Analyze the measured noise of all encoders
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@@ -3,7 +3,7 @@
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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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<!-- 2021-02-02 mar. 18:46 -->
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<!-- 2021-02-03 mer. 11:20 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Encoder Renishaw Vionic - Test Bench</title>
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<meta name="generator" content="Org mode" />
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@@ -39,23 +39,23 @@
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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="#org3a55927">1. Encoder Model</a></li>
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<li><a href="#orgde74ebc">2. Noise Measurement</a>
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<li><a href="#org691fd8d">1. Encoder Model</a></li>
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<li><a href="#org6d49234">2. Noise Measurement</a>
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<ul>
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<li><a href="#org835e359">2.1. Test Bench</a></li>
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<li><a href="#org52a3f6f">2.2. Results</a></li>
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<li><a href="#orga5ff56c">2.1. Test Bench</a></li>
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<li><a href="#org14877fe">2.2. Results</a></li>
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</ul>
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</li>
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<li><a href="#orge941dff">3. Linearity Measurement</a>
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<li><a href="#org2b0bcde">3. Linearity Measurement</a>
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<ul>
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<li><a href="#orga2e857a">3.1. Test Bench</a></li>
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<li><a href="#orgc7f59c3">3.2. Results</a></li>
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<li><a href="#org175ba6f">3.1. Test Bench</a></li>
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<li><a href="#org69056ec">3.2. Results</a></li>
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</ul>
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</li>
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<li><a href="#org42e063d">4. Dynamical Measurement</a>
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<li><a href="#org5ca0c03">4. Dynamical Measurement</a>
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<ul>
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<li><a href="#org4e0f29a">4.1. Test Bench</a></li>
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<li><a href="#orgb2f1f77">4.2. Results</a></li>
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<li><a href="#orgde9a37d">4.1. Test Bench</a></li>
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<li><a href="#org8bc51db">4.2. Results</a></li>
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</ul>
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</li>
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</ul>
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@@ -65,7 +65,7 @@
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<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
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<hr>
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<div class="note" id="orgf92d65f">
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<div class="note" id="org978e8ad">
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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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@@ -90,14 +90,24 @@ In particular, we would like to measure:
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</ul>
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<div id="orgddb4738" class="figure">
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<div id="orgf372152" 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-org3a55927" class="outline-2">
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<h2 id="org3a55927"><span class="section-number-2">1</span> Encoder Model</h2>
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<ul class="org-ul">
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<li>1: 2YA275</li>
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<li>2: 2YA274</li>
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<li>3: 2YA273</li>
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<li>4: 2YA270</li>
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<li>5: 2YA272</li>
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<li>6: 2YA271</li>
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<li>7: 2YJ313</li>
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</ul>
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<div id="outline-container-org691fd8d" class="outline-2">
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<h2 id="org691fd8d"><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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@@ -109,27 +119,27 @@ It is also characterized by its measurement noise \(n\) that can be described by
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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="#orga0a431c">2</a>.
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The model of the encoder is shown in Figure <a href="#orgb6cf5b4">2</a>.
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</p>
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<div id="orga0a431c" class="figure">
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<div id="orgb6cf5b4" 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="#org70392dd">4</a>.
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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="#orgd00343b">4</a>.
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</p>
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<div id="org27d4d98" class="figure">
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<div id="org2725c4b" 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="org212ba69" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="org20632fc" 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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@@ -174,7 +184,7 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
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</table>
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<div id="org70392dd" class="figure">
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<div id="orgd00343b" 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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@@ -183,15 +193,15 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
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</div>
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<div id="outline-container-orgde74ebc" class="outline-2">
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<h2 id="orgde74ebc"><span class="section-number-2">2</span> Noise Measurement</h2>
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<div id="outline-container-org6d49234" class="outline-2">
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<h2 id="org6d49234"><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="orgcac09c5"></a>
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<a id="org4cb96c9"></a>
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</p>
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</div>
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<div id="outline-container-org835e359" class="outline-3">
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<h3 id="org835e359"><span class="section-number-3">2.1</span> Test Bench</h3>
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<div id="outline-container-orga5ff56c" class="outline-3">
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<h3 id="orga5ff56c"><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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@@ -200,63 +210,84 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\).
