Compare commits
12 Commits
983b300650
...
master
| Author | SHA1 | Date | |
|---|---|---|---|
| 4776c89343 | |||
| 195c5b5598 | |||
| 9a06c0995f | |||
| 73dc280ab3 | |||
| 15d8508bf0 | |||
| bc5876f32f | |||
| 080b788768 | |||
| 30177e4809 | |||
| 006cb20df1 | |||
| 53ffaaa793 | |||
| 0296f80900 | |||
| d924339f63 |
BIN
figs/IMG_20210211_170551.jpg
Normal file
BIN
figs/IMG_20210211_170551.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 3.4 MiB |
BIN
figs/IMG_20210211_170554.jpg
Normal file
BIN
figs/IMG_20210211_170554.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 236 KiB |
BIN
figs/IMG_20210211_170607.jpg
Normal file
BIN
figs/IMG_20210211_170607.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 268 KiB |
BIN
figs/vionic_drifts_linear_fit.pdf
Normal file
BIN
figs/vionic_drifts_linear_fit.pdf
Normal file
Binary file not shown.
BIN
figs/vionic_drifts_linear_fit.png
Normal file
BIN
figs/vionic_drifts_linear_fit.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 20 KiB |
BIN
figs/vionic_drifts_time.pdf
Normal file
BIN
figs/vionic_drifts_time.pdf
Normal file
Binary file not shown.
BIN
figs/vionic_drifts_time.png
Normal file
BIN
figs/vionic_drifts_time.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 20 KiB |
Binary file not shown.
Binary file not shown.
|
Before Width: | Height: | Size: 66 KiB After Width: | Height: | Size: 80 KiB |
1274
figs/vionic_noise_asd_combined.pdf
Normal file
1274
figs/vionic_noise_asd_combined.pdf
Normal file
File diff suppressed because it is too large
Load Diff
BIN
figs/vionic_noise_asd_combined.png
Normal file
BIN
figs/vionic_noise_asd_combined.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 86 KiB |
BIN
figs/vionic_noise_asd_low_freq.pdf
Normal file
BIN
figs/vionic_noise_asd_low_freq.pdf
Normal file
Binary file not shown.
BIN
figs/vionic_noise_asd_low_freq.png
Normal file
BIN
figs/vionic_noise_asd_low_freq.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 57 KiB |
Binary file not shown.
Binary file not shown.
|
Before Width: | Height: | Size: 67 KiB After Width: | Height: | Size: 86 KiB |
BIN
figs/vionic_noise_cas_model.pdf
Normal file
BIN
figs/vionic_noise_cas_model.pdf
Normal file
Binary file not shown.
BIN
figs/vionic_noise_cas_model.png
Normal file
BIN
figs/vionic_noise_cas_model.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 53 KiB |
BIN
figs/vionic_noise_raw_lpf.pdf
Normal file
BIN
figs/vionic_noise_raw_lpf.pdf
Normal file
Binary file not shown.
BIN
figs/vionic_noise_raw_lpf.png
Normal file
BIN
figs/vionic_noise_raw_lpf.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 35 KiB |
Binary file not shown.
Binary file not shown.
|
Before Width: | Height: | Size: 38 KiB After Width: | Height: | Size: 57 KiB |
BIN
matlab/mat/noise_meas_100Hz_without_AGC.mat
Normal file
BIN
matlab/mat/noise_meas_100Hz_without_AGC.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_100s_20kHz_2.mat
Normal file
BIN
matlab/mat/noise_meas_100s_20kHz_2.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_100s_20kHz_3.mat
Normal file
BIN
matlab/mat/noise_meas_100s_20kHz_3.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_100s_20kHz_4.mat
Normal file
BIN
matlab/mat/noise_meas_100s_20kHz_4.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_100s_20kHz_5.mat
Normal file
BIN
matlab/mat/noise_meas_100s_20kHz_5.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_100s_20kHz_6.mat
Normal file
BIN
matlab/mat/noise_meas_100s_20kHz_6.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_100s_20kHz_7.mat
Normal file
BIN
matlab/mat/noise_meas_100s_20kHz_7.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_40h_100Hz_1.mat
Normal file
BIN
matlab/mat/noise_meas_40h_100Hz_1.mat
Normal file
Binary file not shown.
BIN
matlab/mat/noise_meas_80h_100Hz_1.mat
Normal file
BIN
matlab/mat/noise_meas_80h_100Hz_1.mat
Normal file
Binary file not shown.
