2020-01-29 20:35:14 +01:00
<?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 >
2020-03-17 11:23:47 +01:00
<!-- 2020 - 03 - 17 mar. 11:21 -->
2020-01-29 20:35:14 +01:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< meta name = "viewport" content = "width=device-width, initial-scale=1" / >
< title > HAC-LAC applied on the Simscape Model< / 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 >
2020-02-25 18:21:17 +01:00
< 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 >
2020-01-29 20:35:14 +01:00
< script type = "text/javascript" >
2020-03-13 17:40:22 +01:00
// @license magnet:?xt=urn:btih:1f739d935676111cfff4b4693e3816e664797050& dn=gpl-3.0.txt GPL-v3-or-Later
2020-01-29 20:35:14 +01:00
<!-- /* --> <![CDATA[/*> <!-- */
2020-03-13 17:40:22 +01:00
function CodeHighlightOn(elem, id)
{
var target = document.getElementById(id);
if(null != target) {
elem.cacheClassElem = elem.className;
elem.cacheClassTarget = target.className;
target.className = "code-highlighted";
elem.className = "code-highlighted";
}
}
function CodeHighlightOff(elem, id)
{
var target = document.getElementById(id);
if(elem.cacheClassElem)
elem.className = elem.cacheClassElem;
if(elem.cacheClassTarget)
target.className = elem.cacheClassTarget;
}
/*]]>*///-->
// @license-end
2020-01-29 20:35:14 +01:00
< / script >
2020-03-13 17:40:22 +01:00
< script >
MathJax = {
tex: { macros: {
bm: ["\\boldsymbol{#1}",1],
}
}
};
< / script >
< script type = "text/javascript"
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">< / script >
2020-01-29 20:35:14 +01:00
< / head >
< body >
< div id = "org-div-home-and-up" >
2020-02-25 18:21:17 +01:00
< a accesskey = "h" href = "./index.html" > UP < / a >
2020-01-29 20:35:14 +01:00
|
2020-02-25 18:21:17 +01:00
< a accesskey = "H" href = "./index.html" > HOME < / a >
2020-01-29 20:35:14 +01:00
< / div > < div id = "content" >
< h1 class = "title" > HAC-LAC applied on the Simscape Model< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2020-03-13 17:40:22 +01:00
< li > < a href = "#org9a782be" > 1. Initialization< / a > < / li >
< li > < a href = "#org5f71356" > 2. Low Authority Control - Direct Velocity Feedback \(\bm{K}_\mathcal{L}\)< / a >
2020-01-29 20:35:14 +01:00
< ul >
2020-03-13 17:40:22 +01:00
< li > < a href = "#orgd91db57" > 2.1. Identification< / a > < / li >
< li > < a href = "#org09c8990" > 2.2. Plant< / a > < / li >
< li > < a href = "#orgc21ad83" > 2.3. Root Locus< / a > < / li >
< li > < a href = "#orgd18d476" > 2.4. Controller and Loop Gain< / a > < / li >
2020-01-29 20:35:14 +01:00
< / ul >
< / li >
2020-03-13 17:40:22 +01:00
< li > < a href = "#orgbba86f0" > 3. High Authority Control - \(\bm{K}_\mathcal{X}\)< / a >
2020-01-29 20:35:14 +01:00
< ul >
2020-03-13 17:40:22 +01:00
< li > < a href = "#orgdd75cdd" > 3.1. Identification of the damped plant< / a > < / li >
< li > < a href = "#orgf70f020" > 3.2. Controller Design< / a > < / li >
2020-01-29 20:35:14 +01:00
< / ul >
< / li >
2020-03-13 17:40:22 +01:00
< li > < a href = "#org5a1507e" > 4. Simulation< / a > < / li >
< li > < a href = "#org9498b7b" > 5. Results< / a > < / li >
2020-01-29 20:35:14 +01:00
< / ul >
< / div >
< / div >
< p >
2020-03-13 17:40:22 +01:00
The position \(\bm{\mathcal{X}}\) of the Sample with respect to the granite is measured.
