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Thomas Dehaeze
2020-03-26 17:25:43 +01:00
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@@ -1,11 +1,10 @@
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<?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 mar. 17:31 -->
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<title>Active Damping applied on the Simscape Model</title>
@@ -203,28 +202,50 @@
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@@ -252,17 +273,17 @@
<ul>
<li><a href="#orgb9bb91c">1.1. Identification of the dynamics for Active Damping</a>
<ul>
<li><a href="#org0f0da06">1.1.1. Identification</a></li>
<li><a href="#org9be7a0a">1.1.1. Identification</a></li>
<li><a href="#org821239d">1.1.2. Obtained Plants for Active Damping</a></li>
</ul>
</li>
<li><a href="#org21a2e91">1.2. Identification of the dynamics for High Authority Control</a>
<ul>
<li><a href="#org9be7a0a">1.2.1. Identification</a></li>
<li><a href="#orgae8b5f6">1.2.1. Identification</a></li>
<li><a href="#orgff85811">1.2.2. Obtained Plants</a></li>
</ul>
</li>
<li><a href="#org81c0932">1.3. Tomography Experiment</a>
<li><a href="#orgd249fa7">1.3. Tomography Experiment</a>
<ul>
<li><a href="#orgd5305ce">1.3.1. Simulation</a></li>
<li><a href="#orgd64a4bc">1.3.2. Results</a></li>
@@ -282,55 +303,55 @@
</li>
<li><a href="#org47c5593">2.4. Variation of the Tilt Angle</a></li>
<li><a href="#org047e39c">2.5. Scans of the Translation Stage</a></li>
<li><a href="#orgcc847b4">2.6. Conclusion</a></li>
<li><a href="#orga3a88c5">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org11ab68f">3. Integral Force Feedback</a>
<ul>
<li><a href="#orgc33df7f">3.1. Control Design</a>
<li><a href="#org7469e89">3.1. Control Design</a>
<ul>
<li><a href="#orgb37aa8c">3.1.1. Plant</a></li>
<li><a href="#orgf48079a">3.1.2. Control Design</a></li>
<li><a href="#orgbe1ed5f">3.1.3. Diagonal Controller</a></li>
<li><a href="#org50113d6">3.1.1. Plant</a></li>
<li><a href="#org0279170">3.1.2. Control Design</a></li>
<li><a href="#orge6bfce6">3.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#org22b777e">3.2. Tomography Experiment</a>
<li><a href="#org93e3515">3.2. Tomography Experiment</a>
<ul>
<li><a href="#org132e692">3.2.1. Simulation with IFF Controller</a></li>
<li><a href="#orgea4037e">3.2.2. Compare with Undamped system</a></li>
<li><a href="#orge17626d">3.2.2. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#org59bf532">3.3. Conclusion</a></li>
<li><a href="#org6bfc3c8">3.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org13393f4">4. Direct Velocity Feedback</a>
<ul>
<li><a href="#org7ffae11">4.1. Control Design</a>
<li><a href="#org6ab2a22">4.1. Control Design</a>
<ul>
<li><a href="#orgf0a922a">4.1.1. Plant</a></li>
<li><a href="#orge6b7551">4.1.2. Control Design</a></li>
<li><a href="#org8d3cc5b">4.1.3. Diagonal Controller</a></li>
<li><a href="#orged52a69">4.1.1. Plant</a></li>
<li><a href="#org44b5b14">4.1.2. Control Design</a></li>
<li><a href="#orgfb28f7d">4.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#orgd249fa7">4.2. Tomography Experiment</a>
<li><a href="#orgdc93329">4.2. Tomography Experiment</a>
<ul>
<li><a href="#orgb9a85e7">4.2.1. Initialize the Simulation</a></li>
<li><a href="#orge17626d">4.2.2. Compare with Undamped system</a></li>
<li><a href="#orgaf91898">4.2.1. Initialize the Simulation</a></li>
<li><a href="#orge68c2e6">4.2.2. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#org70b25db">4.3. Conclusion</a></li>
<li><a href="#orgdd6b994">4.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8f2508f">5. Inertial Control</a>
<ul>
<li><a href="#org0279170">5.1. Control Design</a>
<li><a href="#org78934a1">5.1. Control Design</a>
<ul>
<li><a href="#org50113d6">5.1.1. Plant</a></li>
<li><a href="#orgbb314af">5.1.2. Control Design</a></li>
<li><a href="#orge6bfce6">5.1.3. Diagonal Controller</a></li>
<li><a href="#orga97b3aa">5.1.1. Plant</a></li>
<li><a href="#org92b0a5f">5.1.2. Control Design</a></li>
<li><a href="#org9e08e48">5.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#orga3a88c5">5.2. Conclusion</a></li>
<li><a href="#org054aff8">5.2. Conclusion</a></li>
</ul>
</li>
<li><a href="#org3557ae9">6. Comparison</a>
@@ -345,16 +366,16 @@
<ul>
<li><a href="#org8642cf5">7.1. prepareLinearizeIdentification</a>
<ul>
