Add new file about optimal stiffness / control

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</div><div id="content">
<h1 class="title">Control of the NASS with optimal stiffness</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgb09af41">1. Low Authority Control - Decentralized Integral Force Feedback</a>
<ul>
<li><a href="#orgf3f8aed">1.1. Initialization</a></li>
<li><a href="#org93676a4">1.2. Identification</a></li>
<li><a href="#org1f2e125">1.3. Controller Design</a></li>
</ul>
</li>
<li><a href="#orgf825c29">2. Primary Control</a>
<ul>
<li><a href="#org611a860">2.1. Identification</a></li>
<li><a href="#orgfef1a3f">2.2. Controller Design</a></li>
</ul>
</li>
<li><a href="#org84f68cc">3. Simulations</a></li>
</ul>
</div>
</div>
<div id="outline-container-orgb09af41" class="outline-2">
<h2 id="orgb09af41"><span class="section-number-2">1</span> Low Authority Control - Decentralized Integral Force Feedback</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-orgf3f8aed" class="outline-3">
<h3 id="orgf3f8aed"><span class="section-number-3">1.1</span> Initialization</h3>
<div class="outline-text-3" id="text-1-1">
<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>
We set the references that corresponds to a tomography experiment.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating-not-filtered'</span>, <span class="org-string">'Rz_period'</span>, 1);
initializeSimscapeConfiguration();
initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-iff'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org93676a4" class="outline-3">
<h3 id="org93676a4"><span class="section-number-3">1.2</span> Identification</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-matlab">Kx = tf(zeros(6));
Kiff = tf(zeros(6));
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">Ms = [1, 10, 50];
Gm_iff = {zeros(length(Ms), 1)};
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'k'</span>, 1e5, <span class="org-string">'c'</span>, 2e2);
</pre>
</div>
</div>
</div>
<div id="outline-container-org1f2e125" class="outline-3">
<h3 id="org1f2e125"><span class="section-number-3">1.3</span> Controller Design</h3>
<div class="outline-text-3" id="text-1-3">
<p>
Root Locus
</p>
<div id="orgf657dfe" class="figure">
<p><img src="figs/opt_stiff_iff_root_locus.png" alt="opt_stiff_iff_root_locus.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Root Locus for the</p>
</div>
<p>
Damping as function of the gain
</p>
</div>
</div>
</div>
<div id="outline-container-orgf825c29" class="outline-2">
<h2 id="orgf825c29"><span class="section-number-2">2</span> Primary Control</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org611a860" class="outline-3">
<h3 id="org611a860"><span class="section-number-3">2.1</span> Identification</h3>
</div>
<div id="outline-container-orgfef1a3f" class="outline-3">
<h3 id="orgfef1a3f"><span class="section-number-3">2.2</span> Controller Design</h3>
</div>
</div>
<div id="outline-container-org84f68cc" class="outline-2">
<h2 id="org84f68cc"><span class="section-number-2">3</span> Simulations</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-08 mer. 17:22</p>
</div>
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<head>
<!-- 2020-04-08 mer. 12:17 -->
<!-- 2020-04-08 mer. 17:20 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Determination of the optimal nano-hexapod&rsquo;s stiffness for reducing the effect of disturbances</title>
@@ -257,7 +257,7 @@
<li><a href="#org78dd34d">2.3. Sensitivity to Stages vibration (Filtering)</a></li>
<li><a href="#orgd4ea2f4">2.4. Effect of Ground motion (Transmissibility).</a></li>
<li><a href="#org0448746">2.5. Direct Forces (Compliance).</a></li>
