2973 lines
132 KiB
HTML
2973 lines
132 KiB
HTML
<?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>
|
|
<!-- 2020-03-25 mer. 19:20 -->
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
|
<title>Subsystems used for the Simscape Models</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>
|
|
<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
|
<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
|
<link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
|
|
<script type="text/javascript" src="./js/jquery.min.js"></script>
|
|
<script type="text/javascript" src="./js/bootstrap.min.js"></script>
|
|
<script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
|
|
<script type="text/javascript" src="./js/readtheorg.js"></script>
|
|
<script type="text/javascript">
|
|
/*
|
|
@licstart The following is the entire license notice for the
|
|
JavaScript code in this tag.
|
|
|
|
Copyright (C) 2012-2020 Free Software Foundation, Inc.
|
|
|
|
The JavaScript code in this tag is free software: you can
|
|
redistribute it and/or modify it under the terms of the GNU
|
|
General Public License (GNU GPL) as published by the Free Software
|
|
Foundation, either version 3 of the License, or (at your option)
|
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
|
|
|
As additional permission under GNU GPL version 3 section 7, you
|
|
may distribute non-source (e.g., minimized or compacted) forms of
|
|
that code without the copy of the GNU GPL normally required by
|
|
section 4, provided you include this license notice and a URL
|
|
through which recipients can access the Corresponding Source.
|
|
|
|
|
|
@licend The above is the entire license notice
|
|
for the JavaScript code in this tag.
|
|
*/
|
|
<!--/*--><![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;
|
|
}
|
|
/*]]>*///-->
|
|
</script>
|
|
</head>
|
|
<body>
|
|
<div id="org-div-home-and-up">
|
|
<a accesskey="h" href="./index.html"> UP </a>
|
|
|
|
|
<a accesskey="H" href="./index.html"> HOME </a>
|
|
</div><div id="content">
|
|
<h1 class="title">Subsystems used for the Simscape Models</h1>
|
|
<div id="table-of-contents">
|
|
<h2>Table of Contents</h2>
|
|
<div id="text-table-of-contents">
|
|
<ul>
|
|
<li><a href="#org6171274">1. Simscape Configuration</a>
|
|
<ul>
|
|
<li><a href="#org15732a0">Function description</a></li>
|
|
<li><a href="#org902a1e1">Optional Parameters</a></li>
|
|
<li><a href="#org44bc280">Structure initialization</a></li>
|
|
<li><a href="#orgd741b2d">Add Type</a></li>
|
|
<li><a href="#org9d366f8">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgdda6840">2. Logging Configuration</a>
|
|
<ul>
|
|
<li><a href="#org8bb169e">Function description</a></li>
|
|
<li><a href="#org737eb2b">Optional Parameters</a></li>
|
|
<li><a href="#orgde70fa0">Structure initialization</a></li>
|
|
<li><a href="#orgd74dc80">Add Type</a></li>
|
|
<li><a href="#org60d91f1">Sampling Time</a></li>
|
|
<li><a href="#org5b7da5e">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org1bf1870">3. Ground</a>
|
|
<ul>
|
|
<li><a href="#orgc616e98">Simscape Model</a></li>
|
|
<li><a href="#org55983d8">Function description</a></li>
|
|
<li><a href="#orgc45d616">Optional Parameters</a></li>
|
|
<li><a href="#orge90a770">Structure initialization</a></li>
|
|
<li><a href="#orgdfb33da">Add Type</a></li>
|
|
<li><a href="#org4c31ca5">Ground Solid properties</a></li>
|
|
<li><a href="#org542691f">Rotation Point</a></li>
|
|
<li><a href="#orge012e41">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orga045749">4. Granite</a>
|
|
<ul>
|
|
<li><a href="#orge6f1ffa">Simscape Model</a></li>
|
|
<li><a href="#orgfe1e8d4">Function description</a></li>
|
|
<li><a href="#orga232b56">Optional Parameters</a></li>
|
|
<li><a href="#org6a319e4">Structure initialization</a></li>
|
|
<li><a href="#org413c06d">Add Granite Type</a></li>
|
|
<li><a href="#org35a416f">Material and Geometry</a></li>
|
|
<li><a href="#org210c84e">Stiffness and Damping properties</a></li>
|
|
<li><a href="#org2848fdf">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#org5d1f420">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgd3ff237">5. Translation Stage</a>
|
|
<ul>
|
|
<li><a href="#org3048997">Simscape Model</a></li>
|
|
<li><a href="#org9f52c55">Function description</a></li>
|
|
<li><a href="#org90522d0">Optional Parameters</a></li>
|
|
<li><a href="#org609c8fb">Structure initialization</a></li>
|
|
<li><a href="#org715e876">Add Translation Stage Type</a></li>
|
|
<li><a href="#orgfca9fc3">Material and Geometry</a></li>
|
|
<li><a href="#orgfb71c1d">Stiffness and Damping properties</a></li>
|
|
<li><a href="#org1e5bb2b">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#org6e13988">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org46b0509">6. Tilt Stage</a>
|
|
<ul>
|
|
<li><a href="#org3834ca7">Simscape Model</a></li>
|
|
<li><a href="#org0ffd9dc">Function description</a></li>
|
|
<li><a href="#orgc4130e8">Optional Parameters</a></li>
|
|
<li><a href="#org5a105fd">Structure initialization</a></li>
|
|
<li><a href="#orgea3a7ba">Add Tilt Type</a></li>
|
|
<li><a href="#orgdfb5814">Material and Geometry</a></li>
|
|
<li><a href="#org1ae49c1">Stiffness and Damping properties</a></li>
|
|
<li><a href="#org8e9e40c">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#org7d54dc1">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgb98f9a6">7. Spindle</a>
|
|
<ul>
|
|
<li><a href="#org127f684">Simscape Model</a></li>
|
|
<li><a href="#orgab0b601">Function description</a></li>
|
|
<li><a href="#org1f40549">Optional Parameters</a></li>
|
|
<li><a href="#org85ca363">Structure initialization</a></li>
|
|
<li><a href="#orge5b17ec">Add Spindle Type</a></li>
|
|
<li><a href="#org1ec9aee">Material and Geometry</a></li>
|
|
<li><a href="#org117f09d">Stiffness and Damping properties</a></li>
|
|
<li><a href="#orgaaa75bf">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#org881ebe0">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org49a14bb">8. Micro Hexapod</a>
|
|
<ul>
|
|
<li><a href="#org156d5c7">Simscape Model</a></li>
|
|
<li><a href="#org4fcfe02">Function description</a></li>
|
|
<li><a href="#org1e9bfc3">Optional Parameters</a></li>
|
|
<li><a href="#org1c650c8">Function content</a></li>
|
|
<li><a href="#orgb34b6c7">Add Type</a></li>
|
|
<li><a href="#orgc0b87f8">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orga55d418">9. Center of gravity compensation</a>
|
|
<ul>
|
|
<li><a href="#org7501cd7">Simscape Model</a></li>
|
|
<li><a href="#org8b06b22">Function description</a></li>
|
|
<li><a href="#org8b0c4a4">Optional Parameters</a></li>
|
|
<li><a href="#org50581f7">Structure initialization</a></li>
|
|
<li><a href="#org5167cf8">Add Type</a></li>
|
|
<li><a href="#orge79b90d">Material and Geometry</a></li>
|
|
<li><a href="#org4a63f45">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org7586ab7">10. Mirror</a>
|
|
<ul>
|
|
<li><a href="#org406058f">Simscape Model</a></li>
|
|
<li><a href="#org090435a">Function description</a></li>
|
|
<li><a href="#org06a58c7">Optional Parameters</a></li>
|
|
<li><a href="#orgfd4ee37">Structure initialization</a></li>
|
|
<li><a href="#orgff14824">Add Mirror Type</a></li>
|
|
<li><a href="#org0144cc7">Material and Geometry</a></li>
|
|
<li><a href="#org505752d">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org4dc3820">11. Nano Hexapod</a>
|
|
<ul>
|
|
<li><a href="#org08f35a2">Simscape Model</a></li>
|
|
<li><a href="#orgb862ff4">Function description</a></li>
|
|
<li><a href="#orgac24dff">Optional Parameters</a></li>
|
|
<li><a href="#org35fbeff">Function content</a></li>
|
|
<li><a href="#org2939880">Add Type</a></li>
|
|
<li><a href="#orgdc2d29f">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org3d615a1">12. Sample</a>
|
|
<ul>
|
|
<li><a href="#orgd8e711f">Simscape Model</a></li>
|
|
<li><a href="#orgec394e5">Function description</a></li>
|
|
<li><a href="#org9a67f8d">Optional Parameters</a></li>
|
|
<li><a href="#org82f944c">Structure initialization</a></li>
|
|
<li><a href="#org2bb1d24">Add Sample Type</a></li>
|
|
<li><a href="#org63af8a7">Material and Geometry</a></li>
|
|
<li><a href="#org91c540d">Stiffness and Damping properties</a></li>
|
|
<li><a href="#org19876e8">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#org23eeae8">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orge9cbdc9">13. Initialize Controller</a>
|
|
<ul>
|
|
<li><a href="#orgb650d4c">Function Declaration and Documentation</a></li>
|
|
<li><a href="#org90273ed">Optional Parameters</a></li>
|
|
<li><a href="#org0f81215">Structure initialization</a></li>
|
|
<li><a href="#org4207f98">Controller Type</a></li>
|
|
<li><a href="#org5fe61c6">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgae5cb57">14. Generate Reference Signals</a>
|
|
<ul>
|
|
<li><a href="#orgc0954ba">Function Declaration and Documentation</a></li>
|
|
<li><a href="#org0c5ed70">Optional Parameters</a></li>
|
|
<li><a href="#orge94c0c2">Initialize Parameters</a></li>
|
|
<li><a href="#org6a6adba">Translation Stage</a></li>
|
|
<li><a href="#orgf61cdf3">Tilt Stage</a></li>
|
|
<li><a href="#org3e7754b">Spindle</a></li>
|
|
<li><a href="#orgaf1747d">Micro Hexapod</a></li>
|
|
<li><a href="#org04d73dc">Axis Compensation</a></li>
|
|
<li><a href="#orgd74c144">Nano Hexapod</a></li>
|
|
<li><a href="#orgd21e485">Save</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org544c9dd">15. Initialize Disturbances</a>
|
|
<ul>
|
|
<li><a href="#org8067551">Function Declaration and Documentation</a></li>
|
|
<li><a href="#org4fe2ec1">Optional Parameters</a></li>
|
|
<li><a href="#orgf744aeb">Load Data</a></li>
|
|
<li><a href="#org6c7d666">Parameters</a></li>
|
|
<li><a href="#orgb2108c4">Ground Motion</a></li>
|
|
<li><a href="#orgb70c65e">Translation Stage - X direction</a></li>
|
|
<li><a href="#org070255a">Translation Stage - Z direction</a></li>
|
|
<li><a href="#orgfd5f32b">Spindle - Z direction</a></li>
|
|
<li><a href="#orgba4d479">Direct Forces</a></li>
|
|
<li><a href="#orgf6d2198">Set initial value to zero</a></li>
|
|
<li><a href="#orgc10a6b1">Save</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgefb8a5e">16. Initialize Position Errors</a>
|
|
<ul>
|
|
<li><a href="#orgc93deeb">Function Declaration and Documentation</a></li>
|
|
<li><a href="#org84b0cbd">Optional Parameters</a></li>
|
|
<li><a href="#orgf35470d">Structure initialization</a></li>
|
|
<li><a href="#orgc890f7d">Type</a></li>
|
|
<li><a href="#org7d50228">Position Errors</a></li>
|
|
<li><a href="#org4d82b1e">Save</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgc87e890">17. Z-Axis Geophone</a></li>
|
|
<li><a href="#orgcbddbd1">18. Z-Axis Accelerometer</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<p>
|
|
The full Simscape Model is represented in Figure <a href="#org742ece0">1</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org742ece0" class="figure">
|
|
<p><img src="figs/images/simscape_picture.png" alt="simscape_picture.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Screenshot of the Multi-Body Model representation</p>
|
|
</div>
|
|
|
|
<p>
|
|
This model is divided into multiple subsystems that are independent.
