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First analysis of the sensor noise

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Thomas Dehaeze
2021-02-02 18:25:28 +01:00
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<head>
<!-- 2021-01-04 lun. 11:44 -->
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<title>Encoder Renishaw Vionic - Test Bench</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Dehaeze Thomas" />
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<div id="org-div-home-and-up">
@@ -30,15 +39,19 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org55157ef">1. Encoder Model</a></li>
<li><a href="#org8ef40ec">2. Test-Bench Description</a></li>
<li><a href="#orgce223ed">3. Measurement procedure</a></li>
<li><a href="#org51852cb">4. Measurement Results</a></li>
<li><a href="#orgd4a4664">1. Encoder Model</a></li>
<li><a href="#org8e70edd">2. Test-Bench Description</a></li>
<li><a href="#orge118b0f">3. Measurement procedure</a></li>
<li><a href="#org8e44240">4. Measurement Results</a>
<ul>
<li><a href="#org7e465e7">4.1. Noise Measurement</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div class="note" id="org4436bab">
<div class="note" id="org4c0c9be">
<p>
You can find below the document of:
</p>
@@ -63,14 +76,14 @@ In particular, we would like to measure:
</ul>
<div id="orgeb4726b" class="figure">
<div id="org13fff85" class="figure">
<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
</div>
<div id="outline-container-org55157ef" class="outline-2">
<h2 id="org55157ef"><span class="section-number-2">1</span> Encoder Model</h2>
<div id="outline-container-orgd4a4664" class="outline-2">
<h2 id="orgd4a4664"><span class="section-number-2">1</span> Encoder Model</h2>
<div class="outline-text-2" id="text-1">
<p>
The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; displacement \(y\) to measured displacement \(y_m\).
@@ -82,52 +95,63 @@ It is also characterized by its measurement noise \(n\) that can be described by
</p>
<p>
The model of the encoder is shown in Figure <a href="#org2d59f14">2</a>.
The model of the encoder is shown in Figure <a href="#org08a4e7a">2</a>.
</p>
<div id="org2d59f14" class="figure">
<div id="org08a4e7a" class="figure">
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
</div>
<table id="org476b3d6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org20ed9a5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-center" />
<col class="org-center" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left"><b>Characteristics</b></th>
<th scope="col" class="org-left"><b>Manual</b></th>
<th scope="col" class="org-center"><b>Manual</b></th>
<th scope="col" class="org-center"><b>Specifications</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Range</td>
<td class="org-center">Ruler length</td>
<td class="org-center">&gt; 200 [um]</td>
</tr>
<tr>
<td class="org-left">Resolution</td>
<td class="org-left">2.5nm</td>
<td class="org-center">2.5 [nm]</td>
<td class="org-center">&lt; 50 [nm rms]</td>
</tr>
<tr>
<td class="org-left">Sub-Divisional Error</td>
<td class="org-left">\(< \pm 15\,nm\)</td>
<td class="org-center">\(< \pm 15\,nm\)</td>
<td class="org-center">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Bandwidth</td>
<td class="org-left">&gt; 50 kHz</td>
<td class="org-center">To be checked</td>
<td class="org-center">&gt; 5 [kHz]</td>
</tr>
</tbody>
</table>
<div id="orgb8bf3d5" class="figure">
<div id="org2068d11" class="figure">
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Expected interpolation errors for the Vionic Encoder</p>
@@ -136,8 +160,8 @@ The model of the encoder is shown in Figure <a href="#org2d59f14">2</a>.
</div>
<div id="outline-container-org8ef40ec" class="outline-2">
<h2 id="org8ef40ec"><span class="section-number-2">2</span> Test-Bench Description</h2>
<div id="outline-container-org8e70edd" class="outline-2">
<h2 id="org8e70edd"><span class="section-number-2">2</span> Test-Bench Description</h2>
<div class="outline-text-2" id="text-2">
<p>
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.
@@ -151,7 +175,7 @@ An actuator should also be there so impose a displacement.
</p>
<p>
One idea is to use the test-bench shown in Figure <a href="#org1fd5a94">4</a>.
One idea is to use the test-bench shown in Figure <a href="#orgfefda93">4</a>.
</p>
<p>
@@ -164,7 +188,7 @@ As the interferometer has a very large bandwidth, we should be able to estimate
</p>
<div id="org1fd5a94" class="figure">
<div id="orgfefda93" class="figure">
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Schematic of the test bench</p>
@@ -172,11 +196,11 @@ As the interferometer has a very large bandwidth, we should be able to estimate
<p>
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.
This can be done by clamping the two as done in the mounting strut tool (Figure <a href="#orgab0ed8d">5</a>).
This can be done by clamping the two as done in the mounting strut tool (Figure <a href="#org742c647">5</a>).
</p>
<div id="orgab0ed8d" class="figure">
<div id="org742c647" class="figure">
<p><img src="figs/test_bench_measure_noise.png" alt="test_bench_measure_noise.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Mounting Strut test bench as a clamping method to measure the encoder noise.</p>
@@ -184,17 +208,70 @@ This can be done by clamping the two as done in the mounting strut tool (Figure
</div>
</div>
<div id="outline-container-orgce223ed" class="outline-2">
<h2 id="orgce223ed"><span class="section-number-2">3</span> Measurement procedure</h2>
<div id="outline-container-orge118b0f" class="outline-2">
<h2 id="orge118b0f"><span class="section-number-2">3</span> Measurement procedure</h2>
</div>
<div id="outline-container-org51852cb" class="outline-2">
<h2 id="org51852cb"><span class="section-number-2">4</span> Measurement Results</h2>
<div id="outline-container-org8e44240" class="outline-2">
<h2 id="org8e44240"><span class="section-number-2">4</span> Measurement Results</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-org7e465e7" class="outline-3">
<h3 id="org7e465e7"><span class="section-number-3">4.1</span> Noise Measurement</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<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>);
x = x <span class="org-type">-</span> mean(x);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
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>);
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>)
hold off;
xlabel(<span class="org-string">'Time [s]'</span>);
ylabel(<span class="org-string">'Displacement [nm]'</span>);
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>
<div id="org3070d03" class="figure">
<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Time domain measurement (raw data and low pass filtered data)</p>
</div>
<div id="orgd593081" class="figure">
<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the measured signal</p>
</div>
<p>
Let&rsquo;s create a transfer function that approximate the measured noise of the encoder.
</p>
<div class="org-src-container">
<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);
</pre>
</div>
<div id="orgd1f9fd9" class="figure">
<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Measured ASD of the noise and modelled one</p>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-01-04 lun. 11:44</p>
<p class="date">Created: 2021-02-02 mar. 18:24</p>
</div>
</body>
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