First analysis of the sensor noise
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<head>
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<!-- 2021-01-04 lun. 11:44 -->
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<!-- 2021-02-02 mar. 18:24 -->
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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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<meta name="author" content="Dehaeze Thomas" />
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src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
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</head>
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<body>
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<div id="org-div-home-and-up">
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@ -30,15 +39,19 @@
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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="#org55157ef">1. Encoder Model</a></li>
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<li><a href="#org8ef40ec">2. Test-Bench Description</a></li>
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<li><a href="#orgce223ed">3. Measurement procedure</a></li>
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<li><a href="#org51852cb">4. Measurement Results</a></li>
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||||
<li><a href="#orgd4a4664">1. Encoder Model</a></li>
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||||
<li><a href="#org8e70edd">2. Test-Bench Description</a></li>
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||||
<li><a href="#orge118b0f">3. Measurement procedure</a></li>
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<li><a href="#org8e44240">4. Measurement Results</a>
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<ul>
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<li><a href="#org7e465e7">4.1. Noise Measurement</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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<div class="note" id="org4436bab">
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<div class="note" id="org4c0c9be">
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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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@ -63,14 +76,14 @@ In particular, we would like to measure:
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</ul>
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<div id="orgeb4726b" class="figure">
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<div id="org13fff85" 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-org55157ef" class="outline-2">
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<h2 id="org55157ef"><span class="section-number-2">1</span> Encoder Model</h2>
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||||
<div id="outline-container-orgd4a4664" class="outline-2">
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||||
<h2 id="orgd4a4664"><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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@ -82,52 +95,63 @@ 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="#org2d59f14">2</a>.
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The model of the encoder is shown in Figure <a href="#org08a4e7a">2</a>.
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</p>
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<div id="org2d59f14" class="figure">
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<div id="org08a4e7a" 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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<table id="org476b3d6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="org20ed9a5" 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-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-left"><b>Manual</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-left">2.5nm</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-left">\(< \pm 15\,nm\)</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-left">> 50 kHz</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="orgb8bf3d5" class="figure">
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<div id="org2068d11" 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 3: </span>Expected interpolation errors for the Vionic Encoder</p>
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@ -136,8 +160,8 @@ The model of the encoder is shown in Figure <a href="#org2d59f14">2</a>.
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</div>
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<div id="outline-container-org8ef40ec" class="outline-2">
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<h2 id="org8ef40ec"><span class="section-number-2">2</span> Test-Bench Description</h2>
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||||
<div id="outline-container-org8e70edd" class="outline-2">
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<h2 id="org8e70edd"><span class="section-number-2">2</span> Test-Bench Description</h2>
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<div class="outline-text-2" id="text-2">
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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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@ -151,7 +175,7 @@ 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="#org1fd5a94">4</a>.
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One idea is to use the test-bench shown in Figure <a href="#orgfefda93">4</a>.
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</p>
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<p>
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@ -164,7 +188,7 @@ 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="org1fd5a94" class="figure">
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<div id="orgfefda93" 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 4: </span>Schematic of the test bench</p>
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@ -172,11 +196,11 @@ As the interferometer has a very large bandwidth, we should be able to estimate
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<p>
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To measure the noise of the sensor, we can also simply measure the output signal when the relative motion between the encoder and the ruler is null.
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This can be done by clamping the two as done in the mounting strut tool (Figure <a href="#orgab0ed8d">5</a>).
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This can be done by clamping the two as done in the mounting strut tool (Figure <a href="#org742c647">5</a>).