|
|
These subsystems are saved in separate files and imported in the main file using a block balled “subsystem reference”.
|
|
</p>
|
|
|
|
<p>
|
|
Each stage is configured (geometry, mass properties, dynamic properties …) using one function.
|
|
</p>
|
|
|
|
<p>
|
|
These functions are defined below.
|
|
</p>
|
|
|
|
<div id="outline-container-org6171274" class="outline-2">
|
|
<h2 id="org6171274"><span class="section-number-2">1</span> Simscape Configuration</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
<a id="orgb590dcf"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org15732a0" class="outline-3">
|
|
<h3 id="org15732a0">Function description</h3>
|
|
<div class="outline-text-3" id="text-org15732a0">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeSimscapeConfiguration</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org902a1e1" class="outline-3">
|
|
<h3 id="org902a1e1">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org902a1e1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.gravity logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org44bc280" class="outline-3">
|
|
<h3 id="org44bc280">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org44bc280">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">conf_simscape = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd741b2d" class="outline-3">
|
|
<h3 id="orgd741b2d">Add Type</h3>
|
|
<div class="outline-text-3" id="text-orgd741b2d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.gravity
|
|
conf_simscape.type = 1;
|
|
<span class="org-keyword">else</span>
|
|
conf_simscape.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9d366f8" class="outline-3">
|
|
<h3 id="org9d366f8">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org9d366f8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/conf_simscape.mat'</span>, <span class="org-string">'conf_simscape'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdda6840" class="outline-2">
|
|
<h2 id="orgdda6840"><span class="section-number-2">2</span> Logging Configuration</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="org1f9c6ac"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org8bb169e" class="outline-3">
|
|
<h3 id="org8bb169e">Function description</h3>
|
|
<div class="outline-text-3" id="text-org8bb169e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeLoggingConfiguration</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org737eb2b" class="outline-3">
|
|
<h3 id="org737eb2b">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org737eb2b">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.log char {mustBeMember(args.log,{<span class="org-string">'none'</span>, <span class="org-string">'all'</span>, <span class="org-string">'forces'</span>})} = <span class="org-string">'none'</span>
|
|
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgde70fa0" class="outline-3">
|
|
<h3 id="orgde70fa0">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgde70fa0">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">conf_log = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd74dc80" class="outline-3">
|
|
<h3 id="orgd74dc80">Add Type</h3>
|
|
<div class="outline-text-3" id="text-orgd74dc80">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.log</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
conf_log.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'all'</span>
|
|
conf_log.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'forces'</span>
|
|
conf_log.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org60d91f1" class="outline-3">
|
|
<h3 id="org60d91f1">Sampling Time</h3>
|
|
<div class="outline-text-3" id="text-org60d91f1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">conf_log.Ts = args.Ts;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5b7da5e" class="outline-3">
|
|
<h3 id="org5b7da5e">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org5b7da5e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/conf_log.mat'</span>, <span class="org-string">'conf_log'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1bf1870" class="outline-2">
|
|
<h2 id="org1bf1870"><span class="section-number-2">3</span> Ground</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="orgbe1f388"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc616e98" class="outline-3">
|
|
<h3 id="orgc616e98">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgc616e98">
|
|
<p>
|
|
The model of the Ground is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>A <b>Cartesian</b> joint that is used to simulation the ground motion</li>
|
|
<li>A solid that represents the ground on which the granite is located</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org31eeec1" class="figure">
|
|
<p><img src="figs/images/simscape_model_ground.png" alt="simscape_model_ground.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Simscape model for the Ground</p>
|
|
</div>
|
|
|
|
|
|
<div id="org342019d" class="figure">
|
|
<p><img src="figs/images/simscape_picture_ground.png" alt="simscape_picture_ground.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Simscape picture for the Ground</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org55983d8" class="outline-3">
|
|
<h3 id="org55983d8">Function description</h3>
|
|
<div class="outline-text-3" id="text-org55983d8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ground]</span> = <span class="org-function-name">initializeGround</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc45d616" class="outline-3">
|
|
<h3 id="orgc45d616">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgc45d616">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>})} = <span class="org-string">'rigid'</span>
|
|
args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) <span class="org-comment">% Rotation point for the ground motion [m]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge90a770" class="outline-3">
|
|
<h3 id="orge90a770">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orge90a770">
|
|
<p>
|
|
First, we initialize the <code>granite</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ground = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdfb33da" class="outline-3">
|
|
<h3 id="orgdfb33da">Add Type</h3>
|
|
<div class="outline-text-3" id="text-orgdfb33da">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
ground.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
ground.type = 1;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4c31ca5" class="outline-3">
|
|
<h3 id="org4c31ca5">Ground Solid properties</h3>
|
|
<div class="outline-text-3" id="text-org4c31ca5">
|
|
<p>
|
|
We set the shape and density of the ground solid element.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ground.shape = [2, 2, 0.5]; <span class="org-comment">% [m]</span>
|
|
ground.density = 2800; <span class="org-comment">% [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org542691f" class="outline-3">
|
|
<h3 id="org542691f">Rotation Point</h3>
|
|
<div class="outline-text-3" id="text-org542691f">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ground.rot_point = args.rot_point;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge012e41" class="outline-3">
|
|
<h3 id="orge012e41">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-orge012e41">
|
|
<p>
|
|
The <code>ground</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ground'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga045749" class="outline-2">
|
|
<h2 id="orga045749"><span class="section-number-2">4</span> Granite</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org82dc444"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orge6f1ffa" class="outline-3">
|
|
<h3 id="orge6f1ffa">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orge6f1ffa">
|
|
<p>
|
|
The Simscape model of the granite is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>A cartesian joint such that the granite can vibrations along x, y and z axis</li>
|
|
<li>A solid</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The output <code>sample_pos</code> corresponds to the impact point of the X-ray.
|
|
</p>
|
|
|
|
|
|
<div id="org3072cb3" class="figure">
|
|
<p><img src="figs/images/simscape_model_granite.png" alt="simscape_model_granite.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Simscape model for the Granite</p>
|
|
</div>
|
|
|
|
|
|
<div id="org089e7b6" class="figure">
|
|
<p><img src="figs/images/simscape_picture_granite.png" alt="simscape_picture_granite.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Simscape picture for the Granite</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfe1e8d4" class="outline-3">
|
|
<h3 id="orgfe1e8d4">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgfe1e8d4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[granite]</span> = <span class="org-function-name">initializeGranite</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga232b56" class="outline-3">
|
|
<h3 id="orga232b56">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orga232b56">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'none'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 <span class="org-comment">% Density [kg/m3]</span>
|
|
args.x0 (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% Rest position of the Joint in the X direction [m]</span>
|
|
args.y0 (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% Rest position of the Joint in the Y direction [m]</span>
|
|
args.z0 (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% Rest position of the Joint in the Z direction [m]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org6a319e4" class="outline-3">
|
|
<h3 id="org6a319e4">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org6a319e4">
|
|
<p>
|
|
First, we initialize the <code>granite</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org413c06d" class="outline-3">
|
|
<h3 id="org413c06d">Add Granite Type</h3>
|
|
<div class="outline-text-3" id="text-org413c06d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
granite.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
granite.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
granite.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
granite.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
granite.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org35a416f" class="outline-3">
|
|
<h3 id="org35a416f">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org35a416f">
|
|
<p>
|
|
Properties of the Material and link to the geometry of the granite.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite.density = args.density; <span class="org-comment">% [kg/m3]</span>
|
|
granite.STEP = <span class="org-string">'./STEPS/granite/granite.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Z-offset for the initial position of the sample with respect to the granite top surface.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite.sample_pos = 0.8; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org210c84e" class="outline-3">
|
|
<h3 id="org210c84e">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org210c84e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite.K = [4e9; 3e8; 8e8]; <span class="org-comment">% [N/m]</span>
|
|
granite.C = [4.0e5; 1.1e5; 9.0e5]; <span class="org-comment">% [N/(m/s)]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2848fdf" class="outline-3">
|
|
<h3 id="org2848fdf">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org2848fdf">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fgm'</span>);
|
|
granite.Deq = <span class="org-type">-</span>Fgm<span class="org-type">'./</span>granite.K;
|
|
<span class="org-keyword">else</span>
|
|
granite.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5d1f420" class="outline-3">
|
|
<h3 id="org5d1f420">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org5d1f420">
|
|
<p>
|
|
The <code>granite</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'granite'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd3ff237" class="outline-2">
|
|
<h2 id="orgd3ff237"><span class="section-number-2">5</span> Translation Stage</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="orga6fcdbd"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org3048997" class="outline-3">
|
|
<h3 id="org3048997">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org3048997">
|
|
<p>
|
|
The Simscape model of the Translation stage consist of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One rigid body for the fixed part of the translation stage</li>
|
|
<li>One rigid body for the moving part of the translation stage</li>
|
|
<li>Four 6-DOF Joints that only have some rigidity in the X and Z directions.