@@ -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>
|
||||
<!-- 2021-02-02 mar. 18:46 -->
|
||||
<!-- 2021-02-12 ven. 18:26 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Encoder Renishaw Vionic - Test Bench</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@@ -39,23 +39,21 @@
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#org3a55927">1. Encoder Model</a></li>
|
||||
<li><a href="#orgde74ebc">2. Noise Measurement</a>
|
||||
<li><a href="#orgfa3d11e">1. Expected Performances</a></li>
|
||||
<li><a href="#orgf23b21b">2. Encoder Model</a></li>
|
||||
<li><a href="#org9c17913">3. Noise Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#org835e359">2.1. Test Bench</a></li>
|
||||
<li><a href="#org52a3f6f">2.2. Results</a></li>
|
||||
<li><a href="#orgb9429ef">3.1. Test Bench</a></li>
|
||||
<li><a href="#orgd9c9c77">3.2. Thermal drifts</a></li>
|
||||
<li><a href="#org8ec1ba2">3.3. Time Domain signals</a></li>
|
||||
<li><a href="#org833451c">3.4. Noise Spectral Density</a></li>
|
||||
<li><a href="#org71a7d07">3.5. Noise Model</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orge941dff">3. Linearity Measurement</a>
|
||||
<li><a href="#org61522ff">4. Linearity Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#orga2e857a">3.1. Test Bench</a></li>
|
||||
<li><a href="#orgc7f59c3">3.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org42e063d">4. Dynamical Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#org4e0f29a">4.1. Test Bench</a></li>
|
||||
<li><a href="#orgb2f1f77">4.2. Results</a></li>
|
||||
<li><a href="#orge455e25">4.1. Test Bench</a></li>
|
||||
<li><a href="#orgc6e5044">4.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
@@ -65,9 +63,9 @@
|
||||
<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
|
||||
<hr>
|
||||
|
||||
<div class="note" id="orgf92d65f">
|
||||
<div class="note" id="orge01a92a">
|
||||
<p>
|
||||
You can find below the document of:
|
||||
You can find below the documentation of:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li><a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Vionic Encoder</a></li>
|
||||
@@ -77,60 +75,81 @@ You can find below the document of:
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We would like to characterize the encoder measurement system.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In this document, we wish to characterize the performances of the encoder measurement system.
|
||||
In particular, we would like to measure:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Power Spectral Density of the measurement noise</li>
|
||||
<li>Bandwidth of the sensor</li>
|
||||
<li>Linearity of the sensor</li>
|
||||
<li>the measurement noise</li>
|
||||
<li>the linearity of the sensor</li>
|
||||
<li>the bandwidth of the sensor</li>
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
This document is structured as follow:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Section <a href="#org5ddac7d">1</a>: the expected performance of the Vionic encoder system are described</li>
|
||||
<li>Section <a href="#org55cdc69">2</a>: a simple model of the encoder is developed</li>
|
||||
<li>Section <a href="#orgb828c8d">3</a>: the noise of the encoder is measured and a model of the noise is identified</li>
|
||||
<li>Section <a href="#org49975c3">4</a>: the linearity of the sensor is estimated</li>
|
||||
</ul>
|
||||
|
||||
<div id="orgddb4738" class="figure">
|
||||
<div id="outline-container-orgfa3d11e" class="outline-2">
|
||||
<h2 id="orgfa3d11e"><span class="section-number-2">1</span> Expected Performances</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
<a id="org5ddac7d"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The Vionic encoder is shown in Figure <a href="#orga0ecb6c">1</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga0ecb6c" 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-org3a55927" class="outline-2">
|
||||
<h2 id="org3a55927"><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 “true” displacement \(y\) to measured displacement \(y_m\).
|
||||
Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
|
||||
From the Renishaw <a href="https://www.renishaw.com/en/how-optical-encoders-work--36979">website</a>:
|
||||
</p>
|
||||
<blockquote>
|
||||
<p>
|
||||
The VIONiC encoder features the third generation of Renishaw’s unique filtering optics that average the contributions from many scale periods and effectively filter out non-periodic features such as dirt.
|
||||
The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector.
|
||||
Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals.
|
||||
These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining <b>bandwidth to beyond 500 kHz</b>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD).
|
||||
Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure <b>ultra-low Sub-Divisional Error (SDE) of typically</b> \(<\pm 15\, nm\).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The model of the encoder is shown in Figure <a href="#orga0a431c">2</a>.
|
||||
This evolution of filtering optics, combined with carefully-selected electronics, provide incremental signals with wide bandwidth achieving a maximum speed of 12 m/s with the lowest positional jitter (noise) of any encoder in its class.
|
||||
Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve <b>jitter of just 1.6 nm RMS</b>.
|
||||
</p>
|
||||
</blockquote>
|
||||
|
||||
<p>
|
||||
The expected interpolation errors (non-linearity) is shown in Figure <a href="#orgc38e53f">2</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga0a431c" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
|
||||
<div id="orgc38e53f" class="figure">
|
||||
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Expected interpolation errors for the Vionic Encoder</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
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>.
