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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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<!-- 2021-06-14 lun. 17:24 -->
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<!-- 2021-06-14 lun. 18:07 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Nano-Hexapod - Test Bench</title>
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<meta name="author" content="Dehaeze Thomas" />
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@ -39,54 +39,54 @@
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org5c42276">1. Encoders fixed to the Struts</a>
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<li><a href="#org4f28452">1. Encoders fixed to the Struts</a>
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<ul>
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<li><a href="#orge93a02f">1.1. Introduction</a></li>
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<li><a href="#org0640b0f">1.2. Identification of the dynamics</a>
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<li><a href="#orgdb58b6b">1.1. Introduction</a></li>
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<li><a href="#orga23f4a3">1.2. Identification of the dynamics</a>
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<ul>
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<li><a href="#org1fc2e33">1.2.1. Load Data</a></li>
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<li><a href="#org27129af">1.2.2. Spectral Analysis - Setup</a></li>
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<li><a href="#orgfe67585">1.2.3. DVF Plant</a></li>
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<li><a href="#org3674942">1.2.4. IFF Plant</a></li>
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<li><a href="#org463f1c5">1.2.1. Load Data</a></li>
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<li><a href="#orga89822b">1.2.2. Spectral Analysis - Setup</a></li>
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<li><a href="#org2ea8050">1.2.3. DVF Plant</a></li>
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<li><a href="#org3af4d82">1.2.4. IFF Plant</a></li>
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</ul>
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</li>
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<li><a href="#org90b8ca8">1.3. Comparison with the Simscape Model</a>
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<li><a href="#org0d5bead">1.3. Comparison with the Simscape Model</a>
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<ul>
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<li><a href="#org7f3653d">1.3.1. Dynamics from Actuator to Force Sensors</a></li>
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<li><a href="#orgf2b8f1a">1.3.2. Dynamics from Actuator to Encoder</a></li>
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<li><a href="#org52ed397">1.3.1. Dynamics from Actuator to Force Sensors</a></li>
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<li><a href="#org6bb92e5">1.3.2. Dynamics from Actuator to Encoder</a></li>
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</ul>
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</li>
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<li><a href="#orgcb40fee">1.4. Integral Force Feedback</a>
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<li><a href="#org9537bdd">1.4. Integral Force Feedback</a>
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<ul>
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<li><a href="#org454aab2">1.4.1. Root Locus and Decentralized Loop gain</a></li>
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<li><a href="#orgf25396d">1.4.2. Multiple Gains - Simulation</a></li>
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<li><a href="#org9e5a43a">1.4.3. Experimental Results - Gains</a>
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<li><a href="#org1092513">1.4.1. Root Locus and Decentralized Loop gain</a></li>
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<li><a href="#orgb15799f">1.4.2. Multiple Gains - Simulation</a></li>
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<li><a href="#orgfc28d74">1.4.3. Experimental Results - Gains</a>
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<ul>
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<li><a href="#org7528195">1.4.3.1. Load Data</a></li>
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<li><a href="#org014c26e">1.4.3.2. Spectral Analysis - Setup</a></li>
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<li><a href="#orga410c78">1.4.3.3. DVF Plant</a></li>
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<li><a href="#org97f2ad7">1.4.3.4. Experimental Results - Comparison of the un-damped and fully damped system</a></li>
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<li><a href="#orgc87e132">1.4.3.1. Load Data</a></li>
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<li><a href="#org082cedd">1.4.3.2. Spectral Analysis - Setup</a></li>
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<li><a href="#orgf617003">1.4.3.3. DVF Plant</a></li>
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<li><a href="#orgfaa6821">1.4.3.4. Experimental Results - Comparison of the un-damped and fully damped system</a></li>
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</ul>
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</li>
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<li><a href="#org38e77db">1.4.4. Experimental Results - Damped Plant with Optimal gain</a>
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<li><a href="#orgc0e0293">1.4.4. Experimental Results - Damped Plant with Optimal gain</a>
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<ul>
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<li><a href="#org5b64143">1.4.4.1. Load Data</a></li>
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<li><a href="#org9d60597">1.4.4.2. Spectral Analysis - Setup</a></li>
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<li><a href="#org5e16098">1.4.4.3. DVF Plant</a></li>
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<li><a href="#org04a0c15">1.4.4.1. Load Data</a></li>
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<li><a href="#org288970e">1.4.4.2. Spectral Analysis - Setup</a></li>
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<li><a href="#orgbe5d7c4">1.4.4.3. DVF Plant</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#orgcf93367">1.5. Modal Analysis</a>
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<li><a href="#org4d2a6a9">1.5. Modal Analysis</a>
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<ul>
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<li><a href="#org4380b82">1.5.1. Effectiveness of the IFF Strategy - Compliance</a></li>
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<li><a href="#org432b9c9">1.5.2. Comparison with the Simscape Model</a></li>
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<li><a href="#org9e1cc1a">1.5.3. Obtained Mode Shapes</a></li>
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<li><a href="#org76f1cc6">1.5.1. Effectiveness of the IFF Strategy - Compliance</a></li>
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<li><a href="#org1c35d39">1.5.2. Comparison with the Simscape Model</a></li>
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<li><a href="#org2fb301f">1.5.3. Obtained Mode Shapes</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#org6382ca3">2. Encoders fixed to the plates</a></li>
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<li><a href="#orgfd9b3f1">2. Encoders fixed to the plates</a></li>
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</ul>
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</div>
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</div>
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@ -95,12 +95,19 @@
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<hr>
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<p>
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In this document, the dynamics of the nano-hexapod shown in Figure <a href="#org19c1f7f">1</a> is identified.
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This document is dedicated to the experimental study of the nano-hexapod shown in Figure <a href="#orgf67b6ef">1</a>.
