1.28125 -2.0625 C 2.046875 -2.421875 2.375 -3.234375 2.078125 -3.875 C 1.890625 -4.28125 1.53125 -4.4375 1.375 -4.5 C 1.5625 -4.953125 1.9375 -5.125 2.046875 -5.171875 C 2.015625 -5.125 1.96875 -5.0625 2.03125 -4.90625 C 2.0625 -4.828125 2.203125 -4.703125 2.390625 -4.78125 C 2.5 -4.84375 2.578125 -4.96875 2.5 -5.140625 Z M 1.453125 -3.578125 C 1.53125 -3.390625 1.90625 -2.609375 1.1875 -2.28125 C 0.46875 -1.9375 0.09375 -2.71875 0.015625 -2.90625 C -0.09375 -3.125 -0.203125 -3.421875 -0.15625 -3.671875 C -0.125 -3.890625 0.046875 -4.109375 0.28125 -4.21875 C 1 -4.546875 1.359375 -3.765625 1.453125 -3.578125 Z M 3.765625 -1 C 3.984375 -0.53125 3.515625 0.109375 2.75 0.46875 C 1.953125 0.84375 1.1875 0.75 0.984375 0.296875 C 0.921875 0.171875 0.75 -0.40625 1.453125 -0.734375 L 2.1875 -1.078125 C 2.453125 -1.203125 3.453125 -1.65625 3.765625 -1 Z M 3.765625 -1 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-8">
|
||||
<path style="stroke:none;" d="M 3.453125 -3.4375 C 3.25 -3.890625 2.90625 -4.1875 2.609375 -4.328125 C 2.03125 -4.609375 1.625 -4.53125 1.046875 -4.40625 L 0.265625 -4.25 C -0.46875 -4.09375 -0.90625 -4.515625 -1.078125 -4.875 C -1.328125 -5.421875 -1.140625 -6.140625 -0.46875 -6.46875 C 0.578125 -6.953125 1.375 -6.359375 1.875 -5.609375 C 1.953125 -5.453125 1.984375 -5.4375 2.09375 -5.484375 C 2.203125 -5.53125 2.171875 -5.578125 2.09375 -5.75 L 1.359375 -7.3125 C 1.28125 -7.484375 1.265625 -7.53125 1.171875 -7.484375 C 1.109375 -7.453125 1.09375 -7.453125 1.09375 -7.328125 C 1.046875 -7.140625 1.09375 -7.28125 1.015625 -6.734375 C 0.796875 -6.84375 0.1875 -7.03125 -0.5625 -6.6875 C -1.515625 -6.234375 -1.84375 -5.1875 -1.46875 -4.375 C -1.171875 -3.734375 -0.625 -3.515625 -0.5625 -3.5 C -0.03125 -3.3125 0.140625 -3.328125 1.1875 -3.5625 C 1.9375 -3.71875 2.03125 -3.734375 2.421875 -3.578125 C 2.421875 -3.578125 2.84375 -3.421875 3.0625 -2.9375 C 3.328125 -2.390625 3.21875 -1.59375 2.46875 -1.25 C 1.859375 -0.953125 0.59375 -0.671875 -0.09375 -2 C -0.140625 -2.09375 -0.171875 -2.15625 -0.28125 -2.109375 C -0.390625 -2.0625 -0.359375 -1.984375 -0.28125 -1.828125 L 0.453125 -0.265625 C 0.515625 -0.109375 0.546875 -0.03125 0.625 -0.0625 C 0.6875 -0.09375 0.703125 -0.125 0.71875 -0.234375 C 0.75 -0.4375 0.71875 -0.296875 0.8125 -0.828125 C 1.515625 -0.59375 2.1875 -0.796875 2.578125 -0.984375 C 3.578125 -1.4375 3.859375 -2.578125 3.453125 -3.4375 Z M 3.453125 -3.4375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-9">
|
||||
<path style="stroke:none;" d="M 3 -2.578125 C 2.984375 -2.625 2.90625 -2.671875 2.84375 -2.640625 C 2.765625 -2.609375 2.78125 -2.53125 2.78125 -2.484375 C 2.875 -1.53125 2.171875 -1.1875 2.046875 -1.125 C 1.671875 -0.953125 1.21875 -1 0.90625 -1.203125 C 0.453125 -1.46875 0.234375 -1.953125 0.078125 -2.296875 L 2.390625 -3.375 C 2.546875 -3.453125 2.59375 -3.46875 2.515625 -3.640625 C 2.125 -4.46875 1.3125 -5.03125 0.28125 -4.546875 C -0.703125 -4.09375 -1.0625 -2.90625 -0.59375 -1.890625 C -0.109375 -0.828125 1.140625 -0.4375 2.109375 -0.890625 C 3.109375 -1.34375 3.09375 -2.390625 3 -2.578125 Z M 1.953125 -3.40625 L -0.015625 -2.484375 C -0.515625 -3.765625 0.140625 -4.234375 0.375 -4.34375 C 0.8125 -4.546875 1.46875 -4.453125 1.953125 -3.40625 Z M 1.953125 -3.40625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-10">
|
||||
<path style="stroke:none;" d="M 6.03125 -2.8125 L 5.90625 -3.0625 L 5.765625 -3 C 5.375 -2.8125 5.171875 -2.75 4.875 -2.921875 L 1.890625 -4.671875 L 2.265625 -6.859375 C 2.40625 -7.53125 3.046875 -7.84375 3.203125 -7.921875 L 3.09375 -8.171875 C 2.703125 -7.96875 2.40625 -7.828125 2.203125 -7.734375 L 1.171875 -7.28125 L 1.28125 -7.03125 C 1.640625 -7.171875 1.890625 -7.046875 1.953125 -6.890625 C 1.984375 -6.828125 1.984375 -6.75 1.96875 -6.640625 L 1.625 -4.828125 L -0.171875 -5.890625 C -0.21875 -5.890625 -0.28125 -5.9375 -0.296875 -6 C -0.34375 -6.078125 -0.265625 -6.28125 0.078125 -6.46875 L -0.03125 -6.71875 C -0.34375 -6.546875 -0.828125 -6.328125 -1.1875 -6.15625 L -2.25 -5.6875 L -2.140625 -5.4375 L -2 -5.5 C -1.453125 -5.75 -1.328125 -5.703125 -1.046875 -5.515625 L 1.5 -4.046875 L 1.046875 -1.4375 C 0.90625 -0.734375 0.265625 -0.4375 0.09375 -0.34375 L 0.21875 -0.09375 C 0.609375 -0.328125 0.921875 -0.46875 1.109375 -0.546875 L 2.125 -0.984375 L 2 -1.234375 C 1.625 -1.078125 1.40625 -1.265625 1.359375 -1.375 C 1.3125 -1.46875 1.328125 -1.546875 1.34375 -1.640625 L 1.765625 -3.875 L 3.96875 -2.59375 C 4.0625 -2.53125 4.0625 -2.53125 4.078125 -2.5 C 4.125 -2.390625 4.015625 -2.171875 3.6875 -2.03125 L 3.8125 -1.78125 C 4.15625 -1.984375 4.59375 -2.171875 4.953125 -2.34375 Z M 6.03125 -2.8125 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-11">
|
||||
<path style="stroke:none;" d="M 1.609375 -2.578125 L 1.375 -3.078125 L -0.859375 -2.046875 L -0.625 -1.546875 Z M 1.609375 -2.578125 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-12">
|
||||
<path style="stroke:none;" d="M 3.65625 -8.140625 L 3.546875 -8.390625 C 3.28125 -8.25 3.046875 -8.125 2.78125 -8 L 1.84375 -7.59375 L 1.953125 -7.34375 C 2.25 -7.484375 2.46875 -7.421875 2.5625 -7.234375 C 2.609375 -7.140625 2.59375 -7.09375 2.5625 -6.953125 L 2.21875 -4.125 L -0.421875 -5.78125 C -0.5 -5.859375 -0.546875 -5.890625 -0.578125 -5.921875 C -0.65625 -6.109375 -0.375 -6.265625 -0.125 -6.375 L -0.234375 -6.625 C -0.546875 -6.453125 -1.03125 -6.234375 -1.390625 -6.0625 L -2.484375 -5.578125 L -2.375 -5.328125 L -2.234375 -5.390625 C -1.75 -5.625 -1.609375 -5.609375 -1.34375 -5.453125 L 1.75 -3.5 L 2.484375 -1.9375 C 2.625 -1.640625 2.625 -1.53125 2 -1.234375 L 1.8125 -1.15625 L 1.9375 -0.90625 C 2.3125 -1.109375 2.71875 -1.3125 3.09375 -1.484375 C 3.5 -1.671875 3.890625 -1.859375 4.3125 -2 L 4.1875 -2.25 L 4 -2.171875 C 3.375 -1.875 3.3125 -1.96875 3.171875 -2.265625 L 2.4375 -3.828125 L 2.875 -7.09375 C 2.90625 -7.421875 3.046875 -7.828125 3.65625 -8.140625 Z M 3.65625 -8.140625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-13">
|
||||