|
||||
The characteristics as advertise in the manual as well as our specifications are shown in Table <a href="#org091f419">1</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org27d4d98" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<table id="org212ba69" 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>
|
||||
<table id="org091f419" 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 compared with the specifications</caption>
|
||||
|
||||
<colgroup>
|
||||
<col class="org-left" />
|
||||
@@ -143,121 +162,313 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
|
||||
<tr>
|
||||
<th scope="col" class="org-left"><b>Characteristics</b></th>
|
||||
<th scope="col" class="org-center"><b>Manual</b></th>
|
||||
<th scope="col" class="org-center"><b>Specifications</b></th>
|
||||
<th scope="col" class="org-center"><b>Specification</b></th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-left">Range</td>
|
||||
<td class="org-center">Ruler length</td>
|
||||
<td class="org-center">> 200 [um]</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Resolution</td>
|
||||
<td class="org-center">2.5 [nm]</td>
|
||||
<td class="org-center">< 50 [nm rms]</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Sub-Divisional Error</td>
|
||||
<td class="org-center">\(< \pm 15\,nm\)</td>
|
||||
<td class="org-center"> </td>
|
||||
<td class="org-left">Time Delay</td>
|
||||
<td class="org-center">< 10 ns</td>
|
||||
<td class="org-center">< 0.5 ms</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Bandwidth</td>
|
||||
<td class="org-center">To be checked</td>
|
||||
<td class="org-center">> 5 [kHz]</td>
|
||||
<td class="org-center">> 500 kHz</td>
|
||||
<td class="org-center">> 5 kHz</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Noise</td>
|
||||
<td class="org-center">< 1.6 nm rms</td>
|
||||
<td class="org-center">< 50 nm rms</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Linearity</td>
|
||||
<td class="org-center">< +/- 15 nm</td>
|
||||
<td class="org-center"> </td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Range</td>
|
||||
<td class="org-center">Ruler length</td>
|
||||
<td class="org-center">> 200 um</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
|
||||
<div id="org70392dd" class="figure">
|
||||
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Expected interpolation errors for the Vionic Encoder</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-orgde74ebc" class="outline-2">
|
||||
<h2 id="orgde74ebc"><span class="section-number-2">2</span> Noise Measurement</h2>
|
||||
<div id="outline-container-orgf23b21b" class="outline-2">
|
||||
<h2 id="orgf23b21b"><span class="section-number-2">2</span> Encoder Model</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="orgcac09c5"></a>
|
||||
<a id="org55cdc69"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\).
|
||||
Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD) \(\Gamma_n(\omega)\).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The model of the encoder is shown in Figure <a href="#org4fdb73a">3</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org4fdb73a" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Model of the Encoder</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
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="#orgc38e53f">2</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org793433f" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org835e359" class="outline-3">
|
||||
<h3 id="org835e359"><span class="section-number-3">2.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9c17913" class="outline-2">
|
||||
<h2 id="org9c17913"><span class="section-number-2">3</span> Noise Measurement</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="orgb828c8d"></a>
|
||||
</p>
|
||||
<p>
|
||||
This part is structured as follow:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Section <a href="#org8cfb922">3.1</a>: the measurement bench is described</li>
|
||||
<li>Section <a href="#orgfd5ce06">3.2</a>: long measurement is performed to estimate the low frequency drifts in the measurement</li>
|
||||
<li>Section <a href="#org4df45c5">3.3</a>: high frequency measurements are performed to estimate the high frequency noise</li>
|
||||
<li>Section <a href="#orgd464562">3.4</a>: the Spectral density of the measurement noise is estimated</li>
|
||||
<li>Section <a href="#orgd6ec52a">3.5</a>: finally, the measured noise is modeled</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb9429ef" class="outline-3">
|
||||
<h3 id="orgb9429ef"><span class="section-number-3">3.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
<a id="org8cfb922"></a>
|
||||
</p>
|
||||
|
||||
<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.
|
||||
Then, the measured signal \(y_m\) corresponds to the noise \(n\).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The measurement bench is shown in Figures <a href="#org4037996">5</a> and <a href="#org06e2754">6</a>.
|
||||
Note that the bench is then covered with a “plastic bubble sheet” in order to keep disturbances as small as possible.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org4037996" class="figure">
|
||||
<p><img src="figs/IMG_20210211_170554.jpg" alt="IMG_20210211_170554.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Top view picture of the measurement bench</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org06e2754" class="figure">
|
||||
<p><img src="figs/IMG_20210211_170607.jpg" alt="IMG_20210211_170607.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Side view picture of the measurement bench</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org52a3f6f" class="outline-3">
|
||||
<h3 id="org52a3f6f"><span class="section-number-3">2.2</span> Results</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<div id="outline-container-orgd9c9c77" class="outline-3">
|
||||
<h3 id="orgd9c9c77"><span class="section-number-3">3.2</span> Thermal drifts</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
First we load the data.
|
||||
<a id="orgfd5ce06"></a>
|
||||
Measured displacement were recording during approximately 40 hours with a sample frequency of 100Hz.
|
||||
A first order low pass filter with a corner frequency of 1Hz
|
||||
</p>
|
||||
|
||||
<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 class="src src-matlab">enc_l = load(<span class="org-string">'mat/noise_meas_40h_100Hz_1.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The time domain data are shown in Figure <a href="#orgc55250e">4</a>.
|
||||
The measured time domain data are shown in Figure <a href="#org1454db4">7</a>.