<li><a href="#org87c7f1d">Function Description</a></li>
<li><a href="#orga92724f">Optional Parameters</a></li>
<li><a href="#orgd2983c1">Initialize the Simulation</a></li>
<li><a href="#org6a968ef">Function Description</a></li>
<li><a href="#orgc14eed3">Optional Parameters</a></li>
<li><a href="#orgc7a07c5">Initialize the Simulation</a></li>
</ul>
</li>
<li><a href="#orgeb73896">7.2. prepareTomographyExperiment</a>
<ul>
<li><a href="#org6a968ef">Function Description</a></li>
<li><a href="#orgc14eed3">Optional Parameters</a></li>
<li><a href="#orgaf91898">Initialize the Simulation</a></li>
<li><a href="#org34e8f09">Function Description</a></li>
<li><a href="#org82d8c08">Optional Parameters</a></li>
<li><a href="#org2ece687">Initialize the Simulation</a></li>
</ul>
</li>
</ul>
@@ -426,8 +447,8 @@ After that, a tomography experiment is simulation without any active damping tec
<h3 id="orgb9bb91c"><span class="section-number-3">1.1</span> Identification of the dynamics for Active Damping</h3>
<div class="outline-text-3" id="text-1-1">
</div>
<div id="outline-container-org0f0da06" class="outline-4">
<h4 id="org0f0da06"><span class="section-number-4">1.1.1</span> Identification</h4>
<div id="outline-container-org9be7a0a" class="outline-4">
<h4 id="org9be7a0a"><span class="section-number-4">1.1.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-1-1">
<p>
We initialize all the stages with the default parameters.
@@ -520,8 +541,8 @@ And we save them for further analysis.
<h3 id="org21a2e91"><span class="section-number-3">1.2</span> Identification of the dynamics for High Authority Control</h3>
<div class="outline-text-3" id="text-1-2">
</div>
<div id="outline-container-org9be7a0a" class="outline-4">
<h4 id="org9be7a0a"><span class="section-number-4">1.2.1</span> Identification</h4>
<div id="outline-container-orgae8b5f6" class="outline-4">
<h4 id="orgae8b5f6"><span class="section-number-4">1.2.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-2-1">
<p>
We initialize all the stages with the default parameters.
@@ -590,8 +611,8 @@ And we save them for further analysis.
</div>
</div>
<div id="outline-container-org81c0932" class="outline-3">
<h3 id="org81c0932"><span class="section-number-3">1.3</span> Tomography Experiment</h3>
<div id="outline-container-orgd249fa7" class="outline-3">
<h3 id="orgd249fa7"><span class="section-number-3">1.3</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-1-3">
</div>
<div id="outline-container-orgd5305ce" class="outline-4">
@@ -979,8 +1000,8 @@ We identify the dynamics at different positions (times) when scanning with the T
</div>
</div>
<div id="outline-container-orgcc847b4" class="outline-3">
<h3 id="orgcc847b4"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-orga3a88c5" class="outline-3">
<h3 id="orga3a88c5"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<table id="orgbd1a9f9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Conclusion on the variability of the system dynamics for active damping</caption>
@@ -1071,12 +1092,12 @@ The control architecture is represented in figure <a href="#org3a1dbf1">29</a> w
</div>
</div>
<div id="outline-container-orgc33df7f" class="outline-3">
<h3 id="orgc33df7f"><span class="section-number-3">3.1</span> Control Design</h3>
<div id="outline-container-org7469e89" class="outline-3">
<h3 id="org7469e89"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1">
</div>
<div id="outline-container-orgb37aa8c" class="outline-4">
<h4 id="orgb37aa8c"><span class="section-number-4">3.1.1</span> Plant</h4>
<div id="outline-container-org50113d6" class="outline-4">
<h4 id="org50113d6"><span class="section-number-4">3.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-3-1-1">
<p>
Let&rsquo;s load the previously identified undamped plant:
@@ -1100,8 +1121,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div>
</div>
<div id="outline-container-orgf48079a" class="outline-4">
<h4 id="orgf48079a"><span class="section-number-4">3.1.2</span> Control Design</h4>
<div id="outline-container-org0279170" class="outline-4">
<h4 id="org0279170"><span class="section-number-4">3.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-3-1-2">
<p>
The controller for each pair of actuator/sensor is:
@@ -1125,8 +1146,8 @@ The corresponding loop gains are shown in figure <a href="#org1f5c623">31</a>.