<path style="stroke:none;" d="M 3.328125 -6.4375 C 2.953125 -7.25 1.78125 -7.5625 0.65625 -7.03125 L -2.25 -5.6875 L -2.140625 -5.4375 L -1.953125 -5.515625 C -1.328125 -5.8125 -1.28125 -5.734375 -1.140625 -5.421875 L 0.84375 -1.171875 C 0.984375 -0.875 1.015625 -0.78125 0.390625 -0.484375 L 0.203125 -0.40625 L 0.328125 -0.15625 C 0.671875 -0.359375 1.125 -0.5625 1.5 -0.734375 C 1.875 -0.90625 2.328125 -1.125 2.703125 -1.265625 L 2.578125 -1.515625 L 2.390625 -1.421875 C 1.765625 -1.140625 1.734375 -1.21875 1.59375 -1.515625 L 0.703125 -3.421875 L 2.046875 -4.046875 C 3.171875 -4.578125 3.6875 -5.671875 3.328125 -6.4375 Z M 2.484375 -6.046875 C 2.65625 -5.703125 3.0625 -4.8125 1.71875 -4.1875 L 0.5625 -3.640625 L -0.4375 -5.796875 C -0.578125 -6.078125 -0.59375 -6.15625 -0.21875 -6.328125 L 0.5625 -6.6875 C 1.890625 -7.3125 2.3125 -6.421875 2.484375 -6.046875 Z M 2.484375 -6.046875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-14">
|
||||
<path style="stroke:none;" d="M 2.6875 -5.21875 L 2.578125 -5.46875 C 2.328125 -5.3125 2.078125 -5.1875 1.96875 -5.140625 C 1.75 -5.046875 1.484375 -4.921875 1.265625 -4.84375 L 1.375 -4.59375 C 1.765625 -4.765625 1.90625 -4.46875 1.90625 -4.4375 C 1.953125 -4.328125 1.953125 -4.234375 1.96875 -4.15625 L 2.03125 -1.84375 L 0.140625 -3.546875 C 0.046875 -3.640625 0.03125 -3.703125 0.03125 -3.703125 C -0.078125 -3.921875 0.1875 -4.046875 0.359375 -4.125 L 0.25 -4.375 L -0.640625 -3.921875 C -0.671875 -3.90625 -1.140625 -3.6875 -1.453125 -3.578125 L -1.34375 -3.328125 C -0.984375 -3.5 -0.8125 -3.5625 -0.625 -3.359375 L 2.0625 -0.96875 L 2.09375 -0.390625 C 2.109375 0.125 2.125 0.78125 1.609375 1.03125 C 1.40625 1.109375 1.21875 1.09375 1.171875 1.078125 C 1.25 1.03125 1.4375 0.875 1.3125 0.59375 C 1.203125 0.390625 0.984375 0.328125 0.8125 0.421875 C 0.609375 0.515625 0.515625 0.703125 0.625 0.90625 C 0.796875 1.28125 1.265625 1.421875 1.6875 1.234375 C 2.203125 0.984375 2.34375 0.34375 2.34375 -0.1875 L 2.203125 -4.28125 C 2.203125 -4.546875 2.203125 -4.953125 2.6875 -5.21875 Z M 2.6875 -5.21875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-15">
|
||||
<path style="stroke:none;" d="M 2.109375 -0.984375 L 1.984375 -1.234375 C 1.46875 -0.984375 1.359375 -0.9375 1.1875 -1.3125 L -1.140625 -6.3125 L -2.28125 -5.671875 L -2.171875 -5.421875 C -1.640625 -5.671875 -1.515625 -5.640625 -1.328125 -5.25 L 0.625 -1.046875 C 0.796875 -0.671875 0.703125 -0.640625 0.171875 -0.390625 L 0.296875 -0.140625 C 0.671875 -0.328125 0.8125 -0.421875 1.1875 -0.59375 C 1.578125 -0.765625 1.71875 -0.8125 2.109375 -0.984375 Z M 2.109375 -0.984375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph0-16">
|
||||
<path style="stroke:none;" d="M 4.375 -2.046875 L 4.25 -2.296875 C 3.703125 -2.03125 3.609375 -2.0625 3.421875 -2.453125 L 1.125 -7.375 L -0.03125 -6.71875 L 0.078125 -6.46875 C 0.625 -6.734375 0.734375 -6.703125 0.921875 -6.3125 L 1.71875 -4.578125 C 1.65625 -4.609375 1.109375 -4.875 0.46875 -4.578125 C -0.53125 -4.109375 -1.03125 -2.921875 -0.546875 -1.859375 C -0.078125 -0.84375 1.140625 -0.4375 2.09375 -0.875 C 2.6875 -1.15625 2.875 -1.65625 2.953125 -1.890625 L 3.203125 -1.390625 Z M 2.703125 -2.453125 C 2.765625 -2.296875 2.78125 -2.28125 2.734375 -2.046875 C 2.65625 -1.5625 2.359375 -1.234375 2.03125 -1.078125 C 1.6875 -0.921875 1.28125 -0.96875 0.90625 -1.21875 C 0.515625 -1.453125 0.296875 -1.921875 0.171875 -2.1875 C 0 -2.5625 -0.171875 -3.015625 -0.09375 -3.4375 C -0.03125 -3.78125 0.15625 -4.203125 0.59375 -4.40625 C 0.921875 -4.5625 1.328125 -4.546875 1.703125 -4.328125 C 1.859375 -4.25 1.875 -4.234375 1.9375 -4.078125 Z M 2.703125 -2.453125 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-1">
|
||||
<path style="stroke:none;" d="M 6.21875 -6.109375 C 6.21875 -6.21875 6.140625 -6.265625 6.078125 -6.3125 C 5.859375 -6.453125 5.75 -6.640625 5.671875 -6.875 C 5.640625 -6.96875 5.609375 -7.09375 5.46875 -7.09375 C 5.328125 -7.09375 5.265625 -6.96875 5.265625 -6.890625 C 5.265625 -6.84375 5.34375 -6.515625 5.5 -6.3125 L 2.15625 -6.3125 C 1.984375 -6.3125 1.8125 -6.3125 1.8125 -6.109375 C 1.8125 -5.90625 1.984375 -5.90625 2.15625 -5.90625 L 5.34375 -5.90625 C 5.203125 -5.78125 4.875 -5.5 4.875 -5.328125 C 4.875 -5.234375 4.96875 -5.125 5.0625 -5.125 C 5.15625 -5.125 5.203125 -5.203125 5.25 -5.25 C 5.375 -5.40625 5.609375 -5.6875 6.046875 -5.90625 C 6.109375 -5.9375 6.21875 -6 6.21875 -6.109375 Z M 6.21875 -6.109375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-2">
|
||||
<path style="stroke:none;" d="M 2.828125 -6.21875 C 2.828125 -6.40625 2.6875 -6.5625 2.453125 -6.5625 C 2.1875 -6.5625 1.921875 -6.3125 1.921875 -6.046875 C 1.921875 -5.859375 2.0625 -5.6875 2.296875 -5.6875 C 2.53125 -5.6875 2.828125 -5.90625 2.828125 -6.21875 Z M 2.90625 -1.421875 C 2.90625 -1.515625 2.828125 -1.515625 2.796875 -1.515625 C 2.6875 -1.515625 2.6875 -1.484375 2.640625 -1.34375 C 2.46875 -0.71875 2.140625 -0.109375 1.625 -0.109375 C 1.453125 -0.109375 1.390625 -0.203125 1.390625 -0.4375 C 1.390625 -0.6875 1.453125 -0.828125 1.671875 -1.4375 L 2.0625 -2.46875 C 2.1875 -2.765625 2.1875 -2.78125 2.28125 -3.046875 C 2.359375 -3.25 2.421875 -3.390625 2.421875 -3.578125 C 2.421875 -4.03125 2.09375 -4.390625 1.59375 -4.390625 C 0.671875 -4.390625 0.28125 -2.953125 0.28125 -2.859375 C 0.28125 -2.765625 0.40625 -2.765625 0.40625 -2.765625 C 0.5 -2.765625 0.515625 -2.78125 0.5625 -2.9375 C 0.828125 -3.875 1.234375 -4.171875 1.5625 -4.171875 C 1.65625 -4.171875 1.8125 -4.171875 1.8125 -3.859375 C 1.8125 -3.640625 1.75 -3.4375 1.703125 -3.34375 C 1.625 -3.078125 1.1875 -1.921875 1.03125 -1.5 C 0.921875 -1.25 0.796875 -0.921875 0.796875 -0.703125 C 0.796875 -0.234375 1.140625 0.109375 1.609375 0.109375 C 2.546875 0.109375 2.90625 -1.328125 2.90625 -1.421875 Z M 2.90625 -1.421875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-3">
|
||||
<path style="stroke:none;" d="M 4.515625 -4.96875 C 4.515625 -5.625 4.34375 -7 3.328125 -7 C 1.953125 -7 0.421875 -4.203125 0.421875 -1.921875 C 0.421875 -1 0.703125 0.109375 1.609375 0.109375 C 3.015625 0.109375 4.515625 -2.75 4.515625 -4.96875 Z M 3.546875 -3.609375 L 1.46875 -3.609375 C 1.640625 -4.25 1.84375 -5.03125 2.234375 -5.75 C 2.5 -6.234375 2.875 -6.78125 3.3125 -6.78125 C 3.8125 -6.78125 3.859375 -6.15625 3.859375 -5.578125 C 3.859375 -5.09375 3.78125 -4.59375 3.546875 -3.609375 Z M 3.453125 -3.296875 C 3.34375 -2.828125 3.140625 -1.984375 2.765625 -1.265625 C 2.421875 -0.59375 2.03125 -0.109375 1.609375 -0.109375 C 1.28125 -0.109375 1.078125 -0.390625 1.078125 -1.328125 C 1.078125 -1.734375 1.140625 -2.3125 1.390625 -3.296875 Z M 3.453125 -3.296875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-4">