|
||||
</p>
|
||||
|
||||
<div id="org1454db4" class="figure">
|
||||
<p><img src="figs/vionic_drifts_time.png" alt="vionic_drifts_time.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Measured thermal drifts</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
<img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
|
||||
The amplitude spectral density is computed and shown in Figure <a href="#orgfb661b7">5</a>.
|
||||
The measured data seems to experience a constant drift after approximately 20 hour.
|
||||
Let’s estimate this drift.
|
||||
</p>
|
||||
|
||||
<pre class="example">
|
||||
The mean drift is approximately 60.9 [nm/hour] or 1.0 [nm/min]
|
||||
</pre>
|
||||
|
||||
<div id="orgfb661b7" class="figure">
|
||||
|
||||
<p>
|
||||
Comparison between the data and the linear fit is shown in Figure <a href="#orgfbe5f53">8</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgfbe5f53" class="figure">
|
||||
<p><img src="figs/vionic_drifts_linear_fit.png" alt="vionic_drifts_linear_fit.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Measured drift and linear fit</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Let’s now estimate the Power Spectral Density of the measured displacement.
|
||||
The obtained low frequency ASD is shown in Figure <a href="#org42f3fad">9</a>.
|
||||
</p>
|
||||
|
||||
<div id="org42f3fad" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd_low_freq.png" alt="vionic_noise_asd_low_freq.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Amplitude Spectral density of the measured displacement</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8ec1ba2" class="outline-3">
|
||||
<h3 id="org8ec1ba2"><span class="section-number-3">3.3</span> Time Domain signals</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
<a id="org4df45c5"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
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="#org28ad5da">10</a>.
|
||||
</p>
|
||||
|
||||
<div id="org28ad5da" class="figure">
|
||||
<p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The time domain data for all the encoders are compared in Figure <a href="#org1656541">11</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
We can see some drifts that are in the order of few nm to 20nm per minute.
|
||||
As shown in Section <a href="#orgfd5ce06">3.2</a>, these drifts should diminish over time down to 1nm/min.
|
||||
</p>
|
||||
|
||||
<div id="org1656541" class="figure">
|
||||
<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Comparison of the time domain measurement</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org833451c" class="outline-3">
|
||||
<h3 id="org833451c"><span class="section-number-3">3.4</span> Noise Spectral Density</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
<a id="orgd464562"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The amplitude spectral densities for all the encoder are computed and shown in Figure <a href="#org7e93bb1">12</a>.
|
||||
</p>
|
||||
|
||||
<div id="org7e93bb1" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signal</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the measured signal</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We can combine these measurements with the low frequency noise computed in Section <a href="#orgfd5ce06">3.2</a>.
|
||||
The obtained ASD is shown in Figure <a href="#org7e54160">13</a>.
|
||||
</p>
|
||||
|
||||
<div id="org7e54160" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd_combined.png" alt="vionic_noise_asd_combined.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Combined low frequency and high frequency noise measurements</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org71a7d07" class="outline-3">
|
||||
<h3 id="org71a7d07"><span class="section-number-3">3.5</span> Noise Model</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<p>
|
||||
<a id="orgd6ec52a"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Let’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 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);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org6d60818">6</a>.
|
||||
The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org5d39757">14</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org6d60818" class="figure">
|
||||
<div id="org5d39757" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Measured ASD of the noise and modelled one</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Measured ASD of the noise and modeled one</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orge941dff" class="outline-2">
|
||||
<h2 id="orge941dff"><span class="section-number-2">3</span> Linearity Measurement</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
|
||||
<p>
|
||||
<a id="org0c843ed"></a>
|
||||
The cumulative amplitude spectrum is now computed and shown in Figure <a href="#org05b258c">15</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
We can see that the Root Mean Square value of the measurement noise is \(\approx 1.6 \, nm\) as advertise in the datasheet.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org05b258c" class="figure">
|
||||
<p><img src="figs/vionic_noise_cas_model.png" alt="vionic_noise_cas_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Meassured CAS of the noise and modeled one</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org61522ff" class="outline-2">
|
||||
<h2 id="org61522ff"><span class="section-number-2">4</span> Linearity Measurement</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="org49975c3"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orga2e857a" class="outline-3">
|
||||
<h3 id="orga2e857a"><span class="section-number-3">3.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<div id="outline-container-orge455e25" class="outline-3">
|
||||
<h3 id="orge455e25"><span class="section-number-3">4.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<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 fine.
|
||||
@@ -265,7 +476,7 @@ 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="#org793dd45">7</a>.
