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Add some test benches

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Thomas Dehaeze 2020-12-17 14:54:16 +01:00
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-12-16 mer. 14:07 -->
<!-- 2020-12-17 jeu. 14:54 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Encoder Renishaw Vionic - Test Bench</title>
<meta name="generator" content="Org mode" />
@ -30,15 +30,15 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org096db33">1. Encoder Model</a></li>
<li><a href="#orga6d0b8e">2. Test-Bench Description</a></li>
<li><a href="#orgfc138a6">3. Measurement procedure</a></li>
<li><a href="#orgcddc280">4. Measurement Results</a></li>
<li><a href="#org52a1b18">1. Encoder Model</a></li>
<li><a href="#org79c9cb0">2. Test-Bench Description</a></li>
<li><a href="#org68a3dfb">3. Measurement procedure</a></li>
<li><a href="#orgf207a65">4. Measurement Results</a></li>
</ul>
</div>
</div>
<div class="note" id="org89964c6">
<div class="note" id="orgf5882b4">
<p>
You can find below the document of:
</p>
@ -57,13 +57,13 @@ We would like to characterize the encoder measurement system.
In particular, we would like to measure:
</p>
<ul class="org-ul">
<li>Bandwidth/dynamics of the sensor</li>
<li>Power Spectral Density of the measurement noise</li>
<li>Linearity/resolution of the sensor</li>
<li>Bandwidth of the sensor</li>
<li>Linearity of the sensor</li>
</ul>
<div id="outline-container-org096db33" class="outline-2">
<h2 id="org096db33"><span class="section-number-2">1</span> Encoder Model</h2>
<div id="outline-container-org52a1b18" class="outline-2">
<h2 id="org52a1b18"><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 \(y_m\).
@ -75,20 +75,62 @@ 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="#org8c743b3">1</a>.
The model of the encoder is shown in Figure <a href="#org131b7a7">1</a>.
</p>
<div id="org8c743b3" class="figure">
<div id="org131b7a7" class="figure">
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Model of the Encoder</p>
</div>
<table id="org00cec14" 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" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left"><b>Characteristics</b></th>
<th scope="col" class="org-left"><b>Manual</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Resolution</td>
<td class="org-left">2.5nm</td>
</tr>
<tr>
<td class="org-left">Sub-Divisional Error</td>
<td class="org-left">\(< \pm 15\,nm\)</td>
</tr>
<tr>
<td class="org-left">Bandwidth</td>
<td class="org-left">&gt; 50 kHz</td>
</tr>
</tbody>
</table>
<div id="orgd22d423" class="figure">
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Expected interpolation errors for the Vionic Encoder</p>
</div>
</div>
</div>
<div id="outline-container-orga6d0b8e" class="outline-2">
<h2 id="orga6d0b8e"><span class="section-number-2">2</span> Test-Bench Description</h2>
<div id="outline-container-org79c9cb0" class="outline-2">
<h2 id="org79c9cb0"><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.
@ -97,23 +139,55 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\).
<p>
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
An interferometer or capacitive sensor should work.
An interferometer or capacitive sensor should work fine.
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="#org1bd058e">3</a>.
</p>
<p>
The APA300ML is used to excite the mass in a broad bandwidth.
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
</p>
<p>
As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder is it is less than the Nyquist frequency (~ 5kHz).
</p>
<div id="org1bd058e" class="figure">
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Schematic of the test bench</p>
</div>
<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="#orgfdf8d08">4</a>).
</p>
<div id="orgfdf8d08" class="figure">
<p><img src="figs/test_bench_measure_noise.png" alt="test_bench_measure_noise.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Mounting Strut test bench as a clamping method to measure the encoder noise.</p>
</div>
</div>
</div>
<div id="outline-container-orgfc138a6" class="outline-2">
<h2 id="orgfc138a6"><span class="section-number-2">3</span> Measurement procedure</h2>
<div id="outline-container-org68a3dfb" class="outline-2">
<h2 id="org68a3dfb"><span class="section-number-2">3</span> Measurement procedure</h2>
</div>
<div id="outline-container-orgcddc280" class="outline-2">
<h2 id="orgcddc280"><span class="section-number-2">4</span> Measurement Results</h2>
<div id="outline-container-orgf207a65" class="outline-2">
<h2 id="orgf207a65"><span class="section-number-2">4</span> Measurement Results</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-12-16 mer. 14:07</p>
<p class="date">Created: 2020-12-17 jeu. 14:54</p>
</div>
</body>
</html>

41
index.org
View File

@ -51,9 +51,9 @@ You can find below the document of:
We would like to characterize the encoder measurement system.
In particular, we would like to measure:
- Bandwidth/dynamics of the sensor
- Power Spectral Density of the measurement noise
- Linearity/resolution of the sensor
- Bandwidth of the sensor
- Linearity of the sensor
* Encoder Model
The Encoder is characterized by its dynamics $G_m(s)$ from the "true" displacement $y$ to measured displacement $y_m$.
@ -85,15 +85,50 @@ The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
#+RESULTS:
[[file:figs/encoder-model-schematic.png]]
#+name: tab:vionic_characteristics_manual
#+caption: Characteristics of the Vionic Encoder
#+attr_latex: :environment tabularx :width \linewidth :align lXX
#+attr_latex: :center t :booktabs t :float t
| *Characteristics* | *Manual* |
|----------------------+----------------|
| Resolution | 2.5nm |
| Sub-Divisional Error | $< \pm 15\,nm$ |
| Bandwidth | > 50 kHz |
#+name: fig:vionic_expected_noise
#+caption: Expected interpolation errors for the Vionic Encoder
[[file:./figs/vionic_expected_noise.png]]
* Test-Bench Description
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.
Then, the measured signal $y_m$ corresponds to the noise $n$.
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
An interferometer or capacitive sensor should work.
An interferometer or capacitive sensor should work fine.
An actuator should also be there so impose a displacement.
One idea is to use the test-bench shown in Figure [[fig:test_bench_encoder_calibration]].
The APA300ML is used to excite the mass in a broad bandwidth.
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder is it is less than the Nyquist frequency (~ 5kHz).
#+name: fig:test_bench_encoder_calibration
#+caption: Schematic of the test bench
[[file:figs/test_bench_encoder_calibration.png]]
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 [[fig:test_bench_measure_noise]]).
#+name: fig:test_bench_measure_noise
#+caption: Mounting Strut test bench as a clamping method to measure the encoder noise.
[[file:figs/test_bench_measure_noise.png]]
* Measurement procedure
* Measurement Results