|
||||
<path style="stroke:none;" d="M 4.921875 -1.421875 C 4.921875 -1.515625 4.84375 -1.515625 4.8125 -1.515625 C 4.71875 -1.515625 4.703125 -1.484375 4.6875 -1.40625 C 4.359375 -0.34375 3.671875 -0.109375 3.359375 -0.109375 C 2.96875 -0.109375 2.8125 -0.421875 2.8125 -0.765625 C 2.8125 -0.984375 2.875 -1.203125 2.984375 -1.640625 L 3.3125 -3 C 3.375 -3.265625 3.609375 -4.171875 4.296875 -4.171875 C 4.359375 -4.171875 4.59375 -4.171875 4.796875 -4.046875 C 4.515625 -4 4.328125 -3.75 4.328125 -3.515625 C 4.328125 -3.34375 4.4375 -3.15625 4.703125 -3.15625 C 4.921875 -3.15625 5.234375 -3.34375 5.234375 -3.734375 C 5.234375 -4.25 4.65625 -4.390625 4.3125 -4.390625 C 3.734375 -4.390625 3.390625 -3.859375 3.265625 -3.640625 C 3.015625 -4.296875 2.484375 -4.390625 2.203125 -4.390625 C 1.15625 -4.390625 0.59375 -3.109375 0.59375 -2.859375 C 0.59375 -2.765625 0.71875 -2.765625 0.71875 -2.765625 C 0.796875 -2.765625 0.828125 -2.78125 0.84375 -2.875 C 1.1875 -3.921875 1.84375 -4.171875 2.171875 -4.171875 C 2.359375 -4.171875 2.71875 -4.078125 2.71875 -3.515625 C 2.71875 -3.203125 2.546875 -2.53125 2.171875 -1.140625 C 2.015625 -0.53125 1.671875 -0.109375 1.234375 -0.109375 C 1.171875 -0.109375 0.9375 -0.109375 0.734375 -0.234375 C 0.984375 -0.28125 1.203125 -0.5 1.203125 -0.78125 C 1.203125 -1.046875 0.984375 -1.125 0.828125 -1.125 C 0.53125 -1.125 0.28125 -0.859375 0.28125 -0.546875 C 0.28125 -0.09375 0.78125 0.109375 1.21875 0.109375 C 1.875 0.109375 2.234375 -0.59375 2.265625 -0.640625 C 2.390625 -0.28125 2.75 0.109375 3.34375 0.109375 C 4.359375 0.109375 4.921875 -1.171875 4.921875 -1.421875 Z M 4.921875 -1.421875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-5">
|
||||
<path style="stroke:none;" d="M 2.015625 -0.015625 C 2.015625 -0.671875 1.765625 -1.046875 1.375 -1.046875 C 1.046875 -1.046875 0.859375 -0.8125 0.859375 -0.53125 C 0.859375 -0.265625 1.046875 0 1.375 0 C 1.5 0 1.625 -0.046875 1.734375 -0.125 C 1.765625 -0.15625 1.78125 -0.15625 1.78125 -0.15625 C 1.78125 -0.15625 1.796875 -0.15625 1.796875 -0.015625 C 1.796875 0.71875 1.453125 1.328125 1.125 1.65625 C 1.015625 1.765625 1.015625 1.78125 1.015625 1.8125 C 1.015625 1.875 1.0625 1.921875 1.109375 1.921875 C 1.21875 1.921875 2.015625 1.15625 2.015625 -0.015625 Z M 2.015625 -0.015625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph1-6">
|
||||
<path style="stroke:none;" d="M 4.828125 -3.78125 C 4.875 -3.921875 4.875 -3.9375 4.875 -4.015625 C 4.875 -4.1875 4.734375 -4.28125 4.578125 -4.28125 C 4.484375 -4.28125 4.328125 -4.21875 4.234375 -4.078125 C 4.21875 -4.03125 4.140625 -3.71875 4.09375 -3.53125 L 3.890625 -2.75 L 3.453125 -0.953125 C 3.40625 -0.8125 2.984375 -0.109375 2.328125 -0.109375 C 1.8125 -0.109375 1.703125 -0.546875 1.703125 -0.921875 C 1.703125 -1.375 1.875 -1.984375 2.21875 -2.859375 C 2.375 -3.265625 2.421875 -3.375 2.421875 -3.578125 C 2.421875 -4.03125 2.09375 -4.390625 1.59375 -4.390625 C 0.65625 -4.390625 0.28125 -2.953125 0.28125 -2.859375 C 0.28125 -2.765625 0.40625 -2.765625 0.40625 -2.765625 C 0.5 -2.765625 0.515625 -2.78125 0.5625 -2.9375 C 0.828125 -3.875 1.234375 -4.171875 1.5625 -4.171875 C 1.65625 -4.171875 1.8125 -4.171875 1.8125 -3.859375 C 1.8125 -3.609375 1.71875 -3.34375 1.65625 -3.15625 C 1.25 -2.109375 1.078125 -1.546875 1.078125 -1.078125 C 1.078125 -0.1875 1.703125 0.109375 2.28125 0.109375 C 2.671875 0.109375 3.015625 -0.0625 3.296875 -0.34375 C 3.15625 0.171875 3.046875 0.671875 2.640625 1.1875 C 2.390625 1.53125 2 1.8125 1.546875 1.8125 C 1.40625 1.8125 0.96875 1.78125 0.796875 1.40625 C 0.953125 1.40625 1.078125 1.40625 1.21875 1.28125 C 1.328125 1.1875 1.421875 1.0625 1.421875 0.875 C 1.421875 0.5625 1.15625 0.53125 1.046875 0.53125 C 0.828125 0.53125 0.5 0.6875 0.5 1.171875 C 0.5 1.671875 0.9375 2.03125 1.546875 2.03125 C 2.578125 2.03125 3.59375 1.140625 3.875 0.015625 Z M 4.828125 -3.78125 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph2-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph2-1">
|
||||
<path style="stroke:none;" d="M 3.890625 -1 C 3.890625 -1.078125 3.796875 -1.078125 3.78125 -1.078125 C 3.6875 -1.078125 3.671875 -1.046875 3.65625 -0.96875 C 3.5 -0.484375 3.09375 -0.125 2.703125 -0.125 C 2.421875 -0.125 2.28125 -0.3125 2.28125 -0.578125 C 2.28125 -0.765625 2.4375 -1.390625 2.640625 -2.15625 C 2.78125 -2.703125 3.09375 -2.875 3.3125 -2.875 C 3.3125 -2.875 3.546875 -2.875 3.6875 -2.78125 C 3.46875 -2.71875 3.390625 -2.515625 3.390625 -2.390625 C 3.390625 -2.234375 3.5 -2.140625 3.671875 -2.140625 C 3.828125 -2.140625 4.046875 -2.265625 4.046875 -2.5625 C 4.046875 -2.953125 3.609375 -3.0625 3.328125 -3.0625 C 2.984375 -3.0625 2.703125 -2.84375 2.546875 -2.578125 C 2.421875 -2.859375 2.109375 -3.0625 1.71875 -3.0625 C 0.9375 -3.0625 0.5 -2.21875 0.5 -2 C 0.5 -1.90625 0.59375 -1.90625 0.609375 -1.90625 C 0.703125 -1.90625 0.703125 -1.9375 0.75 -2.03125 C 0.921875 -2.578125 1.359375 -2.875 1.703125 -2.875 C 1.921875 -2.875 2.109375 -2.75 2.109375 -2.40625 C 2.109375 -2.28125 2.03125 -1.921875 1.96875 -1.6875 L 1.734375 -0.734375 C 1.65625 -0.5 1.4375 -0.125 1.078125 -0.125 C 1.0625 -0.125 0.84375 -0.125 0.703125 -0.21875 C 0.984375 -0.3125 1.015625 -0.5625 1.015625 -0.609375 C 1.015625 -0.765625 0.890625 -0.859375 0.734375 -0.859375 C 0.53125 -0.859375 0.328125 -0.703125 0.328125 -0.4375 C 0.328125 -0.09375 0.71875 0.0625 1.0625 0.0625 C 1.390625 0.0625 1.671875 -0.125 1.84375 -0.421875 C 2.015625 -0.0625 2.390625 0.0625 2.671875 0.0625 C 3.46875 0.0625 3.890625 -0.796875 3.890625 -1 Z M 3.890625 -1 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph2-2">
|
||||
