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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-03-13 ven. 10:34 -->
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<!-- 2020-03-16 lun. 11:21 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Stewart Platform - Vibration Isolation</title>
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@ -250,28 +249,28 @@
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<li><a href="#orgf86b757">1. HAC-LAC (Cascade) Control - Integral Control</a>
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<ul>
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<li><a href="#org3a9f4d4">1.1. Introduction</a></li>
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<li><a href="#org42643f7">1.2. Initialization</a></li>
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<li><a href="#orgd24dcff">1.3. Identification</a>
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<li><a href="#org58e2ab0">1.2. Initialization</a></li>
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<li><a href="#orgab56a44">1.3. Identification</a>
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<ul>
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<li><a href="#org8048e33">1.3.1. HAC - Without LAC</a></li>
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<li><a href="#org937f315">1.3.2. HAC - IFF</a></li>
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<li><a href="#org83d8630">1.3.3. HAC - DVF</a></li>
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<li><a href="#org2309d71">1.3.1. HAC - Without LAC</a></li>
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<li><a href="#orgd3d2942">1.3.2. HAC - IFF</a></li>
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<li><a href="#org492aabc">1.3.3. HAC - DVF</a></li>
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</ul>
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</li>
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<li><a href="#org4d7a6d8">1.4. Control Architecture</a></li>
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<li><a href="#org3e1b1b7">1.5. 6x6 Plant Comparison</a></li>
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<li><a href="#org22da139">1.6. HAC - DVF</a>
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<li><a href="#org14108ef">1.6. HAC - DVF</a>
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<ul>
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<li><a href="#orgc0e6f7d">1.6.1. Plant</a></li>
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<li><a href="#org91edbdd">1.6.2. Controller Design</a></li>
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<li><a href="#org5e71990">1.6.3. Obtained Performance</a></li>
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<li><a href="#org71d45ac">1.6.1. Plant</a></li>
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<li><a href="#org8236bd6">1.6.2. Controller Design</a></li>
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<li><a href="#org7810516">1.6.3. Obtained Performance</a></li>
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</ul>
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</li>
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<li><a href="#orgd3d2942">1.7. HAC - IFF</a>
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<li><a href="#org55f17b6">1.7. HAC - IFF</a>
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<ul>
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<li><a href="#org71d45ac">1.7.1. Plant</a></li>
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<li><a href="#org8236bd6">1.7.2. Controller Design</a></li>
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<li><a href="#org7810516">1.7.3. Obtained Performance</a></li>
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<li><a href="#org87cf3a4">1.7.1. Plant</a></li>
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<li><a href="#org6d26667">1.7.2. Controller Design</a></li>
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<li><a href="#orgef0abff">1.7.3. Obtained Performance</a></li>
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</ul>
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</li>
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<li><a href="#org81c1767">1.8. Comparison</a></li>
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@ -279,11 +278,11 @@
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</li>
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<li><a href="#org6f94eba">2. MIMO Analysis</a>
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<ul>
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<li><a href="#orgc26d5f4">2.1. Initialization</a></li>
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<li><a href="#org308b8f7">2.2. Identification</a>
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<li><a href="#org925bb20">2.1. Initialization</a></li>
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<li><a href="#org57c87f0">2.2. Identification</a>
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<ul>
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<li><a href="#org2309d71">2.2.1. HAC - Without LAC</a></li>
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<li><a href="#org492aabc">2.2.2. HAC - DVF</a></li>
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<li><a href="#org661b495">2.2.1. HAC - Without LAC</a></li>
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<li><a href="#orgdd8b824">2.2.2. HAC - DVF</a></li>
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<li><a href="#orgf606814">2.2.3. Cartesian Frame</a></li>
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</ul>
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</li>
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@ -292,13 +291,13 @@
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</li>
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<li><a href="#orgc8479b7">3. Diagonal Control based on the damped plant</a>
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<ul>
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<li><a href="#orga3f0f82">3.1. Initialization</a></li>
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<li><a href="#orgab56a44">3.2. Identification</a></li>
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<li><a href="#org99665a2">3.1. Initialization</a></li>
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<li><a href="#org42a5e98">3.2. Identification</a></li>
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<li><a href="#orgae85e0d">3.3. Steady State Decoupling</a>
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<ul>
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<li><a href="#org1e2bbe7">3.3.1. Pre-Compensator Design</a></li>
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<li><a href="#org077e6f6">3.3.2. Diagonal Control Design</a></li>
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<li><a href="#org4e0fae0">3.3.3. Results</a></li>
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<li><a href="#orgf7c304f">3.3.3. Results</a></li>
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</ul>
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</li>
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<li><a href="#orgad35bf9">3.4. Decoupling at Crossover</a></li>
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@ -306,10 +305,10 @@
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</li>
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<li><a href="#org846cef9">4. Time Domain Simulation</a>
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<ul>
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<li><a href="#org58e2ab0">4.1. Initialization</a></li>
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<li><a href="#org2a9e89f">4.1. Initialization</a></li>
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<li><a href="#org8dbc004">4.2. HAC IFF</a></li>
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<li><a href="#org7dc4716">4.3. HAC-DVF</a></li>
