tdehaeze/nass-micro-station-measurements
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update analysis on control systems

Browse Source
This commit is contained in:
Thomas Dehaeze 2019-05-17 10:42:55 +02:00
parent 48e3b909d0
commit 34de51c0cf
8 changed files with 225 additions and 333 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

BIN
disturbance-control-system/figs/psd_marble_comp.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 180 KiB

After

Width:  |  Height:  |  Size: 186 KiB

BIN
disturbance-control-system/figs/psd_marble_comp_high_freq.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 230 KiB

After

Width:  |  Height:  |  Size: 229 KiB

BIN
disturbance-control-system/figs/psd_sample_comp.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 183 KiB

After

Width:  |  Height:  |  Size: 189 KiB

BIN
disturbance-control-system/figs/psd_sample_comp_high_freq.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 217 KiB

After

Width:  |  Height:  |  Size: 223 KiB

BIN
disturbance-control-system/figs/time_domain_marble.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 111 KiB

After

Width:  |  Height:  |  Size: 100 KiB

BIN
disturbance-control-system/figs/time_domain_sample.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 122 KiB

After

Width:  |  Height:  |  Size: 112 KiB

402
disturbance-control-system/index.html
View File

@ -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>
<!-- 2019-05-15 mer. 17:24 -->
<!-- 2019-05-17 ven. 10:40 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Effect on the control system of each stages on the vibration of the station</title>
@ -258,67 +258,78 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgbbaaa98">1. Effect of all the control systems on the Sample vibrations</a>
<li><a href="#orga4a36da">1. Effect of all the control systems on the Sample vibrations</a>
<ul>
<li><a href="#org06b693f">1.1. Experimental Setup</a></li>
<li><a href="#orgd47a227">1.2. Load data</a></li>
<li><a href="#orgef1cef2">1.3. Analysis - Time Domain</a></li>
<li><a href="#orgab71525">1.4. Analysis - Frequency Domain</a>
<li><a href="#org112de2c">1.1. Experimental Setup</a></li>
<li><a href="#org544eed6">1.2. Load data</a></li>
<li><a href="#org0e43e73">1.3. Analysis - Time Domain</a></li>
<li><a href="#org608c1ca">1.4. Analysis - Frequency Domain</a>
<ul>
<li><a href="#org93314dd">1.4.1. Vibrations at the sample location</a></li>
<li><a href="#org39db171">1.4.2. Vibrations on the marble</a></li>
<li><a href="#orgd88ef09">1.4.1. Vibrations at the sample location</a></li>
<li><a href="#orgac51e85">1.4.2. Vibrations on the marble</a></li>
</ul>
</li>
<li><a href="#org8f07d2e">1.5. Effect of the control system on the transmissibility from ground to sample</a></li>
<li><a href="#org47a7f4c">1.6. Conclusion</a></li>
<li><a href="#org32639df">1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org96b6d66">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a>
<li><a href="#org1b7e339">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a>
<ul>
<li><a href="#org21aea52">2.1. Experimental Setup</a></li>
<li><a href="#orgf9fa5d1">2.2. Load data</a></li>
<li><a href="#orgb1aceca">2.3. Voltage to Velocity</a></li>
<li><a href="#org9deea89">2.4. Analysis - Time Domain</a></li>
<li><a href="#orga52ae70">2.5. Analysis - Frequency Domain</a>
<li><a href="#org2ce1110">2.1. Experimental Setup</a></li>
<li><a href="#orgd3b1acb">2.2. Load data</a></li>
<li><a href="#orgc93b66c">2.3. Voltage to Velocity</a></li>
<li><a href="#org484ddf0">2.4. Analysis - Time Domain</a></li>
<li><a href="#orgdc28818">2.5. Analysis - Frequency Domain</a>
<ul>
<li><a href="#orgc044b46">2.5.1. Vibrations at the sample location</a></li>
<li><a href="#orgff12b0a">2.5.2. Vibrations on the marble</a></li>
<li><a href="#org0b21a2a">2.5.1. Vibrations at the sample location</a></li>
<li><a href="#org99943a5">2.5.2. Vibrations on the marble</a></li>
</ul>
</li>
<li><a href="#orgf832269">2.6. Conclusion</a></li>
<li><a href="#orga2778aa">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org76bb785">3. Effect of the Symetrie Driver</a>
<li><a href="#orgf76ae8c">3. Effect of the Symetrie Driver</a>
<ul>
<li><a href="#org3e3d670">3.1. Experimental Setup</a></li>
<li><a href="#org2c5eb48">3.2. Load data</a></li>
<li><a href="#org7b92812">3.3. Analysis - Time Domain</a></li>
<li><a href="#orgd042971">3.4. Analysis - Frequency Domain</a>
<li><a href="#org11e22fa">3.1. Experimental Setup</a></li>
<li><a href="#org1837038">3.2. Load data</a></li>
<li><a href="#orge2bd074">3.3. Analysis - Time Domain</a></li>
<li><a href="#org1903625">3.4. Analysis - Frequency Domain</a>
<ul>
<li><a href="#orgdc25bb2">3.4.1. Vibrations at the sample location</a></li>
<li><a href="#orgb1f3c6c">3.4.1. Vibrations at the sample location</a></li>
</ul>
</li>
<li><a href="#org2a573c2">3.5. Conclusion</a></li>
<li><a href="#orgbb3e3c0">3.5. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<p>
For all the measurements shown here:
This file is organized as follow:
</p>
<ul class="org-ul">