<path style="stroke:none;" d="M 3.859375 -2.625 C 3.890625 -2.71875 3.890625 -2.734375 3.890625 -2.78125 C 3.890625 -2.90625 3.78125 -3 3.671875 -3 C 3.59375 -3 3.453125 -2.96875 3.375 -2.828125 C 3.359375 -2.78125 3.296875 -2.5625 3.265625 -2.421875 L 3.125 -1.84375 L 2.84375 -0.734375 C 2.84375 -0.734375 2.53125 -0.125 1.984375 -0.125 C 1.515625 -0.125 1.515625 -0.578125 1.515625 -0.703125 C 1.515625 -1.078125 1.671875 -1.515625 1.890625 -2.046875 C 1.96875 -2.28125 2 -2.359375 2 -2.46875 C 2 -2.8125 1.71875 -3.0625 1.34375 -3.0625 C 0.640625 -3.0625 0.328125 -2.125 0.328125 -2 C 0.328125 -1.90625 0.421875 -1.90625 0.4375 -1.90625 C 0.546875 -1.90625 0.546875 -1.953125 0.5625 -2.015625 C 0.75 -2.59375 1.046875 -2.875 1.328125 -2.875 C 1.4375 -2.875 1.5 -2.796875 1.5 -2.625 C 1.5 -2.46875 1.4375 -2.3125 1.390625 -2.21875 C 1.0625 -1.375 1 -1.125 1 -0.8125 C 1 -0.703125 1 -0.375 1.265625 -0.140625 C 1.484375 0.03125 1.765625 0.0625 1.953125 0.0625 C 2.234375 0.0625 2.484375 -0.03125 2.71875 -0.25 C 2.625 0.140625 2.546875 0.4375 2.265625 0.78125 C 2.078125 1 1.796875 1.21875 1.421875 1.21875 C 1.375 1.21875 1.046875 1.21875 0.90625 1 C 1.28125 0.953125 1.28125 0.609375 1.28125 0.609375 C 1.28125 0.390625 1.078125 0.34375 1.015625 0.34375 C 0.828125 0.34375 0.609375 0.484375 0.609375 0.8125 C 0.609375 1.15625 0.9375 1.421875 1.4375 1.421875 C 2.140625 1.421875 2.984375 0.875 3.203125 0 Z M 3.859375 -2.625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph2-3">
|
||||
<path style="stroke:none;" d="M 3.46875 -1.015625 C 3.46875 -1.09375 3.390625 -1.09375 3.34375 -1.09375 C 3.265625 -1.09375 3.25 -1.0625 3.21875 -0.984375 C 3.09375 -0.640625 2.671875 -0.46875 2.34375 -0.46875 C 2.171875 -0.46875 2 -0.5 1.828125 -0.546875 C 1.515625 -0.625 1.453125 -0.625 1.328125 -0.625 C 1.328125 -0.625 1.203125 -0.625 1.171875 -0.609375 C 1.34375 -0.796875 1.46875 -0.921875 2.0625 -1.390625 C 2.21875 -1.515625 2.734375 -1.9375 2.9375 -2.125 C 3.359375 -2.546875 3.625 -2.90625 3.625 -2.984375 C 3.625 -3.0625 3.53125 -3.0625 3.5 -3.0625 C 3.4375 -3.0625 3.421875 -3.046875 3.390625 -3 C 3.171875 -2.671875 3.03125 -2.578125 2.859375 -2.578125 C 2.78125 -2.578125 2.671875 -2.578125 2.46875 -2.78125 C 2.21875 -3.015625 2.078125 -3.0625 1.90625 -3.0625 C 1.359375 -3.0625 0.984375 -2.46875 0.984375 -2.25 C 0.984375 -2.1875 1.046875 -2.171875 1.09375 -2.171875 C 1.1875 -2.171875 1.203125 -2.1875 1.21875 -2.265625 C 1.328125 -2.515625 1.71875 -2.53125 1.828125 -2.53125 C 1.984375 -2.53125 2.171875 -2.484375 2.265625 -2.46875 C 2.65625 -2.375 2.703125 -2.375 2.875 -2.375 C 2.6875 -2.1875 2.5625 -2.0625 1.90625 -1.53125 C 1.359375 -1.109375 1.171875 -0.9375 1.046875 -0.796875 C 0.625 -0.375 0.421875 -0.078125 0.421875 -0.015625 C 0.421875 0.0625 0.515625 0.0625 0.546875 0.0625 C 0.609375 0.0625 0.625 0.0625 0.65625 0 C 0.84375 -0.265625 1.0625 -0.421875 1.296875 -0.421875 C 1.390625 -0.421875 1.484375 -0.421875 1.671875 -0.25 C 1.890625 -0.03125 2.03125 0.0625 2.25 0.0625 C 3 0.0625 3.46875 -0.765625 3.46875 -1.015625 Z M 3.46875 -1.015625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph3-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph3-1">
|
||||
<path style="stroke:none;" d="M 3.0625 -8.15625 C 3.015625 -8.265625 2.921875 -8.265625 2.84375 -8.28125 C 2.578125 -8.3125 2.40625 -8.453125 2.234375 -8.625 C 2.171875 -8.703125 2.078125 -8.796875 1.953125 -8.734375 C 1.828125 -8.671875 1.828125 -8.53125 1.859375 -8.46875 C 1.875 -8.421875 2.09375 -8.171875 2.3125 -8.046875 L -0.71875 -6.625 C -0.875 -6.5625 -1.03125 -6.484375 -0.9375 -6.296875 C -0.859375 -6.125 -0.703125 -6.203125 -0.546875 -6.265625 L 2.34375 -7.625 C 2.28125 -7.4375 2.09375 -7.046875 2.171875 -6.890625 C 2.203125 -6.8125 2.328125 -6.734375 2.421875 -6.78125 C 2.5 -6.8125 2.515625 -6.921875 2.546875 -6.984375 C 2.59375 -7.171875 2.671875 -7.53125 2.984375 -7.921875 C 3.015625 -7.953125 3.109375 -8.0625 3.0625 -8.15625 Z M 3.0625 -8.15625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph3-2">
|
||||
<path style="stroke:none;" d="M -0.0625 -6.828125 C -0.140625 -7 -0.328125 -7.09375 -0.546875 -6.984375 C -0.78125 -6.875 -0.9375 -6.53125 -0.828125 -6.296875 C -0.734375 -6.125 -0.53125 -6.03125 -0.328125 -6.125 C -0.109375 -6.21875 0.0625 -6.546875 -0.0625 -6.828125 Z M 2.046875 -2.515625 C 2 -2.609375 1.921875 -2.5625 1.890625 -2.5625 C 1.796875 -2.515625 1.8125 -2.484375 1.828125 -2.328125 C 1.9375 -1.703125 1.890625 -1 1.421875 -0.78125 C 1.265625 -0.703125 1.1875 -0.78125 1.078125 -0.984375 C 0.96875 -1.21875 0.96875 -1.359375 0.90625 -2 L 0.828125 -3.109375 C 0.8125 -3.421875 0.8125 -3.4375 0.78125 -3.734375 C 0.765625 -3.953125 0.75 -4.109375 0.671875 -4.28125 C 0.484375 -4.6875 0.03125 -4.875 -0.421875 -4.65625 C -1.25 -4.265625 -1 -2.796875 -0.953125 -2.71875 C -0.921875 -2.625 -0.796875 -2.671875 -0.796875 -2.671875 C -0.71875 -2.71875 -0.703125 -2.734375 -0.71875 -2.890625 C -0.890625 -3.859375 -0.640625 -4.296875 -0.34375 -4.4375 C -0.265625 -4.484375 -0.125 -4.546875 0.015625 -4.265625 C 0.109375 -4.0625 0.140625 -3.84375 0.140625 -3.75 C 0.171875 -3.484375 0.265625 -2.234375 0.296875 -1.796875 C 0.296875 -1.53125 0.328125 -1.171875 0.421875 -0.984375 C 0.625 -0.5625 1.078125 -0.390625 1.5 -0.59375 C 2.359375 -0.984375 2.078125 -2.4375 2.046875 -2.515625 Z M 2.046875 -2.515625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph4-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph4-1">
|
||||
<path style="stroke:none;" d="M 3.53125 -2.75 C 3.5 -2.828125 3.40625 -2.78125 3.40625 -2.78125 C 3.3125 -2.734375 3.296875 -2.71875 3.328125 -2.53125 C 3.40625 -2.203125 3.46875 -1.75 3.203125 -1.625 C 3.046875 -1.546875 2.921875 -1.671875 2.84375 -1.84375 C 2.796875 -1.953125 2.75 -2.1875 2.71875 -2.390625 L 2.578125 -3.015625 L 2.46875 -3.640625 C 2.421875 -3.8125 2.375 -4.125 2.359375 -4.15625 C 2.296875 -4.28125 2.15625 -4.3125 2.0625 -4.265625 C 1.828125 -4.15625 1.859375 -3.953125 1.890625 -3.734375 L 2.1875 -2.25 C 2.21875 -2.125 2.28125 -1.859375 2.265625 -1.84375 C 2.234375 -1.59375 2.140625 -1.140625 1.75 -0.953125 C 1.328125 -0.75 1.125 -1.171875 1.078125 -1.28125 C 0.90625 -1.640625 0.859375 -2.171875 0.828125 -2.703125 C 0.8125 -2.875 0.8125 -2.984375 0.765625 -3.078125 C 0.625 -3.40625 0.234375 -3.5 -0.09375 -3.34375 C -0.71875 -3.046875 -0.59375 -2.046875 -0.546875 -1.953125 C -0.515625 -1.875 -0.4375 -1.90625 -0.421875 -1.921875 C -0.3125 -1.96875 -0.328125 -2 -0.34375 -2.0625 C -0.421875 -2.65625 -0.265625 -3.046875 -0.03125 -3.15625 C 0.078125 -3.21875 0.15625 -3.15625 0.234375 -3 C 0.296875 -2.859375 0.3125 -2.71875 0.328125 -2.53125 C 0.375 -1.515625 0.46875 -1.328125 0.546875 -1.15625 C 0.59375 -1.0625 0.734375 -0.765625 1.078125 -0.671875 C 1.3125 -0.59375 1.59375 -0.65625 1.796875 -0.765625 C 2.21875 -0.953125 2.3125 -1.265625 2.421875 -1.5625 C 2.765625 -1.21875 3.1875 -1.40625 3.265625 -1.4375 C 3.46875 -1.546875 3.578125 -1.75 3.59375 -2 C 3.625 -2.3125 3.546875 -2.71875 3.53125 -2.75 Z M 3.53125 -2.75 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph4-2">