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<li><a href="#orgf7c304f">4.4. Results</a></li>
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<li><a href="#org65730fb">4.4. Results</a></li>
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</ul>
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</li>
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<li><a href="#org69ebad1">5. Functions</a>
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@ -364,8 +363,8 @@ First, the LAC loop is closed (the LAC control is described <a href="active-damp
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</div>
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</div>
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<div id="outline-container-org42643f7" class="outline-3">
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<h3 id="org42643f7"><span class="section-number-3">1.2</span> Initialization</h3>
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<div id="outline-container-org58e2ab0" class="outline-3">
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<h3 id="org58e2ab0"><span class="section-number-3">1.2</span> Initialization</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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We first initialize the Stewart platform.
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@ -396,8 +395,8 @@ payload = initializePayload(<span class="org-string">'type'</span>, <span class=
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</div>
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</div>
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<div id="outline-container-orgd24dcff" class="outline-3">
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<h3 id="orgd24dcff"><span class="section-number-3">1.3</span> Identification</h3>
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<div id="outline-container-orgab56a44" class="outline-3">
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<h3 id="orgab56a44"><span class="section-number-3">1.3</span> Identification</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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We identify the transfer function from the actuator forces \(\bm{\tau}\) to the absolute displacement of the mobile platform \(\bm{\mathcal{X}}\) in three different cases:
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@ -409,8 +408,8 @@ We identify the transfer function from the actuator forces \(\bm{\tau}\) to the
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</ul>
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</div>
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<div id="outline-container-org8048e33" class="outline-4">
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<h4 id="org8048e33"><span class="section-number-4">1.3.1</span> HAC - Without LAC</h4>
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<div id="outline-container-org2309d71" class="outline-4">
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<h4 id="org2309d71"><span class="section-number-4">1.3.1</span> HAC - Without LAC</h4>
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<div class="outline-text-4" id="text-1-3-1">
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<div class="org-src-container">
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<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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@ -435,8 +434,8 @@ G_ol.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string
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</div>
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</div>
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<div id="outline-container-org937f315" class="outline-4">
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<h4 id="org937f315"><span class="section-number-4">1.3.2</span> HAC - IFF</h4>
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<div id="outline-container-orgd3d2942" class="outline-4">
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<h4 id="orgd3d2942"><span class="section-number-4">1.3.2</span> HAC - IFF</h4>
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<div class="outline-text-4" id="text-1-3-2">
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<div class="org-src-container">
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<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'iff'</span>);
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@ -462,8 +461,8 @@ G_iff.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-strin
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</div>
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</div>
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<div id="outline-container-org83d8630" class="outline-4">
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<h4 id="org83d8630"><span class="section-number-4">1.3.3</span> HAC - DVF</h4>
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<div id="outline-container-org492aabc" class="outline-4">
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<h4 id="org492aabc"><span class="section-number-4">1.3.3</span> HAC - DVF</h4>
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<div class="outline-text-4" id="text-1-3-3">
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<div class="org-src-container">
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<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
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@ -527,12 +526,12 @@ We then design a controller based on the transfer functions from \(\bm{\mathcal{
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</div>
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</div>
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<div id="outline-container-org22da139" class="outline-3">
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<h3 id="org22da139"><span class="section-number-3">1.6</span> HAC - DVF</h3>
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<div id="outline-container-org14108ef" class="outline-3">
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<h3 id="org14108ef"><span class="section-number-3">1.6</span> HAC - DVF</h3>
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<div class="outline-text-3" id="text-1-6">
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</div>
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<div id="outline-container-orgc0e6f7d" class="outline-4">
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<h4 id="orgc0e6f7d"><span class="section-number-4">1.6.1</span> Plant</h4>
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<div id="outline-container-org71d45ac" class="outline-4">
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<h4 id="org71d45ac"><span class="section-number-4">1.6.1</span> Plant</h4>
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<div class="outline-text-4" id="text-1-6-1">
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<div id="org487a558" class="figure">
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@ -543,8 +542,8 @@ We then design a controller based on the transfer functions from \(\bm{\mathcal{
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</div>
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</div>
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<div id="outline-container-org91edbdd" class="outline-4">
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<h4 id="org91edbdd"><span class="section-number-4">1.6.2</span> Controller Design</h4>
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<div id="outline-container-org8236bd6" class="outline-4">
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<h4 id="org8236bd6"><span class="section-number-4">1.6.2</span> Controller Design</h4>
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<div class="outline-text-4" id="text-1-6-2">
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<p>
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We design a diagonal controller with equal bandwidth for the 6 terms.
