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Thomas Dehaeze
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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>
<!-- 2020-02-11 mar. 15:26 -->
<!-- 2020-02-11 mar. 15:50 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Stewart Platform - Decentralized Active Damping</title>
@@ -268,28 +268,28 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgd59c804">Inertial Control</a>
<li><a href="#orgd59c804">1. Inertial Control</a>
<ul>
<li><a href="#org5f749c8">Identification of the Dynamics</a></li>
<li><a href="#org543be7a">Effect of the Flexible Joint stiffness on the Dynamics</a></li>
<li><a href="#org9a605b4">Obtained Damping</a></li>
<li><a href="#org42a74ed">Conclusion</a></li>
<li><a href="#org5f749c8">1.1. Identification of the Dynamics</a></li>
<li><a href="#org41a6913">1.2. Effect of the Flexible Joint stiffness on the Dynamics</a></li>
<li><a href="#orgbcd94dc">1.3. Obtained Damping</a></li>
<li><a href="#orgb81ed64">1.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org74c7eb4">Integral Force Feedback</a>
<li><a href="#org74c7eb4">2. Integral Force Feedback</a>
<ul>
<li><a href="#orgc96f772">Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#orgd119d8a">Effect of the Flexible Joint stiffness on the Dynamics</a></li>
<li><a href="#org2b5e45a">Obtained Damping</a></li>
<li><a href="#org39ddf1e">Conclusion</a></li>
<li><a href="#org04cb1dc">2.1. Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#org7f576ce">2.2. Effect of the Flexible Joint stiffness on the Dynamics</a></li>
<li><a href="#orgb927f01">2.3. Obtained Damping</a></li>
<li><a href="#orgf5f2135">2.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org08917d6">Direct Velocity Feedback</a>
<li><a href="#org08917d6">3. Direct Velocity Feedback</a>
<ul>
<li><a href="#org243b924">Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#orgcdb3ee5">Effect of the Flexible Joint stiffness on the Dynamics</a></li>
<li><a href="#orgff0cbf9">Obtained Damping</a></li>
<li><a href="#org4027234">Conclusion</a></li>
<li><a href="#orgbfe0af6">3.1. Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#org62438da">3.2. Effect of the Flexible Joint stiffness on the Dynamics</a></li>
<li><a href="#orgb4fcddf">3.3. Obtained Damping</a></li>
<li><a href="#org31a4bb6">3.4. Conclusion</a></li>
</ul>
</li>
</ul>
@@ -300,22 +300,22 @@ for the JavaScript code in this tag.
The following decentralized active damping techniques are briefly studied:
</p>
<ul class="org-ul">
<li>Inertial Control (proportional feedback of the absolute velocity): Section <a href="#orgeb37c7d">No description for this link</a></li>
<li>Integral Force Feedback: Section <a href="#orgab5e6b5">No description for this link</a></li>
<li>Direct feedback of the relative velocity of each strut: Section <a href="#org0aa816a">No description for this link</a></li>
<li>Inertial Control (proportional feedback of the absolute velocity): Section <a href="#orgeb37c7d">1</a></li>
<li>Integral Force Feedback: Section <a href="#orgab5e6b5">2</a></li>
<li>Direct feedback of the relative velocity of each strut: Section <a href="#org0aa816a">3</a></li>
</ul>
<div id="outline-container-orgd59c804" class="outline-2">
<h2 id="orgd59c804">Inertial Control</h2>
<div class="outline-text-2" id="text-orgd59c804">
<h2 id="orgd59c804"><span class="section-number-2">1</span> Inertial Control</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orgeb37c7d"></a>
</p>
</div>
<div id="outline-container-org5f749c8" class="outline-3">
<h3 id="org5f749c8">Identification of the Dynamics</h3>
<div class="outline-text-3" id="text-org5f749c8">
<h3 id="org5f749c8"><span class="section-number-3">1.1</span> Identification of the Dynamics</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-matlab">stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
@@ -362,9 +362,9 @@ The transfer function from actuator forces to force sensors is shown in Figure <
</div>
</div>
<div id="outline-container-org543be7a" class="outline-3">
<h3 id="org543be7a">Effect of the Flexible Joint stiffness on the Dynamics</h3>
<div class="outline-text-3" id="text-org543be7a">
<div id="outline-container-org41a6913" class="outline-3">
<h3 id="org41a6913"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness on the Dynamics</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
</p>
@@ -388,9 +388,9 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
</div>
</div>
<div id="outline-container-org9a605b4" class="outline-3">
<h3 id="org9a605b4">Obtained Damping</h3>
<div class="outline-text-3" id="text-org9a605b4">
<div id="outline-container-orgbcd94dc" class="outline-3">
<h3 id="orgbcd94dc"><span class="section-number-3">1.3</span> Obtained Damping</h3>
<div class="outline-text-3" id="text-1-3">
<p>
The control is a performed in a decentralized manner.