|
||||
<path style="stroke:none;" d="M 2.3125 -3.875 C 2.078125 -4.359375 1.78125 -4.234375 1.75 -4.21875 C 1.59375 -4.140625 1.484375 -3.890625 1.5625 -3.71875 C 1.609375 -3.609375 1.71875 -3.59375 1.765625 -3.5625 C 1.90625 -3.53125 2.109375 -3.4375 2.234375 -3.171875 C 2.359375 -2.890625 2.59375 -1.34375 1.84375 -0.984375 C 1.328125 -0.75 1.109375 -1.203125 1.0625 -1.328125 C 0.921875 -1.609375 0.875 -2 0.828125 -2.6875 C 0.8125 -2.875 0.828125 -2.96875 0.765625 -3.078125 C 0.625 -3.40625 0.234375 -3.5 -0.09375 -3.34375 C -0.71875 -3.046875 -0.59375 -2.046875 -0.546875 -1.953125 C -0.515625 -1.875 -0.4375 -1.90625 -0.421875 -1.921875 C -0.3125 -1.96875 -0.328125 -2 -0.34375 -2.0625 C -0.421875 -2.65625 -0.28125 -3.046875 -0.03125 -3.15625 C 0.078125 -3.21875 0.15625 -3.15625 0.234375 -3 C 0.296875 -2.859375 0.3125 -2.71875 0.328125 -2.53125 C 0.375 -1.71875 0.421875 -1.40625 0.53125 -1.1875 C 0.828125 -0.5625 1.421875 -0.578125 1.90625 -0.8125 C 2.953125 -1.296875 2.546875 -3.34375 2.3125 -3.875 Z M 2.3125 -3.875 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph5-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph5-1">
|
||||
<path style="stroke:none;" d="M 4.40625 -2.484375 C 4.40625 -3.546875 3.53125 -4.40625 2.484375 -4.40625 C 1.40625 -4.40625 0.5625 -3.53125 0.5625 -2.484375 C 0.5625 -1.421875 1.4375 -0.5625 2.46875 -0.5625 C 3.5625 -0.5625 4.40625 -1.4375 4.40625 -2.484375 Z M 4.40625 -2.484375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph6-0">
|
||||
<path style="stroke:none;" d=""/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph6-1">
|
||||
<path style="stroke:none;" d="M 3.296875 2.390625 C 3.296875 2.359375 3.296875 2.328125 3.125 2.171875 C 1.875 0.921875 1.5625 -0.96875 1.5625 -2.484375 C 1.5625 -4.21875 1.9375 -5.9375 3.15625 -7.1875 C 3.296875 -7.296875 3.296875 -7.328125 3.296875 -7.359375 C 3.296875 -7.421875 3.25 -7.453125 3.1875 -7.453125 C 3.09375 -7.453125 2.203125 -6.78125 1.609375 -5.515625 C 1.109375 -4.421875 0.984375 -3.3125 0.984375 -2.484375 C 0.984375 -1.703125 1.09375 -0.5 1.640625 0.609375 C 2.234375 1.84375 3.09375 2.484375 3.1875 2.484375 C 3.25 2.484375 3.296875 2.453125 3.296875 2.390625 Z M 3.296875 2.390625 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph6-2">
|
||||
<path style="stroke:none;" d="M 2.875 -2.484375 C 2.875 -3.265625 2.765625 -4.46875 2.21875 -5.578125 C 1.625 -6.8125 0.765625 -7.453125 0.671875 -7.453125 C 0.609375 -7.453125 0.5625 -7.40625 0.5625 -7.359375 C 0.5625 -7.328125 0.5625 -7.296875 0.75 -7.125 C 1.734375 -6.140625 2.296875 -4.5625 2.296875 -2.484375 C 2.296875 -0.78125 1.921875 0.96875 0.703125 2.21875 C 0.5625 2.328125 0.5625 2.359375 0.5625 2.390625 C 0.5625 2.4375 0.609375 2.484375 0.671875 2.484375 C 0.765625 2.484375 1.65625 1.8125 2.25 0.546875 C 2.75 -0.546875 2.875 -1.65625 2.875 -2.484375 Z M 2.875 -2.484375 "/>
|
||||
</symbol>
|
||||
<symbol overflow="visible" id="glyph6-3">
|
||||
<path style="stroke:none;" d="M 6.734375 -1.609375 L 6.484375 -1.609375 C 6.421875 -1.34375 6.390625 -1.125 6.296875 -0.890625 C 6.25 -0.71875 6.21875 -0.640625 5.640625 -0.640625 L 4.84375 -0.640625 C 4.984375 -1.203125 5.28125 -1.671875 5.734375 -2.328125 C 6.203125 -3.046875 6.609375 -3.734375 6.609375 -4.515625 C 6.609375 -5.890625 5.265625 -7 3.59375 -7 C 1.875 -7 0.5625 -5.875 0.5625 -4.515625 C 0.5625 -3.734375 0.96875 -3.046875 1.4375 -2.328125 C 1.875 -1.671875 2.1875 -1.203125 2.3125 -0.640625 L 1.515625 -0.640625 C 0.9375 -0.640625 0.921875 -0.71875 0.859375 -0.875 C 0.78125 -1.109375 0.734375 -1.359375 0.6875 -1.609375 L 0.4375 -1.609375 L 0.765625 0 L 2.359375 0 C 2.578125 0 2.609375 0 2.609375 -0.203125 C 2.609375 -0.90625 2.296875 -1.78125 2.0625 -2.421875 C 1.859375 -2.984375 1.578125 -3.78125 1.578125 -4.515625 C 1.578125 -6.109375 2.671875 -6.78125 3.578125 -6.78125 C 4.53125 -6.78125 5.578125 -6.078125 5.578125 -4.515625 C 5.578125 -3.78125 5.3125 -3.015625 5.03125 -2.203125 C 4.875 -1.78125 4.5625 -0.890625 4.5625 -0.203125 C 4.5625 0 4.59375 0 4.8125 0 L 6.40625 0 Z M 6.734375 -1.609375 "/>
|
||||
</symbol>
|
||||
</g>
|
||||
<clipPath id="clip1">
|
||||
<path d="M 6 0.0585938 L 247.367188 0.0585938 L 247.367188 242 L 6 242 Z M 6 0.0585938 "/>
|
||||
</clipPath>
|
||||
<clipPath id="clip2">
|
||||
<path d="M 2 208 L 39 208 L 39 245.550781 L 2 245.550781 Z M 2 208 "/>
|
||||
</clipPath>
|
||||
</defs>
|
||||
<g id="surface1">
|
||||
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(59.999084%,59.999084%,59.999084%);fill-opacity:1;" d="M 246.375 114.066406 C 246.375 51.648438 195.777344 1.050781 133.359375 1.050781 C 70.941406 1.050781 20.34375 51.648438 20.34375 114.066406 C 20.34375 176.480469 70.941406 227.078125 133.359375 227.078125 C 195.777344 227.078125 246.375 176.480469 246.375 114.066406 Z M 246.375 114.066406 "/>
|
||||
<g clip-path="url(#clip1)" clip-rule="nonzero">
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 113.389044 -0.00146372 C 113.389044 62.622233 62.62462 113.386657 0.00092327 113.386657 C -62.622773 113.386657 -113.387198 62.622233 -113.387198 -0.00146372 C -113.387198 -62.621241 -62.622773 -113.385666 0.00092327 -113.385666 C 62.62462 -113.385666 113.389044 -62.621241 113.389044 -0.00146372 Z M 113.389044 -0.00146372 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-1" x="61.90895" y="42.376231"/>
|
||||
<use xlink:href="#glyph0-2" x="68.035519" y="39.51936"/>
|
||||
<use xlink:href="#glyph0-3" x="72.197925" y="37.578395"/>