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</p>
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<div id="orgab0ed8d" class="figure">
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||||
<div id="org742c647" class="figure">
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<p><img src="figs/test_bench_measure_noise.png" alt="test_bench_measure_noise.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Mounting Strut test bench as a clamping method to measure the encoder noise.</p>
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@ -184,17 +208,70 @@ This can be done by clamping the two as done in the mounting strut tool (Figure
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</div>
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</div>
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||||
<div id="outline-container-orgce223ed" class="outline-2">
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||||
<h2 id="orgce223ed"><span class="section-number-2">3</span> Measurement procedure</h2>
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||||
<div id="outline-container-orge118b0f" class="outline-2">
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<h2 id="orge118b0f"><span class="section-number-2">3</span> Measurement procedure</h2>
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</div>
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||||
<div id="outline-container-org51852cb" class="outline-2">
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<h2 id="org51852cb"><span class="section-number-2">4</span> Measurement Results</h2>
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<div id="outline-container-org8e44240" class="outline-2">
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<h2 id="org8e44240"><span class="section-number-2">4</span> Measurement Results</h2>
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<div class="outline-text-2" id="text-4">
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</div>
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<div id="outline-container-org7e465e7" class="outline-3">
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<h3 id="org7e465e7"><span class="section-number-3">4.1</span> Noise Measurement</h3>
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<div class="outline-text-3" id="text-4-1">
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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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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot(t, 1e9<span class="org-type">*</span>x, <span class="org-string">'.'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Raw'</span>);
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plot(t, 1e9<span class="org-type">*</span>lsim(1<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>500), x, t), <span class="org-string">'DisplayName'</span>, <span class="org-string">'LPF - 500Hz'</span>)
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hold off;
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xlabel(<span class="org-string">'Time [s]'</span>);
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ylabel(<span class="org-string">'Displacement [nm]'</span>);
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legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
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</pre>
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</div>
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<div id="org3070d03" 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>Time domain measurement (raw data and low pass filtered data)</p>
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</div>
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<div id="orgd593081" 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 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>
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</div>
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<div id="orgd1f9fd9" 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 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>
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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: 2021-01-04 lun. 11:44</p>
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<p class="date">Created: 2021-02-02 mar. 18:24</p>
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</div>
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</body>
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</html>
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114
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114
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@ -94,12 +94,13 @@ The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
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#+caption: Characteristics of the Vionic Encoder
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#+attr_latex: :environment tabularx :width \linewidth :align lXX
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#+attr_latex: :center t :booktabs t :float t
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| *Characteristics* | *Manual* |
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|----------------------+----------------|
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| Resolution | 2.5nm |
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| Sub-Divisional Error | $< \pm 15\,nm$ |
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| Bandwidth | > 50 kHz |
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| <l> | <c> | <c> |
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| *Characteristics* | *Manual* | *Specifications* |
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|----------------------+----------------+------------------|
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| Range | Ruler length | > 200 [um] |
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| Resolution | 2.5 [nm] | < 50 [nm rms] |
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| Sub-Divisional Error | $< \pm 15\,nm$ | |
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| Bandwidth | To be checked | > 5 [kHz] |
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#+name: fig:vionic_expected_noise
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#+caption: Expected interpolation errors for the Vionic Encoder
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@ -136,3 +137,104 @@ This can be done by clamping the two as done in the mounting strut tool (Figure
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* Measurement procedure
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* Measurement Results
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** Noise Measurement
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*** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :tangle no
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addpath('./matlab/mat/');
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addpath('./matlab/');
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#+end_src
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#+begin_src matlab :eval no
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addpath('./mat/');
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#+end_src
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*** Analysis :ignore:
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#+begin_src matlab
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load('noise_meas_100s_20kHz.mat', 't', 'x');
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x = x - mean(x);
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#+end_src
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#+begin_src matlab
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figure;
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hold on;
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plot(t, 1e9*x, '.', 'DisplayName', 'Raw');
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plot(t, 1e9*lsim(1/(1 + s/2/pi/500), x, t), 'DisplayName', 'LPF - 500Hz')
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hold off;
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xlabel('Time [s]');
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ylabel('Displacement [nm]');
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legend('location', 'northeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/vionic_noise_time.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:vionic_noise_time
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#+caption: Time domain measurement (raw data and low pass filtered data)
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#+RESULTS:
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[[file:figs/vionic_noise_time.png]]
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#+begin_src matlab :exports none
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% Compute sampling Frequency
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Ts = (t(end) - t(1))/(length(t)-1);
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Fs = 1/Ts;
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#+end_src
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#+begin_src matlab :exports none
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% Hannning Windows
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win = hanning(ceil(0.5*Fs));
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[pxx, f] = pwelch(x, win, [], [], Fs);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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plot(f, sqrt(pxx));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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xlim([1, Fs/2]);
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ylim([1e-11, 1e-9]);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/vionic_noise_asd.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_asd
|
||||
#+caption: Amplitude Spectral Density of the measured signal
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd.png]]
|
||||
|
||||
Let's create a transfer function that approximate the measured noise of the encoder.
|
||||
#+begin_src matlab
|
||||
Gn_e = 1.8e-11/(1 + s/2/pi/5e3);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(pxx));
|
||||
plot(f, abs(squeeze(freqresp(Gn_e, f, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
|
||||
xlim([1, Fs/2]);
|
||||
ylim([1e-11, 1e-9]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_noise_asd_model.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_asd_model
|
||||
#+caption: Measured ASD of the noise and modelled one
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd_model.png]]
|
||||
|
||||
Loading…
Reference in New Issue
Block a user