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</p>
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<div class="note" id="org1ec7b22">
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<div id="orgf67b6ef" class="figure">
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<p><img src="figs/IMG_20210608_152917.jpg" alt="IMG_20210608_152917.jpg" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Nano-Hexapod</p>
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</div>
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<div class="note" id="org75105c3">
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<p>
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Here are the documentation of the equipment used for this test bench:
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Here are the documentation of the equipment used for this test bench (lots of them are shwon in Figure <a href="#org800f7b8">2</a>):
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</p>
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<ul class="org-ul">
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<li>Voltage Amplifier: PiezoDrive <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
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@ -113,27 +120,25 @@ Here are the documentation of the equipment used for this test bench:
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</div>
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<div id="org19c1f7f" class="figure">
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<p><img src="figs/IMG_20210608_152917.jpg" alt="IMG_20210608_152917.jpg" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Nano-Hexapod</p>
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</div>
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<div id="org224dec6" class="figure">
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<div id="org800f7b8" class="figure">
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<p><img src="figs/IMG_20210608_154722.jpg" alt="IMG_20210608_154722.jpg" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Nano-Hexapod and the control electronics</p>
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</div>
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<p>
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In Figure <a href="#orgc1fc8a4">3</a> is shown a block diagram of the experimental setup.
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When possible, the notations are consistent with this diagram and summarized in Table <a href="#org211ae1e">1</a>.
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</p>
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<div id="orgd82bcd1" class="figure">
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<div id="orgc1fc8a4" class="figure">
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<p><img src="figs/nano_hexapod_signals.png" alt="nano_hexapod_signals.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Block diagram of the system with named signals</p>
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</div>
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<table id="orga3794c2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="org211ae1e" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> List of signals</caption>
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<colgroup>
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@ -250,25 +255,50 @@ Here are the documentation of the equipment used for this test bench:
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</tbody>
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</table>
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<div id="outline-container-org5c42276" class="outline-2">
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<h2 id="org5c42276"><span class="section-number-2">1</span> Encoders fixed to the Struts</h2>
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<p>
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This document is divided in the following sections:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org7e4eeef">1</a>: the encoders are fixed to the struts</li>
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<li>Section <a href="#org6f5eb76">2</a>: the encoders are fixed to the plates</li>
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</ul>
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<div id="outline-container-org4f28452" class="outline-2">
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<h2 id="org4f28452"><span class="section-number-2">1</span> Encoders fixed to the Struts</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org7e4eeef"></a>
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</p>
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</div>
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<div id="outline-container-orge93a02f" class="outline-3">
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<h3 id="orge93a02f"><span class="section-number-3">1.1</span> Introduction</h3>
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<div id="outline-container-orgdb58b6b" class="outline-3">
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<h3 id="orgdb58b6b"><span class="section-number-3">1.1</span> Introduction</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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In this section, the encoders are fixed to the struts.
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</p>
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<p>
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It is divided in the following sections:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org9c2cb86">1.2</a>: the transfer function matrix from the actuators to the force sensors and to the encoders is experimentally identified.</li>
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<li>Section <a href="#org860409f">1.3</a>: the obtained FRF matrix is compared with the dynamics of the simscape model</li>
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<li>Section <a href="#org941b355">1.4</a>: decentralized Integral Force Feedback (IFF) is applied and its performances are evaluated.</li>
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<li>Section <a href="#orgb37d2f8">1.5</a>: a modal analysis of the nano-hexapod is performed</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org0640b0f" class="outline-3">
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<h3 id="org0640b0f"><span class="section-number-3">1.2</span> Identification of the dynamics</h3>
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<div id="outline-container-orga23f4a3" class="outline-3">
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<h3 id="orga23f4a3"><span class="section-number-3">1.2</span> Identification of the dynamics</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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<a id="org9c2cb86"></a>
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</p>
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</div>
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<div id="outline-container-org1fc2e33" class="outline-4">
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<h4 id="org1fc2e33"><span class="section-number-4">1.2.1</span> Load Data</h4>
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<div id="outline-container-org463f1c5" class="outline-4">
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<h4 id="org463f1c5"><span class="section-number-4">1.2.1</span> Load Data</h4>
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<div class="outline-text-4" id="text-1-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load Identification Data</span></span>
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@ -283,8 +313,8 @@ meas_data_lf = {};
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</div>
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</div>
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<div id="outline-container-org27129af" class="outline-4">
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<h4 id="org27129af"><span class="section-number-4">1.2.2</span> Spectral Analysis - Setup</h4>
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<div id="outline-container-orga89822b" class="outline-4">
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<h4 id="orga89822b"><span class="section-number-4">1.2.2</span> Spectral Analysis - Setup</h4>
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<div class="outline-text-4" id="text-1-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Setup useful variables</span></span>
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@ -307,11 +337,11 @@ i_hf = f <span class="org-type">></span> 250; <span class="org-comment">% Poi
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</div>
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</div>
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<div id="outline-container-orgfe67585" class="outline-4">
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<h4 id="orgfe67585"><span class="section-number-4">1.2.3</span> DVF Plant</h4>
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<div id="outline-container-org2ea8050" class="outline-4">
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<h4 id="org2ea8050"><span class="section-number-4">1.2.3</span> DVF Plant</h4>
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<div class="outline-text-4" id="text-1-2-3">
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<p>
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First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure <a href="#org47768a4">4</a>).
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First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure <a href="#org83cc12f">4</a>).
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</p>
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<div class="org-src-container">
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@ -327,14 +357,14 @@ coh_dvf_hf = zeros(length(f), 6, 6);
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</div>
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<div id="org47768a4" class="figure">
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<div id="org83cc12f" class="figure">
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<p><img src="figs/enc_struts_dvf_coh.png" alt="enc_struts_dvf_coh.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Obtained coherence for the DVF plant</p>
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</div>
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<p>
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#orgff1ab10">5</a>).