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</div>
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</div>
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<div id="outline-container-org52a3f6f" class="outline-3">
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<h3 id="org52a3f6f"><span class="section-number-3">2.2</span> Results</h3>
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<div id="outline-container-org14877fe" class="outline-3">
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<h3 id="org14877fe"><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 class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load Data</span></span>
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enc1 = load(<span class="org-string">'noise_meas_100s_20kHz_1.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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enc2 = load(<span class="org-string">'noise_meas_100s_20kHz_2.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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enc3 = load(<span class="org-string">'noise_meas_100s_20kHz_3.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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enc4 = load(<span class="org-string">'noise_meas_100s_20kHz_4.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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enc6 = load(<span class="org-string">'noise_meas_100s_20kHz_6.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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enc7 = load(<span class="org-string">'noise_meas_100s_20kHz_7.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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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="#orgc55250e">4</a>.
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The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure <a href="#org72fd239">5</a>.
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</p>
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<div id="org72fd239" class="figure">
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<p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</p>
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</div>
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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="#orgfb661b7">5</a>.
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The time domain data for all the encoders are compared in Figure <a href="#orgf7f2fda">6</a>.
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</p>
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<div id="orgf7f2fda" class="figure">
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<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Comparison of the time domain measurement</p>
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</div>
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<div id="orgfb661b7" class="figure">
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<p>
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The amplitude spectral density is computed and shown in Figure <a href="#orgf3c083c">7</a>.
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</p>
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<div id="orgf3c083c" 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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<p><span class="figure-number">Figure 7: </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 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>1e4);
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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="#org6d60818">6</a>.
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The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org8714af7">8</a>.
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</p>
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<div id="org6d60818" class="figure">
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<div id="org8714af7" 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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<p><span class="figure-number">Figure 8: </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-orge941dff" class="outline-2">
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<h2 id="orge941dff"><span class="section-number-2">3</span> Linearity Measurement</h2>
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<div id="outline-container-org2b0bcde" class="outline-2">
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<h2 id="org2b0bcde"><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="org0c843ed"></a>
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<a id="orgc339bfd"></a>
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</p>
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</div>
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<div id="outline-container-orga2e857a" class="outline-3">
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<h3 id="orga2e857a"><span class="section-number-3">3.1</span> Test Bench</h3>
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<div id="outline-container-org175ba6f" class="outline-3">
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<h3 id="org175ba6f"><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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@@ -265,7 +296,7 @@ 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="#org793dd45">7</a>.
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One idea is to use the test-bench shown in Figure <a href="#org30ec1c0">9</a>.
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</p>
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<p>
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@@ -278,38 +309,38 @@ As the interferometer has a very large bandwidth, we should be able to estimate
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</p>
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<div id="org793dd45" class="figure">
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<div id="org30ec1c0" 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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<p><span class="figure-number">Figure 9: </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-orgc7f59c3" class="outline-3">
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<h3 id="orgc7f59c3"><span class="section-number-3">3.2</span> Results</h3>
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<div id="outline-container-org69056ec" class="outline-3">
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<h3 id="org69056ec"><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-org42e063d" class="outline-2">
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<h2 id="org42e063d"><span class="section-number-2">4</span> Dynamical Measurement</h2>
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<div id="outline-container-org5ca0c03" class="outline-2">
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<h2 id="org5ca0c03"><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="org2b52f4b"></a>
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<a id="org71dc40b"></a>
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</p>
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</div>
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<div id="outline-container-org4e0f29a" class="outline-3">
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<h3 id="org4e0f29a"><span class="section-number-3">4.1</span> Test Bench</h3>
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<div id="outline-container-orgde9a37d" class="outline-3">
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<h3 id="orgde9a37d"><span class="section-number-3">4.1</span> Test Bench</h3>
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</div>
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<div id="outline-container-orgb2f1f77" class="outline-3">
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<h3 id="orgb2f1f77"><span class="section-number-3">4.2</span> Results</h3>
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<div id="outline-container-org8bc51db" class="outline-3">
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<h3 id="org8bc51db"><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. 18:46</p>
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<p class="date">Created: 2021-02-03 mer. 11:20</p>
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</div>
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</body>
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</html>
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