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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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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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<!-- 2021-06-08 mar. 21:51 -->
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<!-- 2021-06-08 mar. 22:15 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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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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<title>Nano-Hexapod - Test Bench</title>
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<meta name="author" content="Dehaeze Thomas" />
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<meta name="author" content="Dehaeze Thomas" />
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@ -22,15 +22,19 @@
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<h2>Table of Contents</h2>
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<div id="text-table-of-contents">
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<ul>
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<ul>
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<li><a href="#org401a850">1. Test-Bench Description</a></li>
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<li><a href="#orge60a691">1. Encoders fixed to the Struts</a>
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<li><a href="#org32d67fc">2. Encoders fixed to the Struts</a>
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<ul>
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<ul>
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<li><a href="#org332ecf2">2.1. Introduction</a></li>
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<li><a href="#org7010817">1.1. Introduction</a></li>
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<li><a href="#orgf904215">2.2. Load Data</a></li>
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<li><a href="#orga8cffa3">1.2. Load Data</a></li>
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<li><a href="#org3689d6b">2.3. Spectral Analysis - Setup</a></li>
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<li><a href="#org46d9ef0">1.3. Spectral Analysis - Setup</a></li>
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<li><a href="#org9ac5c69">2.4. DVF Plant</a></li>
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<li><a href="#org8d17470">1.4. DVF Plant</a></li>
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<li><a href="#org4f1737c">2.5. IFF Plant</a></li>
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<li><a href="#org22119eb">1.5. IFF Plant</a></li>
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<li><a href="#org4238e67">2.6. Jacobian</a></li>
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<li><a href="#org9f943b4">1.6. Jacobian</a>
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<ul>
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<li><a href="#org31b15c3">1.6.1. DVF Plant</a></li>
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<li><a href="#org6b0e225">1.6.2. IFF Plant</a></li>
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</ul>
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</li>
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</ul>
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</ul>
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</li>
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</li>
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</ul>
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</ul>
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<p>This report is also available as a <a href="./test-bench-nano-hexapod.pdf">pdf</a>.</p>
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<p>This report is also available as a <a href="./test-bench-nano-hexapod.pdf">pdf</a>.</p>
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<hr>
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<hr>
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<div id="outline-container-org401a850" class="outline-2">
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<div class="note" id="org6b76075">
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<h2 id="org401a850"><span class="section-number-2">1</span> Test-Bench Description</h2>
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<div class="outline-text-2" id="text-1">
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<div class="note" id="orgdb43d80">
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<p>
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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:
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</p>
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</p>
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@ -58,32 +59,30 @@ Here are the documentation of the equipment used for this test bench:
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</div>
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</div>
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<div id="org00dd2c1" class="figure">
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<div id="org6594005" class="figure">
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<p><img src="figs/IMG_20210608_152917.jpg" alt="IMG_20210608_152917.jpg" />
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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>
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<p><span class="figure-number">Figure 1: </span>Nano-Hexapod</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>
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<div id="org0f5d79a" class="figure">
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<div id="org0571a2e" class="figure">
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<p><img src="figs/IMG_20210608_154722.jpg" alt="IMG_20210608_154722.jpg" />
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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>
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<p><span class="figure-number">Figure 2: </span>Nano-Hexapod and the control electronics</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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</div>
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<div id="outline-container-orge60a691" class="outline-2">
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<h2 id="orge60a691"><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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</div>
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</div>
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<div id="outline-container-org7010817" class="outline-3">
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<h3 id="org7010817"><span class="section-number-3">1.1</span> Introduction</h3>
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</div>
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</div>
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<div id="outline-container-org32d67fc" class="outline-2">
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<div id="outline-container-orga8cffa3" class="outline-3">
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<h2 id="org32d67fc"><span class="section-number-2">2</span> Encoders fixed to the Struts</h2>
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<h3 id="orga8cffa3"><span class="section-number-3">1.2</span> Load Data</h3>
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<div class="outline-text-2" id="text-2">
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<div class="outline-text-3" id="text-1-2">
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</div>
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<div id="outline-container-org332ecf2" class="outline-3">
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<h3 id="org332ecf2"><span class="section-number-3">2.1</span> Introduction</h3>
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</div>
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<div id="outline-container-orgf904215" class="outline-3">
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<h3 id="orgf904215"><span class="section-number-3">2.2</span> Load Data</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab">meas_data_lf = {};
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<pre class="src src-matlab">meas_data_lf = {};
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@ -96,9 +95,9 @@ Here are the documentation of the equipment used for this test bench:
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org3689d6b" class="outline-3">
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<div id="outline-container-org46d9ef0" class="outline-3">
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<h3 id="org3689d6b"><span class="section-number-3">2.3</span> Spectral Analysis - Setup</h3>
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<h3 id="org46d9ef0"><span class="section-number-3">1.3</span> Spectral Analysis - Setup</h3>
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<div class="outline-text-3" id="text-2-3">
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<div class="outline-text-3" id="text-1-3">
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-comment">% Sampling Time [s]</span>
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<pre class="src src-matlab"><span class="org-comment">% Sampling Time [s]</span>
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Ts = (meas_data_lf{1}.t(end) <span class="org-type">-</span> (meas_data_lf{1}.t(1)))<span class="org-type">/</span>(length(meas_data_lf{1}.t)<span class="org-type">-</span>1);
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Ts = (meas_data_lf{1}.t(end) <span class="org-type">-</span> (meas_data_lf{1}.t(1)))<span class="org-type">/</span>(length(meas_data_lf{1}.t)<span class="org-type">-</span>1);
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@ -127,11 +126,11 @@ 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>
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</div>
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<div id="outline-container-org9ac5c69" class="outline-3">
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<div id="outline-container-org8d17470" class="outline-3">
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<h3 id="org9ac5c69"><span class="section-number-3">2.4</span> DVF Plant</h3>
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<h3 id="org8d17470"><span class="section-number-3">1.4</span> DVF Plant</h3>
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<div class="outline-text-3" id="text-2-4">
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<div class="outline-text-3" id="text-1-4">
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<p>
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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="#orga941078">3</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="#org67e2048">3</a>).