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#org18fb1d6">5</a>).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% DVF Plant (transfer function from u to dLm)</span></span>
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@ -349,7 +379,7 @@ G_dvf_hf = zeros(length(f), 6, 6);
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</div>
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<div id="orgff1ab10" class="figure">
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||||
<div id="org18fb1d6" class="figure">
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||||
<p><img src="figs/enc_struts_dvf_frf.png" alt="enc_struts_dvf_frf.png" />
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||||
</p>
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||||
<p><span class="figure-number">Figure 5: </span>Measured FRF for the DVF plant</p>
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||||
@ -358,11 +388,11 @@ G_dvf_hf = zeros(length(f), 6, 6);
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||||
</div>
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||||
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||||
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||||
<div id="outline-container-org3674942" class="outline-4">
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<h4 id="org3674942"><span class="section-number-4">1.2.4</span> IFF Plant</h4>
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||||
<div id="outline-container-org3af4d82" class="outline-4">
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<h4 id="org3af4d82"><span class="section-number-4">1.2.4</span> IFF Plant</h4>
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||||
<div class="outline-text-4" id="text-1-2-4">
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||||
<p>
|
||||
First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure <a href="#org5d46af6">6</a>).
|
||||
First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure <a href="#org01dd40a">6</a>).
|
||||
</p>
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||||
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<div class="org-src-container">
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||||
@ -379,14 +409,14 @@ coh_iff_hf = zeros(length(f), 6, 6);
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</div>
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||||
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||||
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||||
<div id="org5d46af6" class="figure">
|
||||
<div id="org01dd40a" class="figure">
|
||||
<p><img src="figs/enc_struts_iff_coh.png" alt="enc_struts_iff_coh.png" />
|
||||
</p>
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||||
<p><span class="figure-number">Figure 6: </span>Obtained coherence for the IFF plant</p>
|
||||
</div>
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||||
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||||
<p>
|
||||
Then the 6x6 transfer function matrix is estimated (Figure <a href="#org7d56a08">7</a>).
|
||||
Then the 6x6 transfer function matrix is estimated (Figure <a href="#org671b27d">7</a>).
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||||
</p>
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||||
<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% IFF Plant</span></span>
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@ -401,7 +431,7 @@ G_iff_hf = zeros(length(f), 6, 6);
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</div>
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<div id="org7d56a08" class="figure">
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<div id="org671b27d" class="figure">
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<p><img src="figs/enc_struts_iff_frf.png" alt="enc_struts_iff_frf.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Measured FRF for the IFF plant</p>
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@ -410,16 +440,18 @@ G_iff_hf = zeros(length(f), 6, 6);
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</div>
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</div>
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||||
<div id="outline-container-org90b8ca8" class="outline-3">
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||||
<h3 id="org90b8ca8"><span class="section-number-3">1.3</span> Comparison with the Simscape Model</h3>
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||||
<div id="outline-container-org0d5bead" class="outline-3">
|
||||
<h3 id="org0d5bead"><span class="section-number-3">1.3</span> Comparison with the Simscape Model</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
<a id="org860409f"></a>
|
||||
</p>
|
||||
<p>
|
||||
In this section, the measured dynamics is compared with the dynamics estimated from the Simscape model.
|
||||
</p>
|
||||
</div>
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||||
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||||
<div id="outline-container-org7f3653d" class="outline-4">
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||||
<h4 id="org7f3653d"><span class="section-number-4">1.3.1</span> Dynamics from Actuator to Force Sensors</h4>
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||||
<div id="outline-container-org52ed397" class="outline-4">
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||||
<h4 id="org52ed397"><span class="section-number-4">1.3.1</span> Dynamics from Actuator to Force Sensors</h4>
|
||||
<div class="outline-text-4" id="text-1-3-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Initialize Nano-Hexapod</span></span>
|
||||
@ -441,14 +473,14 @@ Giff = exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts)<sp
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgaec8567" class="figure">
|
||||
<div id="orgfe01cea" class="figure">
|
||||
<p><img src="figs/enc_struts_iff_comp_simscape.png" alt="enc_struts_iff_comp_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Diagonal elements of the IFF Plant</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orged3779d" class="figure">
|
||||
<div id="org37f6405" class="figure">
|
||||
<p><img src="figs/enc_struts_iff_comp_offdiag_simscape.png" alt="enc_struts_iff_comp_offdiag_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Off diagonal elements of the IFF Plant</p>
|
||||
@ -456,8 +488,8 @@ Giff = exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts)<sp
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf2b8f1a" class="outline-4">
|
||||
<h4 id="orgf2b8f1a"><span class="section-number-4">1.3.2</span> Dynamics from Actuator to Encoder</h4>
|
||||
<div id="outline-container-org6bb92e5" class="outline-4">
|
||||
<h4 id="org6bb92e5"><span class="section-number-4">1.3.2</span> Dynamics from Actuator to Encoder</h4>
|
||||