|
||||
One idea is to use the test-bench shown in Figure <a href="#org177aa2c">16</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -278,38 +489,22 @@ As the interferometer has a very large bandwidth, we should be able to estimate
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org793dd45" class="figure">
|
||||
<div id="org177aa2c" class="figure">
|
||||
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Schematic of the test bench</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Schematic of the test bench</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc7f59c3" class="outline-3">
|
||||
<h3 id="orgc7f59c3"><span class="section-number-3">3.2</span> Results</h3>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org42e063d" class="outline-2">
|
||||
<h2 id="org42e063d"><span class="section-number-2">4</span> Dynamical Measurement</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="org2b52f4b"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org4e0f29a" class="outline-3">
|
||||
<h3 id="org4e0f29a"><span class="section-number-3">4.1</span> Test Bench</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb2f1f77" class="outline-3">
|
||||
<h3 id="orgb2f1f77"><span class="section-number-3">4.2</span> Results</h3>
|
||||
<div id="outline-container-orgc6e5044" class="outline-3">
|
||||
<h3 id="orgc6e5044"><span class="section-number-3">4.2</span> Results</h3>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-02-02 mar. 18:46</p>
|
||||
<p class="date">Created: 2021-02-12 ven. 18:26</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -16,7 +16,6 @@
|
||||
#+LaTeX_CLASS: scrreprt
|
||||
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
|
||||
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
|
||||
#+EXPORT_FILE_NAME: test-bench-vionic.tex
|
||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||
#+PROPERTY: header-args:matlab+ :comments org
|
||||
@@ -50,28 +49,75 @@
|
||||
* Introduction :ignore:
|
||||
|
||||
#+begin_note
|
||||
You can find below the document of:
|
||||
You can find below the documentation of:
|
||||
- [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic Encoder]]
|
||||
- [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Linear Scale]]
|
||||
#+end_note
|
||||
|
||||
We would like to characterize the encoder measurement system.
|
||||
|
||||
In this document, we wish to characterize the performances of the encoder measurement system.
|
||||
In particular, we would like to measure:
|
||||
- Power Spectral Density of the measurement noise
|
||||
- Bandwidth of the sensor
|
||||
- Linearity of the sensor
|
||||
- the measurement noise
|
||||
- the linearity of the sensor
|
||||
- the bandwidth of the sensor
|
||||
|
||||
This document is structured as follow:
|
||||
- Section [[sec:vionic_expected_performances]]: the expected performance of the Vionic encoder system are described
|
||||
- Section [[sec:encoder_model]]: a simple model of the encoder is developed
|
||||
- Section [[sec:noise_measurement]]: the noise of the encoder is measured and a model of the noise is identified
|
||||
- Section [[sec:linearity_measurement]]: the linearity of the sensor is estimated
|
||||
|
||||
* Expected Performances
|
||||
<<sec:vionic_expected_performances>>
|
||||
|
||||
The Vionic encoder is shown in Figure [[fig:encoder_vionic]].
|
||||
|
||||
#+name: fig:encoder_vionic
|
||||
#+caption: Picture of the Vionic Encoder
|
||||
#+attr_latex: :width 0.6\linewidth
|
||||
[[file:figs/encoder_vionic.png]]
|
||||
|
||||
From the Renishaw [[https://www.renishaw.com/en/how-optical-encoders-work--36979][website]]:
|
||||
#+begin_quote
|
||||
The VIONiC encoder features the third generation of Renishaw's unique filtering optics that average the contributions from many scale periods and effectively filter out non-periodic features such as dirt.
|
||||
The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector.
|
||||
Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals.
|
||||
These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining *bandwidth to beyond 500 kHz*.
|
||||
|
||||
Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure *ultra-low Sub-Divisional Error (SDE) of typically* $<\pm 15\, nm$.
|
||||
|
||||
This evolution of filtering optics, combined with carefully-selected electronics, provide incremental signals with wide bandwidth achieving a maximum speed of 12 m/s with the lowest positional jitter (noise) of any encoder in its class.
|
||||
Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve *jitter of just 1.6 nm RMS*.
|
||||
#+end_quote
|
||||
|
||||
The expected interpolation errors (non-linearity) is shown in Figure [[fig:vionic_expected_noise]].
|
||||
|
||||
#+name: fig:vionic_expected_noise
|
||||
#+attr_latex: :width \linewidth
|
||||
#+caption: Expected interpolation errors for the Vionic Encoder
|
||||
[[file:./figs/vionic_expected_noise.png]]
|
||||
|
||||
The characteristics as advertise in the manual as well as our specifications are shown in Table [[tab:vionic_characteristics]].
|
||||
|
||||
#+name: tab:vionic_characteristics
|
||||
#+caption: Characteristics of the Vionic compared with the specifications
|
||||
#+attr_latex: :environment tabularx :width 0.6\linewidth :align lcc
|
||||
#+attr_latex: :center t :booktabs t :float t
|
||||
| <l> | <c> | <c> |
|
||||
| *Characteristics* | *Manual* | *Specification* |
|
||||
|-------------------+--------------+-----------------|
|
||||
| Time Delay | < 10 ns | < 0.5 ms |
|
||||
| Bandwidth | > 500 kHz | > 5 kHz |
|
||||
| Noise | < 1.6 nm rms | < 50 nm rms |
|
||||
| Linearity | < +/- 15 nm | |
|
||||
| Range | Ruler length | > 200 um |
|
||||
|
||||
* Encoder Model
|
||||
<<sec:encoder_model>>
|
||||
|
||||
The Encoder is characterized by its dynamics $G_m(s)$ from the "true" displacement $y$ to measured displacement $y_m$.