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@ -579,8 +578,8 @@ Finally, we pre-multiply the diagonal controller by \(\bm{J}^{-T}\) prior implem
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</div>
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</div>
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<div id="outline-container-org5e71990" class="outline-4">
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<h4 id="org5e71990"><span class="section-number-4">1.6.3</span> Obtained Performance</h4>
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<div id="outline-container-org7810516" class="outline-4">
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<h4 id="org7810516"><span class="section-number-4">1.6.3</span> Obtained Performance</h4>
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<div class="outline-text-4" id="text-1-6-3">
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<p>
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We identify the transmissibility and compliance of the system.
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@ -617,12 +616,12 @@ We identify the transmissibility and compliance of the system.
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</div>
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</div>
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<div id="outline-container-orgd3d2942" class="outline-3">
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<h3 id="orgd3d2942"><span class="section-number-3">1.7</span> HAC - IFF</h3>
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<div id="outline-container-org55f17b6" class="outline-3">
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<h3 id="org55f17b6"><span class="section-number-3">1.7</span> HAC - IFF</h3>
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<div class="outline-text-3" id="text-1-7">
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</div>
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<div id="outline-container-org71d45ac" class="outline-4">
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<h4 id="org71d45ac"><span class="section-number-4">1.7.1</span> Plant</h4>
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<div id="outline-container-org87cf3a4" class="outline-4">
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<h4 id="org87cf3a4"><span class="section-number-4">1.7.1</span> Plant</h4>
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<div class="outline-text-4" id="text-1-7-1">
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<div id="org0fc8dea" class="figure">
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@ -633,8 +632,8 @@ We identify the transmissibility and compliance of the system.
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</div>
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</div>
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<div id="outline-container-org8236bd6" class="outline-4">
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<h4 id="org8236bd6"><span class="section-number-4">1.7.2</span> Controller Design</h4>
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<div id="outline-container-org6d26667" class="outline-4">
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<h4 id="org6d26667"><span class="section-number-4">1.7.2</span> Controller Design</h4>
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<div class="outline-text-4" id="text-1-7-2">
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<p>
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We design a diagonal controller with equal bandwidth for the 6 terms.
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@ -669,8 +668,8 @@ Finally, we pre-multiply the diagonal controller by \(\bm{J}^{-T}\) prior implem
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</div>
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</div>
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<div id="outline-container-org7810516" class="outline-4">
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<h4 id="org7810516"><span class="section-number-4">1.7.3</span> Obtained Performance</h4>
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<div id="outline-container-orgef0abff" class="outline-4">
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<h4 id="orgef0abff"><span class="section-number-4">1.7.3</span> Obtained Performance</h4>
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<div class="outline-text-4" id="text-1-7-3">
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<p>
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We identify the transmissibility and compliance of the system.
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@ -826,8 +825,8 @@ Let’s define the system as shown in figure <a href="#orgac8f77c">13</a>.