|
||||
<use xlink:href="#glyph0-4" x="75.435352" y="36.068756"/>
|
||||
<use xlink:href="#glyph0-3" x="79.597758" y="34.127791"/>
|
||||
<use xlink:href="#glyph0-5" x="82.835185" y="32.618151"/>
|
||||
<use xlink:href="#glyph0-6" x="85.147632" y="31.539837"/>
|
||||
<use xlink:href="#glyph0-7" x="89.772528" y="29.38321"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-8" x="96.713111" y="26.146757"/>
|
||||
<use xlink:href="#glyph0-3" x="101.338006" y="23.990129"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-4" x="104.567334" y="22.484267"/>
|
||||
<use xlink:href="#glyph0-7" x="108.72974" y="20.543302"/>
|
||||
<use xlink:href="#glyph0-9" x="112.892146" y="18.602337"/>
|
||||
</g>
|
||||
<path style="fill-rule:nonzero;fill:rgb(79.998779%,79.998779%,79.998779%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -35.647437 -97.944313 L -97.945846 35.646896 L 35.649283 97.945305 L 97.943773 -35.649824 Z M -35.647437 -97.944313 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-10" x="43.395968" y="85.954598"/>
|
||||
<use xlink:href="#glyph0-11" x="49.638362" y="83.043717"/>
|
||||
<use xlink:href="#glyph0-12" x="52.4133" y="81.749741"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-8" x="61.433871" y="77.543372"/>
|
||||
<use xlink:href="#glyph0-3" x="66.058766" y="75.386744"/>
|
||||
<use xlink:href="#glyph0-4" x="69.296193" y="73.877105"/>
|
||||
<use xlink:href="#glyph0-7" x="73.458599" y="71.93614"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-9" x="77.612905" y="69.998952"/>
|
||||
</g>
|
||||
<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -13.712095 -37.672092 L -37.669705 13.711554 L 13.710022 37.669165 L 37.671552 -13.710563 Z M -13.712095 -37.672092 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-13" x="120.798851" y="144.979055"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-4" x="126.228851" y="142.447001"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph0-14" x="130.164467" y="140.61179"/>
|
||||
<use xlink:href="#glyph0-15" x="134.557712" y="138.563182"/>
|
||||
<use xlink:href="#glyph0-2" x="136.87016" y="137.484868"/>
|
||||
<use xlink:href="#glyph0-4" x="141.032566" y="135.543903"/>
|
||||
<use xlink:href="#glyph0-16" x="145.194972" y="133.602938"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -25.692859 -11.978309 L -30.830832 -14.376814 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 11.981688 -25.691327 L 14.376273 -30.8293 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -21.244653 -34.928705 L -40.413092 6.175077 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -26.382625 -37.32329 L -35.968805 -16.771399 L -30.830832 -14.376814 L -21.244653 -34.928705 Z M -26.382625 -37.32329 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -26.382625 -37.32329 L -30.830832 -14.376814 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -35.968805 -16.771399 L -21.244653 -34.928705 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 3.927886 -41.955696 L 1.529382 -36.817723 L 27.223165 -24.840877 L 29.61775 -29.97885 Z M 3.927886 -41.955696 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 29.61775 -29.97885 L 1.529382 -36.817723 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 3.927886 -41.955696 L 27.223165 -24.840877 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -48.30621 -50.675748 L -32.892292 -43.488073 L -35.286877 -38.350101 L -50.700795 -45.537776 Z M -48.30621 -50.675748 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -30.583927 -39.282852 L -33.636926 -40.709414 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.055438 0.00118717 L 1.606788 1.682043 L 3.088754 0.000746652 L 1.607588 -1.682646 Z M 6.055438 0.00118717 " transform="matrix(0.903323,-0.421212,-0.421212,-0.903323,100.311736,154.414975)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -53.00916 -49.742997 L -49.956162 -48.316435 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.053948 -0.00119667 L 1.606954 1.683211 L 3.087264 -0.00163719 L 1.607754 -1.681478 Z M 6.053948 -0.00119667 " transform="matrix(-0.903323,0.421212,0.421212,0.903323,83.08636,162.447181)"/>
|
||||
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -35.968805 -16.771399 L -41.106778 -19.169903 L -41.40855 -22.058299 L -46.221236 -18.805425 L -46.824781 -24.582215 L -51.637466 -21.33326 L -52.241011 -27.11005 L -57.057616 -23.857177 L -57.661161 -29.633967 L -60.067504 -28.011449 L -66.796641 -31.146749 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -40.413092 6.175077 L -45.551065 3.780492 L -45.852838 0.892097 L -50.669442 4.14497 L -51.272987 -1.635739 L -56.085673 1.617135 L -56.689218 -4.159655 L -61.501903 -0.910701 L -62.105449 -6.687491 L -66.922053 -3.434617 L -67.525598 -9.211407 L -69.931941 -7.588889 L -76.382821 -10.594858 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 42.966289 -51.898515 L 35.778614 -36.484597 L 30.640642 -38.883102 L 37.828317 -54.29702 Z M 42.966289 -51.898515 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 31.577312 -34.176233 L 32.999955 -37.23315 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.052701 0.000344825 L 1.609259 1.683096 L 3.086017 -0.0000956979 L 1.610059 -1.681593 Z M 6.052701 0.000344825 " transform="matrix(-0.421212,-0.903323,-0.903323,0.421212,166.026342,150.693959)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 42.033538 -56.605384 L 40.610895 -53.548467 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.05316 0.00128928 L 1.609718 1.68404 L 3.086476 0.000848753 L 1.608862 -1.6842 Z M 6.05316 0.00128928 " transform="matrix(0.421212,0.903323,0.903323,-0.421212,174.058549,167.919305)"/>
|
||||