2020-01-29 20:35:14 +01:00
< / p >
2020-03-13 17:40:22 +01:00
< p >
It is then compare to the wanted position of the Sample \(\bm{r}_\mathcal{X}\) in order to obtain the position error \(\bm{\epsilon}_\mathcal{X}\) of the Sample with respect to a frame attached to the Stewart top platform.
< / p >
2020-03-17 11:23:47 +01:00
< div id = "org250b69d" class = "figure" >
2020-03-13 17:40:22 +01:00
< p > < img src = "figs/hac_lac_control_schematic.png" alt = "hac_lac_control_schematic.png" / >
< / p >
2020-03-17 11:23:47 +01:00
< p > < span class = "figure-number" > Figure 1: < / span > HAC-LAC Control Architecture used for the Control of the NASS< / p >
2020-01-29 20:35:14 +01:00
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-org9a782be" class = "outline-2" >
< h2 id = "org9a782be" > < span class = "section-number-2" > 1< / span > Initialization< / h2 >
< div class = "outline-text-2" id = "text-1" >
2020-01-29 20:35:14 +01:00
< p >
We initialize all the stages with the default parameters.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
< / pre >
< / div >
< p >
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeNanoHexapod(< span class = "org-string" > 'actuator'< / span > , < span class = "org-string" > 'piezo'< / span > );
2020-03-13 17:40:22 +01:00
initializeSample(< span class = "org-string" > 'mass'< / span > , 1);
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< p >
2020-03-13 17:40:22 +01:00
We set the references that corresponds to a tomography experiment.
2020-01-29 20:35:14 +01:00
< / p >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > initializeReferences(< span class = "org-string" > 'Rz_type'< / span > , < span class = "org-string" > 'rotating'< / span > , < span class = "org-string" > 'Rz_period'< / span > , 1);
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > initializeDisturbances();
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< p >
2020-03-13 17:40:22 +01:00
Open Loop.
2020-01-29 20:35:14 +01:00
< / p >
< div class = "org-src-container" >
2020-02-25 18:10:20 +01:00
< pre class = "src src-matlab" > initializeController(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'open-loop'< / span > );
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< p >
2020-03-13 17:40:22 +01:00
And we put some gravity.
2020-01-29 20:35:14 +01:00
< / p >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > initializeSimscapeConfiguration(< span class = "org-string" > 'gravity'< / span > , < span class = "org-constant" > true< / span > );
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
2020-03-13 17:40:22 +01:00
< p >
We log the signals.
< / p >
2020-01-29 20:35:14 +01:00
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > initializeLoggingConfiguration(< span class = "org-string" > 'log'< / span > , < span class = "org-string" > 'all'< / span > );
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< / div >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-org5f71356" class = "outline-2" >
< h2 id = "org5f71356" > < span class = "section-number-2" > 2< / span > Low Authority Control - Direct Velocity Feedback \(\bm{K}_\mathcal{L}\)< / h2 >
< div class = "outline-text-2" id = "text-2" >
< p >
The first loop closed corresponds to a direct velocity feedback loop.
2020-01-29 20:35:14 +01:00
< / p >
2020-03-13 17:40:22 +01:00
< p >
The design of the associated decentralized controller is explained in < a href = "active_damping.html" > this< / a > file.