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</table>
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</div>
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<div id="outline-container-orgc26d5f4" class="outline-3">
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<h3 id="orgc26d5f4"><span class="section-number-3">2.1</span> Initialization</h3>
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<div id="outline-container-org925bb20" class="outline-3">
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||||
<h3 id="org925bb20"><span class="section-number-3">2.1</span> Initialization</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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We first initialize the Stewart platform.
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@ -858,12 +857,12 @@ payload = initializePayload(<span class="org-string">'type'</span>, <span class=
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</div>
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</div>
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<div id="outline-container-org308b8f7" class="outline-3">
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<h3 id="org308b8f7"><span class="section-number-3">2.2</span> Identification</h3>
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<div id="outline-container-org57c87f0" class="outline-3">
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<h3 id="org57c87f0"><span class="section-number-3">2.2</span> Identification</h3>
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<div class="outline-text-3" id="text-2-2">
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</div>
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<div id="outline-container-org2309d71" class="outline-4">
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<h4 id="org2309d71"><span class="section-number-4">2.2.1</span> HAC - Without LAC</h4>
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<div id="outline-container-org661b495" class="outline-4">
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<h4 id="org661b495"><span class="section-number-4">2.2.1</span> HAC - Without LAC</h4>
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<div class="outline-text-4" id="text-2-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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@ -888,8 +887,8 @@ G_ol.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string
|
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</div>
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||||
</div>
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||||
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||||
<div id="outline-container-org492aabc" class="outline-4">
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<h4 id="org492aabc"><span class="section-number-4">2.2.2</span> HAC - DVF</h4>
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<div id="outline-container-orgdd8b824" class="outline-4">
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<h4 id="orgdd8b824"><span class="section-number-4">2.2.2</span> HAC - DVF</h4>
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<div class="outline-text-4" id="text-2-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
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@ -987,8 +986,8 @@ There are mainly three different cases:
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</ol>
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</div>
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<div id="outline-container-orga3f0f82" class="outline-3">
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<h3 id="orga3f0f82"><span class="section-number-3">3.1</span> Initialization</h3>
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<div id="outline-container-org99665a2" class="outline-3">
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||||
<h3 id="org99665a2"><span class="section-number-3">3.1</span> Initialization</h3>
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<div class="outline-text-3" id="text-3-1">
|
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<p>
|
||||
We first initialize the Stewart platform.
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@ -1019,8 +1018,8 @@ payload = initializePayload(<span class="org-string">'type'</span>, <span class=
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</div>
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</div>
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||||
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||||
<div id="outline-container-orgab56a44" class="outline-3">
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<h3 id="orgab56a44"><span class="section-number-3">3.2</span> Identification</h3>
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<div id="outline-container-org42a5e98" class="outline-3">
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<h3 id="org42a5e98"><span class="section-number-3">3.2</span> Identification</h3>
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<div class="outline-text-3" id="text-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
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@ -1135,8 +1134,8 @@ The overall controller is then \(K(s) = W_1 K_s(s)\) as shown in Figure <a href=
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</div>
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</div>
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|
||||
<div id="outline-container-org4e0fae0" class="outline-4">
|
||||
<h4 id="org4e0fae0"><span class="section-number-4">3.3.3</span> Results</h4>
|
||||
<div id="outline-container-orgf7c304f" class="outline-4">
|
||||
<h4 id="orgf7c304f"><span class="section-number-4">3.3.3</span> Results</h4>
|
||||
<div class="outline-text-4" id="text-3-3-3">
|
||||
<p>
|
||||
We identify the transmissibility and compliance of the Stewart platform under open-loop and closed-loop control.
|
||||
@ -1184,8 +1183,8 @@ The results are shown in figure
|
||||
<h2 id="org846cef9"><span class="section-number-2">4</span> Time Domain Simulation</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org58e2ab0" class="outline-3">
|
||||
<h3 id="org58e2ab0"><span class="section-number-3">4.1</span> Initialization</h3>
|
||||
<div id="outline-container-org2a9e89f" class="outline-3">
|
||||
<h3 id="org2a9e89f"><span class="section-number-3">4.1</span> Initialization</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
We first initialize the Stewart platform.