<div class="outline-text-4" id="text-1-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Initialization of the Nano-Hexapod</span></span>
|
||||
@ -479,14 +511,14 @@ Gdvf = exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts)<sp
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org2041eb7" class="figure">
|
||||
<div id="org27467a4" class="figure">
|
||||
<p><img src="figs/enc_struts_dvf_comp_simscape.png" alt="enc_struts_dvf_comp_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Diagonal elements of the DVF Plant</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgeb4abcc" class="figure">
|
||||
<div id="orgf864568" class="figure">
|
||||
<p><img src="figs/enc_struts_dvf_comp_offdiag_simscape.png" alt="enc_struts_dvf_comp_offdiag_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Off diagonal elements of the DVF Plant</p>
|
||||
@ -495,12 +527,15 @@ Gdvf = exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts)<sp
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcb40fee" class="outline-3">
|
||||
<h3 id="orgcb40fee"><span class="section-number-3">1.4</span> Integral Force Feedback</h3>
|
||||
<div id="outline-container-org9537bdd" class="outline-3">
|
||||
<h3 id="org9537bdd"><span class="section-number-3">1.4</span> Integral Force Feedback</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<p>
|
||||
<a id="org941b355"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org454aab2" class="outline-4">
|
||||
<h4 id="org454aab2"><span class="section-number-4">1.4.1</span> Root Locus and Decentralized Loop gain</h4>
|
||||
<div id="outline-container-org1092513" class="outline-4">
|
||||
<h4 id="org1092513"><span class="section-number-4">1.4.1</span> Root Locus and Decentralized Loop gain</h4>
|
||||
<div class="outline-text-4" id="text-1-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% IFF Controller</span></span>
|
||||
@ -512,7 +547,7 @@ Kiff_g1 = (1<span class="org-type">/</span>(s <span class="org-type">+</span> 2<
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd9ca9de" class="figure">
|
||||
<div id="orgbecd90a" class="figure">
|
||||
<p><img src="figs/enc_struts_iff_root_locus.png" alt="enc_struts_iff_root_locus.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Root Locus for the IFF control strategy</p>
|
||||
@ -528,7 +563,7 @@ Kiff = g<span class="org-type">*</span>Kiff_g1;
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org428110f" class="figure">
|
||||
<div id="org67421cd" class="figure">
|
||||
<p><img src="figs/enc_struts_iff_opt_loop_gain.png" alt="enc_struts_iff_opt_loop_gain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Bode plot of the “decentralized loop gain” \(G_\text{iff}(i,i) \times K_\text{iff}(i,i)\)</p>
|
||||
@ -536,8 +571,8 @@ Kiff = g<span class="org-type">*</span>Kiff_g1;
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf25396d" class="outline-4">
|
||||
<h4 id="orgf25396d"><span class="section-number-4">1.4.2</span> Multiple Gains - Simulation</h4>
|
||||
<div id="outline-container-orgb15799f" class="outline-4">
|
||||
<h4 id="orgb15799f"><span class="section-number-4">1.4.2</span> Multiple Gains - Simulation</h4>
|
||||
<div class="outline-text-4" id="text-1-4-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Tested IFF gains</span></span>
|
||||
@ -573,7 +608,7 @@ io(io_i) = linio([mdl, <span class="org-string">'/D'</span>], 1, <span class="o
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgf455f45" class="figure">
|
||||
<div id="org5e12ba5" class="figure">
|
||||
<p><img src="figs/enc_struts_iff_gains_effect_dvf_plant.png" alt="enc_struts_iff_gains_effect_dvf_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Effect of the IFF gain \(g\) on the transfer function from \(\bm{\tau}\) to \(d\bm{\mathcal{L}}_m\)</p>
|
||||
@ -581,16 +616,16 @@ io(io_i) = linio([mdl, <span class="org-string">'/D'</span>], 1, <span class="o
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9e5a43a" class="outline-4">
|
||||
<h4 id="org9e5a43a"><span class="section-number-4">1.4.3</span> Experimental Results - Gains</h4>
|
||||
<div id="outline-container-orgfc28d74" class="outline-4">
|
||||
<h4 id="orgfc28d74"><span class="section-number-4">1.4.3</span> Experimental Results - Gains</h4>
|
||||
<div class="outline-text-4" id="text-1-4-3">
|
||||
<p>
|
||||
Let’s look at the damping introduced by IFF as a function of the IFF gain and compare that with the results obtained using the Simscape model.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7528195" class="outline-5">
|
||||
<h5 id="org7528195"><span class="section-number-5">1.4.3.1</span> Load Data</h5>
|
||||
<div id="outline-container-orgc87e132" class="outline-5">
|
||||
<h5 id="orgc87e132"><span class="section-number-5">1.4.3.1</span> Load Data</h5>
|
||||
<div class="outline-text-5" id="text-1-4-3-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load Identification Data</span></span>
|
||||
@ -604,8 +639,8 @@ meas_iff_gains = {};
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org014c26e" class="outline-5">
|
||||
<h5 id="org014c26e"><span class="section-number-5">1.4.3.2</span> Spectral Analysis - Setup</h5>
|
||||
<div id="outline-container-org082cedd" class="outline-5">
|
||||
<h5 id="org082cedd"><span class="section-number-5">1.4.3.2</span> Spectral Analysis - Setup</h5>
|
||||
<div class="outline-text-5" id="text-1-4-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Setup useful variables</span></span>
|
||||
@ -625,8 +660,8 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga410c78" class="outline-5">
|
||||
<h5 id="orga410c78"><span class="section-number-5">1.4.3.3</span> DVF Plant</h5>
|
||||
<div id="outline-container-orgf617003" class="outline-5">
|
||||
<h5 id="orgf617003"><span class="section-number-5">1.4.3.3</span> DVF Plant</h5>
|
||||
<div class="outline-text-5" id="text-1-4-3-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% DVF Plant (transfer function from u to dLm)</span></span>
|
||||
@ -639,20 +674,20 @@ G_iff_gains = {};
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org4661cd1" class="figure">
|
||||
<div id="org16336f2" class="figure">
|
||||
<p><img src="figs/comp_iff_gains_dvf_plant.png" alt="comp_iff_gains_dvf_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Transfer function from \(u\) to \(d\mathcal{L}_m\) for multiple values of the IFF gain</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org106c1ed" class="figure">
|
||||
<div id="orgcef8028" class="figure">
|
||||
<p><img src="figs/comp_iff_gains_dvf_plant_zoom.png" alt="comp_iff_gains_dvf_plant_zoom.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Transfer function from \(u\) to \(d\mathcal{L}_m\) for multiple values of the IFF gain (Zoom)</p>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org2517529">
|
||||
<div class="important" id="orgf90d42d">
|
||||
<p>
|
||||
The IFF control strategy is very effective for the damping of the suspension modes.