<li><a href="#org6791692">2.6. Conclusion</a></li>
<li><a href="#org08f24cd">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org6527e58">3. Effect of granite stiffness</a>
@@ -270,7 +270,7 @@
</li>
<li><a href="#org9215f81">3.2. Soft Granite</a></li>
<li><a href="#org8878556">3.3. Effect of the Granite transfer function</a></li>
<li><a href="#orga001da4">3.4. Conclusion</a></li>
<li><a href="#orgbc8931e">3.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8a88fb0">4. Open Loop Budget Error</a>
@@ -278,7 +278,7 @@
<li><a href="#org6bd588f">4.1. Noise Budgeting - Theory</a></li>
<li><a href="#orgcc86f59">4.2. Power Spectral Densities</a></li>
<li><a href="#orgef96b89">4.3. Cumulative Amplitude Spectrum</a></li>
<li><a href="#org4352c0d">4.4. Conclusion</a></li>
<li><a href="#org18bab44">4.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org34c0f38">5. Closed Loop Budget Error</a>
@@ -287,7 +287,7 @@
<li><a href="#orgf2d36a1">5.2. Reduction thanks to feedback - Required bandwidth</a></li>
</ul>
</li>
<li><a href="#org08f24cd">6. Conclusion</a></li>
<li><a href="#orgd9198a1">6. Conclusion</a></li>
</ul>
</div>
</div>
@@ -497,8 +497,8 @@ The effect of direct forces/torques applied on the sample (cable forces for inst
</div>
</div>
<div id="outline-container-org6791692" class="outline-3">
<h3 id="org6791692"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-org08f24cd" class="outline-3">
<h3 id="org08f24cd"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<p>
@@ -678,8 +678,8 @@ From Figures <a href="#orgc4c14fb">11</a> and <a href="#org533cc4b">12</a>, we s
</div>
</div>
<div id="outline-container-orga001da4" class="outline-3">
<h3 id="orga001da4"><span class="section-number-3">3.4</span> Conclusion</h3>
<div id="outline-container-orgbc8931e" class="outline-3">
<h3 id="orgbc8931e"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4">
<div class="important">
<p>
@@ -848,8 +848,8 @@ The black dashed line corresponds to the performance objective of a sample vibra
</div>
</div>
<div id="outline-container-org4352c0d" class="outline-3">
<h3 id="org4352c0d"><span class="section-number-3">4.4</span> Conclusion</h3>
<div id="outline-container-org18bab44" class="outline-3">
<h3 id="org18bab44"><span class="section-number-3">4.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-4">
<div class="important">
<p>
@@ -1012,8 +1012,8 @@ The obtained required bandwidth (approximate upper and lower bounds) to obtained
</div>
</div>
<div id="outline-container-org08f24cd" class="outline-2">
<h2 id="org08f24cd"><span class="section-number-2">6</span> Conclusion</h2>
<div id="outline-container-orgd9198a1" class="outline-2">
<h2 id="orgd9198a1"><span class="section-number-2">6</span> Conclusion</h2>
<div class="outline-text-2" id="text-6">
<div class="important">
<p>
@@ -1021,7 +1021,7 @@ From Figure <a href="#orgd677910">23</a> and Table <a href="#org5ab4860">1</a>,
</p>
<ul class="org-ul">
<li>For a soft nano-hexapod (\(k < 10^4\ [N/m]\)), the required bandwidth is \(\omega_c \approx 50-100\ Hz\)</li>
<li>For a nano-hexapods with \(10^5 < k < 10^6\ [N/m]\)), the required bandwidth is \(\omega_c \approx 150-300\ Hz\)</li>
<li>For a nano-hexapods with \(10^5 < k < 10^6\ [N/m]\), the required bandwidth is \(\omega_c \approx 150-300\ Hz\)</li>
<li>For a stiff nano-hexapods (\(k > 10^7\ [N/m]\)), the required bandwidth is \(\omega_c \approx 250-500\ Hz\)</li>
</ul>
@@ -1031,7 +1031,7 @@ From Figure <a href="#orgd677910">23</a> and Table <a href="#org5ab4860">1</a>,
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-08 mer. 12:17</p>
<p class="date">Created: 2020-04-08 mer. 17:20</p>
</div>
</body>
</html>