<li>geophones used are L22 with a resonance frequency of 1Hz</li>
<li>the signals are amplified with voltage amplifiers with a gain of 60dB</li>
<li>the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz</li>
<li>Section <a href="#orgd3ccbfb">1</a>:
<ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one by one</li>
</ul></li>
<li>Section <a href="#orgf536384">2</a>:
<ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one at a time</li>
</ul></li>
<li>Section <a href="#orgbb23a6a">3</a>:
<ul class="org-ul">
<li>We check if the Symetrie driver induces some vibrations when placed on the marble</li>
</ul></li>
</ul>
<div id="outline-container-orgbbaaa98" class="outline-2">
<h2 id="orgbbaaa98"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2>
<div id="outline-container-orga4a36da" class="outline-2">
<h2 id="orga4a36da"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orgdddc824"></a>
<a id="orgd3ccbfb"></a>
</p>
<div class="note">
<p>
@ -328,17 +339,26 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_cont
</div>
</div>
<div id="outline-container-org06b693f" class="outline-3">
<h3 id="org06b693f"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div id="outline-container-org112de2c" class="outline-3">
<h3 id="org112de2c"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We here measure the signals of two geophones:
We here measure the signals of two L22 geophones:
</p>
<ul class="org-ul">
<li>One is located on top of the Sample platform</li>
<li>One is located on the marble</li>
</ul>
<p>
The signals are amplified with voltage amplifiers with the following settings:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
<li>AC/DC option set on AC</li>
<li>Low pass filter set at 1kHz</li>
</ul>
<p>
The signal from the top geophone does not go trought the slip-ring.
</p>
@ -348,7 +368,7 @@ First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s.
</p>
<table id="org3dc1795" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgfb3379b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup>
@ -468,8 +488,8 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div>
</div>
<div id="outline-container-orgd47a227" class="outline-3">
<h3 id="orgd47a227"><span class="section-number-3">1.2</span> Load data</h3>
<div id="outline-container-org544eed6" class="outline-3">
<h3 id="org544eed6"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We load the data of the z axis of two geophones.
@ -486,26 +506,26 @@ d8 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-s
</div>
</div>
<div id="outline-container-orgef1cef2" class="outline-3">
<h3 id="orgef1cef2"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div id="outline-container-org0e43e73" class="outline-3">
<h3 id="org0e43e73"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-1-3">
<p>
First, we can look at the time domain data and compare all the measurements:
</p>
<ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#orge122156">1</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org812d3e0">2</a>)</li>
<li>comparison for the geophone at the sample location (figure <a href="#org9d0687f">1</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org2241d7c">2</a>)</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry, Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -514,22 +534,21 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="orge122156" class="figure">
<div id="org9d0687f" class="figure">
<p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry, Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -538,7 +557,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org812d3e0" class="figure">
<div id="org2241d7c" class="figure">
<p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
@ -546,8 +565,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
<div id="outline-container-orgab71525" class="outline-3">
<h3 id="orgab71525"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div id="outline-container-org608c1ca" class="outline-3">
<h3 id="org608c1ca"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-matlab">dt = d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -558,8 +577,8 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div>
</div>
<div id="outline-container-org93314dd" class="outline-4">
<h4 id="org93314dd"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
<div id="outline-container-orgd88ef09" class="outline-4">
<h4 id="orgd88ef09"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-1-4-1">
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -575,17 +594,18 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
</div>
<p>
And we compare all the signals (figures <a href="#org7432b3d">3</a> and <a href="#orgefd2377">4</a>).
And we compare all the signals (figures <a href="#org4e15d4a">3</a> and <a href="#org17050df">4</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry, Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>fgm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxxgm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-k', 'DisplayName', 'Ground Velocity'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -596,7 +616,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org7432b3d" class="figure">