|
|
The rigidity in rotation comes from the fact that we use multiple joints that are located at different points</li>
|
|
<li>One 6-DOF joint that represent the Actuator.
|
|
It is used to impose the motion in the Y direction</li>
|
|
<li>One 6-DOF joint to inject force disturbance in the X and Z directions</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgb5e657d" class="figure">
|
|
<p><img src="figs/images/simscape_model_ty.png" alt="simscape_model_ty.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Simscape model for the Translation Stage</p>
|
|
</div>
|
|
|
|
|
|
<div id="org55b7d60" class="figure">
|
|
<p><img src="figs/images/simscape_picture_ty.png" alt="simscape_picture_ty.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Simscape picture for the Translation Stage</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9f52c55" class="outline-3">
|
|
<h3 id="org9f52c55">Function description</h3>
|
|
<div class="outline-text-3" id="text-org9f52c55">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ty]</span> = <span class="org-function-name">initializeTy</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org90522d0" class="outline-3">
|
|
<h3 id="org90522d0">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org90522d0">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org609c8fb" class="outline-3">
|
|
<h3 id="org609c8fb">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org609c8fb">
|
|
<p>
|
|
First, we initialize the <code>ty</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org715e876" class="outline-3">
|
|
<h3 id="org715e876">Add Translation Stage Type</h3>
|
|
<div class="outline-text-3" id="text-org715e876">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
ty.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
ty.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
ty.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
ty.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
ty.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfca9fc3" class="outline-3">
|
|
<h3 id="orgfca9fc3">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-orgfca9fc3">
|
|
<p>
|
|
Define the density of the materials as well as the geometry (STEP files).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Ty Granite frame</span>
|
|
ty.granite_frame.density = 7800; <span class="org-comment">% [kg/m3] => 43kg</span>
|
|
ty.granite_frame.STEP = <span class="org-string">'./STEPS/Ty/Ty_Granite_Frame.STEP'</span>;
|
|
|
|
<span class="org-comment">% Guide Translation Ty</span>
|
|
ty.guide.density = 7800; <span class="org-comment">% [kg/m3] => 76kg</span>
|
|
ty.guide.STEP = <span class="org-string">'./STEPS/ty/Ty_Guide.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty - Guide_Translation12</span>
|
|
ty.guide12.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ty.guide12.STEP = <span class="org-string">'./STEPS/Ty/Ty_Guide_12.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty - Guide_Translation11</span>
|
|
ty.guide11.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ty.guide11.STEP = <span class="org-string">'./STEPS/ty/Ty_Guide_11.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty - Guide_Translation22</span>
|
|
ty.guide22.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ty.guide22.STEP = <span class="org-string">'./STEPS/ty/Ty_Guide_22.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty - Guide_Translation21</span>
|
|
ty.guide21.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ty.guide21.STEP = <span class="org-string">'./STEPS/Ty/Ty_Guide_21.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty - Plateau translation</span>
|
|
ty.frame.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ty.frame.STEP = <span class="org-string">'./STEPS/ty/Ty_Stage.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty Stator Part</span>
|
|
ty.stator.density = 5400; <span class="org-comment">% [kg/m3]</span>
|
|
ty.stator.STEP = <span class="org-string">'./STEPS/ty/Ty_Motor_Stator.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ty Rotor Part</span>
|
|
ty.rotor.density = 5400; <span class="org-comment">% [kg/m3]</span>
|
|
ty.rotor.STEP = <span class="org-string">'./STEPS/ty/Ty_Motor_Rotor.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfb71c1d" class="outline-3">
|
|
<h3 id="orgfb71c1d">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-orgfb71c1d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; <span class="org-comment">% [N/m, N*m/rad]</span>
|
|
ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 2e4]; <span class="org-comment">% [N/(m/s), N*m/(rad/s)]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1e5bb2b" class="outline-3">
|
|
<h3 id="org1e5bb2b">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org1e5bb2b">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Ftym'</span>);
|
|
ty.Deq = <span class="org-type">-</span>Ftym<span class="org-type">'./</span>ty.K;
|
|
<span class="org-keyword">else</span>
|
|
ty.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6e13988" class="outline-3">
|
|
<h3 id="org6e13988">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org6e13988">
|
|
<p>
|
|
The <code>ty</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ty'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org46b0509" class="outline-2">
|
|
<h2 id="org46b0509"><span class="section-number-2">6</span> Tilt Stage</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="orga630083"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org3834ca7" class="outline-3">
|
|
<h3 id="org3834ca7">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org3834ca7">
|
|
<p>
|
|
The Simscape model of the Tilt stage is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Two solid bodies for the two part of the stage</li>
|
|
<li><b>Four</b> 6-DOF joints to model the flexibility of the stage.
|
|
These joints are virtually located along the rotation axis and are connecting the two solid bodies.
|
|
These joints have some translation stiffness in the u-v-w directions aligned with the joint.
|
|
The stiffness in rotation between the two solids is due to the fact that the 4 joints are connecting the two solids are different locations</li>
|
|
<li>A Bushing Joint used for the Actuator.
|
|
The Ry motion is imposed by the input.</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgee25bbf" class="figure">
|
|
<p><img src="figs/images/simscape_model_ry.png" alt="simscape_model_ry.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Simscape model for the Tilt Stage</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgcb39e81" class="figure">
|
|
<p><img src="figs/images/simscape_picture_ry.png" alt="simscape_picture_ry.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Simscape picture for the Tilt Stage</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0ffd9dc" class="outline-3">
|
|
<h3 id="org0ffd9dc">Function description</h3>
|
|
<div class="outline-text-3" id="text-org0ffd9dc">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ry]</span> = <span class="org-function-name">initializeRy</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc4130e8" class="outline-3">
|
|
<h3 id="orgc4130e8">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgc4130e8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
args.Ry_init (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5a105fd" class="outline-3">
|
|
<h3 id="org5a105fd">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org5a105fd">
|
|
<p>
|
|
First, we initialize the <code>ry</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgea3a7ba" class="outline-3">
|
|
<h3 id="orgea3a7ba">Add Tilt Type</h3>
|
|
<div class="outline-text-3" id="text-orgea3a7ba">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
ry.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
ry.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
ry.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
ry.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
ry.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdfb5814" class="outline-3">
|
|
<h3 id="orgdfb5814">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-orgdfb5814">
|
|
<p>
|
|
Properties of the Material and link to the geometry of the Tilt stage.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Ry - Guide for the tilt stage</span>
|
|
ry.guide.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ry.guide.STEP = <span class="org-string">'./STEPS/ry/Tilt_Guide.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ry - Rotor of the motor</span>
|
|
ry.rotor.density = 2400; <span class="org-comment">% [kg/m3]</span>
|
|
ry.rotor.STEP = <span class="org-string">'./STEPS/ry/Tilt_Motor_Axis.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ry - Motor</span>
|
|
ry.motor.density = 3200; <span class="org-comment">% [kg/m3]</span>
|
|
ry.motor.STEP = <span class="org-string">'./STEPS/ry/Tilt_Motor.STEP'</span>;
|
|
|
|
<span class="org-comment">% Ry - Plateau Tilt</span>
|
|
ry.stage.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ry.stage.STEP = <span class="org-string">'./STEPS/ry/Tilt_Stage.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Z-Offset so that the center of rotation matches the sample center;
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry.z_offset = 0.58178; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry.Ry_init = args.Ry_init; <span class="org-comment">% [rad]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1ae49c1" class="outline-3">
|
|
<h3 id="org1ae49c1">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org1ae49c1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8];
|
|
ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8e9e40c" class="outline-3">
|
|
<h3 id="org8e9e40c">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org8e9e40c">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fym'</span>);
|
|
ry.Deq = <span class="org-type">-</span>Fym<span class="org-type">'./</span>ry.K;
|
|
<span class="org-keyword">else</span>
|
|
ry.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7d54dc1" class="outline-3">
|
|
<h3 id="org7d54dc1">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org7d54dc1">
|
|
<p>
|
|
The <code>ry</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ry'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb98f9a6" class="outline-2">
|
|
<h2 id="orgb98f9a6"><span class="section-number-2">7</span> Spindle</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<p>
|
|
<a id="org85f7685"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org127f684" class="outline-3">
|
|
<h3 id="org127f684">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org127f684">
|
|
<p>
|
|
The Simscape model of the Spindle is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Two rigid bodies: the stator and the rotor</li>
|
|
<li>A Bushing Joint that is used both as the actuator (the Rz motion is imposed by the input) and as the force perturbation in the Z direction.</li>
|
|
<li>The Bushing joint has some flexibility in the X-Y-Z directions as well as in Rx and Ry rotations</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgf8cd2b8" class="figure">
|
|
<p><img src="figs/images/simscape_model_rz.png" alt="simscape_model_rz.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Simscape model for the Spindle</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8f17d51" class="figure">
|
|
<p><img src="figs/images/simscape_picture_rz.png" alt="simscape_picture_rz.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Simscape picture for the Spindle</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgab0b601" class="outline-3">
|
|
<h3 id="orgab0b601">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgab0b601">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[rz]</span> = <span class="org-function-name">initializeRz</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1f40549" class="outline-3">
|
|
<h3 id="org1f40549">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org1f40549">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org85ca363" class="outline-3">
|
|
<h3 id="org85ca363">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org85ca363">
|
|
<p>
|
|
First, we initialize the <code>rz</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">rz = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge5b17ec" class="outline-3">
|
|
<h3 id="orge5b17ec">Add Spindle Type</h3>
|
|
<div class="outline-text-3" id="text-orge5b17ec">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
rz.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
rz.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
rz.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
rz.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
rz.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1ec9aee" class="outline-3">
|
|
<h3 id="org1ec9aee">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org1ec9aee">