|
||||
Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
|
||||
|
||||
It is also characterized by its measurement noise $n$ that can be described by its Power Spectral Density (PSD).
|
||||
It is also characterized by its measurement noise $n$ that can be described by its Power Spectral Density (PSD) $\Gamma_n(\omega)$.
|
||||
|
||||
The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
|
||||
|
||||
@@ -121,31 +167,37 @@ We can also use a transfer function $G_n(s)$ to shape a noise $\tilde{n}$ with u
|
||||
#+RESULTS:
|
||||
[[file:figs/encoder-model-schematic-with-asd.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
|
||||
| <l> | <c> | <c> |
|
||||
| *Characteristics* | *Manual* | *Specifications* |
|
||||
|----------------------+----------------+------------------|
|
||||
| Range | Ruler length | > 200 [um] |
|
||||
| Resolution | 2.5 [nm] | < 50 [nm rms] |
|
||||
| Sub-Divisional Error | $< \pm 15\,nm$ | |
|
||||
| Bandwidth | To be checked | > 5 [kHz] |
|
||||
|
||||
#+name: fig:vionic_expected_noise
|
||||
#+attr_latex: :width \linewidth
|
||||
#+caption: Expected interpolation errors for the Vionic Encoder
|
||||
[[file:./figs/vionic_expected_noise.png]]
|
||||
|
||||
|
||||
* Noise Measurement
|
||||
<<sec:noise_measurement>>
|
||||
|
||||
** Introduction :ignore:
|
||||
|
||||
This part is structured as follow:
|
||||
- Section [[sec:noise_bench]]: the measurement bench is described
|
||||
- Section [[sec:thermal_drifts]]: long measurement is performed to estimate the low frequency drifts in the measurement
|
||||
- Section [[sec:vionic_noise_time]]: high frequency measurements are performed to estimate the high frequency noise
|
||||
- Section [[sec:noise_asd]]: the Spectral density of the measurement noise is estimated
|
||||
- Section [[sec:vionic_noise_model]]: finally, the measured noise is modeled
|
||||
|
||||
** Test Bench
|
||||
<<sec:noise_bench>>
|
||||
|
||||
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 $n$.
|
||||
|
||||
The measurement bench is shown in Figures [[fig:meas_bench_top_view]] and [[fig:meas_bench_side_view]].
|
||||
Note that the bench is then covered with a "plastic bubble sheet" in order to keep disturbances as small as possible.
|
||||
|
||||
#+name: fig:meas_bench_top_view
|
||||
#+caption: Top view picture of the measurement bench
|
||||
#+attr_latex: :width 0.8\linewidth
|
||||
[[file:figs/IMG_20210211_170554.jpg]]
|
||||
|
||||
#+name: fig:meas_bench_side_view
|
||||
#+caption: Side view picture of the measurement bench
|
||||
#+attr_latex: :width 0.8\linewidth
|
||||
[[file:figs/IMG_20210211_170607.jpg]]
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
@@ -164,23 +216,170 @@ addpath('./matlab/');
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
** Results
|
||||
First we load the data.
|
||||
** Thermal drifts
|
||||
<<sec:thermal_drifts>>
|
||||
Measured displacement were recording during approximately 40 hours with a sample frequency of 100Hz.
|
||||
A first order low pass filter with a corner frequency of 1Hz
|
||||
|
||||
#+begin_src matlab
|
||||
load('noise_meas_100s_20kHz.mat', 't', 'x');
|
||||
x = x - mean(x);
|
||||
enc_l = load('mat/noise_meas_40h_100Hz_1.mat', 't', 'x');
|
||||
#+end_src
|
||||
|
||||
The measured time domain data are shown in Figure [[fig:vionic_drifts_time]].
|
||||
#+begin_src matlab :exports none
|
||||
enc_l.x = enc_l.x(enc_l.t > 5); % Remove first 5 seconds
|
||||
enc_l.t = enc_l.t(enc_l.t > 5); % Remove first 5 seconds
|
||||
enc_l.t = enc_l.t - enc_l.t(1); % Start at 0
|
||||
|
||||
enc_l.x = enc_l.x - mean(enc_l.x(enc_l.t < 1)); % Start at zero displacement
|
||||
#+end_src
|
||||
|
||||
The time domain data are shown in Figure [[fig:vionic_noise_time]].
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(t, 1e9*x, '.', 'DisplayName', 'Raw');
|
||||
plot(t, 1e9*lsim(1/(1 + s/2/pi/500), x, t), 'DisplayName', 'LPF - 500Hz')
|
||||
plot(enc_l.t/3600, 1e9*enc_l.x, '-');
|
||||
hold off;
|
||||
xlabel('Time [h]');
|
||||
ylabel('Displacement [nm]');
|
||||
xlim([0, 40]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_drifts_time.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_drifts_time
|
||||
#+caption: Measured thermal drifts
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_drifts_time.png]]
|
||||
|
||||
The measured data seems to experience a constant drift after approximately 20 hour.
|
||||
Let's estimate this drift.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
t0 = 20*3600; % Start time [s]
|
||||
x_stab = enc_l.x(enc_l.t > t0);
|
||||
x_stab = x_stab - x_stab(1);
|
||||
t_stab = enc_l.t(enc_l.t > t0);
|
||||
t_stab = t_stab - t_stab(1);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
sprintf('The mean drift is approximately %.1f [nm/hour] or %.1f [nm/min]', 3600*1e9*(t_stab\x_stab), 60*1e9*(t_stab\x_stab))
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: The mean drift is approximately 60.9 [nm/hour] or 1.0 [nm/min]
|
||||
|
||||
Comparison between the data and the linear fit is shown in Figure [[fig:vionic_drifts_linear_fit]].