<div id="org4e15d4a" class="figure">
<p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
@ -604,7 +624,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div id="orgefd2377" class="figure">
<div id="org17050df" class="figure">
<p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -612,8 +632,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
<div id="outline-container-org39db171" class="outline-4">
<h4 id="org39db171"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
<div id="outline-container-orgac51e85" class="outline-4">
<h4 id="orgac51e85"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-1-4-2">
<p>
Now we plot the same curves for the geophone located on the marble.
@ -629,17 +649,18 @@ Now we plot the same curves for the geophone located on the marble.
</div>
<p>
And we compare the Amplitude Spectral Densities (figures <a href="#orga0ae73f">5</a> and <a href="#orgcfb23f8">6</a>)
And we compare the Amplitude Spectral Densities (figures <a href="#org66e8748">5</a> and <a href="#orge872d6b">6</a>)
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry, Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR, Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz, SR'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa, Rz'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>fgm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxxgm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-k', 'DisplayName', 'Ground Velocity'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -650,7 +671,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="orga0ae73f" class="figure">
<div id="org66e8748" class="figure">
<p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
@ -658,7 +679,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div id="orgcfb23f8" class="figure">
<div id="orge872d6b" class="figure">
<p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -666,102 +687,25 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
</div>
<div id="outline-container-org8f07d2e" class="outline-3">
<h3 id="org8f07d2e"><span class="section-number-3">1.5</span> Effect of the control system on the transmissibility from ground to sample</h3>
<div id="outline-container-org32639df" class="outline-3">
<h3 id="org32639df"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<p>
As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure <a href="#orgd9f2aae">7</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T3, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T3<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T4<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T5<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T6<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T7<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T8<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgd9f2aae" class="figure">
<p><img src="figs/trans_comp.png" alt="trans_comp.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of the transfer function from the geophone on the marble to the geophone at the sample location</p>
</div>
</div>
</div>
<div id="outline-container-org47a7f4c" class="outline-3">
<h3 id="org47a7f4c"><span class="section-number-3">1.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-6">
<div class="important">
<ul class="org-ul">
<li>The control system of the Ty stage induces a lot of vibrations of the marble</li>
</ul>
</div>
<div class="note">
<ul class="org-ul">
<li>Why it seems that the measurement noise at high frequency is the limiting factor when the slip ring is ON but not when it is OFF?</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org96b6d66" class="outline-2">
<h2 id="org96b6d66"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2>
<div id="outline-container-org1b7e339" class="outline-2">
<h2 id="org1b7e339"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org0b65553"></a>
<a id="orgf536384"></a>
</p>
<div class="note">
<p>
@ -771,8 +715,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_cont
</div>
</div>
<div id="outline-container-org21aea52" class="outline-3">
<h3 id="org21aea52"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div id="outline-container-org2ce1110" class="outline-3">
<h3 id="org2ce1110"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We here measure the signals of two geophones:
@ -795,7 +739,7 @@ Each measurement are done during 100s.
</p>
<p>
The settings of the voltage amplifier are shown on figure <a href="#orga2e0c1e">8</a>:
The settings of the voltage amplifier are shown on figure <a href="#orgdaac4d3">7</a>:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
@ -807,7 +751,7 @@ The settings of the voltage amplifier are shown on figure <a href="#orga2e0c1e">
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
</p>
<table id="org879a5e4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org400e399" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup>
@ -926,16 +870,16 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</table>