2020-01-29 20:35:14 +01:00
< / p >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-orgd91db57" class = "outline-3" >
< h3 id = "orgd91db57" > < span class = "section-number-3" > 2.1< / span > Identification< / h3 >
< div class = "outline-text-3" id = "text-2-1" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'nass_model'< / span > ;
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Inputs< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Micro-Station'< / span > ], 3, < span class = "org-string" > 'openoutput'< / span > , [], < span class = "org-string" > 'Dnlm'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Relative Motion Outputs< / span >
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G_dvf = linearize(mdl, io, 0);
G_dvf.InputName = {< span class = "org-string" > 'Fnl1'< / span > , < span class = "org-string" > 'Fnl2'< / span > , < span class = "org-string" > 'Fnl3'< / span > , < span class = "org-string" > 'Fnl4'< / span > , < span class = "org-string" > 'Fnl5'< / span > , < span class = "org-string" > 'Fnl6'< / span > };
G_dvf.OutputName = {< span class = "org-string" > 'Dnlm1'< / span > , < span class = "org-string" > 'Dnlm2'< / span > , < span class = "org-string" > 'Dnlm3'< / span > , < span class = "org-string" > 'Dnlm4'< / span > , < span class = "org-string" > 'Dnlm5'< / span > , < span class = "org-string" > 'Dnlm6'< / span > };
< / pre >
2020-01-29 20:35:14 +01:00
< / div >
< / div >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-org09c8990" class = "outline-3" >
< h3 id = "org09c8990" > < span class = "section-number-3" > 2.2< / span > Plant< / h3 >
2020-01-29 20:35:14 +01:00
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-orgc21ad83" class = "outline-3" >
< h3 id = "orgc21ad83" > < span class = "section-number-3" > 2.3< / span > Root Locus< / h3 >
2020-01-29 20:35:14 +01:00
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-orgd18d476" class = "outline-3" >
< h3 id = "orgd18d476" > < span class = "section-number-3" > 2.4< / span > Controller and Loop Gain< / h3 >
< div class = "outline-text-3" id = "text-2-4" >
2020-01-29 20:35:14 +01:00
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > K_dvf = s< span class = "org-type" > *< / span > 15000< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > 10000);
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > K_dvf = < span class = "org-type" > -< / span > K_dvf< span class = "org-type" > *< / span > eye(6);
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< / div >
< / div >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-orgbba86f0" class = "outline-2" >
< h2 id = "orgbba86f0" > < span class = "section-number-2" > 3< / span > High Authority Control - \(\bm{K}_\mathcal{X}\)< / h2 >
< div class = "outline-text-2" id = "text-3" >
2020-01-29 20:35:14 +01:00
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-orgdd75cdd" class = "outline-3" >
< h3 id = "orgdd75cdd" > < span class = "section-number-3" > 3.1< / span > Identification of the damped plant< / h3 >
< div class = "outline-text-3" id = "text-3-1" >
2020-01-29 20:35:14 +01:00
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > Kx = tf(zeros(6));
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > initializeController(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'hac-dvf'< / span > );
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'nass_model'< / span > ;
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'input'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Inputs< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Tracking Error'< / span > ], 1, < span class = "org-string" > 'output'< / span > , [], < span class = "org-string" > 'En'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Position Errror< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, 0);
G.InputName = {< span class = "org-string" > 'Fnl1'< / span > , < span class = "org-string" > 'Fnl2'< / span > , < span class = "org-string" > 'Fnl3'< / span > , < span class = "org-string" > 'Fnl4'< / span > , < span class = "org-string" > 'Fnl5'< / span > , < span class = "org-string" > 'Fnl6'< / span > };
G.OutputName = {< span class = "org-string" > 'Ex'< / span > , < span class = "org-string" > 'Ey'< / span > , < span class = "org-string" > 'Ez'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< p >
2020-03-13 17:40:22 +01:00
The minus sine is put here because there is already a minus sign included due to the computation of the position error.