The \(6 \times 6\) control is a diagonal matrix with pure proportional action on the diagonal:
@@ -421,9 +421,9 @@ The root locus is shown in figure <a href="#org9af9e33">3</a> and the obtained p
</div>
</div>
<div id="outline-container-org42a74ed" class="outline-3">
<h3 id="org42a74ed">Conclusion</h3>
<div class="outline-text-3" id="text-org42a74ed">
<div id="outline-container-orgb81ed64" class="outline-3">
<h3 id="orgb81ed64"><span class="section-number-3">1.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-4">
<div class="important">
<p>
Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
@@ -435,16 +435,16 @@ Joint stiffness does increase the resonance frequencies of the system but does n
</div>
<div id="outline-container-org74c7eb4" class="outline-2">
<h2 id="org74c7eb4">Integral Force Feedback</h2>
<div class="outline-text-2" id="text-org74c7eb4">
<h2 id="org74c7eb4"><span class="section-number-2">2</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgab5e6b5"></a>
</p>
</div>
<div id="outline-container-orgc96f772" class="outline-3">
<h3 id="orgc96f772">Identification of the Dynamics with perfect Joints</h3>
<div class="outline-text-3" id="text-orgc96f772">
<div id="outline-container-org04cb1dc" class="outline-3">
<h3 id="org04cb1dc"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We first initialize the Stewart platform without joint stiffness.
</p>
@@ -498,9 +498,9 @@ The transfer function from actuator forces to force sensors is shown in Figure <
</div>
</div>
<div id="outline-container-orgd119d8a" class="outline-3">
<h3 id="orgd119d8a">Effect of the Flexible Joint stiffness on the Dynamics</h3>
<div class="outline-text-3" id="text-orgd119d8a">
<div id="outline-container-org7f576ce" class="outline-3">
<h3 id="org7f576ce"><span class="section-number-3">2.2</span> Effect of the Flexible Joint stiffness on the Dynamics</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
</p>
@@ -524,9 +524,9 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
</div>
</div>
<div id="outline-container-org2b5e45a" class="outline-3">
<h3 id="org2b5e45a">Obtained Damping</h3>
<div class="outline-text-3" id="text-org2b5e45a">
<div id="outline-container-orgb927f01" class="outline-3">
<h3 id="orgb927f01"><span class="section-number-3">2.3</span> Obtained Damping</h3>
<div class="outline-text-3" id="text-2-3">
<p>
The control is a performed in a decentralized manner.
The \(6 \times 6\) control is a diagonal matrix with pure integration action on the diagonal:
@@ -557,9 +557,9 @@ The root locus is shown in figure <a href="#orge21bbea">7</a> and the obtained p
</div>
</div>
<div id="outline-container-org39ddf1e" class="outline-3">
<h3 id="org39ddf1e">Conclusion</h3>
<div class="outline-text-3" id="text-org39ddf1e">
<div id="outline-container-orgf5f2135" class="outline-3">
<h3 id="orgf5f2135"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4">
<div class="important">
<p>
The joint stiffness has a huge impact on the attainable active damping performance when using force sensors.
@@ -572,16 +572,16 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
</div>
<div id="outline-container-org08917d6" class="outline-2">
<h2 id="org08917d6">Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-org08917d6">
<h2 id="org08917d6"><span class="section-number-2">3</span> Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org0aa816a"></a>
</p>
</div>
<div id="outline-container-org243b924" class="outline-3">
<h3 id="org243b924">Identification of the Dynamics with perfect Joints</h3>
<div class="outline-text-3" id="text-org243b924">
<div id="outline-container-orgbfe0af6" class="outline-3">
<h3 id="orgbfe0af6"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
<div class="outline-text-3" id="text-3-1">
<p>
We first initialize the Stewart platform without joint stiffness.
</p>
@@ -635,9 +635,9 @@ The transfer function from actuator forces to relative motion sensors is shown i
</div>
<div id="outline-container-orgcdb3ee5" class="outline-3">
<h3 id="orgcdb3ee5">Effect of the Flexible Joint stiffness on the Dynamics</h3>
<div class="outline-text-3" id="text-orgcdb3ee5">
<div id="outline-container-org62438da" class="outline-3">
<h3 id="org62438da"><span class="section-number-3">3.2</span> Effect of the Flexible Joint stiffness on the Dynamics</h3>
<div class="outline-text-3" id="text-3-2">
<p>
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
</p>
@@ -661,9 +661,9 @@ The new dynamics from force actuator to relative motion sensor is shown in Figur
</div>
</div>
<div id="outline-container-orgff0cbf9" class="outline-3">
<h3 id="orgff0cbf9">Obtained Damping</h3>
<div class="outline-text-3" id="text-orgff0cbf9">
<div id="outline-container-orgb4fcddf" class="outline-3">
<h3 id="orgb4fcddf"><span class="section-number-3">3.3</span> Obtained Damping</h3>
<div class="outline-text-3" id="text-3-3">
<p>
The control is a performed in a decentralized manner.
The \(6 \times 6\) control is a diagonal matrix with pure derivative action on the diagonal:
@@ -694,9 +694,9 @@ The root locus is shown in figure <a href="#org277d60d">11</a> and the obtained
</div>
</div>
<div id="outline-container-org4027234" class="outline-3">
<h3 id="org4027234">Conclusion</h3>
<div class="outline-text-3" id="text-org4027234">
<div id="outline-container-org31a4bb6" class="outline-3">
<h3 id="org31a4bb6"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4">
<div class="important">
<p>
Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
@@ -709,7 +709,7 @@ Joint stiffness does increase the resonance frequencies of the system but does n
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-11 mar. 15:26</p>
<p class="date">Created: 2020-02-11 mar. 15:50</p>
</div>
</body>
</html>