|
|
<p>
|
|
Properties of the Material and link to the geometry of the spindle.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Spindle - Slip Ring</span>
|
|
rz.slipring.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
rz.slipring.STEP = <span class="org-string">'./STEPS/rz/Spindle_Slip_Ring.STEP'</span>;
|
|
|
|
<span class="org-comment">% Spindle - Rotor</span>
|
|
rz.rotor.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
rz.rotor.STEP = <span class="org-string">'./STEPS/rz/Spindle_Rotor.STEP'</span>;
|
|
|
|
<span class="org-comment">% Spindle - Stator</span>
|
|
rz.stator.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
rz.stator.STEP = <span class="org-string">'./STEPS/rz/Spindle_Stator.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org117f09d" class="outline-3">
|
|
<h3 id="org117f09d">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org117f09d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7];
|
|
rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaaa75bf" class="outline-3">
|
|
<h3 id="orgaaa75bf">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-orgaaa75bf">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fzm'</span>);
|
|
rz.Deq = <span class="org-type">-</span>Fzm<span class="org-type">'./</span>rz.K;
|
|
<span class="org-keyword">else</span>
|
|
rz.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org881ebe0" class="outline-3">
|
|
<h3 id="org881ebe0">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org881ebe0">
|
|
<p>
|
|
The <code>rz</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'rz'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org49a14bb" class="outline-2">
|
|
<h2 id="org49a14bb"><span class="section-number-2">8</span> Micro Hexapod</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<p>
|
|
<a id="org01254ae"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org156d5c7" class="outline-3">
|
|
<h3 id="org156d5c7">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org156d5c7">
|
|
|
|
<div id="org13345ec" class="figure">
|
|
<p><img src="figs/images/simscape_model_micro_hexapod.png" alt="simscape_model_micro_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Simscape model for the Micro-Hexapod</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga63e01a" class="figure">
|
|
<p><img src="figs/images/simscape_picture_micro_hexapod.png" alt="simscape_picture_micro_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Simscape picture for the Micro-Hexapod</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4fcfe02" class="outline-3">
|
|
<h3 id="org4fcfe02">Function description</h3>
|
|
<div class="outline-text-3" id="text-org4fcfe02">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[micro_hexapod]</span> = <span class="org-function-name">initializeMicroHexapod</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1e9bfc3" class="outline-3">
|
|
<h3 id="org1e9bfc3">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org1e9bfc3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
<span class="org-comment">% initializeFramesPositions</span>
|
|
args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e<span class="org-type">-</span>3
|
|
args.MO_B (1,1) double {mustBeNumeric} = 270e<span class="org-type">-</span>3
|
|
<span class="org-comment">% generateGeneralConfiguration</span>
|
|
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 50e<span class="org-type">-</span>3
|
|
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 175.5e<span class="org-type">-</span>3
|
|
args.FTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>10, 10, 120<span class="org-type">-</span>10, 120<span class="org-type">+</span>10, 240<span class="org-type">-</span>10, 240<span class="org-type">+</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 45e<span class="org-type">-</span>3
|
|
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 118e<span class="org-type">-</span>3
|
|
args.MTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>60<span class="org-type">+</span>10, 60<span class="org-type">-</span>10, 60<span class="org-type">+</span>10, 180<span class="org-type">-</span>10, 180<span class="org-type">+</span>10, <span class="org-type">-</span>60<span class="org-type">-</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
<span class="org-comment">% initializeStrutDynamics</span>
|
|
args.Ki (6,1) double {mustBeNumeric, mustBeNonnegative} = 2e7<span class="org-type">*</span>ones(6,1)
|
|
args.Ci (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3<span class="org-type">*</span>ones(6,1)
|
|
<span class="org-comment">% initializeCylindricalPlatforms</span>
|
|
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 10
|
|
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 26e<span class="org-type">-</span>3
|
|
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 207.5e<span class="org-type">-</span>3
|
|
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 10
|
|
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 26e<span class="org-type">-</span>3
|
|
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e<span class="org-type">-</span>3
|
|
<span class="org-comment">% initializeCylindricalStruts</span>
|
|
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 25e<span class="org-type">-</span>3
|
|
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 25e<span class="org-type">-</span>3
|
|
<span class="org-comment">% inverseKinematics</span>
|
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
|
<span class="org-comment">% Force that stiffness of each joint should apply at t=0</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1c650c8" class="outline-3">
|
|
<h3 id="org1c650c8">Function content</h3>
|
|
<div class="outline-text-3" id="text-org1c650c8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">micro_hexapod = initializeFramesPositions(<span class="org-string">'H'</span>, args.H, <span class="org-string">'MO_B'</span>, args.MO_B);
|
|
micro_hexapod = generateGeneralConfiguration(micro_hexapod, <span class="org-string">'FH'</span>, args.FH, <span class="org-string">'FR'</span>, args.FR, <span class="org-string">'FTh'</span>, args.FTh, <span class="org-string">'MH'</span>, args.MH, <span class="org-string">'MR'</span>, args.MR, <span class="org-string">'MTh'</span>, args.MTh);
|
|
micro_hexapod = computeJointsPose(micro_hexapod);
|
|
micro_hexapod = initializeStrutDynamics(micro_hexapod, <span class="org-string">'Ki'</span>, args.Ki, <span class="org-string">'Ci'</span>, args.Ci);
|
|
micro_hexapod = initializeCylindricalPlatforms(micro_hexapod, <span class="org-string">'Fpm'</span>, args.Fpm, <span class="org-string">'Fph'</span>, args.Fph, <span class="org-string">'Fpr'</span>, args.Fpr, <span class="org-string">'Mpm'</span>, args.Mpm, <span class="org-string">'Mph'</span>, args.Mph, <span class="org-string">'Mpr'</span>, args.Mpr);
|
|
micro_hexapod = initializeCylindricalStruts(micro_hexapod, <span class="org-string">'Fsm'</span>, args.Fsm, <span class="org-string">'Fsh'</span>, args.Fsh, <span class="org-string">'Fsr'</span>, args.Fsr, <span class="org-string">'Msm'</span>, args.Msm, <span class="org-string">'Msh'</span>, args.Msh, <span class="org-string">'Msr'</span>, args.Msr);
|
|
micro_hexapod = computeJacobian(micro_hexapod);
|
|
[Li, dLi] = inverseKinematics(micro_hexapod, <span class="org-string">'AP'</span>, args.AP, <span class="org-string">'ARB'</span>, args.ARB);
|
|
micro_hexapod.Li = Li;
|
|
micro_hexapod.dLi = dLi;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Equilibrium position of the each joint.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fhm'</span>);
|
|
micro_hexapod.dLeq = <span class="org-type">-</span>Fhm<span class="org-type">'./</span>args.Ki;
|
|
<span class="org-keyword">else</span>
|
|
micro_hexapod.dLeq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb34b6c7" class="outline-3">
|
|
<h3 id="orgb34b6c7">Add Type</h3>
|
|
<div class="outline-text-3" id="text-orgb34b6c7">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
micro_hexapod.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
micro_hexapod.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
micro_hexapod.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
micro_hexapod.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
micro_hexapod.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc0b87f8" class="outline-3">
|
|
<h3 id="orgc0b87f8">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-orgc0b87f8">
|
|
<p>
|
|
The <code>micro_hexapod</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'micro_hexapod'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga55d418" class="outline-2">
|
|
<h2 id="orga55d418"><span class="section-number-2">9</span> Center of gravity compensation</h2>
|
|
<div class="outline-text-2" id="text-9">
|
|
<p>
|
|
<a id="org9989724"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org7501cd7" class="outline-3">
|
|
<h3 id="org7501cd7">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org7501cd7">
|
|
<p>
|
|
The Simscape model of the Center of gravity compensator is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One main solid that is connected to two other solids (the masses to position of center of mass) through two revolute joints</li>
|
|
<li>The angle of both revolute joints is set by the input</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orge09d585" class="figure">
|
|
<p><img src="figs/images/simscape_model_axisc.png" alt="simscape_model_axisc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Simscape model for the Center of Mass compensation system</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga3d0932" class="figure">
|
|
<p><img src="figs/images/simscape_picture_axisc.png" alt="simscape_picture_axisc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Simscape picture for the Center of Mass compensation system</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8b06b22" class="outline-3">
|
|
<h3 id="org8b06b22">Function description</h3>
|
|
<div class="outline-text-3" id="text-org8b06b22">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[axisc]</span> = <span class="org-function-name">initializeAxisc</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8b0c4a4" class="outline-3">
|
|
<h3 id="org8b0c4a4">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org8b0c4a4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>})} = <span class="org-string">'flexible'</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org50581f7" class="outline-3">
|
|
<h3 id="org50581f7">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org50581f7">
|
|
<p>
|
|
First, we initialize the <code>axisc</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">axisc = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5167cf8" class="outline-3">
|
|
<h3 id="org5167cf8">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org5167cf8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
axisc.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
axisc.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
axisc.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge79b90d" class="outline-3">
|
|
<h3 id="orge79b90d">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-orge79b90d">
|
|
<p>
|
|
Properties of the Material and link to the geometry files.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Structure</span>
|
|
axisc.structure.density = 3400; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.structure.STEP = <span class="org-string">'./STEPS/axisc/axisc_structure.STEP'</span>;
|
|
|
|
<span class="org-comment">% Wheel</span>
|
|
axisc.wheel.density = 2700; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.wheel.STEP = <span class="org-string">'./STEPS/axisc/axisc_wheel.STEP'</span>;
|
|
|
|
<span class="org-comment">% Mass</span>
|
|
axisc.mass.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.mass.STEP = <span class="org-string">'./STEPS/axisc/axisc_mass.STEP'</span>;
|
|
|
|
<span class="org-comment">% Gear</span>
|
|
axisc.gear.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.gear.STEP = <span class="org-string">'./STEPS/axisc/axisc_gear.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4a63f45" class="outline-3">
|
|
<h3 id="org4a63f45">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org4a63f45">
|
|
<p>
|
|
The <code>axisc</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'axisc'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7586ab7" class="outline-2">
|
|
<h2 id="org7586ab7"><span class="section-number-2">10</span> Mirror</h2>
|
|
<div class="outline-text-2" id="text-10">
|
|
<p>
|
|
<a id="org3d670bf"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org406058f" class="outline-3">
|
|
<h3 id="org406058f">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org406058f">
|
|
<p>
|
|
The Simscape Model of the mirror is just a solid body.