<div id="orga2e0c1e" class="figure">
<div id="orgdaac4d3" class="figure">
<p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 8: </span>Voltage amplifier settings for the measurement</p>
<p><span class="figure-number">Figure 7: </span>Voltage amplifier settings for the measurement</p>
</div>
</div>
</div>
<div id="outline-container-orgf9fa5d1" class="outline-3">
<h3 id="orgf9fa5d1"><span class="section-number-3">2.2</span> Load data</h3>
<div id="outline-container-orgd3b1acb" class="outline-3">
<h3 id="orgd3b1acb"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We load the data of the z axis of two geophones.
@ -952,8 +896,8 @@ d_he = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org
</div>
</div>
<div id="outline-container-orgb1aceca" class="outline-3">
<h3 id="orgb1aceca"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
<div id="outline-container-orgc93b66c" class="outline-3">
<h3 id="orgc93b66c"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/MEGA/These/meas/src/index.html">here</a>).
@ -980,16 +924,16 @@ d_he<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">
</div>
</div>
<div id="outline-container-org9deea89" class="outline-3">
<h3 id="org9deea89"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
<div id="outline-container-org484ddf0" class="outline-3">
<h3 id="org484ddf0"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
First, we can look at the time domain data and compare all the measurements:
</p>
<ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#org0c06ee9">9</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org45a64e1">10</a>)</li>
<li>relative displacement of the sample with respect to the marble (figure <a href="#org45a64e1">10</a>)</li>
<li>comparison for the geophone at the sample location (figure <a href="#org1e830e0">8</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org60ee9ec">9</a>)</li>
<li>relative displacement of the sample with respect to the marble (figure <a href="#org60ee9ec">9</a>)</li>
</ul>
<div class="org-src-container">
@ -1009,10 +953,10 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org0c06ee9" class="figure">
<div id="org1e830e0" class="figure">
<p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
<p><span class="figure-number">Figure 8: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div>
@ -1033,10 +977,10 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org45a64e1" class="figure">
<div id="org60ee9ec" class="figure">
<p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
<p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
</div>
<div class="org-src-container">
@ -1056,16 +1000,16 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="orgbad8646" class="figure">
<div id="org3220e1a" class="figure">
<p><img src="figs/time_domain_relative_disp.png" alt="time_domain_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Relative displacement of the sample with respect to the marble</p>
<p><span class="figure-number">Figure 10: </span>Relative displacement of the sample with respect to the marble</p>
</div>
</div>
</div>
<div id="outline-container-orga52ae70" class="outline-3">
<h3 id="orga52ae70"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
<div id="outline-container-orgdc28818" class="outline-3">
<h3 id="orgdc28818"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-matlab">dt = d_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -1076,8 +1020,8 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div>
</div>
<div id="outline-container-orgc044b46" class="outline-4">
<h4 id="orgc044b46"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
<div id="outline-container-org0b21a2a" class="outline-4">
<h4 id="org0b21a2a"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-2-5-1">
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -1093,7 +1037,7 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
</div>
<p>
And we compare all the signals (figures <a href="#org87295b7">12</a> and <a href="#orgd42d7db">13</a>).
And we compare all the signals (figures <a href="#org41d7152">11</a> and <a href="#orgdc87af3">12</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
@ -1114,24 +1058,24 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org87295b7" class="figure">
<div id="org41d7152" class="figure">
<p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity</p>
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the sample velocity</p>
</div>
<div id="orgd42d7db" class="figure">
<div id="orgdc87af3" class="figure">
<p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p>
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p>
</div>
</div>
</div>
<div id="outline-container-orgff12b0a" class="outline-4">
<h4 id="orgff12b0a"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
<div id="outline-container-org99943a5" class="outline-4">
<h4 id="org99943a5"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-2-5-2">
<p>
Now we plot the same curves for the geophone located on the marble.
@ -1147,7 +1091,7 @@ Now we plot the same curves for the geophone located on the marble.
</div>
<p>