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 3.927886 -41.959615 L 6.322472 -47.097587 L 9.210867 -47.39936 L 5.957993 -52.212045 L 11.738702 -52.815591 L 8.485829 -57.628276 L 14.262619 -58.231821 L 11.013664 -63.048426 L 16.790454 -63.651971 L 15.164017 -66.058314 L 18.303236 -72.787451 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -8.574122 -35.273588 L -6.175618 -40.41156 L -3.287223 -40.713333 L -6.540096 -45.529937 L -0.763306 -46.133483 L -4.012261 -50.946168 L 1.764529 -51.549713 L -1.488344 -56.362399 L 4.292365 -56.965944 L 1.039491 -61.782548 L 6.816281 -62.386093 L 3.563408 -67.198779 L 9.344117 -67.802324 L 7.71768 -70.208667 L 10.594318 -76.381288 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -113.387198 -113.385666 L -61.325543 -113.385666 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.05384 0.00157449 L 1.609552 1.682879 L 3.087062 0.00157449 L 1.609552 -1.683649 Z M 6.05384 0.00157449 " transform="matrix(0.996715,0,0,-0.996715,69.403548,227.079694)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-1" x="71.105638" y="237.978532"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-2" x="72.641576" y="240.252039"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph2-1" x="76.062301" y="241.742127"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -113.387198 -113.385666 L -113.387198 -61.32793 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.051453 -0.0000423547 L 1.607165 1.681262 L 3.088594 -0.0000423547 L 1.607165 -1.681347 Z M 6.051453 -0.0000423547 " transform="matrix(0,-0.996715,-0.996715,0,20.343708,178.019854)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-1" x="6.809556" y="171.561441"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-2" x="8.344497" y="173.834947"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph2-2" x="11.766219" y="175.324039"/>
|
||||
</g>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -111.686297 -113.385666 C -111.686297 -112.448995 -112.446608 -111.684765 -113.387198 -111.684765 C -114.327788 -111.684765 -115.088098 -112.448995 -115.088098 -113.385666 C -115.088098 -114.326255 -114.327788 -115.086566 -113.387198 -115.086566 C -112.446608 -115.086566 -111.686297 -114.326255 -111.686297 -113.385666 Z M -111.686297 -113.385666 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<g clip-path="url(#clip2)" clip-rule="nonzero">
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -109.134947 -113.385666 C -109.134947 -111.03811 -111.039642 -109.133415 -113.387198 -109.133415 C -115.734753 -109.133415 -117.639448 -111.03811 -117.639448 -113.385666 C -117.639448 -115.73714 -115.734753 -117.637916 -113.387198 -117.637916 C -111.039642 -117.637916 -109.134947 -115.73714 -109.134947 -113.385666 Z M -109.134947 -113.385666 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-1" x="2.27251" y="228.743969"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-2" x="3.808447" y="231.017476"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph2-3" x="7.229173" y="232.506568"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00092327 -0.00146372 L 47.183268 22.000503 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.052359 0.000510492 L 1.608917 1.683262 L 3.085675 0.0000699691 L 1.609717 -1.681427 Z M 6.052359 0.000510492 " transform="matrix(0.903323,-0.421212,-0.421212,-0.903323,177.822044,93.331036)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph3-1" x="176.077036" y="85.793095"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph3-2" x="178.429901" y="87.204479"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph4-1" x="182.159458" y="87.108391"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00092327 -0.00146372 L -22.001044 47.180881 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.053976 0.000352813 L 1.610534 1.683104 L 3.087292 -0.0000877097 L 1.609678 -1.685137 Z M 6.053976 0.000352813 " transform="matrix(-0.421212,-0.903323,-0.903323,0.421212,112.624543,69.601358)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph3-1" x="97.963495" y="70.058954"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph3-2" x="100.31636" y="71.470338"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph4-2" x="104.046339" y="71.375153"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-dasharray:2.98883,2.98883;stroke-miterlimit:10;" d="M 0.00092327 -0.00146372 L 56.694984 -0.00146372 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 42.519509 -0.00146372 C 42.519509 6.20643 41.159573 12.34378 38.537678 17.971643 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-3" x="178.538543" y="108.340814"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph5-1" x="130.875638" y="116.271674"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph6-1" x="106.515927" y="116.547764"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-4" x="110.3772" y="116.547764"/>
|
||||
<use xlink:href="#glyph1-5" x="116.052122" y="116.547764"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph1-6" x="120.468929" y="116.547764"/>
|
||||
</g>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph6-2" x="125.690727" y="116.547764"/>
|
||||
</g>
|
||||
<path style="fill:none;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.21357 -0.00146372 C 99.21357 21.773194 92.04549 42.909035 78.896826 60.157103 " transform="matrix(0.996715,0,0,-0.996715,133.358455,114.064947)"/>
|
||||
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.99628;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 6.053653 -0.00146221 L 1.609367 1.684941 L 3.088612 0.000405489 L 1.608324 -1.681639 Z M 6.053653 -0.00146221 " transform="matrix(-0.621003,-0.779531,-0.779531,0.621003,213.750386,56.325385)"/>
|
||||
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
|
||||
<use xlink:href="#glyph6-3" x="215.304364" y="83.663151"/>
|
||||
</g>
|
||||
</g>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 55 KiB |
147
tikz/index.org
147
tikz/index.org
@ -58,11 +58,11 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
% Force Sensors
|
||||
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
|
||||
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
|
||||
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) -- ($(au) + (0, -0.5)$);
|
||||
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) node[above=0.1, rotate=\thetau]{$f_{u}$} -- ($(au) + (0, -0.5)$);
|
||||
|
||||
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
|
||||
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
|
||||
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$);
|
||||
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) node[left=0.1, rotate=\thetau]{$f_{v}$} -- ($(av) + ( 0.5, 0)$);