|
||||
It however does not damp the modes at 200Hz, 300Hz and 400Hz (flexible modes of the APA).
|
||||
@ -667,29 +702,40 @@ Also, the experimental results and the models obtained from the Simscape model a
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org97f2ad7" class="outline-5">
|
||||
<h5 id="org97f2ad7"><span class="section-number-5">1.4.3.4</span> Experimental Results - Comparison of the un-damped and fully damped system</h5>
|
||||
<div id="outline-container-orgfaa6821" class="outline-5">
|
||||
<h5 id="orgfaa6821"><span class="section-number-5">1.4.3.4</span> Experimental Results - Comparison of the un-damped and fully damped system</h5>
|
||||
<div class="outline-text-5" id="text-1-4-3-4">
|
||||
|
||||
<div id="org58aadc4" class="figure">
|
||||
<div id="org16f8986" class="figure">
|
||||
<p><img src="figs/comp_undamped_opt_iff_gain_diagonal.png" alt="comp_undamped_opt_iff_gain_diagonal.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Comparison of the diagonal elements of the tranfer function from \(\bm{u}\) to \(d\bm{\mathcal{L}}_m\) without active damping and with optimal IFF gain</p>
|
||||
</div>
|
||||
|
||||
<div class="question" id="orgb8cc006">
|
||||
<p>
|
||||
A series of modes at around 205Hz are also damped.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Are these damped modes at 205Hz additional “suspension” modes or flexible modes of the struts?
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org38e77db" class="outline-4">
|
||||
<h4 id="org38e77db"><span class="section-number-4">1.4.4</span> Experimental Results - Damped Plant with Optimal gain</h4>
|
||||
<div id="outline-container-orgc0e0293" class="outline-4">
|
||||
<h4 id="orgc0e0293"><span class="section-number-4">1.4.4</span> Experimental Results - Damped Plant with Optimal gain</h4>
|
||||
<div class="outline-text-4" id="text-1-4-4">
|
||||
<p>
|
||||
Let’s now look at the \(6 \times 6\) damped plant with the optimal gain \(g = 400\).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5b64143" class="outline-5">
|
||||
<h5 id="org5b64143"><span class="section-number-5">1.4.4.1</span> Load Data</h5>
|
||||
<div id="outline-container-org04a0c15" class="outline-5">
|
||||
<h5 id="org04a0c15"><span class="section-number-5">1.4.4.1</span> Load Data</h5>
|
||||
<div class="outline-text-5" id="text-1-4-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load Identification Data</span></span>
|
||||
@ -703,8 +749,8 @@ meas_iff_struts = {};
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9d60597" class="outline-5">
|
||||
<h5 id="org9d60597"><span class="section-number-5">1.4.4.2</span> Spectral Analysis - Setup</h5>
|
||||
<div id="outline-container-org288970e" class="outline-5">
|
||||
<h5 id="org288970e"><span class="section-number-5">1.4.4.2</span> Spectral Analysis - Setup</h5>
|
||||
<div class="outline-text-5" id="text-1-4-4-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Setup useful variables</span></span>
|
||||
@ -724,8 +770,8 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5e16098" class="outline-5">
|
||||
<h5 id="org5e16098"><span class="section-number-5">1.4.4.3</span> DVF Plant</h5>
|
||||
<div id="outline-container-orgbe5d7c4" class="outline-5">
|
||||
<h5 id="orgbe5d7c4"><span class="section-number-5">1.4.4.3</span> DVF Plant</h5>
|
||||
<div class="outline-text-5" id="text-1-4-4-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% DVF Plant (transfer function from u to dLm)</span></span>
|
||||
@ -738,23 +784,23 @@ G_iff_opt = {};
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org863be1b" class="figure">
|
||||
<div id="org02df88f" class="figure">
|
||||
<p><img src="figs/damped_iff_plant_comp_diagonal.png" alt="damped_iff_plant_comp_diagonal.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Comparison of the diagonal elements of the transfer functions from \(\bm{u}\) to \(d\bm{\mathcal{L}}_m\) with active damping (IFF) applied with an optimal gain \(g = 400\)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org071cb05" class="figure">
|
||||
<div id="orgc6361cd" class="figure">
|
||||
<p><img src="figs/damped_iff_plant_comp_off_diagonal.png" alt="damped_iff_plant_comp_off_diagonal.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Comparison of the off-diagonal elements of the transfer functions from \(\bm{u}\) to \(d\bm{\mathcal{L}}_m\) with active damping (IFF) applied with an optimal gain \(g = 400\)</p>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org57eccf4">
|
||||
<div class="important" id="org1353115">
|
||||
<p>
|
||||
With the IFF control strategy applied and the optimal gain used, the suspension modes are very well dapmed.
|
||||
Remains the undamped flexible modes of the APA, and the modes of the plates.
|
||||
With the IFF control strategy applied and the optimal gain used, the suspension modes are very well damped.
|
||||
Remains the undamped flexible modes of the APA (200Hz, 300Hz, 400Hz), and the modes of the plates (700Hz).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -767,34 +813,36 @@ The Simscape model and the experimental results are in very good agreement.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcf93367" class="outline-3">
|
||||
<h3 id="orgcf93367"><span class="section-number-3">1.5</span> Modal Analysis</h3>
|
||||
<div id="outline-container-org4d2a6a9" class="outline-3">
|
||||
<h3 id="org4d2a6a9"><span class="section-number-3">1.5</span> Modal Analysis</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<p>
|
||||
Several 3-axis accelerometers are fixed on the top platform of the nano-hexapod as shown in Figure <a href="#orgbafa9c1">22</a>.