</div>
</div>
<div id="outline-container-orgbe1ed5f" class="outline-4">
<h4 id="orgbe1ed5f"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4>
<div id="outline-container-orge6bfce6" class="outline-4">
<h4 id="orge6bfce6"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-3-1-3">
<p>
We create the diagonal controller and we add a minus sign as we have a positive
@@ -1148,8 +1169,8 @@ We save the controller for further analysis.
</div>
</div>
<div id="outline-container-org22b777e" class="outline-3">
<h3 id="org22b777e"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
<div id="outline-container-org93e3515" class="outline-3">
<h3 id="org93e3515"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-3-2">
</div>
<div id="outline-container-org132e692" class="outline-4">
@@ -1201,8 +1222,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-orgea4037e" class="outline-4">
<h4 id="orgea4037e"><span class="section-number-4">3.2.2</span> Compare with Undamped system</h4>
<div id="outline-container-orge17626d" class="outline-4">
<h4 id="orge17626d"><span class="section-number-4">3.2.2</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-3-2-2">
<div id="org7547861" class="figure">
@@ -1228,8 +1249,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-org59bf532" class="outline-3">
<h3 id="org59bf532"><span class="section-number-3">3.3</span> Conclusion</h3>
<div id="outline-container-org6bfc3c8" class="outline-3">
<h3 id="org6bfc3c8"><span class="section-number-3">3.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-3">
<div class="important">
<p>
@@ -1264,12 +1285,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
</p>
</div>
<div id="outline-container-org7ffae11" class="outline-3">
<h3 id="org7ffae11"><span class="section-number-3">4.1</span> Control Design</h3>
<div id="outline-container-org6ab2a22" class="outline-3">
<h3 id="org6ab2a22"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1">
</div>
<div id="outline-container-orgf0a922a" class="outline-4">
<h4 id="orgf0a922a"><span class="section-number-4">4.1.1</span> Plant</h4>
<div id="outline-container-orged52a69" class="outline-4">
<h4 id="orged52a69"><span class="section-number-4">4.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-4-1-1">
<p>
Let&rsquo;s load the undamped plant:
@@ -1293,8 +1314,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div>
</div>
<div id="outline-container-orge6b7551" class="outline-4">
<h4 id="orge6b7551"><span class="section-number-4">4.1.2</span> Control Design</h4>
<div id="outline-container-org44b5b14" class="outline-4">
<h4 id="org44b5b14"><span class="section-number-4">4.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-4-1-2">
<p>
The Direct Velocity Feedback is defined below.
@@ -1318,8 +1339,8 @@ The obtained loop gains are shown in figure <a href="#org3568457">36</a>.
</div>
</div>
<div id="outline-container-org8d3cc5b" class="outline-4">
<h4 id="org8d3cc5b"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4>
<div id="outline-container-orgfb28f7d" class="outline-4">
<h4 id="orgfb28f7d"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-4-1-3">
<p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@@ -1340,12 +1361,12 @@ We save the controller for further analysis.
</div>
</div>
<div id="outline-container-orgd249fa7" class="outline-3">
<h3 id="orgd249fa7"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
<div id="outline-container-orgdc93329" class="outline-3">
<h3 id="orgdc93329"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-4-2">
</div>
<div id="outline-container-orgb9a85e7" class="outline-4">
<h4 id="orgb9a85e7"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4>
<div id="outline-container-orgaf91898" class="outline-4">
<h4 id="orgaf91898"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-4-2-1">
<p>
We initialize elements for the tomography experiment.
