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Thomas Dehaeze
2020-11-10 12:53:45 +01:00
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-11-10 mar. 11:16 -->
<!-- 2020-11-10 mar. 12:53 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Encoder - Test Bench</title>
<meta name="generator" content="Org mode" />
@@ -26,19 +26,19 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgaf79dd3">1. Experimental Setup</a></li>
<li><a href="#org7a3b4de">2. Noise Spectral Density of the Encoder</a>
<li><a href="#org5ac16f2">1. Experimental Setup</a></li>
<li><a href="#org7441659">2. Noise Spectral Density of the Encoder</a>
<ul>
<li><a href="#orgfbf4ee1">2.1. Load Data</a></li>
<li><a href="#org6c853de">2.2. Time Domain Results</a></li>
<li><a href="#orgd135f83">2.3. Frequency Domain Noise</a></li>
<li><a href="#orgfface02">2.1. Load Data</a></li>
<li><a href="#orgeab98b2">2.2. Time Domain Results</a></li>
<li><a href="#org9d7a1b2">2.3. Frequency Domain Noise</a></li>
</ul>
</li>
<li><a href="#org1e07ca4">3. Dynamics from Actuator to Encoder</a>
<li><a href="#orga15f5e0">3. Dynamics from Actuator to Encoder</a>
<ul>
<li><a href="#orga05d6d1">3.1. Load Data</a></li>
<li><a href="#orga8a55da">3.2. Excitation and Measured Signals</a></li>
<li><a href="#org4873d25">3.3. Identification</a></li>
<li><a href="#org371d2a2">3.1. Load Data</a></li>
<li><a href="#orgb2df3c8">3.2. Excitation and Measured Signals</a></li>
<li><a href="#orgfb97858">3.3. Identification</a></li>
</ul>
</li>
</ul>
@@ -53,23 +53,23 @@ In this document, we wish to study the use of an encoder in parallel with an Amp
The document is divided into the following Sections:
</p>
<ul class="org-ul">
<li>Section <a href="#org05b69c6">1</a>: the test-bench used is described</li>
<li>Section <a href="#org0031eaa">2</a>: the noise spectral density of the encoder is estimated</li>
<li>Section <a href="#org8178907">3</a>: the dynamics from the amplified piezoelectric actuator to the encoder measured displacement is identified</li>
<li>Section <a href="#org973b24d">1</a>: the test-bench used is described</li>
<li>Section <a href="#org7331cce">2</a>: the noise spectral density of the encoder is estimated</li>
<li>Section <a href="#org9fb1af3">3</a>: the dynamics from the amplified piezoelectric actuator to the encoder measured displacement is identified</li>
</ul>
<div id="outline-container-orgaf79dd3" class="outline-2">
<h2 id="orgaf79dd3"><span class="section-number-2">1</span> Experimental Setup</h2>
<div id="outline-container-org5ac16f2" class="outline-2">
<h2 id="org5ac16f2"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org05b69c6"></a>
<a id="org973b24d"></a>
</p>
<p>
The experimental Setup is schematically represented in Figure <a href="#org54243a1">1</a>.
The experimental Setup is schematically represented in Figure <a href="#org2529a80">1</a>.
</p>
<div class="note" id="orgba61b71">
<div class="note" id="org3cc7332">
<p>
Here are the equipment used in the test bench:
</p>
@@ -89,21 +89,21 @@ The displacement of the mass (relative to the mechanical frame) is measured both
</p>
<div id="org54243a1" class="figure">
<div id="org2529a80" class="figure">
<p><img src="figs/exp_setup_schematic.png" alt="exp_setup_schematic.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Schematic of the Experiment</p>
</div>
<div id="orgc63322f" class="figure">
<div id="orgdf4e259" class="figure">
<p><img src="figs/IMG_20201023_153905.jpg" alt="IMG_20201023_153905.jpg" />
</p>
<p><span class="figure-number">Figure 2: </span>Side View of the encoder</p>
</div>
<div id="org795dc71" class="figure">
<div id="orga98f1bf" class="figure">
<p><img src="figs/IMG_20201023_153914.jpg" alt="IMG_20201023_153914.jpg" />
</p>
<p><span class="figure-number">Figure 3: </span>Front View of the encoder</p>
@@ -111,11 +111,11 @@ The displacement of the mass (relative to the mechanical frame) is measured both
</div>
</div>
<div id="outline-container-org7a3b4de" class="outline-2">
<h2 id="org7a3b4de"><span class="section-number-2">2</span> Noise Spectral Density of the Encoder</h2>
<div id="outline-container-org7441659" class="outline-2">
<h2 id="org7441659"><span class="section-number-2">2</span> Noise Spectral Density of the Encoder</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org0031eaa"></a>
<a id="org7331cce"></a>
</p>
<p>
The goal in this section is the estimate the noise of both the encoder and the intereferometer.