|
||||
|
||||
% Spring and Actuator for U
|
||||
\draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
|
||||
@ -70,6 +70,10 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
|
||||
\draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
|
||||
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k_v$} (kv|-0,-2.6);
|
||||
|
||||
% Displacement measurement
|
||||
\draw[<->, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1 , -0.8);
|
||||
\draw[<->, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1);
|
||||
\end{scope}
|
||||
|
||||
% Inertial Frame
|
||||
@ -85,11 +89,144 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
\node[] at (0,0) {$\bullet$};
|
||||
\node[left] at (0,0) {$(x, y)$};
|
||||
|
||||
% \draw[->] (-4, -4) -- ++(\thetau:2) node[above]{$\vec{i}_u$};
|
||||
% \draw[->] (-4, -4) -- ++(\thetau+90:2) node[left]{$\vec{i}_u$};
|
||||
% \draw[] (-2.5, -4) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
|
||||
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
[[file:figs/rotating_xy_platform.png]]
|
||||
|
||||
* X-Y Rotating Positioning Platform with Springs in parallel
|
||||
#+begin_src latex :file rotating_xy_platform_springs.pdf
|
||||
\begin{tikzpicture}
|
||||
% Angle
|
||||
\def\thetau{25}
|
||||
|
||||
% Rotational Stage
|
||||
\draw[fill=black!40!white] (0, 0) circle (4);
|
||||
|
||||
% Label
|
||||
\node[anchor=north west, rotate=\thetau] at (-2.8, 2.8) {\small Rotating Stage};
|
||||
|
||||
% Rotating Scope
|
||||
\begin{scope}[rotate=\thetau]
|
||||
% Rotating Frame
|
||||
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
|
||||
% Label
|
||||
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
|
||||
|
||||
% Mass
|
||||
\draw[fill=white] (-1, -1) rectangle (1, 1);
|
||||
% Label
|
||||
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
|
||||
|
||||
% Attached Points
|
||||
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
|
||||
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
|
||||
|
||||
% Force Sensors
|
||||
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
|
||||
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
|
||||
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) -- ($(au) + (0, -0.5)$);
|
||||
|
||||
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
|
||||
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
|
||||
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$);
|
||||
|
||||
% Spring and Actuator for U
|
||||
\draw[actuator={0.6}{0.2}] (actu) -- (actu-|-2.6,0);
|
||||
\draw[spring=0.2] (ku) -- (ku-|-2.6,0);
|
||||
\draw[spring=0.2] (-1, 0.8) -- (-1, 0.8-|-2.6,0);
|
||||
|
||||
\draw[actuator={0.6}{0.2}] (actv) -- (actv|-0,-2.6);
|
||||
\draw[spring=0.2] (kv) -- (kv|-0,-2.6);
|
||||
\draw[spring=0.2] (-0.8, -1) -- (-0.8, -1|-0,-2.6);
|
||||
|
||||
% Displacement measurement
|
||||
\draw[<->, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1 , -0.8);
|
||||
\draw[<->, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1);
|
||||
\end{scope}
|
||||
|
||||
% Inertial Frame
|
||||
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
|
||||
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
|
||||
\draw[fill, color=black] (-4, -4) circle (0.06);
|
||||
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
|
||||
|
||||
\draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
|
||||
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
|
||||
\draw[dashed] (0, 0) -- ++(2, 0);
|
||||
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
|
||||
\node[] at (0,0) {$\bullet$};
|
||||
\node[left] at (0,0) {$(x, y)$};
|
||||
|
||||
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+begin_src latex :file rotating_xy_platform_springs.pdf
|
||||
\begin{tikzpicture}
|
||||
% Angle
|
||||
\def\thetau{25}
|
||||
|
||||
% Rotational Stage
|
||||
\draw[fill=black!40!white] (0, 0) circle (4);
|
||||
|
||||
% Label
|
||||
\node[anchor=north west, rotate=\thetau] at (-2.8, 2.8) {\small Rotating Stage};
|
||||
|
||||
% Rotating Scope
|
||||
\begin{scope}[rotate=\thetau]
|
||||
% Rotating Frame
|
||||
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
|
||||
% Label
|
||||
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
|
||||
|
||||
% Mass
|
||||
\draw[fill=white] (-1, -1) rectangle (1, 1);
|
||||
% Label
|
||||
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
|
||||
|
||||
% Attached Points
|
||||
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
|
||||
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
|
||||
\draw[] ($(au) + (0, -0.8)$) -- ($(au) + (0, 0.8)$)coordinate(kpu);
|
||||
|
||||
% Force Sensors
|
||||
\draw[fill=white] ($(au) + (-0.2, -0.8)$) rectangle (au);
|
||||
\draw[] ($(au) + (-0.2, -0.8)$)coordinate(actu) -- (au);
|
||||
\draw[] ($(au) + (-0.2, 0)$)coordinate(ku) -- ($(au) + (0, -0.8)$);
|
||||
|
||||
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
|
||||
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
|
||||
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$);
|
||||
|
||||
% Spring and Actuator for U
|
||||
\draw[actuator={0.6}{0.2}] (actu) -- (actu-|-2.6,0);
|
||||
\draw[spring=0.2] (ku) -- (ku-|-2.6,0);
|
||||
\draw[spring=0.2] (kpu) -- (kpu-|-2.6,0);
|
||||
|
||||
\draw[actuator={0.6}{0.2}] (actv) -- (actv|-0,-2.6);
|
||||
\draw[spring=0.2] (kv) -- (kv|-0,-2.6);
|
||||
\draw[spring=0.2] (-0.8, -1) -- (-0.8, -1|-0,-2.6);
|
||||
\end{scope}
|
||||
|
||||
% Inertial Frame
|
||||
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
|
||||
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
|
||||
\draw[fill, color=black] (-4, -4) circle (0.06);
|
||||
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
|
||||
|
||||
\draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
|
||||
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
|
||||
\draw[dashed] (0, 0) -- ++(2, 0);
|
||||
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
|
||||
\node[] at (0,0) {$\bullet$};
|
||||
\node[left] at (0,0) {$(x, y)$};
|
||||
|
||||
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
[[file:figs/rotating_xy_platform_springs.png]]
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user