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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2021-02-11 jeu. 15:21 --> <!-- 2021-02-12 ven. 18:26 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Encoder Renishaw Vionic - Test Bench</title> <title>Encoder Renishaw Vionic - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -39,21 +39,21 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgacaf822">1. Expected Performances</a></li> <li><a href="#orgfa3d11e">1. Expected Performances</a></li>
<li><a href="#orgd1b48b9">2. Encoder Model</a></li> <li><a href="#orgf23b21b">2. Encoder Model</a></li>
<li><a href="#org9947f0d">3. Noise Measurement</a> <li><a href="#org9c17913">3. Noise Measurement</a>
<ul> <ul>
<li><a href="#org7dd6ce0">3.1. Test Bench</a></li> <li><a href="#orgb9429ef">3.1. Test Bench</a></li>
<li><a href="#orgd61ad80">3.2. Thermal drifts</a></li> <li><a href="#orgd9c9c77">3.2. Thermal drifts</a></li>
<li><a href="#org8f23c76">3.3. Time Domain signals</a></li> <li><a href="#org8ec1ba2">3.3. Time Domain signals</a></li>
<li><a href="#orgbd6cefe">3.4. Noise Spectral Density</a></li> <li><a href="#org833451c">3.4. Noise Spectral Density</a></li>
<li><a href="#orgc14197f">3.5. Noise Model</a></li> <li><a href="#org71a7d07">3.5. Noise Model</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgbc58807">4. Linearity Measurement</a> <li><a href="#org61522ff">4. Linearity Measurement</a>
<ul> <ul>
<li><a href="#org38d4317">4.1. Test Bench</a></li> <li><a href="#orge455e25">4.1. Test Bench</a></li>
<li><a href="#org9a6927b">4.2. Results</a></li> <li><a href="#orgc6e5044">4.2. Results</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -63,7 +63,7 @@
<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p> <p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
<hr> <hr>
<div class="note" id="org34d0504"> <div class="note" id="orge01a92a">
<p> <p>
You can find below the documentation of: You can find below the documentation of:
</p> </p>
@ -88,25 +88,25 @@ In particular, we would like to measure:
This document is structured as follow: This document is structured as follow:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Section <a href="#orgafe2cb7">1</a>: the expected performance of the Vionic encoder system are described</li> <li>Section <a href="#org5ddac7d">1</a>: the expected performance of the Vionic encoder system are described</li>
<li>Section <a href="#org1d1f36e">2</a>: a simple model of the encoder is developed</li> <li>Section <a href="#org55cdc69">2</a>: a simple model of the encoder is developed</li>
<li>Section <a href="#orgf70a154">3</a>: the noise of the encoder is measured and a model of the noise is identified</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="#org3767bd5">4</a>: the linearity of the sensor is estimated</li> <li>Section <a href="#org49975c3">4</a>: the linearity of the sensor is estimated</li>
</ul> </ul>
<div id="outline-container-orgacaf822" class="outline-2"> <div id="outline-container-orgfa3d11e" class="outline-2">
<h2 id="orgacaf822"><span class="section-number-2">1</span> Expected Performances</h2> <h2 id="orgfa3d11e"><span class="section-number-2">1</span> Expected Performances</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="orgafe2cb7"></a> <a id="org5ddac7d"></a>
</p> </p>
<p> <p>
The Vionic encoder is shown in Figure <a href="#org300cb52">1</a>. The Vionic encoder is shown in Figure <a href="#orga0ecb6c">1</a>.
</p> </p>
<div id="org300cb52" class="figure"> <div id="orga0ecb6c" class="figure">
<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" /> <p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p> <p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
@ -134,21 +134,21 @@ Interpolation is within the readhead, with fine resolution versions being furthe
</blockquote> </blockquote>
<p> <p>
The expected interpolation errors (non-linearity) is shown in Figure <a href="#org74b94f4">2</a>. The expected interpolation errors (non-linearity) is shown in Figure <a href="#orgc38e53f">2</a>.
</p> </p>
<div id="org74b94f4" class="figure"> <div id="orgc38e53f" class="figure">
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" /> <p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Expected interpolation errors for the Vionic Encoder</p> <p><span class="figure-number">Figure 2: </span>Expected interpolation errors for the Vionic Encoder</p>
</div> </div>
<p> <p>
The characteristics as advertise in the manual as well as our specifications are shown in Table <a href="#org12ad600">1</a>. The characteristics as advertise in the manual as well as our specifications are shown in Table <a href="#org091f419">1</a>.