And we compare the Amplitude Spectral Densities (figures <a href="#org7f25560">14</a> and <a href="#orgc96b599">15</a>)
And we compare the Amplitude Spectral Densities (figures <a href="#orge453472">13</a> and <a href="#orgcaf65b1">14</a>)
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
@ -1168,25 +1112,25 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org7f25560" class="figure">
<div id="orge453472" class="figure">
<p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity</p>
<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the marble velocity</p>
</div>
<div id="orgc96b599" class="figure">
<div id="orgcaf65b1" class="figure">
<p><img src="figs/psd_marble_comp_lpf_high_freq.png" alt="psd_marble_comp_lpf_high_freq.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p>
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgf832269" class="outline-3">
<h3 id="orgf832269"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-orga2778aa" class="outline-3">
<h3 id="orga2778aa"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<ul class="org-ul">
@ -1199,11 +1143,11 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
<div id="outline-container-org76bb785" class="outline-2">
<h2 id="org76bb785"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
<div id="outline-container-orgf76ae8c" class="outline-2">
<h2 id="orgf76ae8c"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orga49b7fb"></a>
<a id="orgbb23a6a"></a>
</p>
<div class="note">
<p>
@ -1213,8 +1157,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_syme
</div>
</div>
<div id="outline-container-org3e3d670" class="outline-3">
<h3 id="org3e3d670"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div id="outline-container-org11e22fa" class="outline-3">
<h3 id="org11e22fa"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-3-1">
<p>
We here measure the signals of two geophones:
@ -1240,9 +1184,9 @@ Each measurement are done during 100s.
The settings of the voltage amplifier are:
</p>
<ul class="org-ul">
<li>DC</li>
<li>60dB</li>
<li>1kHz</li>
<li>gain of 60dB</li>
<li>AC/DC option set on DC</li>
<li>Low pass filter set at 1kHz</li>
</ul>
<p>
@ -1294,8 +1238,8 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div>
</div>
<div id="outline-container-org2c5eb48" class="outline-3">
<h3 id="org2c5eb48"><span class="section-number-3">3.2</span> Load data</h3>
<div id="outline-container-org1837038" class="outline-3">
<h3 id="org1837038"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2">
<p>
We load the data of the z axis of two geophones.
@ -1308,8 +1252,8 @@ d_19 = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class=
</div>
</div>
<div id="outline-container-org7b92812" class="outline-3">
<h3 id="org7b92812"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div id="outline-container-orge2bd074" class="outline-3">
<h3 id="orge2bd074"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-3-3">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
@ -1324,16 +1268,16 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="org6d6c3ee" class="figure">
<div id="org50d06bc" class="figure">
<p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
<p><span class="figure-number">Figure 15: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div>
</div>
</div>
<div id="outline-container-orgd042971" class="outline-3">
<h3 id="orgd042971"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div id="outline-container-org1903625" class="outline-3">
<h3 id="org1903625"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-3-4">
<div class="org-src-container">
<pre class="src src-matlab">dt = d_18<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d_18<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -1344,8 +1288,8 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div>
</div>
<div id="outline-container-orgdc25bb2" class="outline-4">
<h4 id="orgdc25bb2"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4>
<div id="outline-container-orgb1f3c6c" class="outline-4">
<h4 id="orgb1f3c6c"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-3-4-1">
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -1371,25 +1315,25 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="orgb3d2af2" class="figure">
<div id="org95f15b9" class="figure">
<p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
<p><span class="figure-number">Figure 16: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div>
<div id="orgdf358e8" class="figure">
<div id="org246e09e" class="figure">
<p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org2a573c2" class="outline-3">
<h3 id="org2a573c2"><span class="section-number-3">3.5</span> Conclusion</h3>
<div id="outline-container-orgbb3e3c0" class="outline-3">
<h3 id="orgbb3e3c0"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
<div class="important">
<p>
@ -1403,7 +1347,7 @@ Even tough the Hexapod's driver vibrates quite a lot, it does not generate signi
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 17:24</p>
<p class="date">Created: 2019-05-17 ven. 10:40</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

