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<!-- 2021-02-02 mar. 18:44 -->
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<title>Encoder Renishaw Vionic - Test Bench</title>
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<meta name="author" content="Dehaeze Thomas" />
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Encoder Renishaw Vionic - Test Bench</h1>
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<div id="table-of-contents">
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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="#orgad23dda">1. Encoder Model</a></li>
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<li><a href="#org6337f06">2. Noise Measurement</a>
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<ul>
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<li><a href="#orgc20e5d1">2.1. Test Bench</a></li>
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<li><a href="#org818aa3a">2.2. Results</a></li>
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</ul>
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</li>
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<li><a href="#orgfb293f3">3. Linearity Measurement</a>
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<ul>
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<li><a href="#orgee55e64">3.1. Test Bench</a></li>
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<li><a href="#org53d1667">3.2. Results</a></li>
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</ul>
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</li>
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<li><a href="#org1f03c19">4. Dynamical Measurement</a>
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<ul>
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<li><a href="#org2650123">4.1. Test Bench</a></li>
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<li><a href="#org26f79d3">4.2. Results</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<hr>
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<p>This report is also available as a <a href="./index.pdf">pdf</a>.</p>
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<hr>
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<div class="note" id="org7fbf5f9">
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<p>
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You can find below the document of:
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</p>
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<ul class="org-ul">
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<li><a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Vionic Encoder</a></li>
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<li><a href="doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf">Linear Scale</a></li>
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</ul>
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</div>
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<p>
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We would like to characterize the encoder measurement system.
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</p>
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<p>
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In particular, we would like to measure:
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</p>
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<ul class="org-ul">
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<li>Power Spectral Density of the measurement noise</li>
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<li>Bandwidth of the sensor</li>
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<li>Linearity of the sensor</li>
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</ul>
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<div id="org136f1cc" class="figure">
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<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
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</div>
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<div id="outline-container-orgad23dda" class="outline-2">
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<h2 id="orgad23dda"><span class="section-number-2">1</span> Encoder Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\).
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Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
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</p>
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<p>
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It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD).
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</p>
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<p>
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The model of the encoder is shown in Figure <a href="#orgb95c9f6">2</a>.
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</p>
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<div id="orgb95c9f6" class="figure">
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<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
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</div>
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<p>
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We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure <a href="#org9d20614">4</a>.
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</p>
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<div id="org985a473" class="figure">
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<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
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</p>
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</div>
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<table id="orgcd45716" 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> Characteristics of the Vionic Encoder</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-center" />
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<col class="org-center" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"><b>Characteristics</b></th>
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<th scope="col" class="org-center"><b>Manual</b></th>
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<th scope="col" class="org-center"><b>Specifications</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Range</td>
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<td class="org-center">Ruler length</td>
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<td class="org-center">> 200 [um]</td>
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</tr>
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<tr>
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<td class="org-left">Resolution</td>
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<td class="org-center">2.5 [nm]</td>
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<td class="org-center">< 50 [nm rms]</td>
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</tr>
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<tr>
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<td class="org-left">Sub-Divisional Error</td>
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<td class="org-center">\(< \pm 15\,nm\)</td>
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<td class="org-center"> </td>
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</tr>
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<tr>
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<td class="org-left">Bandwidth</td>
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<td class="org-center">To be checked</td>
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<td class="org-center">> 5 [kHz]</td>
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</tr>
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</tbody>
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</table>
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<div id="org9d20614" class="figure">
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<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Expected interpolation errors for the Vionic Encoder</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org6337f06" class="outline-2">
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<h2 id="org6337f06"><span class="section-number-2">2</span> Noise Measurement</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org93db977"></a>
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</p>
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</div>
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<div id="outline-container-orgc20e5d1" class="outline-3">
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<h3 id="orgc20e5d1"><span class="section-number-3">2.1</span> Test Bench</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
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Then, the measured signal \(y_m\) corresponds to the noise \(n\).
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</p>
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</div>
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</div>
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<div id="outline-container-org818aa3a" class="outline-3">
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<h3 id="org818aa3a"><span class="section-number-3">2.2</span> Results</h3>
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<div class="outline-text-3" id="text-2-2">
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<p>
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First we load the data.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'noise_meas_100s_20kHz.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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x = x <span class="org-type">-</span> mean(x);
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</pre>
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</div>
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<p>
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The time domain data are shown in Figure <a href="#orgb5a687f">4</a>.
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</p>
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<p>
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<img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
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The amplitude spectral density is computed and shown in Figure <a href="#org5702aa0">5</a>.
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</p>
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<div id="org5702aa0" class="figure">
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<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signal</p>
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</div>
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<p>
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Let’s create a transfer function that approximate the measured noise of the encoder.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Gn_e = 1.8e<span class="org-type">-</span>11<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>5e3);
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</pre>
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</div>
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<p>
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The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#orgbbcd196">6</a>.
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</p>
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<div id="orgbbcd196" class="figure">
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<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Measured ASD of the noise and modelled one</p>
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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-orgfb293f3" class="outline-2">
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<h2 id="orgfb293f3"><span class="section-number-2">3</span> Linearity Measurement</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org0812023"></a>
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</p>
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</div>
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<div id="outline-container-orgee55e64" class="outline-3">
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<h3 id="orgee55e64"><span class="section-number-3">3.1</span> Test Bench</h3>
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<div class="outline-text-3" id="text-3-1">
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<p>
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In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
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An interferometer or capacitive sensor should work fine.
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An actuator should also be there so impose a displacement.
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</p>
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<p>
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One idea is to use the test-bench shown in Figure <a href="#org00b4ff5">7</a>.
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</p>
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<p>
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The APA300ML is used to excite the mass in a broad bandwidth.
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The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
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</p>
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<p>
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As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder if it is less than the Nyquist frequency that can be around 10kHz.
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</p>
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<div id="org00b4ff5" class="figure">
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<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Schematic of the test bench</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org53d1667" class="outline-3">
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<h3 id="org53d1667"><span class="section-number-3">3.2</span> Results</h3>
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</div>
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</div>
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<div id="outline-container-org1f03c19" class="outline-2">
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<h2 id="org1f03c19"><span class="section-number-2">4</span> Dynamical Measurement</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="org02907d6"></a>
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</p>
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</div>
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<div id="outline-container-org2650123" class="outline-3">
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<h3 id="org2650123"><span class="section-number-3">4.1</span> Test Bench</h3>
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</div>
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<div id="outline-container-org26f79d3" class="outline-3">
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<h3 id="org26f79d3"><span class="section-number-3">4.2</span> Results</h3>
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</div>
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</div>
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</div>
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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="date">Created: 2021-02-02 mar. 18:44</p>
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</div>
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</body>
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</html>
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