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Thomas Dehaeze
2020-03-03 15:53:02 +01:00
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-02-28 ven. 17:34 -->
<!-- 2020-03-02 lun. 17:57 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Stewart Platform - Vibration Isolation</title>
@@ -249,28 +249,28 @@
<li><a href="#org272e7f8">1. HAC-LAC (Cascade) Control - Integral Control</a>
<ul>
<li><a href="#orga5c9b98">1.1. Introduction</a></li>
<li><a href="#org9ad2582">1.2. Initialization</a></li>
<li><a href="#org03823a6">1.3. Identification</a>
<li><a href="#org5907395">1.2. Initialization</a></li>
<li><a href="#org080a6bd">1.3. Identification</a>
<ul>
<li><a href="#org4d582a9">1.3.1. HAC - Without LAC</a></li>
<li><a href="#orge0108ff">1.3.2. HAC - IFF</a></li>
<li><a href="#org1afe87f">1.3.3. HAC - DVF</a></li>
<li><a href="#org183dcef">1.3.1. HAC - Without LAC</a></li>
<li><a href="#orgc3e7950">1.3.2. HAC - IFF</a></li>
<li><a href="#orgd4db8b6">1.3.3. HAC - DVF</a></li>
</ul>
</li>
<li><a href="#org61a6098">1.4. Control Architecture</a></li>
<li><a href="#orgdca8b1b">1.5. 6x6 Plant Comparison</a></li>
<li><a href="#orgc2459c7">1.6. HAC - DVF</a>
<li><a href="#org7c72eb7">1.6. HAC - DVF</a>
<ul>
<li><a href="#org54f5bbf">1.6.1. Plant</a></li>
<li><a href="#orga9fb0f5">1.6.2. Controller Design</a></li>
<li><a href="#orgf520b4e">1.6.3. Obtained Performance</a></li>
<li><a href="#org673a1cd">1.6.1. Plant</a></li>
<li><a href="#org652bff1">1.6.2. Controller Design</a></li>
<li><a href="#orge39d6bb">1.6.3. Obtained Performance</a></li>
</ul>
</li>
<li><a href="#org8c50a0f">1.7. HAC - IFF</a>
<li><a href="#org09a49c0">1.7. HAC - IFF</a>
<ul>
<li><a href="#orgd015268">1.7.1. Plant</a></li>
<li><a href="#orgb1bd3ac">1.7.2. Controller Design</a></li>
<li><a href="#orgdcdc645">1.7.3. Obtained Performance</a></li>
<li><a href="#org5d68208">1.7.1. Plant</a></li>
<li><a href="#orge650cdd">1.7.2. Controller Design</a></li>
<li><a href="#orge5a568c">1.7.3. Obtained Performance</a></li>
</ul>
</li>
<li><a href="#org9224c01">1.8. Comparison</a></li>
@@ -278,11 +278,11 @@
</li>
<li><a href="#orgde62390">2. MIMO Analysis</a>
<ul>
<li><a href="#org550055f">2.1. Initialization</a></li>
<li><a href="#org23449b8">2.2. Identification</a>
<li><a href="#org56a7ed4">2.1. Initialization</a></li>
<li><a href="#org7b6441f">2.2. Identification</a>
<ul>
<li><a href="#orgd47a3c0">2.2.1. HAC - Without LAC</a></li>
<li><a href="#org1c3609b">2.2.2. HAC - DVF</a></li>
<li><a href="#org33f5d7c">2.2.1. HAC - Without LAC</a></li>
<li><a href="#org9420024">2.2.2. HAC - DVF</a></li>
<li><a href="#orgf7913d5">2.2.3. Cartesian Frame</a></li>
</ul>
</li>
@@ -291,8 +291,8 @@
</li>
<li><a href="#orgebf6121">3. Diagonal Control based on the damped plant</a>
<ul>
<li><a href="#org7d2e4bb">3.1. Initialization</a></li>
<li><a href="#orgb047e7e">3.2. Identification</a></li>
<li><a href="#orgc3f9713">3.1. Initialization</a></li>
<li><a href="#org7e03b59">3.2. Identification</a></li>
<li><a href="#orgab6bc6f">3.3. Steady State Decoupling</a>
<ul>
<li><a href="#orga589a4a">3.3.1. Pre-Compensator Design</a></li>
@@ -355,8 +355,8 @@ First, the LAC loop is closed (the LAC control is described <a href="active-damp
</div>
</div>
<div id="outline-container-org9ad2582" class="outline-3">
<h3 id="org9ad2582"><span class="section-number-3">1.2</span> Initialization</h3>
<div id="outline-container-org5907395" class="outline-3">
<h3 id="org5907395"><span class="section-number-3">1.2</span> Initialization</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We first initialize the Stewart platform.