156
disturbance-control-system/index.org
View File

@ -29,10 +29,16 @@
#+PROPERTY: header-args:shell :eval no-export
:END:
For all the measurements shown here:
- geophones used are L22 with a resonance frequency of 1Hz
- the signals are amplified with voltage amplifiers with a gain of 60dB
- the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz
This file is organized as follow:
- Section [[sec:effect_control_all]]:
- One geophone on the marble and one at the sample location
- Each stage is turned on one by one
- Section [[sec:effect_control_one]]:
- One geophone on the marble and one at the sample location
- Each stage is turned on one at a time
- Section [[sec:effect_symetrie_driver]]:
- We check if the Symetrie driver induces some vibrations when placed on the marble
* Effect of all the control systems on the Sample vibrations
:PROPERTIES:
@ -62,10 +68,15 @@ For all the measurements shown here:
#+end_note
** Experimental Setup
We here measure the signals of two geophones:
We here measure the signals of two L22 geophones:
- One is located on top of the Sample platform
- One is located on the marble
The signals are amplified with voltage amplifiers with the following settings:
- gain of 60dB
- AC/DC option set on AC
- Low pass filter set at 1kHz
The signal from the top geophone does not go trought the slip-ring.
First, all the control systems are turned ON, then, they are turned one by one.
@ -92,6 +103,7 @@ Each of the =mat= file contains one array =data= with 3 columns:
** 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>>
addpath('../src');
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
@ -100,7 +112,7 @@ Each of the =mat= file contains one array =data= with 3 columns:
** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
#+begin_src matlab
d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
@ -114,15 +126,15 @@ First, we can look at the time domain data and compare all the measurements:
- comparison for the geophone at the sample location (figure [[fig:time_domain_sample]])
- comparison for the geophone on the granite (figure [[fig:time_domain_marble]])
#+begin_src matlab :results none
#+begin_src matlab
figure;
hold on;
plot(d3(:, 3), d3(:, 2), 'DisplayName', 'All ON');
plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Ty OFF');
plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Ry OFF');
plot(d6(:, 3), d6(:, 2), 'DisplayName', 'S-R OFF');
plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Rz OFF');
plot(d8(:, 3), d8(:, 2), 'DisplayName', 'Hexa OFF');
plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
@ -140,16 +152,15 @@ First, we can look at the time domain data and compare all the measurements:
#+RESULTS: fig:time_domain_sample
[[file:figs/time_domain_sample.png]]
#+begin_src matlab :results none
figure;
hold on;
plot(d3(:, 3), d3(:, 1), 'DisplayName', 'All ON');
plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Ty OFF');
plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Ry OFF');
plot(d6(:, 3), d6(:, 1), 'DisplayName', 'S-R OFF');
plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Rz OFF');
plot(d8(:, 3), d8(:, 1), 'DisplayName', 'Hexa OFF');
plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
@ -168,7 +179,7 @@ First, we can look at the time domain data and compare all the measurements:
[[file:figs/time_domain_marble.png]]
** Analysis - Frequency Domain
#+begin_src matlab :results none
#+begin_src matlab
dt = d3(2, 3) - d3(1, 3);
Fs = 1/dt;
@ -190,12 +201,13 @@ And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sa