|
|
The output <code>mirror_center</code> corresponds to the center of the Sphere and is the point of measurement for the metrology
|
|
</p>
|
|
|
|
|
|
<div id="org281f48a" class="figure">
|
|
<p><img src="figs/images/simscape_model_mirror.png" alt="simscape_model_mirror.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Simscape model for the Mirror</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgf4fa701" class="figure">
|
|
<p><img src="figs/images/simscape_picture_mirror.png" alt="simscape_picture_mirror.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Simscape picture for the Mirror</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org090435a" class="outline-3">
|
|
<h3 id="org090435a">Function description</h3>
|
|
<div class="outline-text-3" id="text-org090435a">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeMirror</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org06a58c7" class="outline-3">
|
|
<h3 id="org06a58c7">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org06a58c7">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>})} = <span class="org-string">'rigid'</span>
|
|
args.shape char {mustBeMember(args.shape,{<span class="org-string">'spherical'</span>, <span class="org-string">'conical'</span>})} = <span class="org-string">'spherical'</span>
|
|
args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45 <span class="org-comment">% [deg]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfd4ee37" class="outline-3">
|
|
<h3 id="orgfd4ee37">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgfd4ee37">
|
|
<p>
|
|
First, we initialize the <code>mirror</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgff14824" class="outline-3">
|
|
<h3 id="orgff14824">Add Mirror Type</h3>
|
|
<div class="outline-text-3" id="text-orgff14824">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
mirror.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
mirror.type = 1;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0144cc7" class="outline-3">
|
|
<h3 id="org0144cc7">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org0144cc7">
|
|
<p>
|
|
We define the geometrical values.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.h = 0.05; <span class="org-comment">% Height of the mirror [m]</span>
|
|
|
|
mirror.thickness = 0.025; <span class="org-comment">% Thickness of the plate supporting the sample [m]</span>
|
|
|
|
mirror.hole_rad = 0.120; <span class="org-comment">% radius of the hole in the mirror [m]</span>
|
|
|
|
mirror.support_rad = 0.1; <span class="org-comment">% radius of the support plate [m]</span>
|
|
|
|
<span class="org-comment">% point of interest offset in z (above the top surfave) [m]</span>
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
mirror.jacobian = 0.20;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
mirror.jacobian = 0.20 <span class="org-type">-</span> mirror.h;
|
|
<span class="org-keyword">end</span>
|
|
|
|
mirror.rad = 0.180; <span class="org-comment">% radius of the mirror (at the bottom surface) [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.density = 2400; <span class="org-comment">% Density of the material [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.cone_length = mirror.rad<span class="org-type">*</span>tand(args.angle)<span class="org-type">+</span>mirror.h<span class="org-type">+</span>mirror.jacobian; <span class="org-comment">% Distance from Apex point of the cone to jacobian point</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Now we define the Shape of the mirror.
|
|
We first start with the internal part.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.shape = [...
|
|
0 mirror.h<span class="org-type">-</span>mirror.thickness
|
|
mirror.hole_rad mirror.h<span class="org-type">-</span>mirror.thickness; ...
|
|
mirror.hole_rad 0; ...
|
|
mirror.rad 0 ...
|
|
];
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then, we define the reflective used part of the mirror.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> strcmp(args.shape, <span class="org-string">'spherical'</span>)
|
|
mirror.sphere_radius = sqrt((mirror.jacobian<span class="org-type">+</span>mirror.h)<span class="org-type">^</span>2<span class="org-type">+</span>mirror.rad<span class="org-type">^</span>2); <span class="org-comment">% Radius of the sphere [mm]</span>
|
|
|
|
<span class="org-keyword">for</span> <span class="org-variable-name">z</span> = <span class="org-constant">linspace(0, mirror.h, 101)</span>
|
|
mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius<span class="org-type">^</span>2<span class="org-type">-</span>(z<span class="org-type">-</span>mirror.jacobian<span class="org-type">-</span>mirror.h)<span class="org-type">^</span>2) z];
|
|
<span class="org-keyword">end</span>
|
|
<span class="org-keyword">elseif</span> strcmp(args.shape, <span class="org-string">'conical'</span>)
|
|
mirror.shape = [mirror.shape; mirror.rad<span class="org-type">+</span>mirror.h<span class="org-type">/</span>tand(args.angle) mirror.h];
|
|
<span class="org-keyword">else</span>
|
|
error(<span class="org-string">'Shape should be either conical or spherical'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we close the shape.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.shape = [mirror.shape; 0 mirror.h];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org505752d" class="outline-3">
|
|
<h3 id="org505752d">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org505752d">
|
|
<p>
|
|
The <code>mirror</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'mirror'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4dc3820" class="outline-2">
|
|
<h2 id="org4dc3820"><span class="section-number-2">11</span> Nano Hexapod</h2>
|
|
<div class="outline-text-2" id="text-11">
|
|
<p>
|
|
<a id="org9a9721e"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org08f35a2" class="outline-3">
|
|
<h3 id="org08f35a2">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org08f35a2">
|
|
|
|
<div id="orga6643fc" class="figure">
|
|
<p><img src="figs/images/simscape_model_nano_hexapod.png" alt="simscape_model_nano_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Simscape model for the Nano Hexapod</p>
|
|
</div>
|
|
|
|
|
|
<div id="org4d9fd08" class="figure">
|
|
<p><img src="figs/images/simscape_picture_nano_hexapod.png" alt="simscape_picture_nano_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Simscape picture for the Nano Hexapod</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb862ff4" class="outline-3">
|
|
<h3 id="orgb862ff4">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgb862ff4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[nano_hexapod]</span> = <span class="org-function-name">initializeNanoHexapod</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgac24dff" class="outline-3">
|
|
<h3 id="orgac24dff">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgac24dff">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>})} = <span class="org-string">'flexible'</span>
|
|
<span class="org-comment">% initializeFramesPositions</span>
|
|
args.H (1,1) double {mustBeNumeric, mustBePositive} = 90e<span class="org-type">-</span>3
|
|
args.MO_B (1,1) double {mustBeNumeric} = 175e<span class="org-type">-</span>3
|
|
<span class="org-comment">% generateGeneralConfiguration</span>
|
|
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e<span class="org-type">-</span>3
|
|
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
args.FTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>10, 10, 120<span class="org-type">-</span>10, 120<span class="org-type">+</span>10, 240<span class="org-type">-</span>10, 240<span class="org-type">+</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e<span class="org-type">-</span>3
|
|
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e<span class="org-type">-</span>3
|
|
args.MTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>60<span class="org-type">+</span>10, 60<span class="org-type">-</span>10, 60<span class="org-type">+</span>10, 180<span class="org-type">-</span>10, 180<span class="org-type">+</span>10, <span class="org-type">-</span>60<span class="org-type">-</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
<span class="org-comment">% initializeStrutDynamics</span>
|
|
args.actuator char {mustBeMember(args.actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
|
|
<span class="org-comment">% initializeCylindricalPlatforms</span>
|
|
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e<span class="org-type">-</span>3
|
|
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e<span class="org-type">-</span>3
|
|
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e<span class="org-type">-</span>3
|
|
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
<span class="org-comment">% initializeCylindricalStruts</span>
|
|
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
|
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e<span class="org-type">-</span>3
|
|
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e<span class="org-type">-</span>3
|
|
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
|
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e<span class="org-type">-</span>3
|
|
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e<span class="org-type">-</span>3
|
|
<span class="org-comment">% inverseKinematics</span>
|
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
|
<span class="org-comment">% Equilibrium position of each leg</span>
|
|
args.dLeq (6,1) double {mustBeNumeric} = zeros(6,1)
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org35fbeff" class="outline-3">
|
|
<h3 id="org35fbeff">Function content</h3>
|
|
<div class="outline-text-3" id="text-org35fbeff">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">nano_hexapod = initializeFramesPositions(<span class="org-string">'H'</span>, args.H, <span class="org-string">'MO_B'</span>, args.MO_B);
|
|
nano_hexapod = generateGeneralConfiguration(nano_hexapod, <span class="org-string">'FH'</span>, args.FH, <span class="org-string">'FR'</span>, args.FR, <span class="org-string">'FTh'</span>, args.FTh, <span class="org-string">'MH'</span>, args.MH, <span class="org-string">'MR'</span>, args.MR, <span class="org-string">'MTh'</span>, args.MTh);
|
|
nano_hexapod = computeJointsPose(nano_hexapod);
|
|
<span class="org-keyword">if</span> strcmp(args.actuator, <span class="org-string">'piezo'</span>)
|
|
nano_hexapod = initializeStrutDynamics(nano_hexapod, <span class="org-string">'Ki'</span>, 1e7<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
|
<span class="org-keyword">elseif</span> strcmp(args.actuator, <span class="org-string">'lorentz'</span>)
|
|
nano_hexapod = initializeStrutDynamics(nano_hexapod, <span class="org-string">'Ki'</span>, 1e4<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
|
<span class="org-keyword">else</span>
|
|
error(<span class="org-string">'args.actuator should be piezo or lorentz'</span>);
|
|
<span class="org-keyword">end</span>
|
|
nano_hexapod = initializeCylindricalPlatforms(nano_hexapod, <span class="org-string">'Fpm'</span>, args.Fpm, <span class="org-string">'Fph'</span>, args.Fph, <span class="org-string">'Fpr'</span>, args.Fpr, <span class="org-string">'Mpm'</span>, args.Mpm, <span class="org-string">'Mph'</span>, args.Mph, <span class="org-string">'Mpr'</span>, args.Mpr);
|
|
nano_hexapod = initializeCylindricalStruts(nano_hexapod, <span class="org-string">'Fsm'</span>, args.Fsm, <span class="org-string">'Fsh'</span>, args.Fsh, <span class="org-string">'Fsr'</span>, args.Fsr, <span class="org-string">'Msm'</span>, args.Msm, <span class="org-string">'Msh'</span>, args.Msh, <span class="org-string">'Msr'</span>, args.Msr);
|
|
nano_hexapod = computeJacobian(nano_hexapod);
|
|
[Li, dLi] = inverseKinematics(nano_hexapod, <span class="org-string">'AP'</span>, args.AP, <span class="org-string">'ARB'</span>, args.ARB);
|
|
nano_hexapod.Li = Li;
|
|
nano_hexapod.dLi = dLi;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">nano_hexapod.dLeq = args.dLeq;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2939880" class="outline-3">
|
|
<h3 id="org2939880">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org2939880">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
nano_hexapod.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
nano_hexapod.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
nano_hexapod.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdc2d29f" class="outline-3">
|
|
<h3 id="orgdc2d29f">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-orgdc2d29f">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3d615a1" class="outline-2">
|
|
<h2 id="org3d615a1"><span class="section-number-2">12</span> Sample</h2>
|
|
<div class="outline-text-2" id="text-12">
|
|
<p>
|
|
<a id="org9f0d804"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd8e711f" class="outline-3">
|
|
<h3 id="orgd8e711f">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgd8e711f">
|
|
<p>
|
|
The Simscape model of the sample environment is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>A rigid transform that can be used to translate the sample (position offset)</li>
|
|
<li>A cartesian joint to add some flexibility to the sample environment mount</li>
|
|
<li>A solid that represent the sample</li>
|
|
<li>An input is added to apply some external forces and torques at the center of the sample environment.