@@ -387,8 +387,8 @@ payload = initializePayload(<span class="org-string">'type'</span>, <span class=
</div>
</div>
<div id="outline-container-org03823a6" class="outline-3">
<h3 id="org03823a6"><span class="section-number-3">1.3</span> Identification</h3>
<div id="outline-container-org080a6bd" class="outline-3">
<h3 id="org080a6bd"><span class="section-number-3">1.3</span> Identification</h3>
<div class="outline-text-3" id="text-1-3">
<p>
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:
@@ -400,8 +400,8 @@ We identify the transfer function from the actuator forces \(\bm{\tau}\) to the
</ul>
</div>
<div id="outline-container-org4d582a9" class="outline-4">
<h4 id="org4d582a9"><span class="section-number-4">1.3.1</span> HAC - Without LAC</h4>
<div id="outline-container-org183dcef" class="outline-4">
<h4 id="org183dcef"><span class="section-number-4">1.3.1</span> HAC - Without LAC</h4>
<div class="outline-text-4" id="text-1-3-1">
<div class="org-src-container">
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
@@ -426,8 +426,8 @@ G_ol.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string
</div>
</div>
<div id="outline-container-orge0108ff" class="outline-4">
<h4 id="orge0108ff"><span class="section-number-4">1.3.2</span> HAC - IFF</h4>
<div id="outline-container-orgc3e7950" class="outline-4">
<h4 id="orgc3e7950"><span class="section-number-4">1.3.2</span> HAC - IFF</h4>
<div class="outline-text-4" id="text-1-3-2">
<div class="org-src-container">
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'iff'</span>);
@@ -453,8 +453,8 @@ G_iff.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-strin
</div>
</div>
<div id="outline-container-org1afe87f" class="outline-4">
<h4 id="org1afe87f"><span class="section-number-4">1.3.3</span> HAC - DVF</h4>
<div id="outline-container-orgd4db8b6" class="outline-4">
<h4 id="orgd4db8b6"><span class="section-number-4">1.3.3</span> HAC - DVF</h4>
<div class="outline-text-4" id="text-1-3-3">
<div class="org-src-container">
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
@@ -518,12 +518,12 @@ We then design a controller based on the transfer functions from \(\bm{\mathcal{
</div>
</div>
<div id="outline-container-orgc2459c7" class="outline-3">
<h3 id="orgc2459c7"><span class="section-number-3">1.6</span> HAC - DVF</h3>
<div id="outline-container-org7c72eb7" class="outline-3">
<h3 id="org7c72eb7"><span class="section-number-3">1.6</span> HAC - DVF</h3>
<div class="outline-text-3" id="text-1-6">
</div>
<div id="outline-container-org54f5bbf" class="outline-4">
<h4 id="org54f5bbf"><span class="section-number-4">1.6.1</span> Plant</h4>
<div id="outline-container-org673a1cd" class="outline-4">
<h4 id="org673a1cd"><span class="section-number-4">1.6.1</span> Plant</h4>
<div class="outline-text-4" id="text-1-6-1">
<div id="orgbe936ef" class="figure">
@@ -534,8 +534,8 @@ We then design a controller based on the transfer functions from \(\bm{\mathcal{
</div>
</div>
<div id="outline-container-orga9fb0f5" class="outline-4">
<h4 id="orga9fb0f5"><span class="section-number-4">1.6.2</span> Controller Design</h4>
<div id="outline-container-org652bff1" class="outline-4">
<h4 id="org652bff1"><span class="section-number-4">1.6.2</span> Controller Design</h4>
<div class="outline-text-4" id="text-1-6-2">
<p>
We design a diagonal controller with equal bandwidth for the 6 terms.
@@ -570,8 +570,8 @@ Finally, we pre-multiply the diagonal controller by \(\bm{J}^{-T}\) prior implem
</div>
</div>
<div id="outline-container-orgf520b4e" class="outline-4">
<h4 id="orgf520b4e"><span class="section-number-4">1.6.3</span> Obtained Performance</h4>
<div id="outline-container-orge39d6bb" class="outline-4">
<h4 id="orge39d6bb"><span class="section-number-4">1.6.3</span> Obtained Performance</h4>
<div class="outline-text-4" id="text-1-6-3">
<p>
We identify the transmissibility and compliance of the system.
@@ -608,12 +608,12 @@ We identify the transmissibility and compliance of the system.