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px3), 'DisplayName', 'All ON');
plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@ -246,12 +258,13 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp]]
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px3), 'DisplayName', 'All ON');
plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@ -287,79 +300,14 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp]]
#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
#+RESULTS: fig:psd_marble_comp_high_freq
[[file:figs/psd_marble_comp_high_freq.png]]
** Effect of the control system on the transmissibility from ground to sample
As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure [[fig:trans_comp]]).
#+begin_src matlab :results none
dt = d3(2, 3) - d3(1, 3);
Fs = 1/dt;
win = hanning(ceil(1*Fs));
#+end_src
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
#+begin_src matlab :results none
[T3, f] = tfestimate(d3(:, 1), d3(:, 2), win, [], [], Fs);
[T4, ~] = tfestimate(d4(:, 1), d4(:, 2), win, [], [], Fs);
[T5, ~] = tfestimate(d5(:, 1), d5(:, 2), win, [], [], Fs);
[T6, ~] = tfestimate(d6(:, 1), d6(:, 2), win, [], [], Fs);
[T7, ~] = tfestimate(d7(:, 1), d7(:, 2), win, [], [], Fs);
[T8, ~] = tfestimate(d8(:, 1), d8(:, 2), win, [], [], Fs);
#+end_src
#+begin_src matlab :results none
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(T3), 'DisplayName', 'All ON');
plot(f, abs(T4), 'DisplayName', 'Ty OFF');
plot(f, abs(T5), 'DisplayName', 'Ry OFF');
plot(f, abs(T6), 'DisplayName', 'S-R OFF');
plot(f, abs(T7), 'DisplayName', 'Rz OFF');
plot(f, abs(T8), 'DisplayName', 'Hexa OFF');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');
legend('Location', 'northwest');
ax2 = subplot(2, 1, 2);
hold on;
plot(f, mod(180+180/pi*phase(T3), 360)-180);
plot(f, mod(180+180/pi*phase(T4), 360)-180);
plot(f, mod(180+180/pi*phase(T5), 360)-180);
plot(f, mod(180+180/pi*phase(T6), 360)-180);
plot(f, mod(180+180/pi*phase(T7), 360)-180);
plot(f, mod(180+180/pi*phase(T8), 360)-180);
hold off;
set(gca, 'xscale', 'log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase');
linkaxes([ax1,ax2],'x');
xlim([1, 500]);
#+end_src
#+NAME: fig:trans_comp
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/trans_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:trans_comp
#+CAPTION: Comparison of the transfer function from the geophone on the marble to the geophone at the sample location
#+RESULTS: fig:trans_comp
[[file:figs/trans_comp.png]]
** Conclusion
#+begin_important
- The control system of the Ty stage induces a lot of vibrations of the marble
- The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz
- The hexapod control system add vibrations of the sample only above 200Hz
- When the Slip-Ring is ON, white noise appears at high frequencies. This is studied [[file:../slip-ring-electrical-noise/index.org][here]]
#+end_important
#+begin_note
- Why it seems that the measurement noise at high frequency is the limiting factor when the slip ring is ON but not when it is OFF?
#+end_note
* Effect of all the control systems on the Sample vibrations - One stage at a time
:PROPERTIES:
:header-args:matlab+: :tangle matlab/effect_control_one.m
@ -716,9 +664,9 @@ All the control systems are turned OFF except the Hexapod one.
Each measurement are done during 100s.
The settings of the voltage amplifier are:
- DC
- 60dB
- 1kHz
- gain of 60dB
- AC/DC option set on DC
- Low pass filter set at 1kHz
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.