</p> </p>
<table id="org12ad600" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <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> <caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic compared with the specifications</caption>
<colgroup> <colgroup>
@ -200,11 +200,11 @@ The characteristics as advertise in the manual as well as our specifications are
</div> </div>
</div> </div>
<div id="outline-container-orgd1b48b9" class="outline-2"> <div id="outline-container-orgf23b21b" class="outline-2">
<h2 id="orgd1b48b9"><span class="section-number-2">2</span> Encoder Model</h2> <h2 id="orgf23b21b"><span class="section-number-2">2</span> Encoder Model</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org1d1f36e"></a> <a id="org55cdc69"></a>
</p> </p>
<p> <p>
@ -217,65 +217,84 @@ It is also characterized by its measurement noise \(n\) that can be described by
</p> </p>
<p> <p>
The model of the encoder is shown in Figure <a href="#orge3dfe4a">3</a>. The model of the encoder is shown in Figure <a href="#org4fdb73a">3</a>.
</p> </p>
<div id="orge3dfe4a" class="figure"> <div id="org4fdb73a" class="figure">
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" /> <p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Model of the Encoder</p> <p><span class="figure-number">Figure 3: </span>Model of the Encoder</p>
</div> </div>
<p> <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="#org74b94f4">2</a>. 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> </p>
<div id="orgb259ef8" class="figure"> <div id="org793433f" class="figure">
<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" /> <p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
</p> </p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org9947f0d" class="outline-2"> <div id="outline-container-org9c17913" class="outline-2">
<h2 id="org9947f0d"><span class="section-number-2">3</span> Noise Measurement</h2> <h2 id="org9c17913"><span class="section-number-2">3</span> Noise Measurement</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="orgf70a154"></a> <a id="orgb828c8d"></a>
</p> </p>
<p> <p>
This part is structured as follow: This part is structured as follow:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Section <a href="#org1bbddb3">3.1</a>: the measurement bench is described</li> <li>Section <a href="#org8cfb922">3.1</a>: the measurement bench is described</li>
<li>Section <a href="#orge37ddeb">3.2</a>: long measurement is performed to estimate the low frequency drifts in the measurement</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="#orgbe1c0e1">3.3</a>: high frequency measurements are performed to estimate the high frequency noise</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="#orgfafa9fd">3.4</a>: the Spectral density of the measurement noise is estimated</li> <li>Section <a href="#orgd464562">3.4</a>: the Spectral density of the measurement noise is estimated</li>
<li>Section <a href="#org2284feb">3.5</a>: finally, the measured noise is modeled</li> <li>Section <a href="#orgd6ec52a">3.5</a>: finally, the measured noise is modeled</li>
</ul> </ul>
</div> </div>
<div id="outline-container-org7dd6ce0" class="outline-3"> <div id="outline-container-orgb9429ef" class="outline-3">
<h3 id="org7dd6ce0"><span class="section-number-3">3.1</span> Test Bench</h3> <h3 id="orgb9429ef"><span class="section-number-3">3.1</span> Test Bench</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
<a id="org1bbddb3"></a> <a id="org8cfb922"></a>
</p> </p>
<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. 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 \(n\). Then, the measured signal \(y_m\) corresponds to the noise \(n\).
</p> </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 &ldquo;plastic bubble sheet&rdquo; 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> </div>
<div id="outline-container-orgd61ad80" class="outline-3"> <div id="outline-container-orgd9c9c77" class="outline-3">
<h3 id="orgd61ad80"><span class="section-number-3">3.2</span> Thermal drifts</h3> <h3 id="orgd9c9c77"><span class="section-number-3">3.2</span> Thermal drifts</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
<a id="orge37ddeb"></a> <a id="orgfd5ce06"></a>
Measured displacement were recording during approximately 40 hours with a sample frequency of 100Hz. 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 A first order low pass filter with a corner frequency of 1Hz
</p> </p>
@ -286,13 +305,13 @@ A first order low pass filter with a corner frequency of 1Hz
</div> </div>
<p> <p>
The measured time domain data are shown in Figure <a href="#org55bfe2a">5</a>. The measured time domain data are shown in Figure <a href="#org1454db4">7</a>.