|
||||
@ -1308,8 +1307,8 @@ K_hac_dvf = inv(stewart.kinematics.J<span class="org-type">'</span>)<span class=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf7c304f" class="outline-3">
|
||||
<h3 id="orgf7c304f"><span class="section-number-3">4.4</span> Results</h3>
|
||||
<div id="outline-container-org65730fb" class="outline-3">
|
||||
<h3 id="org65730fb"><span class="section-number-3">4.4</span> Results</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
@ -1418,7 +1417,7 @@ ylabel(<span class="org-string">'Orientation error [rad]'</span>);
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-03-13 ven. 10:34</p>
|
||||
<p class="date">Created: 2020-03-16 lun. 11:21</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -46,6 +46,8 @@ Things to add:
|
||||
- cite:beijen18_exper_estim_trans_matric_indus
|
||||
- cite:xie17_model_contr_hybrid_passiv_activ
|
||||
- cite:chi15_desig_exper_study_vcm_based
|
||||
- cite:guo08_cascad_contr_hydraul_driven_paral
|
||||
- cite:zheng18_stewar_isolat_with_high_static
|
||||
|
||||
* Books
|
||||
| | <c> |
|
||||
|
||||
@ -610,7 +610,7 @@ This will simplify the design of the controller as all the elements of the diago
|
||||
#+end_src
|
||||
|
||||
#+name: fig:plant_centralized_L
|
||||
#+caption: Diagonal and off-diagonal elements of the plant $\bm{K}\bm{G}$ ([[./figs/plant_centralized_L.png][png]], [[./figs/plant_centralized_L.pdf][pdf]])
|
||||
#+caption: Diagonal and off-diagonal elements of the plant $\bm{J}\bm{G}$ ([[./figs/plant_centralized_L.png][png]], [[./figs/plant_centralized_L.pdf][pdf]])
|
||||
[[file:figs/plant_centralized_L.png]]
|
||||
|
||||
We can see that this *totally decouples the system at low frequency*.
|
||||
|
||||
@ -39,17 +39,6 @@
|
||||
:END:
|
||||
|
||||
* Introduction :ignore:
|
||||
Control architectures can be divided in different ways.
|
||||
|
||||
It can depend on the sensor used:
|
||||
- Sensors located in each strut: relative motion, force sensor, inertial sensor
|
||||
- Sensors measuring the relative motion between the fixed base and the mobile platform
|
||||
- Inertial sensors located on the mobile platform
|
||||
|
||||
It can also depends on the control objective:
|
||||
- Reference Tracking
|
||||
- Active Damping
|
||||
- Vibration Isolation
|
||||
|
||||
* HAC-LAC (Cascade) Control - Integral Control
|
||||
** Introduction
|
||||
|
||||
30
org/ref.bib
30
org/ref.bib
@ -1330,3 +1330,33 @@
|
||||
url = {https://doi.org/10.1016/j.actaastro.2020.02.033},
|
||||
tags = {parallel robot},
|
||||
}
|
||||
|
||||
@article{guo08_cascad_contr_hydraul_driven_paral,
|
||||
author = {HongBo Guo and YongGuang Liu and GuiRong Liu and HongRen
|
||||
Li},
|
||||
title = {Cascade Control of a Hydraulically Driven 6-dof Parallel
|
||||
Robot Manipulator Based on a Sliding Mode},
|
||||
journal = {Control Engineering Practice},
|
||||
volume = 16,
|
||||
number = 9,
|
||||
pages = {1055-1068},
|
||||
year = 2008,
|
||||
doi = {10.1016/j.conengprac.2007.11.005},
|
||||
url = {https://doi.org/10.1016/j.conengprac.2007.11.005},
|
||||
tags = {parallel robot},
|
||||
}
|
||||
|
||||
@article{zheng18_stewar_isolat_with_high_static,
|
||||
author = {Yisheng Zheng and Qingpin Li and Bo Yan and Yajun Luo and
|
||||
Xinong Zhang},
|
||||
title = {A Stewart Isolator With High-Static-Low-Dynamic Stiffness
|
||||
Struts Based on Negative Stiffness Magnetic Springs},
|
||||
journal = {Journal of Sound and Vibration},
|
||||
volume = 422,
|
||||
number = {nil},
|
||||
pages = {390-408},
|
||||
year = 2018,
|
||||
doi = {10.1016/j.jsv.2018.02.046},
|
||||
url = {https://doi.org/10.1016/j.jsv.2018.02.046},
|
||||
tags = {parallel robot},
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user