@@ -127,15 +127,15 @@ Ideally, a mechanical part would clamp the two together, we here suppose that th
</p>
</div>
<div id="outline-container-orgfbf4ee1" class="outline-3">
<h3 id="orgfbf4ee1"><span class="section-number-3">2.1</span> Load Data</h3>
<div id="outline-container-orgfface02" class="outline-3">
<h3 id="orgfface02"><span class="section-number-3">2.1</span> Load Data</h3>
<div class="outline-text-3" id="text-2-1">
<p>
The measurement data are loaded and the offset are removed using the <code>detrend</code> command.
</p>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_huddle_test.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'t'</span>);
<pre class="src src-matlab">load(<span class="org-string">'int_enc_huddle_test.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'t'</span>);
</pre>
</div>
@@ -147,22 +147,22 @@ encoder = detrend(encoder, 0);
</div>
</div>
<div id="outline-container-org6c853de" class="outline-3">
<h3 id="org6c853de"><span class="section-number-3">2.2</span> Time Domain Results</h3>
<div id="outline-container-orgeab98b2" class="outline-3">
<h3 id="orgeab98b2"><span class="section-number-3">2.2</span> Time Domain Results</h3>
<div class="outline-text-3" id="text-2-2">
<p>
The measurement of both the encoder and interferometer are shown in Figure <a href="#org332769b">4</a>.
The measurement of both the encoder and interferometer are shown in Figure <a href="#orgc0bfd00">4</a>.
</p>
<div id="org332769b" class="figure">
<div id="orgc0bfd00" class="figure">
<p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Huddle test - Time domain signals</p>
</div>
<p>
The raw signals are filtered with a Low Pass filter (defined below) such that we can see the low frequency motion (Figure <a href="#orgc5b97b7">5</a>).
The raw signals are filtered with a Low Pass filter (defined below) such that we can see the low frequency motion (Figure <a href="#org2bb066f">5</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">G_lpf = 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>10);
@@ -170,7 +170,7 @@ The raw signals are filtered with a Low Pass filter (defined below) such that we
</div>
<div id="orgc5b97b7" class="figure">
<div id="org2bb066f" class="figure">
<p><img src="figs/huddle_test_time_domain_filtered.png" alt="huddle_test_time_domain_filtered.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Huddle test - Time domain signals filtered with a LPF at 10Hz</p>
@@ -178,8 +178,8 @@ The raw signals are filtered with a Low Pass filter (defined below) such that we
</div>
</div>
<div id="outline-container-orgd135f83" class="outline-3">
<h3 id="orgd135f83"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
<div id="outline-container-org9d7a1b2" class="outline-3">
<h3 id="org9d7a1b2"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
<div class="outline-text-3" id="text-2-3">
<p>
The noise of the measurement (supposing there is no motion) is now translated in the frequency domain by computed the Amplitude Spectral Density.
@@ -195,7 +195,7 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div>
<p>
The comparison of the ASD of the encoder and interferometer are shown in Figure <a href="#orgd76ad0f">6</a>.
The comparison of the ASD of the encoder and interferometer are shown in Figure <a href="#org7272303">6</a>.