|
||||
<a id="orgb37d2f8"></a>
|
||||
</p>
|
||||
<p>
|
||||
Several 3-axis accelerometers are fixed on the top platform of the nano-hexapod as shown in Figure <a href="#orgcc43dbe">22</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org30849ed" class="figure">
|
||||
<div id="org6f43329" class="figure">
|
||||
<p><img src="figs/accelerometers_nano_hexapod.jpg" alt="accelerometers_nano_hexapod.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Location of the accelerometers on top of the nano-hexapod</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The top platform is then excited using an instrumented hammer as shown in Figure <a href="#orge948ff2">21</a>.
|
||||
The top platform is then excited using an instrumented hammer as shown in Figure <a href="#org5333181">21</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orge948ff2" class="figure">
|
||||
<div id="org5333181" class="figure">
|
||||
<p><img src="figs/hammer_excitation_compliance_meas.jpg" alt="hammer_excitation_compliance_meas.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Example of an excitation using an instrumented hammer</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4380b82" class="outline-4">
|
||||
<h4 id="org4380b82"><span class="section-number-4">1.5.1</span> Effectiveness of the IFF Strategy - Compliance</h4>
|
||||
<div id="outline-container-org76f1cc6" class="outline-4">
|
||||
<h4 id="org76f1cc6"><span class="section-number-4">1.5.1</span> Effectiveness of the IFF Strategy - Compliance</h4>
|
||||
<div class="outline-text-4" id="text-1-5-1">
|
||||
<p>
|
||||
In this section, we wish to estimated the effectiveness of the IFF strategy concerning the compliance.
|
||||
@ -828,28 +876,32 @@ d_frf_iff = 10<span class="org-type">/</span>5<span class="org-type">*</span>(fr
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The vertical compliance (magnitude of the transfer function from a vertical force applied on the top plate to the vertical motion of the top plate) is shown in Figure <a href="#orgbafa9c1">22</a>.
|
||||
The vertical compliance (magnitude of the transfer function from a vertical force applied on the top plate to the vertical motion of the top plate) is shown in Figure <a href="#orgcc43dbe">22</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgbafa9c1" class="figure">
|
||||
<div id="orgcc43dbe" class="figure">
|
||||
<p><img src="figs/compliance_vertical_comp_iff.png" alt="compliance_vertical_comp_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Measured vertical compliance with and without IFF</p>
|
||||
</div>
|
||||
|
||||
<div class="important" id="orgada0906">
|
||||
<div class="important" id="org38045ac">
|
||||
<p>
|
||||
From Figure <a href="#orgbafa9c1">22</a>, it is clear that the IFF control strategy is very effective in damping the suspensions modes of the nano-hexapode.
|
||||
From Figure <a href="#orgcc43dbe">22</a>, it is clear that the IFF control strategy is very effective in damping the suspensions modes of the nano-hexapode.
|
||||
It also has the effect of degrading (slightly) the vertical compliance at low frequency.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It also seems some damping can be added to the modes at around 205Hz which are flexible modes of the struts.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org432b9c9" class="outline-4">
|
||||
<h4 id="org432b9c9"><span class="section-number-4">1.5.2</span> Comparison with the Simscape Model</h4>
|
||||
<div id="outline-container-org1c35d39" class="outline-4">
|
||||
<h4 id="org1c35d39"><span class="section-number-4">1.5.2</span> Comparison with the Simscape Model</h4>
|
||||
<div class="outline-text-4" id="text-1-5-2">
|
||||
<p>
|
||||
Let’s now compare the measured vertical compliance with the vertical compliance as estimated from the Simscape model.
|
||||
@ -857,11 +909,11 @@ Let’s now compare the measured vertical compliance with the vertical compl
|
||||
|
||||
<p>
|
||||
The transfer function from a vertical external force to the absolute motion of the top platform is identified (with and without IFF) using the Simscape model.
|
||||
The comparison is done in Figure <a href="#org871a1cd">23</a>.
|
||||
Again, the model is quire accurate!
|
||||
The comparison is done in Figure <a href="#org8a08cb4">23</a>.
|
||||
Again, the model is quite accurate!
|
||||
</p>
|
||||
|
||||
<div id="org871a1cd" class="figure">
|
||||
<div id="org8a08cb4" class="figure">
|
||||
<p><img src="figs/compliance_vertical_comp_model_iff.png" alt="compliance_vertical_comp_model_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 23: </span>Measured vertical compliance with and without IFF</p>
|
||||
@ -869,40 +921,40 @@ Again, the model is quire accurate!
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9e1cc1a" class="outline-4">
|
||||
<h4 id="org9e1cc1a"><span class="section-number-4">1.5.3</span> Obtained Mode Shapes</h4>
|
||||
<div id="outline-container-org2fb301f" class="outline-4">
|
||||
<h4 id="org2fb301f"><span class="section-number-4">1.5.3</span> Obtained Mode Shapes</h4>
|
||||
<div class="outline-text-4" id="text-1-5-3">
|
||||
<p>
|
||||
Then, several excitation are performed using the instrumented Hammer and the mode shapes are extracted.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
We can observe the mode shapes of the first 6 modes that are the suspension modes (the plate is behaving as a solid body) in Figure <a href="#org46cb63b">24</a>.
|
||||
We can observe the mode shapes of the first 6 modes that are the suspension modes (the plate is behaving as a solid body) in Figure <a href="#org5b33924">24</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org46cb63b" class="figure">
|
||||
<div id="org5b33924" class="figure">
|
||||
<p><img src="figs/mode_shapes_annotated.gif" alt="mode_shapes_annotated.gif" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 24: </span>Measured mode shapes for the first six modes</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Then, there is a mode at 692Hz which corresponds to a flexible mode of the top plate (Figure <a href="#org46cb63b">24</a>).
|
||||
Then, there is a mode at 692Hz which corresponds to a flexible mode of the top plate (Figure <a href="#org5b33924">24</a>).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org04d65e3" class="figure">
|
||||
<div id="orgb4a4a07" class="figure">
|
||||
<p><img src="figs/ModeShapeFlex1_crop.gif" alt="ModeShapeFlex1_crop.gif" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 25: </span>First flexible mode at 692Hz</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained modes are summarized in Table <a href="#org3a99570">2</a>.