</p> </p>
<div id="org55bfe2a" class="figure"> <div id="org1454db4" class="figure">
<p><img src="figs/vionic_drifts_time.png" alt="vionic_drifts_time.png" /> <p><img src="figs/vionic_drifts_time.png" alt="vionic_drifts_time.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Measured thermal drifts</p> <p><span class="figure-number">Figure 7: </span>Measured thermal drifts</p>
</div> </div>
<p> <p>
@ -306,33 +325,33 @@ The mean drift is approximately 60.9 [nm/hour] or 1.0 [nm/min]
<p> <p>
Comparison between the data and the linear fit is shown in Figure <a href="#org1085735">6</a>. Comparison between the data and the linear fit is shown in Figure <a href="#orgfbe5f53">8</a>.
</p> </p>
<div id="org1085735" class="figure"> <div id="orgfbe5f53" class="figure">
<p><img src="figs/vionic_drifts_linear_fit.png" alt="vionic_drifts_linear_fit.png" /> <p><img src="figs/vionic_drifts_linear_fit.png" alt="vionic_drifts_linear_fit.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Measured drift and linear fit</p> <p><span class="figure-number">Figure 8: </span>Measured drift and linear fit</p>
</div> </div>
<p> <p>
Let&rsquo;s now estimate the Power Spectral Density of the measured displacement. Let&rsquo;s now estimate the Power Spectral Density of the measured displacement.
The obtained low frequency ASD is shown in Figure <a href="#orgf2675d7">7</a>. The obtained low frequency ASD is shown in Figure <a href="#org42f3fad">9</a>.
</p> </p>
<div id="orgf2675d7" class="figure"> <div id="org42f3fad" class="figure">
<p><img src="figs/vionic_noise_asd_low_freq.png" alt="vionic_noise_asd_low_freq.png" /> <p><img src="figs/vionic_noise_asd_low_freq.png" alt="vionic_noise_asd_low_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral density of the measured displacement</p> <p><span class="figure-number">Figure 9: </span>Amplitude Spectral density of the measured displacement</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org8f23c76" class="outline-3"> <div id="outline-container-org8ec1ba2" class="outline-3">
<h3 id="org8f23c76"><span class="section-number-3">3.3</span> Time Domain signals</h3> <h3 id="org8ec1ba2"><span class="section-number-3">3.3</span> Time Domain signals</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
<a id="orgbe1c0e1"></a> <a id="org4df45c5"></a>
</p> </p>
<p> <p>
@ -340,67 +359,67 @@ Then, and for all the 7 encoders, we record the measured motion during 100s with
</p> </p>
<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="#orgbd876dc">8</a>. 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> </p>
<div id="orgbd876dc" class="figure"> <div id="org28ad5da" class="figure">
<p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" /> <p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</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> </div>
<p> <p>
The time domain data for all the encoders are compared in Figure <a href="#org63a82cb">9</a>. The time domain data for all the encoders are compared in Figure <a href="#org1656541">11</a>.
</p> </p>
<p> <p>
We can see some drifts that are in the order of few nm to 20nm per minute. We can see some drifts that are in the order of few nm to 20nm per minute.
As shown in Section <a href="#orge37ddeb">3.2</a>, these drifts should diminish over time down to 1nm/min. As shown in Section <a href="#orgfd5ce06">3.2</a>, these drifts should diminish over time down to 1nm/min.
</p> </p>
<div id="org63a82cb" class="figure"> <div id="org1656541" class="figure">
<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" /> <p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Comparison of the time domain measurement</p> <p><span class="figure-number">Figure 11: </span>Comparison of the time domain measurement</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgbd6cefe" class="outline-3"> <div id="outline-container-org833451c" class="outline-3">
<h3 id="orgbd6cefe"><span class="section-number-3">3.4</span> Noise Spectral Density</h3> <h3 id="org833451c"><span class="section-number-3">3.4</span> Noise Spectral Density</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<p> <p>
<a id="orgfafa9fd"></a> <a id="orgd464562"></a>
</p> </p>
<p> <p>
The amplitude spectral densities for all the encoder are computed and shown in Figure <a href="#org4b13cc6">10</a>. The amplitude spectral densities for all the encoder are computed and shown in Figure <a href="#org7e93bb1">12</a>.