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</p>
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</p>
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<div class="org-src-container">
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<div class="org-src-container">
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@ -148,14 +147,14 @@ coh_dvf_hf = zeros(length(f), 6, 6);
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</div>
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</div>
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<div id="orga941078" class="figure">
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<div id="org67e2048" 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><img src="figs/enc_struts_dvf_coh.png" alt="enc_struts_dvf_coh.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 3: </span>Obtained coherence for the DVF plant</p>
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<p><span class="figure-number">Figure 3: </span>Obtained coherence for the DVF plant</p>
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</div>
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</div>
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<p>
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<p>
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#org9c350f6">4</a>).
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#org4e87d8b">4</a>).
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</p>
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</p>
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<div class="org-src-container">
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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</span></span>
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% DVF Plant</span></span>
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@ -170,7 +169,7 @@ G_dvf_hf = zeros(length(f), 6, 6);
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</div>
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</div>
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<div id="org9c350f6" class="figure">
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<div id="org4e87d8b" 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><img src="figs/enc_struts_dvf_frf.png" alt="enc_struts_dvf_frf.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 4: </span>Measured FRF for the DVF plant</p>
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<p><span class="figure-number">Figure 4: </span>Measured FRF for the DVF plant</p>
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@ -179,11 +178,11 @@ G_dvf_hf = zeros(length(f), 6, 6);
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</div>
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</div>
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<div id="outline-container-org4f1737c" class="outline-3">
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<div id="outline-container-org22119eb" class="outline-3">
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<h3 id="org4f1737c"><span class="section-number-3">2.5</span> IFF Plant</h3>
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<h3 id="org22119eb"><span class="section-number-3">1.5</span> IFF Plant</h3>
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<div class="outline-text-3" id="text-2-5">
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<div class="outline-text-3" id="text-1-5">
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<p>
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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="#org2a3d572">5</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="#org38ac16f">5</a>).
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</p>
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</p>
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<div class="org-src-container">
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<div class="org-src-container">
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@ -200,14 +199,14 @@ coh_iff_hf = zeros(length(f), 6, 6);
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</div>
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<div id="org2a3d572" class="figure">
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<div id="org38ac16f" class="figure">
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<p><img src="figs/enc_struts_iff_coh.png" alt="enc_struts_iff_coh.png" />
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<p><img src="figs/enc_struts_iff_coh.png" alt="enc_struts_iff_coh.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 5: </span>Obtained coherence for the IFF plant</p>
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<p><span class="figure-number">Figure 5: </span>Obtained coherence for the IFF 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="#orgaacf7b8">6</a>).
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#org0b97d99">6</a>).
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</p>
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</p>
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<div class="org-src-container">
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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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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% IFF Plant</span></span>
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</div>
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<div id="orgaacf7b8" class="figure">
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<div id="org0b97d99" 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><img src="figs/enc_struts_iff_frf.png" alt="enc_struts_iff_frf.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 6: </span>Measured FRF for the IFF plant</p>
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<p><span class="figure-number">Figure 6: </span>Measured FRF for the IFF plant</p>
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</div>
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</div>
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<div id="outline-container-org9f943b4" class="outline-3">
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<h3 id="org4238e67"><span class="section-number-3">2.6</span> Jacobian</h3>
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<h3 id="org9f943b4"><span class="section-number-3">1.6</span> Jacobian</h3>
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<div class="outline-text-3" id="text-2-6">
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<div class="outline-text-3" id="text-1-6">
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'jacobian.mat'</span>, <span class="org-string">'J'</span>);
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<pre class="src src-matlab">load(<span class="org-string">'jacobian.mat'</span>, <span class="org-string">'J'</span>);
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</pre>
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<h4 id="org31b15c3"><span class="section-number-4">1.6.1</span> DVF Plant</h4>
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<div class="outline-text-4" id="text-1-6-1">
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab">G_dvf_J_lf = G_dvf_lf(i_lf, <span class="org-constant">i</span>, <span class="org-constant">j</span>)
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<pre class="src src-matlab">G_dvf_J_lf = permute(pagemtimes(inv(J), pagemtimes(permute(G_dvf_lf, [2 3 1]), inv(J<span class="org-type">'</span>))), [3 1 2]);
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G_dvf_J_hf = permute(pagemtimes(inv(J), pagemtimes(permute(G_dvf_hf, [2 3 1]), inv(J<span class="org-type">'</span>))), [3 1 2]);
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</pre>
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<p>
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#+end_src</p>
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<h4 id="org6b0e225"><span class="section-number-4">1.6.2</span> IFF Plant</h4>
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<pre class="src src-matlab">G_iff_J_lf = permute(pagemtimes(inv(J), pagemtimes(permute(G_iff_lf, [2 3 1]), inv(J<span class="org-type">'</span>))), [3 1 2]);
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G_iff_J_hf = permute(pagemtimes(inv(J), pagemtimes(permute(G_iff_hf, [2 3 1]), inv(J<span class="org-type">'</span>))), [3 1 2]);
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2021-06-08 mar. 21:51</p>
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<p class="date">Created: 2021-06-08 mar. 22:15</p>
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