|
||||
The obtained modes are summarized in Table <a href="#org0c9e4da">2</a>.
|
||||
</p>
|
||||
|
||||
<table id="org3a99570" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org0c9e4da" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 2:</span> Description of the identified modes</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -914,8 +966,8 @@ The obtained modes are summarized in Table <a href="#org3a99570">2</a>.
|
||||
</colgroup>
|
||||
<thead>
|
||||
<tr>
|
||||
<th scope="col" class="org-right">Mode Number</th>
|
||||
<th scope="col" class="org-right">Frequency [Hz]</th>
|
||||
<th scope="col" class="org-right">Mode</th>
|
||||
<th scope="col" class="org-right">Freq. [Hz]</th>
|
||||
<th scope="col" class="org-left">Description</th>
|
||||
</tr>
|
||||
</thead>
|
||||
@ -923,13 +975,13 @@ The obtained modes are summarized in Table <a href="#org3a99570">2</a>.
|
||||
<tr>
|
||||
<td class="org-right">1</td>
|
||||
<td class="org-right">105</td>
|
||||
<td class="org-left">Suspension Mode: ~Y-translation</td>
|
||||
<td class="org-left">Suspension Mode: Y-translation</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-right">107</td>
|
||||
<td class="org-left">Suspension Mode: ~X-translation</td>
|
||||
<td class="org-left">Suspension Mode: X-translation</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
@ -941,13 +993,13 @@ The obtained modes are summarized in Table <a href="#org3a99570">2</a>.
|
||||
<tr>
|
||||
<td class="org-right">4</td>
|
||||
<td class="org-right">161</td>
|
||||
<td class="org-left">Suspension Mode: ~Y-tilt</td>
|
||||
<td class="org-left">Suspension Mode: Y-tilt</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">5</td>
|
||||
<td class="org-right">162</td>
|
||||
<td class="org-left">Suspension Mode: ~X-tilt</td>
|
||||
<td class="org-left">Suspension Mode: X-tilt</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
@ -968,13 +1020,18 @@ The obtained modes are summarized in Table <a href="#org3a99570">2</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6382ca3" class="outline-2">
|
||||
<h2 id="org6382ca3"><span class="section-number-2">2</span> Encoders fixed to the plates</h2>
|
||||
<div id="outline-container-orgfd9b3f1" class="outline-2">
|
||||
<h2 id="orgfd9b3f1"><span class="section-number-2">2</span> Encoders fixed to the plates</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org6f5eb76"></a>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-06-14 lun. 17:24</p>
|
||||
<p class="date">Created: 2021-06-14 lun. 18:07</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -49,10 +49,15 @@
|
||||
#+latex: \clearpage
|
||||
|
||||
* Introduction :ignore:
|
||||
In this document, the dynamics of the nano-hexapod shown in Figure [[fig:picture_bench_granite_nano_hexapod]] is identified.
|
||||
This document is dedicated to the experimental study of the nano-hexapod shown in Figure [[fig:picture_bench_granite_nano_hexapod]].
|
||||
|
||||
#+name: fig:picture_bench_granite_nano_hexapod
|
||||
#+caption: Nano-Hexapod
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/IMG_20210608_152917.jpg]]
|
||||
|
||||
#+begin_note
|
||||
Here are the documentation of the equipment used for this test bench:
|
||||
Here are the documentation of the equipment used for this test bench (lots of them are shwon in Figure [[fig:picture_bench_granite_overview]]):
|
||||
- Voltage Amplifier: PiezoDrive [[file:doc/PD200-V7-R1.pdf][PD200]]
|
||||
- Amplified Piezoelectric Actuator: Cedrat [[file:doc/APA300ML.pdf][APA300ML]]
|
||||
- DAC/ADC: Speedgoat [[file:doc/IO131-OEM-Datasheet.pdf][IO313]]
|
||||
@ -60,16 +65,14 @@ Here are the documentation of the equipment used for this test bench:
|
||||
- Interferometers: Attocube
|
||||
#+end_note
|
||||
|
||||
#+name: fig:picture_bench_granite_nano_hexapod
|
||||
#+caption: Nano-Hexapod
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/IMG_20210608_152917.jpg]]
|
||||
|
||||
#+name: fig:picture_bench_granite_overview
|
||||
#+caption: Nano-Hexapod and the control electronics
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/IMG_20210608_154722.jpg]]
|
||||
|
||||
In Figure [[fig:nano_hexapod_signals]] is shown a block diagram of the experimental setup.
|
||||
When possible, the notations are consistent with this diagram and summarized in Table [[tab:list_signals]].
|
||||
|
||||
#+begin_src latex :file nano_hexapod_signals.pdf
|
||||
\definecolor{instrumentation}{rgb}{0, 0.447, 0.741}
|
||||
\definecolor{mechanics}{rgb}{0.8500, 0.325, 0.098}
|
||||
@ -112,7 +115,6 @@ Here are the documentation of the equipment used for this test bench:
|
||||
#+name: fig:nano_hexapod_signals
|
||||
#+caption: Block diagram of the system with named signals
|
||||
#+attr_latex: :scale 1
|
||||
#+RESULTS:
|
||||
[[file:figs/nano_hexapod_signals.png]]
|
||||
|
||||
#+name: tab:list_signals
|
||||
@ -136,10 +138,22 @@ Here are the documentation of the equipment used for this test bench:
|
||||
| Motion of the top platform | =[m,rad]= | =dX= | $d\bm{\mathcal{X}}$ | $d\mathcal{X}_i$ |
|
||||
| Metrology measured displacement | =[m,rad]= | =dXm= | $d\bm{\mathcal{X}}_m$ | $d\mathcal{X}_{m,i}$ |
|
||||
|
||||
This document is divided in the following sections:
|
||||
- Section [[sec:encoders_struts]]: the encoders are fixed to the struts
|
||||
- Section [[sec:encoders_plates]]: the encoders are fixed to the plates
|
||||
|
||||
* Encoders fixed to the Struts
|
||||
<<sec:encoders_struts>>
|
||||
|
||||
** Introduction
|
||||
In this section, the encoders are fixed to the struts.