</p> </p>
<div id="org4b13cc6" class="figure"> <div id="org7e93bb1" class="figure">
<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" /> <p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </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> </div>
<p> <p>
We can combine these measurements with the low frequency noise computed in Section <a href="#orge37ddeb">3.2</a>. 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="#orgec960f3">11</a>. The obtained ASD is shown in Figure <a href="#org7e54160">13</a>.
</p> </p>
<div id="orgec960f3" class="figure"> <div id="org7e54160" class="figure">
<p><img src="figs/vionic_noise_asd_combined.png" alt="vionic_noise_asd_combined.png" /> <p><img src="figs/vionic_noise_asd_combined.png" alt="vionic_noise_asd_combined.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Combined low frequency and high frequency noise measurements</p> <p><span class="figure-number">Figure 13: </span>Combined low frequency and high frequency noise measurements</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgc14197f" class="outline-3"> <div id="outline-container-org71a7d07" class="outline-3">
<h3 id="orgc14197f"><span class="section-number-3">3.5</span> Noise Model</h3> <h3 id="org71a7d07"><span class="section-number-3">3.5</span> Noise Model</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<p> <p>
<a id="org2284feb"></a> <a id="orgd6ec52a"></a>
</p> </p>
<p> <p>
@ -412,18 +431,18 @@ Let&rsquo;s create a transfer function that approximate the measured noise of th
</div> </div>
<p> <p>
The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org904aecb">12</a>. The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org5d39757">14</a>.
</p> </p>
<div id="org904aecb" class="figure"> <div id="org5d39757" class="figure">
<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" /> <p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Measured ASD of the noise and modeled one</p> <p><span class="figure-number">Figure 14: </span>Measured ASD of the noise and modeled one</p>
</div> </div>
<p> <p>
The cumulative amplitude spectrum is now computed and shown in Figure <a href="#orgff7d2cd">13</a>. The cumulative amplitude spectrum is now computed and shown in Figure <a href="#org05b258c">15</a>.
</p> </p>
<p> <p>
@ -431,24 +450,24 @@ We can see that the Root Mean Square value of the measurement noise is \(\approx
</p> </p>
<div id="orgff7d2cd" class="figure"> <div id="org05b258c" class="figure">
<p><img src="figs/vionic_noise_cas_model.png" alt="vionic_noise_cas_model.png" /> <p><img src="figs/vionic_noise_cas_model.png" alt="vionic_noise_cas_model.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Meassured CAS of the noise and modeled one</p> <p><span class="figure-number">Figure 15: </span>Meassured CAS of the noise and modeled one</p>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgbc58807" class="outline-2"> <div id="outline-container-org61522ff" class="outline-2">
<h2 id="orgbc58807"><span class="section-number-2">4</span> Linearity Measurement</h2> <h2 id="org61522ff"><span class="section-number-2">4</span> Linearity Measurement</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<p> <p>
<a id="org3767bd5"></a> <a id="org49975c3"></a>
</p> </p>
</div> </div>
<div id="outline-container-org38d4317" class="outline-3"> <div id="outline-container-orge455e25" class="outline-3">
<h3 id="org38d4317"><span class="section-number-3">4.1</span> Test Bench</h3> <h3 id="orge455e25"><span class="section-number-3">4.1</span> Test Bench</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p> <p>
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity. In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
@ -457,7 +476,7 @@ An actuator should also be there so impose a displacement.
</p> </p>
<p> <p>
One idea is to use the test-bench shown in Figure <a href="#org5a7f983">14</a>. One idea is to use the test-bench shown in Figure <a href="#org177aa2c">16</a>.
</p> </p>
<p> <p>
@ -470,22 +489,22 @@ As the interferometer has a very large bandwidth, we should be able to estimate
</p> </p>
<div id="org5a7f983" class="figure"> <div id="org177aa2c" class="figure">
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" /> <p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </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>
</div> </div>
<div id="outline-container-org9a6927b" class="outline-3"> <div id="outline-container-orgc6e5044" class="outline-3">
<h3 id="org9a6927b"><span class="section-number-3">4.2</span> Results</h3> <h3 id="orgc6e5044"><span class="section-number-3">4.2</span> Results</h3>
</div> </div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-02-11 jeu. 15:21</p> <p class="date">Created: 2021-02-12 ven. 18:26</p>
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@ -185,6 +185,19 @@ This part is structured as follow:
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. 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 $n$. 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: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>

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