</p>
<p>
@@ -203,7 +203,7 @@ It is clear that although the encoder exhibit higher frequency noise, is it more
</p>
<div id="orgd76ad0f" class="figure">
<div id="org7272303" class="figure">
<p><img src="figs/huddle_test_asd.png" alt="huddle_test_asd.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signals during the Huddle test</p>
@@ -212,25 +212,25 @@ It is clear that although the encoder exhibit higher frequency noise, is it more
</div>
</div>
<div id="outline-container-org1e07ca4" class="outline-2">
<h2 id="org1e07ca4"><span class="section-number-2">3</span> Dynamics from Actuator to Encoder</h2>
<div id="outline-container-orga15f5e0" class="outline-2">
<h2 id="orga15f5e0"><span class="section-number-2">3</span> Dynamics from Actuator to Encoder</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org8178907"></a>
<a id="org9fb1af3"></a>
</p>
<p>
Now the dynamics from the force actuator to the measurement by the encoder is identified.
</p>
</div>
<div id="outline-container-orga05d6d1" class="outline-3">
<h3 id="orga05d6d1"><span class="section-number-3">3.1</span> Load Data</h3>
<div id="outline-container-org371d2a2" class="outline-3">
<h3 id="org371d2a2"><span class="section-number-3">3.1</span> Load Data</h3>
<div class="outline-text-3" id="text-3-1">
<p>
As usual, the measurement data are loaded.
</p>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_id_noise_bis.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>);
<pre class="src src-matlab">load(<span class="org-string">'int_enc_id_noise_bis.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>);
</pre>
</div>
@@ -257,18 +257,18 @@ u = detrend(u, 0);
</div>
</div>
<div id="outline-container-orga8a55da" class="outline-3">
<h3 id="orga8a55da"><span class="section-number-3">3.2</span> Excitation and Measured Signals</h3>
<div id="outline-container-orgb2df3c8" class="outline-3">
<h3 id="orgb2df3c8"><span class="section-number-3">3.2</span> Excitation and Measured Signals</h3>
<div class="outline-text-3" id="text-3-2">
<p>
The excitation signal is a white noise filtered by a low pass filter to not excite too much the high frequency modes.
</p>
<p>
The excitation signal is shown in Figure <a href="#org8db32e3">7</a>.
The excitation signal is shown in Figure <a href="#org0fde08c">7</a>.
</p>
<div id="org8db32e3" class="figure">
<div id="org0fde08c" class="figure">
<p><img src="figs/encoder_identification_excitation_time.png" alt="encoder_identification_excitation_time.png" />
</p>
</div>
@@ -277,15 +277,15 @@ The excitation signal is shown in Figure <a href="#org8db32e3">7</a>.
The measured motion by the interferometer and encoder is shown in Figure
</p>
<div id="org10991a6" class="figure">
<div id="orgefc6685" class="figure">
<p><img src="figs/encoder_identification_motion.png" alt="encoder_identification_motion.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-org4873d25" class="outline-3">
<h3 id="org4873d25"><span class="section-number-3">3.3</span> Identification</h3>
<div id="outline-container-orgfb97858" class="outline-3">
<h3 id="orgfb97858"><span class="section-number-3">3.3</span> Identification</h3>
<div class="outline-text-3" id="text-3-3">
<p>
Now the dynamics from the voltage sent to the voltage amplitude driving the APA95ML to the measured displacement by both the encoder and interferometer are computed.
@@ -304,22 +304,22 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div>
<p>
The obtained coherence is shown in Figure <a href="#org0b95482">9</a>.
The obtained coherence is shown in Figure <a href="#org1795d67">9</a>.
It is shown that the identification is good until 500Hz for the interferometer and until 1kHz for the encoder.
</p>
<div id="org0b95482" class="figure">
<div id="org1795d67" class="figure">
<p><img src="figs/identification_dynamics_coherence.png" alt="identification_dynamics_coherence.png" />
</p>
</div>
<p>
The compared dynamics as measured by the intereferometer and encoder are shown in Figure <a href="#orgb017bd4">10</a>.
The compared dynamics as measured by the intereferometer and encoder are shown in Figure <a href="#org4ea418f">10</a>.
</p>
<div id="orgb017bd4" class="figure">
<div id="org4ea418f" class="figure">
<p><img src="figs/identification_dynamics_bode.png" alt="identification_dynamics_bode.png" />
</p>
</div>
@@ -334,7 +334,7 @@ The second resonance at around 900Hz most likely corresponds to the resonance of
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-10 mar. 11:16</p>
<p class="date">Created: 2020-11-10 mar. 12:53</p>
</div>
</body>
</html>