|
|
This could be the case for cable forces for instance.</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org4bf20ba" class="figure">
|
|
<p><img src="figs/images/simscape_model_sample.png" alt="simscape_model_sample.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Simscape model for the Sample</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgfaf9137" class="figure">
|
|
<p><img src="figs/images/simscape_picture_sample.png" alt="simscape_picture_sample.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </span>Simscape picture for the Sample</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgec394e5" class="outline-3">
|
|
<h3 id="orgec394e5">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgec394e5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[sample]</span> = <span class="org-function-name">initializeSample</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9a67f8d" class="outline-3">
|
|
<h3 id="org9a67f8d">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org9a67f8d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'none'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 <span class="org-comment">% [m]</span>
|
|
args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 <span class="org-comment">% [m]</span>
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 <span class="org-comment">% [kg]</span>
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 100 <span class="org-comment">% [Hz]</span>
|
|
args.offset (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org82f944c" class="outline-3">
|
|
<h3 id="org82f944c">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org82f944c">
|
|
<p>
|
|
First, we initialize the <code>sample</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2bb1d24" class="outline-3">
|
|
<h3 id="org2bb1d24">Add Sample Type</h3>
|
|
<div class="outline-text-3" id="text-org2bb1d24">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
sample.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
sample.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
sample.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
sample.type = 3;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org63af8a7" class="outline-3">
|
|
<h3 id="org63af8a7">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org63af8a7">
|
|
<p>
|
|
We define the geometrical parameters of the sample as well as its mass and position.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.radius = args.radius; <span class="org-comment">% [m]</span>
|
|
sample.height = args.height; <span class="org-comment">% [m]</span>
|
|
sample.mass = args.mass; <span class="org-comment">% [kg]</span>
|
|
sample.offset = args.offset; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org91c540d" class="outline-3">
|
|
<h3 id="org91c540d">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org91c540d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.K = ones(3,1) <span class="org-type">*</span> sample.mass <span class="org-type">*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span> <span class="org-type">*</span> args.freq)<span class="org-type">^</span>2; <span class="org-comment">% [N/m]</span>
|
|
sample.C = 0.1 <span class="org-type">*</span> sqrt(sample.K<span class="org-type">*</span>sample.mass); <span class="org-comment">% [N/(m/s)]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org19876e8" class="outline-3">
|
|
<h3 id="org19876e8">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org19876e8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fsm'</span>);
|
|
sample.Deq = <span class="org-type">-</span>Fsm<span class="org-type">'./</span>sample.K;
|
|
<span class="org-keyword">else</span>
|
|
sample.Deq = zeros(3,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org23eeae8" class="outline-3">
|
|
<h3 id="org23eeae8">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org23eeae8">
|
|
<p>
|
|
The <code>sample</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'sample'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge9cbdc9" class="outline-2">
|
|
<h2 id="orge9cbdc9"><span class="section-number-2">13</span> Initialize Controller</h2>
|
|
<div class="outline-text-2" id="text-13">
|
|
<p>
|
|
<a id="orgd0062b9"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb650d4c" class="outline-3">
|
|
<h3 id="orgb650d4c">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-orgb650d4c">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeController</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org90273ed" class="outline-3">
|
|
<h3 id="org90273ed">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org90273ed">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'open-loop'</span>, <span class="org-string">'iff'</span>, <span class="org-string">'dvf'</span>, <span class="org-string">'hac-dvf'</span>, <span class="org-string">'ref-track-L'</span>, <span class="org-string">'ref-track-iff-L'</span>, <span class="org-string">'cascade-hac-lac'</span>, <span class="org-string">'hac-iff'</span>})} = <span class="org-string">'open-loop'</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0f81215" class="outline-3">
|
|
<h3 id="org0f81215">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org0f81215">
|
|
<p>
|
|
First, we initialize the <code>controller</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">controller = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4207f98" class="outline-3">
|
|
<h3 id="org4207f98">Controller Type</h3>
|
|
<div class="outline-text-3" id="text-org4207f98">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'open-loop'</span>
|
|
controller.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'dvf'</span>
|
|
controller.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'iff'</span>
|
|
controller.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'hac-dvf'</span>
|
|
controller.type = 4;
|
|
<span class="org-keyword">case</span> <span class="org-string">'ref-track-L'</span>
|
|
controller.type = 5;
|
|
<span class="org-keyword">case</span> <span class="org-string">'ref-track-iff-L'</span>
|
|
controller.type = 6;
|
|
<span class="org-keyword">case</span> <span class="org-string">'cascade-hac-lac'</span>
|
|
controller.type = 7;
|
|
<span class="org-keyword">case</span> <span class="org-string">'hac-iff'</span>
|
|
controller.type = 8;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5fe61c6" class="outline-3">
|
|
<h3 id="org5fe61c6">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org5fe61c6">
|
|
<p>
|
|
The <code>controller</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/controller.mat'</span>, <span class="org-string">'controller'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgae5cb57" class="outline-2">
|
|
<h2 id="orgae5cb57"><span class="section-number-2">14</span> Generate Reference Signals</h2>
|
|
<div class="outline-text-2" id="text-14">
|
|
<p>
|
|
<a id="org5ace526"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc0954ba" class="outline-3">
|
|
<h3 id="orgc0954ba">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-orgc0954ba">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ref]</span> = <span class="org-function-name">initializeReferences</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0c5ed70" class="outline-3">
|
|
<h3 id="org0c5ed70">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org0c5ed70">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
<span class="org-comment">% Sampling Frequency [s]</span>
|
|
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3
|
|
<span class="org-comment">% Maximum simulation time [s]</span>
|
|
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
|
|
<span class="org-comment">% Either "constant" / "triangular" / "sinusoidal"</span>
|
|
args.Dy_type char {mustBeMember(args.Dy_type,{<span class="org-string">'constant'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'sinusoidal'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Amplitude of the displacement [m]</span>
|
|
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-comment">% Period of the displacement [s]</span>
|
|
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-comment">% Either "constant" / "triangular" / "sinusoidal"</span>
|
|
args.Ry_type char {mustBeMember(args.Ry_type,{<span class="org-string">'constant'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'sinusoidal'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Amplitude [rad]</span>
|
|
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-comment">% Period of the displacement [s]</span>
|
|
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-comment">% Either "constant" / "rotating"</span>
|
|
args.Rz_type char {mustBeMember(args.Rz_type,{<span class="org-string">'constant'</span>, <span class="org-string">'rotating'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial angle [rad]</span>
|
|
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-comment">% Period of the rotating [s]</span>
|
|
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-comment">% For now, only constant is implemented</span>
|
|
args.Dh_type char {mustBeMember(args.Dh_type,{<span class="org-string">'constant'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)</span>
|
|
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
|
|
<span class="org-comment">% For now, only constant is implemented</span>
|
|
args.Rm_type char {mustBeMember(args.Rm_type,{<span class="org-string">'constant'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial position of the two masses</span>
|
|
args.Rm_pos (2,1) double {mustBeNumeric} = [0; <span class="org-constant">pi</span>]
|
|
<span class="org-comment">% For now, only constant is implemented</span>
|
|
args.Dn_type char {mustBeMember(args.Dn_type,{<span class="org-string">'constant'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial position [m,m,m,rad,rad,rad] of the top platform</span>
|
|
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orge94c0c2" class="outline-3">
|
|
<h3 id="orge94c0c2">Initialize Parameters</h3>
|
|