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(t_stab/3600, 1e9*x_stab, '-');
|
||||
plot(t_stab/3600, 1e9*t_stab*(t_stab\x_stab), 'k--');
|
||||
hold off;
|
||||
xlabel('Time [h]');
|
||||
ylabel('Displacement [nm]');
|
||||
xlim([0, 20]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_drifts_linear_fit.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_drifts_linear_fit
|
||||
#+caption: Measured drift and linear fit
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_drifts_linear_fit.png]]
|
||||
|
||||
Let's now estimate the Power Spectral Density of the measured displacement.
|
||||
The obtained low frequency ASD is shown in Figure [[fig:vionic_noise_asd_low_freq]].
|
||||
#+begin_src matlab :exports none
|
||||
% Compute sampling Frequency
|
||||
Ts = (enc_l.t(end) - enc_l.t(1))/(length(enc_l.t)-1);
|
||||
Fs = 1/Ts;
|
||||
|
||||
% Hannning Windows
|
||||
win = hanning(ceil(60*10/Ts));
|
||||
|
||||
[pxx_l, f_l] = pwelch(x_stab, win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f_l, sqrt(pxx_l))
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
|
||||
xlim([1e-2, 1e0]);
|
||||
ylim([1e-11, 1e-8]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_noise_asd_low_freq.pdf', 'width', 'side', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_asd_low_freq
|
||||
#+caption: Amplitude Spectral density of the measured displacement
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd_low_freq.png]]
|
||||
|
||||
** Time Domain signals
|
||||
<<sec:vionic_noise_time>>
|
||||
|
||||
Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%% Load all the measurements
|
||||
enc = {};
|
||||
for i = 1:7
|
||||
enc(i) = {load(['mat/noise_meas_100s_20kHz_' num2str(i) '.mat'], 't', 'x')};
|
||||
end
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%% Remove initial offset
|
||||
for i = 1:7
|
||||
enc{i}.x = enc{i}.x - mean(enc{i}.x(1:1000));
|
||||
end
|
||||
#+end_src
|
||||
|
||||
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 [[fig:vionic_noise_raw_lpf]].
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(enc{1}.t, 1e9*enc{1}.x, '.', 'DisplayName', 'Enc 1 - Raw');
|
||||
plot(enc{1}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{1}.x, enc{1}.t), '-', 'DisplayName', 'Enc 1 - LPF');
|
||||
hold off;
|
||||
xlabel('Time [s]');
|
||||
ylabel('Displacement [nm]');
|
||||
legend('location', 'northeast');
|
||||
legend('location', 'northwest');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_noise_raw_lpf.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_raw_lpf
|
||||
#+caption: Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_raw_lpf.png]]
|
||||
|
||||
The time domain data for all the encoders are compared in Figure [[fig:vionic_noise_time]].
|
||||
|
||||
We can see some drifts that are in the order of few nm to 20nm per minute.
|
||||
As shown in Section [[sec:thermal_drifts]], these drifts should diminish over time down to 1nm/min.
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
for i=1:7
|
||||
plot(enc{i}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{i}.x, enc{i}.t), '.', ...
|
||||
'DisplayName', sprintf('Enc %i', i));
|
||||
end
|
||||
hold off;
|
||||
xlabel('Time [s]');
|
||||
ylabel('Displacement [nm]');
|
||||
legend('location', 'northwest');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
@@ -188,31 +387,43 @@ exportFig('figs/vionic_noise_time.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_time
|
||||
#+caption: Time domain measurement (raw data and low pass filtered data)
|
||||
#+caption: Comparison of the time domain measurement
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_time.png]]
|
||||
The amplitude spectral density is computed and shown in Figure [[fig:vionic_noise_asd]].
|
||||
|
||||
** Noise Spectral Density
|
||||
<<sec:noise_asd>>
|
||||
|
||||
The amplitude spectral densities for all the encoder are computed and shown in Figure [[fig:vionic_noise_asd]].