@@ -1393,8 +1414,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-orge17626d" class="outline-4">
<h4 id="orge17626d"><span class="section-number-4">4.2.2</span> Compare with Undamped system</h4>
<div id="outline-container-orge68c2e6" class="outline-4">
<h4 id="orge68c2e6"><span class="section-number-4">4.2.2</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-4-2-2">
<div id="orgfe01054" class="figure">
@@ -1420,8 +1441,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-org70b25db" class="outline-3">
<h3 id="org70b25db"><span class="section-number-3">4.3</span> Conclusion</h3>
<div id="outline-container-orgdd6b994" class="outline-3">
<h3 id="orgdd6b994"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3">
<div class="important">
<p>
@@ -1453,12 +1474,12 @@ In Inertial Control, a feedback is applied between the measured <b>absolute</b>
</p>
</div>
<div id="outline-container-org0279170" class="outline-3">
<h3 id="org0279170"><span class="section-number-3">5.1</span> Control Design</h3>
<div id="outline-container-org78934a1" class="outline-3">
<h3 id="org78934a1"><span class="section-number-3">5.1</span> Control Design</h3>
<div class="outline-text-3" id="text-5-1">
</div>
<div id="outline-container-org50113d6" class="outline-4">
<h4 id="org50113d6"><span class="section-number-4">5.1.1</span> Plant</h4>
<div id="outline-container-orga97b3aa" class="outline-4">
<h4 id="orga97b3aa"><span class="section-number-4">5.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-5-1-1">
<p>
Let&rsquo;s load the undamped plant:
@@ -1482,8 +1503,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div>
</div>
<div id="outline-container-orgbb314af" class="outline-4">
<h4 id="orgbb314af"><span class="section-number-4">5.1.2</span> Control Design</h4>
<div id="outline-container-org92b0a5f" class="outline-4">
<h4 id="org92b0a5f"><span class="section-number-4">5.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-5-1-2">
<p>
The controller is defined below and the obtained loop gain is shown in figure <a href="#orga2f6fdb">41</a>.
@@ -1503,8 +1524,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div>
</div>
<div id="outline-container-orge6bfce6" class="outline-4">
<h4 id="orge6bfce6"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4>
<div id="outline-container-org9e08e48" class="outline-4">
<h4 id="org9e08e48"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-5-1-3">
<p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@@ -1525,8 +1546,8 @@ We save the controller for further analysis.
</div>
</div>
<div id="outline-container-orga3a88c5" class="outline-3">
<h3 id="orga3a88c5"><span class="section-number-3">5.2</span> Conclusion</h3>
<div id="outline-container-org054aff8" class="outline-3">
<h3 id="org054aff8"><span class="section-number-3">5.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-2">
<div class="important">
<p>
@@ -1702,9 +1723,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
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<h4 id="org87c7f1d">Function Description</h4>
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<h4 id="org6a968ef">Function Description</h4>
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<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareLinearizeIdentification</span>(<span class="org-variable-name">args</span>)
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@@ -1712,9 +1733,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
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<h4 id="orga92724f">Optional Parameters</h4>
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<h4 id="orgc14eed3">Optional Parameters</h4>
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<pre class="src src-matlab">arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
@@ -1725,9 +1746,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
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<h4 id="orgd2983c1">Initialize the Simulation</h4>
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<h4 id="orgc7a07c5">Initialize the Simulation</h4>
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We initialize all the stages with the default parameters.
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@@ -1800,9 +1821,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
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<h4 id="org6a968ef">Function Description</h4>
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<h4 id="org34e8f09">Function Description</h4>
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<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>)
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@@ -1810,9 +1831,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
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<pre class="src src-matlab">arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
@@ -1824,9 +1845,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
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<h4 id="orgaf91898">Initialize the Simulation</h4>
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<h4 id="org2ece687">Initialize the Simulation</h4>
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We initialize all the stages with the default parameters.
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@@ -1894,7 +1915,7 @@ We log the signals.
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<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-03-17 mar. 17:31</p>
<p class="date">Created: 2020-03-26 jeu. 17:25</p>
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