<div class="outline-text-3" id="text-orge94c0c2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Set Sampling Time</span></span>
|
|
Ts = args.Ts;
|
|
Tmax = args.Tmax;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Low Pass Filter to filter out the references</span></span>
|
|
s = zpk(<span class="org-string">'s'</span>);
|
|
w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10;
|
|
xi = 1;
|
|
H_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> 2<span class="org-type">*</span>xi<span class="org-type">/</span>w0<span class="org-type">*</span>s <span class="org-type">+</span> s<span class="org-type">^</span>2<span class="org-type">/</span>w0<span class="org-type">^</span>2);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6a6adba" class="outline-3">
|
|
<h3 id="org6a6adba">Translation Stage</h3>
|
|
<div class="outline-text-3" id="text-org6a6adba">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Translation stage - Dy</span></span>
|
|
t = 0<span class="org-type">:</span>Ts<span class="org-type">:</span>Tmax; <span class="org-comment">% Time Vector [s]</span>
|
|
Dy = zeros(length(t), 1);
|
|
Dyd = zeros(length(t), 1);
|
|
Dydd = zeros(length(t), 1);
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Dy_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Dy<span class="org-type">(:) </span>= args.Dy_amplitude;
|
|
Dyd<span class="org-type">(:) </span>= 0;
|
|
Dydd<span class="org-type">(:) </span>= 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
|
|
<span class="org-comment">% This is done to unsure that we start with no displacement</span>
|
|
Dy_raw = args.Dy_amplitude<span class="org-type">*</span>sawtooth(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>t<span class="org-type">/</span>args.Dy_period,1<span class="org-type">/</span>2);
|
|
i0 = find(t<span class="org-type">>=</span>args.Dy_period<span class="org-type">/</span>4,1);
|
|
Dy(1<span class="org-type">:</span>end<span class="org-type">-</span>i0<span class="org-type">+</span>1) = Dy_raw(i0<span class="org-type">:</span>end);
|
|
Dy(end<span class="org-type">-</span>i0<span class="org-type">+</span>2<span class="org-type">:</span>end) = Dy_raw(end); <span class="org-comment">% we fix the last value</span>
|
|
|
|
<span class="org-comment">% The signal is filtered out</span>
|
|
Dy = lsim(H_lpf, Dy, t);
|
|
Dyd = lsim(H_lpf<span class="org-type">*</span>s, Dy, t);
|
|
Dydd = lsim(H_lpf<span class="org-type">*</span>s<span class="org-type">^</span>2, Dy, t);
|
|
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
|
|
Dy<span class="org-type">(:) </span>= args.Dy_amplitude<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>t);
|
|
Dyd = args.Dy_amplitude<span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>cos(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>t);
|
|
Dydd = <span class="org-type">-</span>args.Dy_amplitude<span class="org-type">*</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period)<span class="org-type">^</span>2<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>t);
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Dy_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Dy = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dy), <span class="org-string">'deriv'</span>, Dyd, <span class="org-string">'dderiv'</span>, Dydd);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf61cdf3" class="outline-3">
|
|
<h3 id="orgf61cdf3">Tilt Stage</h3>
|
|
<div class="outline-text-3" id="text-orgf61cdf3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Tilt Stage - Ry</span></span>
|
|
t = 0<span class="org-type">:</span>Ts<span class="org-type">:</span>Tmax; <span class="org-comment">% Time Vector [s]</span>
|
|
Ry = zeros(length(t), 1);
|
|
Ryd = zeros(length(t), 1);
|
|
Rydd = zeros(length(t), 1);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Ry_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Ry<span class="org-type">(:) </span>= args.Ry_amplitude;
|
|
Ryd<span class="org-type">(:) </span>= 0;
|
|
Rydd<span class="org-type">(:) </span>= 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
|
|
Ry_raw = args.Ry_amplitude<span class="org-type">*</span>sawtooth(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>t<span class="org-type">/</span>args.Ry_period,1<span class="org-type">/</span>2);
|
|
i0 = find(t<span class="org-type">>=</span>args.Ry_period<span class="org-type">/</span>4,1);
|
|
Ry(1<span class="org-type">:</span>end<span class="org-type">-</span>i0<span class="org-type">+</span>1) = Ry_raw(i0<span class="org-type">:</span>end);
|
|
Ry(end<span class="org-type">-</span>i0<span class="org-type">+</span>2<span class="org-type">:</span>end) = Ry_raw(end); <span class="org-comment">% we fix the last value</span>
|
|
|
|
<span class="org-comment">% The signal is filtered out</span>
|
|
Ry = lsim(H_lpf, Ry, t);
|
|
Ryd = lsim(H_lpf<span class="org-type">*</span>s, Ry, t);
|
|
Rydd = lsim(H_lpf<span class="org-type">*</span>s<span class="org-type">^</span>2, Ry, t);
|
|
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
|
|
Ry<span class="org-type">(:) </span>= args.Ry_amplitude<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>t);
|
|
|
|
Ryd = args.Ry_amplitude<span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>cos(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>t);
|
|
Rydd = <span class="org-type">-</span>args.Ry_amplitude<span class="org-type">*</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period)<span class="org-type">^</span>2<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>t);
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Ry_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Ry = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Ry), <span class="org-string">'deriv'</span>, Ryd, <span class="org-string">'dderiv'</span>, Rydd);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3e7754b" class="outline-3">
|
|
<h3 id="org3e7754b">Spindle</h3>
|
|
<div class="outline-text-3" id="text-org3e7754b">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Spindle - Rz</span></span>
|
|
t = 0<span class="org-type">:</span>Ts<span class="org-type">:</span>Tmax; <span class="org-comment">% Time Vector [s]</span>
|
|
Rz = zeros(length(t), 1);
|
|
Rzd = zeros(length(t), 1);
|
|
Rzdd = zeros(length(t), 1);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Rz_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Rz<span class="org-type">(:) </span>= args.Rz_amplitude;
|
|
Rzd<span class="org-type">(:) </span>= 0;
|
|
Rzdd<span class="org-type">(:) </span>= 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rotating'</span>
|
|
Rz<span class="org-type">(:) </span>= 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Rz_period<span class="org-type">*</span>t;
|
|
|
|
<span class="org-comment">% The signal is filtered out</span>
|
|
Rz = lsim(H_lpf, Rz, t);
|
|
Rzd = lsim(H_lpf<span class="org-type">*</span>s, Rz, t);
|
|
Rzdd = lsim(H_lpf<span class="org-type">*</span>s<span class="org-type">^</span>2, Rz, t);
|
|
|
|
<span class="org-comment">% We add the angle offset</span>
|
|
Rz = Rz <span class="org-type">+</span> args.Rz_amplitude;
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Rz_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Rz = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Rz), <span class="org-string">'deriv'</span>, Rzd, <span class="org-string">'dderiv'</span>, Rzdd);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaf1747d" class="outline-3">
|
|
<h3 id="orgaf1747d">Micro Hexapod</h3>
|
|
<div class="outline-text-3" id="text-orgaf1747d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
|
|
t = [0, Ts];
|
|
Dh = zeros(length(t), 6);
|
|
Dhl = zeros(length(t), 6);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Dh_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Dh = [args.Dh_pos, args.Dh_pos];
|
|
|
|
load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'micro_hexapod'</span>);
|
|
|
|
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
|
|
|
|
tx = args.Dh_pos(4);
|
|
ty = args.Dh_pos(5);
|
|
tz = args.Dh_pos(6);
|
|
|
|
ARB = [cos(tz) <span class="org-type">-</span>sin(tz) 0;
|
|
sin(tz) cos(tz) 0;
|
|
0 0 1]<span class="org-type">*</span>...
|
|
[ cos(ty) 0 sin(ty);
|
|
0 1 0;
|
|
<span class="org-type">-</span>sin(ty) 0 cos(ty)]<span class="org-type">*</span>...
|
|
[1 0 0;
|
|
0 cos(tx) <span class="org-type">-</span>sin(tx);
|
|
0 sin(tx) cos(tx)];
|
|
|
|
[<span class="org-type">~</span>, Dhl] = inverseKinematics(micro_hexapod, <span class="org-string">'AP'</span>, AP, <span class="org-string">'ARB'</span>, ARB);
|
|
Dhl = [Dhl, Dhl];
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Dh_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Dh = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dh));
|
|
Dhl = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dhl));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org04d73dc" class="outline-3">
|
|
<h3 id="org04d73dc">Axis Compensation</h3>
|
|
<div class="outline-text-3" id="text-org04d73dc">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Axis Compensation - Rm</span></span>
|
|
t = [0, Ts];
|
|
|
|
Rm = [args.Rm_pos, args.Rm_pos];
|
|
Rm = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Rm));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd74c144" class="outline-3">
|
|
<h3 id="orgd74c144">Nano Hexapod</h3>
|
|
<div class="outline-text-3" id="text-orgd74c144">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Nano-Hexapod</span></span>
|
|
t = [0, Ts];
|
|
Dn = zeros(length(t), 6);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Dn_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Dn = [args.Dn_pos, args.Dn_pos];
|
|
|
|
load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
|
|
|
|
AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)];
|
|
|
|
tx = args.Dn_pos(4);
|
|
ty = args.Dn_pos(5);
|
|
tz = args.Dn_pos(6);
|
|
|
|
ARB = [cos(tz) <span class="org-type">-</span>sin(tz) 0;
|
|
sin(tz) cos(tz) 0;
|
|
0 0 1]<span class="org-type">*</span>...
|
|
[ cos(ty) 0 sin(ty);
|
|
0 1 0;
|
|
<span class="org-type">-</span>sin(ty) 0 cos(ty)]<span class="org-type">*</span>...