|
||||
#+begin_src matlab :exports none
|
||||
% Compute sampling Frequency
|
||||
Ts = (t(end) - t(1))/(length(t)-1);
|
||||
Ts = (enc{1}.t(end) - enc{1}.t(1))/(length(enc{1}.t)-1);
|
||||
Fs = 1/Ts;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
% Hannning Windows
|
||||
win = hanning(ceil(0.5*Fs));
|
||||
win = hanning(ceil(0.5/Ts));
|
||||
|
||||
[pxx, f] = pwelch(x, win, [], [], Fs);
|
||||
[pxx, f] = pwelch(enc{1}.x, win, [], [], Fs);
|
||||
enc{1}.pxx = pxx;
|
||||
|
||||
for i=2:7
|
||||
[pxx, ~] = pwelch(enc{i}.x, win, [], [], Fs);
|
||||
enc{i}.pxx = pxx;
|
||||
end
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
plot(f, sqrt(pxx));
|
||||
hold on;
|
||||
for i=1:7
|
||||
plot(f, sqrt(enc{i}.pxx), ...
|
||||
'DisplayName', sprintf('Enc %i', i));
|
||||
end
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
|
||||
xlim([1, Fs/2]);
|
||||
xlim([10, Fs/2]);
|
||||
ylim([1e-11, 1e-9]);
|
||||
legend('location', 'northeast');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
@@ -224,9 +435,36 @@ exportFig('figs/vionic_noise_asd.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd.png]]
|
||||
|
||||
We can combine these measurements with the low frequency noise computed in Section [[sec:thermal_drifts]].
|
||||
The obtained ASD is shown in Figure [[fig:vionic_noise_asd_combined]].
|
||||
#+begin_src matlab :exports none
|
||||
[pxx_h, f_h] = pwelch(enc{2}.x, hanning(ceil(10/Ts)), [], [], Fs);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f_h(f_h>0.6), sqrt(pxx_h(f_h>0.6)), 'k-');
|
||||
plot(f_l(f_l<1), sqrt(pxx_l(f_l<1)), 'k-')
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
|
||||
xlim([1e-2, Fs/2]);
|
||||
ylim([1e-12, 1e-8]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_noise_asd_combined.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_asd_combined
|
||||
#+caption: Combined low frequency and high frequency noise measurements
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd_combined.png]]
|
||||
|
||||
** Noise Model
|
||||
<<sec:vionic_noise_model>>
|
||||
|
||||
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);
|
||||
Gn_e = 1.8e-11/(1 + s/2/pi/1e4);
|
||||
#+end_src
|
||||
|
||||
The amplitude of the transfer function and the measured ASD are shown in Figure [[fig:vionic_noise_asd_model]].
|
||||
@@ -234,13 +472,18 @@ The amplitude of the transfer function and the measured ASD are shown in Figure
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(pxx));
|
||||
plot(f, abs(squeeze(freqresp(Gn_e, f, 'Hz'))), 'k--');
|
||||
plot(f, sqrt(enc{1}.pxx), 'color', [0, 0, 0, 0.5], 'DisplayName', '$\Gamma_n(\omega)$');
|
||||
for i=2:7
|
||||
plot(f, sqrt(enc{i}.pxx), 'color', [0, 0, 0, 0.5], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(f, abs(squeeze(freqresp(Gn_e, f, 'Hz'))), 'r-', 'DisplayName', '$|G_n(j\omega)|$');
|
||||
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]);
|
||||
xlim([10, Fs/2]);
|
||||
ylim([1e-11, 1e-10]);
|
||||
legend('location', 'northeast');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
@@ -248,9 +491,47 @@ 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
|
||||
#+caption: Measured ASD of the noise and modeled one
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd_model.png]]
|
||||
|
||||
The cumulative amplitude spectrum is now computed and shown in Figure [[fig:vionic_noise_cas_model]].
|
||||
|
||||
We can see that the Root Mean Square value of the measurement noise is $\approx 1.6 \, nm$ as advertise in the datasheet.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
for i = 1:7
|
||||
enc{i}.CPS = flip(-cumtrapz(flip(f), flip(enc{i}.pxx)));
|
||||
end
|
||||
|
||||
CAS_Gn = flip(-cumtrapz(flip(f), flip(abs(squeeze(freqresp(Gn_e, f, 'Hz'))).^2)));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(enc{1}.CPS), 'color', [0, 0, 0, 0.5], 'DisplayName', '$CAS_n(\omega)$');
|
||||
for i=2:7
|
||||
plot(f, sqrt(enc{i}.CPS), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off');
|
||||
end
|
||||
plot(f, sqrt(CAS_Gn), 'r-', 'DisplayName', 'model');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('CPS [$m$]');
|
||||
xlim([10, Fs/2]);
|
||||
ylim([1e-10, 1e-8]);
|
||||
legend('location', 'northeast');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/vionic_noise_cas_model.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:vionic_noise_cas_model
|
||||
#+caption: Meassured CAS of the noise and modeled one
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_cas_model.png]]
|
||||
|
||||
* Linearity Measurement
|
||||
<<sec:linearity_measurement>>
|
||||
** Test Bench
|
||||
@@ -289,26 +570,3 @@ addpath('./mat/');
|
||||
|
||||
** Results
|
||||
|
||||
* Dynamical Measurement
|
||||
<<sec:dynamical_measurement>>
|
||||
** Test Bench
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('./matlab/mat/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
** Results
|
||||
|
||||
Binary file not shown.
Reference in New Issue
Block a user