|
||||
|
||||
It is divided in the following sections:
|
||||
- Section [[sec:enc_struts_plant_id]]: the transfer function matrix from the actuators to the force sensors and to the encoders is experimentally identified.
|
||||
- Section [[sec:enc_struts_comp_simscape]]: the obtained FRF matrix is compared with the dynamics of the simscape model
|
||||
- Section [[sec:enc_struts_iff]]: decentralized Integral Force Feedback (IFF) is applied and its performances are evaluated.
|
||||
- Section [[sec:enc_struts_modal_analysis]]: a modal analysis of the nano-hexapod is performed
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
@ -161,6 +175,7 @@ addpath('./src/');
|
||||
#+end_src
|
||||
|
||||
** Identification of the dynamics
|
||||
<<sec:enc_struts_plant_id>>
|
||||
*** Load Data
|
||||
#+begin_src matlab
|
||||
%% Load Identification Data
|
||||
@ -614,6 +629,7 @@ exportFig('figs/enc_struts_iff_cart_frf.pdf', 'width', 'wide', 'height', 'tall')
|
||||
[[file:figs/enc_struts_iff_cart_frf.png]]
|
||||
|
||||
** Comparison with the Simscape Model
|
||||
<<sec:enc_struts_comp_simscape>>
|
||||
*** Introduction :ignore:
|
||||
In this section, the measured dynamics is compared with the dynamics estimated from the Simscape model.
|
||||
|
||||
@ -893,6 +909,7 @@ exportFig('figs/enc_struts_dvf_comp_offdiag_simscape.pdf', 'width', 'wide', 'hei
|
||||
[[file:figs/enc_struts_dvf_comp_offdiag_simscape.png]]
|
||||
|
||||
** Integral Force Feedback
|
||||
<<sec:enc_struts_iff>>
|
||||
*** Root Locus and Decentralized Loop gain
|
||||
#+begin_src matlab
|
||||
%% IFF Controller
|
||||
@ -1263,6 +1280,12 @@ exportFig('figs/comp_undamped_opt_iff_gain_diagonal.pdf', 'width', 'wide', 'heig
|
||||
#+RESULTS:
|
||||
[[file:figs/comp_undamped_opt_iff_gain_diagonal.png]]
|
||||
|
||||
#+begin_question
|
||||
A series of modes at around 205Hz are also damped.
|
||||
|
||||
Are these damped modes at 205Hz additional "suspension" modes or flexible modes of the struts?
|
||||
#+end_question
|
||||
|
||||
*** Experimental Results - Damped Plant with Optimal gain
|
||||
**** Introduction :ignore:
|
||||
Let's now look at the $6 \times 6$ damped plant with the optimal gain $g = 400$.
|
||||
@ -1435,13 +1458,14 @@ exportFig('figs/damped_iff_plant_comp_off_diagonal.pdf', 'width', 'wide', 'heigh
|
||||
[[file:figs/damped_iff_plant_comp_off_diagonal.png]]
|
||||
|
||||
#+begin_important
|
||||
With the IFF control strategy applied and the optimal gain used, the suspension modes are very well dapmed.
|
||||
Remains the undamped flexible modes of the APA, and the modes of the plates.
|
||||
With the IFF control strategy applied and the optimal gain used, the suspension modes are very well damped.
|
||||
Remains the undamped flexible modes of the APA (200Hz, 300Hz, 400Hz), and the modes of the plates (700Hz).
|
||||
|
||||
The Simscape model and the experimental results are in very good agreement.
|
||||
#+end_important
|
||||
|
||||
** Modal Analysis
|
||||
<<sec:enc_struts_modal_analysis>>
|
||||
*** Introduction :ignore:
|
||||
Several 3-axis accelerometers are fixed on the top platform of the nano-hexapod as shown in Figure [[fig:compliance_vertical_comp_iff]].
|
||||
|
||||
@ -1503,6 +1527,8 @@ exportFig('figs/compliance_vertical_comp_iff.pdf', 'width', 'wide', 'height', 'n
|
||||
#+begin_important
|
||||
From Figure [[fig:compliance_vertical_comp_iff]], it is clear that the IFF control strategy is very effective in damping the suspensions modes of the nano-hexapode.
|
||||
It also has the effect of degrading (slightly) the vertical compliance at low frequency.
|
||||
|
||||
It also seems some damping can be added to the modes at around 205Hz which are flexible modes of the struts.
|
||||
#+end_important
|
||||
|
||||
*** Comparison with the Simscape Model
|
||||
@ -1539,7 +1565,7 @@ G_compl_z_iff = linearize(mdl, io, 0.0, options);
|
||||
#+end_src
|
||||
|
||||
The comparison is done in Figure [[fig:compliance_vertical_comp_model_iff]].
|
||||
Again, the model is quire accurate!
|
||||
Again, the model is quite accurate!
|
||||
#+begin_src matlab :exports none
|
||||
%% Comparison of the measured compliance and the one obtained from the model
|
||||
freqs = 2*logspace(1,3,1000);
|
||||
@ -1601,4 +1627,6 @@ The obtained modes are summarized in Table [[tab:description_modes]].
|
||||
| 7 | 692 | (flexible) Membrane mode of the top platform |
|
||||
|
||||
* Encoders fixed to the plates
|
||||
<<sec:encoders_plates>>
|
||||
|
||||
** Introduction :ignore:
|
||||
|
||||
Binary file not shown.
Loading…
Reference in New Issue
Block a user