|
|
[1 0 0;
|
|
0 cos(tx) <span class="org-type">-</span>sin(tx);
|
|
0 sin(tx) cos(tx)];
|
|
|
|
[<span class="org-type">~</span>, Dnl] = inverseKinematics(nano_hexapod, <span class="org-string">'AP'</span>, AP, <span class="org-string">'ARB'</span>, ARB);
|
|
Dnl = [Dnl, Dnl];
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Dn_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Dn = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dn));
|
|
Dnl = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dnl));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd21e485" class="outline-3">
|
|
<h3 id="orgd21e485">Save</h3>
|
|
<div class="outline-text-3" id="text-orgd21e485">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
|
|
save(<span class="org-string">'./mat/nass_references.mat'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>, <span class="org-string">'Dh'</span>, <span class="org-string">'Dhl'</span>, <span class="org-string">'Rm'</span>, <span class="org-string">'Dn'</span>, <span class="org-string">'Dnl'</span>, <span class="org-string">'Ts'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org544c9dd" class="outline-2">
|
|
<h2 id="org544c9dd"><span class="section-number-2">15</span> Initialize Disturbances</h2>
|
|
<div class="outline-text-2" id="text-15">
|
|
<p>
|
|
<a id="org199c5f8"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org8067551" class="outline-3">
|
|
<h3 id="org8067551">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-org8067551">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeDisturbances</span>(<span class="org-variable-name">args</span>)
|
|
<span class="org-comment">% initializeDisturbances - Initialize the disturbances</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Syntax: [] = initializeDisturbances(args)</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Inputs:</span>
|
|
<span class="org-comment">% - args -</span>
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4fe2ec1" class="outline-3">
|
|
<h3 id="org4fe2ec1">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org4fe2ec1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
<span class="org-comment">% Global parameter to enable or disable the disturbances</span>
|
|
args.enable logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Ground Motion - X direction</span>
|
|
args.Dwx logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Ground Motion - Y direction</span>
|
|
args.Dwy logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Ground Motion - Z direction</span>
|
|
args.Dwz logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Translation Stage - X direction</span>
|
|
args.Fty_x logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Translation Stage - Z direction</span>
|
|
args.Fty_z logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Spindle - Z direction</span>
|
|
args.Frz_z logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgf744aeb" class="outline-3">
|
|
<h3 id="orgf744aeb">Load Data</h3>
|
|
<div class="outline-text-3" id="text-orgf744aeb">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We remove the first frequency point that usually is very large.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org6c7d666" class="outline-3">
|
|
<h3 id="org6c7d666">Parameters</h3>
|
|
<div class="outline-text-3" id="text-org6c7d666">
|
|
<p>
|
|
We define some parameters that will be used in the algorithm.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Fs = 2<span class="org-type">*</span>dist_f.f(end); <span class="org-comment">% Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]</span>
|
|
N = 2<span class="org-type">*</span>length(dist_f.f); <span class="org-comment">% Number of Samples match the one of the wanted PSD</span>
|
|
T0 = N<span class="org-type">/</span>Fs; <span class="org-comment">% Signal Duration [s]</span>
|
|
df = 1<span class="org-type">/</span>T0; <span class="org-comment">% Frequency resolution of the DFT [Hz]</span>
|
|
<span class="org-comment">% Also equal to (dist_f.f(2)-dist_f.f(1))</span>
|
|
t = linspace(0, T0, N<span class="org-type">+</span>1)<span class="org-type">'</span>; <span class="org-comment">% Time Vector [s]</span>
|
|
Ts = 1<span class="org-type">/</span>Fs; <span class="org-comment">% Sampling Time [s]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb2108c4" class="outline-3">
|
|
<h3 id="orgb2108c4">Ground Motion</h3>
|
|
<div class="outline-text-3" id="text-orgb2108c4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">phi = dist_f.psd_gm;
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Dwx <span class="org-type">&&</span> args.enable
|
|
rng<span class="org-type">(111);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
Dwx = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Ground Motion - x direction [m]</span>
|
|
<span class="org-keyword">else</span>
|
|
Dwx = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Dwy <span class="org-type">&&</span> args.enable
|
|
rng<span class="org-type">(112);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
Dwy = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Ground Motion - y direction [m]</span>
|
|
<span class="org-keyword">else</span>
|
|
Dwy = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Dwy <span class="org-type">&&</span> args.enable
|
|
rng<span class="org-type">(113);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
Dwz = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Ground Motion - z direction [m]</span>
|
|
<span class="org-keyword">else</span>
|
|
Dwz = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb70c65e" class="outline-3">
|
|
<h3 id="orgb70c65e">Translation Stage - X direction</h3>
|
|
<div class="outline-text-3" id="text-orgb70c65e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Fty_x <span class="org-type">&&</span> args.enable
|
|
phi = dist_f.psd_ty; <span class="org-comment">% TODO - we take here the vertical direction which is wrong but approximate</span>
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
rng<span class="org-type">(121);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
u = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Disturbance Force Ty x [N]</span>
|
|
Fty_x = u;
|
|
<span class="org-keyword">else</span>
|
|
Fty_x = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org070255a" class="outline-3">
|
|
<h3 id="org070255a">Translation Stage - Z direction</h3>
|
|
<div class="outline-text-3" id="text-org070255a">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Fty_z <span class="org-type">&&</span> args.enable
|
|
phi = dist_f.psd_ty;
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
rng<span class="org-type">(122);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
u = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Disturbance Force Ty z [N]</span>
|
|
Fty_z = u;
|
|
<span class="org-keyword">else</span>
|
|
Fty_z = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfd5f32b" class="outline-3">
|
|
<h3 id="orgfd5f32b">Spindle - Z direction</h3>
|
|
<div class="outline-text-3" id="text-orgfd5f32b">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Frz_z <span class="org-type">&&</span> args.enable
|
|
phi = dist_f.psd_rz;
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
rng<span class="org-type">(131);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
u = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Disturbance Force Rz z [N]</span>
|
|
Frz_z = u;
|
|
<span class="org-keyword">else</span>
|
|
Frz_z = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgba4d479" class="outline-3">
|
|
<h3 id="orgba4d479">Direct Forces</h3>
|
|
<div class="outline-text-3" id="text-orgba4d479">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">u = zeros(length(t), 6);
|
|
Fd = u;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf6d2198" class="outline-3">
|
|
<h3 id="orgf6d2198">Set initial value to zero</h3>
|
|
<div class="outline-text-3" id="text-orgf6d2198">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Dwx = Dwx <span class="org-type">-</span> Dwx(1);
|
|
Dwy = Dwy <span class="org-type">-</span> Dwy(1);
|
|
Dwz = Dwz <span class="org-type">-</span> Dwz(1);
|
|
Fty_x = Fty_x <span class="org-type">-</span> Fty_x(1);
|
|
Fty_z = Fty_z <span class="org-type">-</span> Fty_z(1);
|
|
Frz_z = Frz_z <span class="org-type">-</span> Frz_z(1);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc10a6b1" class="outline-3">
|
|
<h3 id="orgc10a6b1">Save</h3>
|
|
<div class="outline-text-3" id="text-orgc10a6b1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/nass_disturbances.mat'</span>, <span class="org-string">'Dwx'</span>, <span class="org-string">'Dwy'</span>, <span class="org-string">'Dwz'</span>, <span class="org-string">'Fty_x'</span>, <span class="org-string">'Fty_z'</span>, <span class="org-string">'Frz_z'</span>, <span class="org-string">'Fd'</span>, <span class="org-string">'Ts'</span>, <span class="org-string">'t'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgefb8a5e" class="outline-2">
|
|
<h2 id="orgefb8a5e"><span class="section-number-2">16</span> Initialize Position Errors</h2>
|
|
<div class="outline-text-2" id="text-16">
|
|
<p>
|
|
<a id="orga39c5fc"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc93deeb" class="outline-3">
|
|
<h3 id="orgc93deeb">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-orgc93deeb">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializePosError</span>(<span class="org-variable-name">args</span>)
|
|
<span class="org-comment">% initializePosError - Initialize the position errors</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Syntax: [] = initializePosError(args)</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Inputs:</span>
|
|
<span class="org-comment">% - args -</span>
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org84b0cbd" class="outline-3">
|
|
<h3 id="org84b0cbd">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org84b0cbd">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.error logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
args.Dy (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
args.Ry (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
args.Rz (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf35470d" class="outline-3">
|
|
<h3 id="orgf35470d">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgf35470d">
|
|
<p>
|
|
First, we initialize the <code>pos_error</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">pos_error = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc890f7d" class="outline-3">
|
|
<h3 id="orgc890f7d">Type</h3>
|
|
<div class="outline-text-3" id="text-orgc890f7d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.error
|
|
pos_error.type = 1;
|
|
<span class="org-keyword">else</span>
|
|
pos_error.type = 0;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7d50228" class="outline-3">
|
|
<h3 id="org7d50228">Position Errors</h3>
|
|
<div class="outline-text-3" id="text-org7d50228">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">pos_error.Dy = args.Dy;
|
|
pos_error.Ry = args.Ry;
|
|
pos_error.Rz = args.Rz;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4d82b1e" class="outline-3">
|
|
<h3 id="org4d82b1e">Save</h3>
|
|
<div class="outline-text-3" id="text-org4d82b1e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/pos_error.mat'</span>, <span class="org-string">'pos_error'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc87e890" class="outline-2">
|
|
<h2 id="orgc87e890"><span class="section-number-2">17</span> Z-Axis Geophone</h2>
|
|
<div class="outline-text-2" id="text-17">
|
|
<p>
|
|
<a id="orgda06de2"></a>
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[geophone]</span> = <span class="org-function-name">initializeZAxisGeophone</span>(<span class="org-variable-name">args</span>)
|
|
arguments
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3 <span class="org-comment">% [kg]</span>
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 1 <span class="org-comment">% [Hz]</span>
|
|
<span class="org-keyword">end</span>
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
|
|
geophone.m = args.mass;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% The Stiffness is set to have the damping resonance frequency</span></span>
|
|
geophone.k = geophone.m <span class="org-type">*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>args.freq)<span class="org-type">^</span>2;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% We set the damping value to have critical damping</span></span>
|
|
geophone.c = 2<span class="org-type">*</span>sqrt(geophone.m <span class="org-type">*</span> geophone.k);
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
|
|
save(<span class="org-string">'./mat/geophone_z_axis.mat'</span>, <span class="org-string">'geophone'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcbddbd1" class="outline-2">
|
|
<h2 id="orgcbddbd1"><span class="section-number-2">18</span> Z-Axis Accelerometer</h2>
|
|
<div class="outline-text-2" id="text-18">
|
|
<p>
|
|
<a id="org071e205"></a>
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[accelerometer]</span> = <span class="org-function-name">initializeZAxisAccelerometer</span>(<span class="org-variable-name">args</span>)
|
|
arguments
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3 <span class="org-comment">% [kg]</span>
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 5e3 <span class="org-comment">% [Hz]</span>
|
|
<span class="org-keyword">end</span>
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
|
|
accelerometer.m = args.mass;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% The Stiffness is set to have the damping resonance frequency</span></span>
|
|
accelerometer.k = accelerometer.m <span class="org-type">*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>args.freq)<span class="org-type">^</span>2;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% We set the damping value to have critical damping</span></span>
|
|
accelerometer.c = 2<span class="org-type">*</span>sqrt(accelerometer.m <span class="org-type">*</span> accelerometer.k);
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Gain correction of the accelerometer to have a unity gain until the resonance</span></span>
|
|
accelerometer.gain = <span class="org-type">-</span>accelerometer.k<span class="org-type">/</span>accelerometer.m;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
|
|
save(<span class="org-string">'./mat/accelerometer_z_axis.mat'</span>, <span class="org-string">'accelerometer'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-03-25 mer. 19:20</p>
|
|
</div>
|
|
</body>
|
|
</html>
|