</div>
</div>
<div id="outline-container-org8c50a0f" class="outline-3">
<h3 id="org8c50a0f"><span class="section-number-3">1.7</span> HAC - IFF</h3>
<div id="outline-container-org09a49c0" class="outline-3">
<h3 id="org09a49c0"><span class="section-number-3">1.7</span> HAC - IFF</h3>
<div class="outline-text-3" id="text-1-7">
</div>
<div id="outline-container-orgd015268" class="outline-4">
<h4 id="orgd015268"><span class="section-number-4">1.7.1</span> Plant</h4>
<div id="outline-container-org5d68208" class="outline-4">
<h4 id="org5d68208"><span class="section-number-4">1.7.1</span> Plant</h4>
<div class="outline-text-4" id="text-1-7-1">
<div id="orgcb10b82" class="figure">
@@ -624,8 +624,8 @@ We identify the transmissibility and compliance of the system.
</div>
</div>
<div id="outline-container-orgb1bd3ac" class="outline-4">
<h4 id="orgb1bd3ac"><span class="section-number-4">1.7.2</span> Controller Design</h4>
<div id="outline-container-orge650cdd" class="outline-4">
<h4 id="orge650cdd"><span class="section-number-4">1.7.2</span> Controller Design</h4>
<div class="outline-text-4" id="text-1-7-2">
<p>
We design a diagonal controller with equal bandwidth for the 6 terms.
@@ -660,8 +660,8 @@ Finally, we pre-multiply the diagonal controller by \(\bm{J}^{-T}\) prior implem
</div>
</div>
<div id="outline-container-orgdcdc645" class="outline-4">
<h4 id="orgdcdc645"><span class="section-number-4">1.7.3</span> Obtained Performance</h4>
<div id="outline-container-orge5a568c" class="outline-4">
<h4 id="orge5a568c"><span class="section-number-4">1.7.3</span> Obtained Performance</h4>
<div class="outline-text-4" id="text-1-7-3">
<p>
We identify the transmissibility and compliance of the system.
@@ -810,8 +810,8 @@ Let&rsquo;s define the system as shown in figure <a href="#orgba6519a">13</a>.
</table>
</div>
<div id="outline-container-org550055f" class="outline-3">
<h3 id="org550055f"><span class="section-number-3">2.1</span> Initialization</h3>
<div id="outline-container-org56a7ed4" class="outline-3">
<h3 id="org56a7ed4"><span class="section-number-3">2.1</span> Initialization</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We first initialize the Stewart platform.
@@ -842,12 +842,12 @@ payload = initializePayload(<span class="org-string">'type'</span>, <span class=
</div>
</div>
<div id="outline-container-org23449b8" class="outline-3">
<h3 id="org23449b8"><span class="section-number-3">2.2</span> Identification</h3>
<div id="outline-container-org7b6441f" class="outline-3">
<h3 id="org7b6441f"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2">
</div>
<div id="outline-container-orgd47a3c0" class="outline-4">
<h4 id="orgd47a3c0"><span class="section-number-4">2.2.1</span> HAC - Without LAC</h4>
<div id="outline-container-org33f5d7c" class="outline-4">
<h4 id="org33f5d7c"><span class="section-number-4">2.2.1</span> HAC - Without LAC</h4>
<div class="outline-text-4" id="text-2-2-1">
<div class="org-src-container">
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
@@ -872,8 +872,8 @@ G_ol.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string
</div>
</div>
<div id="outline-container-org1c3609b" class="outline-4">
<h4 id="org1c3609b"><span class="section-number-4">2.2.2</span> HAC - DVF</h4>
<div id="outline-container-org9420024" class="outline-4">
<h4 id="org9420024"><span class="section-number-4">2.2.2</span> HAC - DVF</h4>
<div class="outline-text-4" id="text-2-2-2">
<div class="org-src-container">
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
@@ -971,8 +971,8 @@ There are mainly three different cases:
</ol>
</div>
<div id="outline-container-org7d2e4bb" class="outline-3">
<h3 id="org7d2e4bb"><span class="section-number-3">3.1</span> Initialization</h3>
<div id="outline-container-orgc3f9713" class="outline-3">
<h3 id="orgc3f9713"><span class="section-number-3">3.1</span> Initialization</h3>
<div class="outline-text-3" id="text-3-1">
<p>
We first initialize the Stewart platform.
@@ -1003,8 +1003,8 @@ payload = initializePayload(<span class="org-string">'type'</span>, <span class=
</div>
</div>
<div id="outline-container-orgb047e7e" class="outline-3">
<h3 id="orgb047e7e"><span class="section-number-3">3.2</span> Identification</h3>
<div id="outline-container-org7e03b59" class="outline-3">
<h3 id="org7e03b59"><span class="section-number-3">3.2</span> Identification</h3>
<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>);
@@ -1239,7 +1239,7 @@ The results are shown in figure
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-28 ven. 17:34</p>
<p class="date">Created: 2020-03-02 lun. 17:57</p>
</div>
</body>
</html>