2020-01-29 20:35:14 +01:00
< / p >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > load(< span class = "org-string" > 'mat/stages.mat'< / span > , < span class = "org-string" > 'nano_hexapod'< / span > );
Gx = < span class = "org-type" > -< / span > G< span class = "org-type" > *< / span > inv(nano_hexapod.J< span class = "org-type" > '< / span > );
Gx.InputName = {< span class = "org-string" > 'Fx'< / span > , < span class = "org-string" > 'Fy'< / span > , < span class = "org-string" > 'Fz'< / span > , < span class = "org-string" > 'Mx'< / span > , < span class = "org-string" > 'My'< / span > , < span class = "org-string" > 'Mz'< / span > };
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< / div >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-orgf70f020" class = "outline-3" >
< h3 id = "orgf70f020" > < span class = "section-number-3" > 3.2< / span > Controller Design< / h3 >
< div class = "outline-text-3" id = "text-3-2" >
2020-01-29 20:35:14 +01:00
< p >
2020-03-13 17:40:22 +01:00
The controller consists of:
2020-01-29 20:35:14 +01:00
< / p >
2020-03-13 17:40:22 +01:00
< ul class = "org-ul" >
< li > A pure integrator< / li >
< li > A Second integrator up to half the wanted bandwidth< / li >
< li > A Lead around the cross-over frequency< / li >
< li > A low pass filter with a cut-off equal to two times the wanted bandwidth< / li >
< / ul >
2020-01-29 20:35:14 +01:00
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > wc = 2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 15; < span class = "org-comment" > % Bandwidth Bandwidth [rad/s]< / span >
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
h = 1.5; < span class = "org-comment" > % Lead parameter< / span >
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
Kx = (1< span class = "org-type" > /< / span > h) < span class = "org-type" > *< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > h)< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > /< / span > h) < span class = "org-type" > *< / span > wc< span class = "org-type" > /< / span > s < span class = "org-type" > *< / span > ((s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > 2 < span class = "org-type" > +< / span > 1)< span class = "org-type" > /< / span > (s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > 2)) < span class = "org-type" > *< / span > (1< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > /< / span > 2));
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
< span class = "org-comment" > % Normalization of the gain of have a loop gain of 1 at frequency wc< / span >
Kx = Kx< span class = "org-type" > .*< / span > diag(1< span class = "org-type" > ./< / span > diag(abs(freqresp(Gx< span class = "org-type" > *< / span > Kx, wc))));
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > isstable(feedback(Gx< span class = "org-type" > *< / span > Kx, eye(6), < span class = "org-type" > -< / span > 1))
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-03-13 17:40:22 +01:00
< pre class = "src src-matlab" > Kx = inv(nano_hexapod.J< span class = "org-type" > '< / span > )< span class = "org-type" > *< / span > Kx;
2020-01-29 20:35:14 +01:00
< / pre >
< / div >
2020-03-13 17:40:22 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > isstable(feedback(G< span class = "org-type" > *< / span > Kx, eye(6), 1))
< / pre >
2020-01-29 20:35:14 +01:00
< / div >
< / div >
< / div >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-org5a1507e" class = "outline-2" >
< h2 id = "org5a1507e" > < span class = "section-number-2" > 4< / span > Simulation< / h2 >
< div class = "outline-text-2" id = "text-4" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'mat/conf_simulink.mat'< / span > );
< span class = "org-matlab-simulink-keyword" > set_param< / span > (< span class = "org-variable-name" > conf_simulink< / span > , < span class = "org-string" > 'StopTime'< / span > , < span class = "org-string" > '1.5'< / span > );
< / pre >
< / div >
2020-01-29 20:35:14 +01:00
2020-03-13 17:40:22 +01:00
< p >
And we simulate the system.
2020-01-29 20:35:14 +01:00
< / p >
2020-03-13 17:40:22 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-simulink-keyword" > sim< / span > (< span class = "org-string" > 'nass_model'< / span > );
< / pre >
2020-01-29 20:35:14 +01:00
< / div >
2020-03-13 17:40:22 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > save(< span class = "org-string" > './mat/tomo_exp_hac_lac.mat'< / span > , < span class = "org-string" > 'simout'< / span > );
< / pre >
2020-01-29 20:35:14 +01:00
< / div >
< / div >
< / div >
2020-03-13 17:40:22 +01:00
< div id = "outline-container-org9498b7b" class = "outline-2" >
< h2 id = "org9498b7b" > < span class = "section-number-2" > 5< / span > Results< / h2 >
< div class = "outline-text-2" id = "text-5" >
2020-03-17 11:23:47 +01:00
< p >
Let’ s load the simulation when no control is applied.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > './mat/experiment_tomography.mat'< / span > , < span class = "org-string" > 'tomo_align_dist'< / span > );
t = tomo_align_dist.t;
MTr = tomo_align_dist.MTr;
< / pre >
< / div >
2020-03-13 17:40:22 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > './mat/tomo_exp_hac_lac.mat'< / span > , < span class = "org-string" > 'simout'< / span > );
< / pre >
< / div >
2020-01-29 20:35:14 +01:00
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2020-03-17 11:23:47 +01:00
< p class = "date" > Created: 2020-03-17 mar. 11:21< / p >
2020-01-29 20:35:14 +01:00
< / div >
< / body >
< / html >
