diff --git a/figs/apa_mode_shapes.gif b/figs/apa_mode_shapes.gif
new file mode 100644
index 0000000..f92b1fc
Binary files /dev/null and b/figs/apa_mode_shapes.gif differ
diff --git a/figs/apa_mode_shapes.png b/figs/apa_mode_shapes.png
new file mode 100644
index 0000000..acd9419
Binary files /dev/null and b/figs/apa_mode_shapes.png differ
diff --git a/test-bench-apa300ml.html b/test-bench-apa300ml.html
index 14de9c8..441f4b3 100644
--- a/test-bench-apa300ml.html
+++ b/test-bench-apa300ml.html
@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
-<!-- 2021-06-09 mer. 19:01 -->
+<!-- 2021-06-14 lun. 23:20 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
<meta name="author" content="Dehaeze Thomas" />
@@ -39,206 +39,206 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
-<li><a href="#org4bb4abb">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
-<li><a href="#org3cda5e6">2. First Basic Measurements</a>
+<li><a href="#org041a21c">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
+<li><a href="#org7edef81">2. First Basic Measurements</a>
<ul>
-<li><a href="#org01cce7d">2.1. Geometrical Measurements</a>
+<li><a href="#org65f942e">2.1. Geometrical Measurements</a>
<ul>
-<li><a href="#org7051010">2.1.1. Measurement Setup</a></li>
-<li><a href="#org3378d62">2.1.2. Measurement Results</a></li>
+<li><a href="#orgdad2385">2.1.1. Measurement Setup</a></li>
+<li><a href="#org499c0e8">2.1.2. Measurement Results</a></li>
</ul>
</li>
-<li><a href="#orge5e6d07">2.2. Electrical Measurements</a></li>
-<li><a href="#orgc0b164d">2.3. Stroke measurement</a>
+<li><a href="#org8b7b7db">2.2. Electrical Measurements</a></li>
+<li><a href="#orgdb9f82c">2.3. Stroke measurement</a>
<ul>
-<li><a href="#org72cef74">2.3.1. Voltage applied on one stack</a></li>
-<li><a href="#orgedd8b54">2.3.2. Voltage applied on two stacks</a></li>
-<li><a href="#org21fe09c">2.3.3. Voltage applied on all three stacks</a></li>
+<li><a href="#org5602516">2.3.1. Voltage applied on one stack</a></li>
+<li><a href="#orged80d8a">2.3.2. Voltage applied on two stacks</a></li>
+<li><a href="#org63e5f31">2.3.3. Voltage applied on all three stacks</a></li>
</ul>
</li>
-<li><a href="#org9017a4d">2.4. Spurious resonances</a>
+<li><a href="#org6049f6f">2.4. Spurious resonances</a>
<ul>
-<li><a href="#org471f1fd">2.4.1. Introduction</a></li>
-<li><a href="#orgc9ac0dd">2.4.2. Setup</a></li>
-<li><a href="#org814855d">2.4.3. Bending - X</a></li>
-<li><a href="#org261cde7">2.4.4. Bending - Y</a></li>
-<li><a href="#org4f5c88d">2.4.5. Torsion - Z</a></li>
-<li><a href="#org76ae8d0">2.4.6. Compare</a></li>
-<li><a href="#orge8afc47">2.4.7. Conclusion</a></li>
+<li><a href="#org9dce8e8">2.4.1. Introduction</a></li>
+<li><a href="#org8dd0475">2.4.2. Setup</a></li>
+<li><a href="#orge844716">2.4.3. Bending - X</a></li>
+<li><a href="#orgff619a3">2.4.4. Bending - Y</a></li>
+<li><a href="#org2083e20">2.4.5. Torsion - Z</a></li>
+<li><a href="#org2c4cad4">2.4.6. Compare</a></li>
+<li><a href="#org88db94d">2.4.7. Conclusion</a></li>
</ul>
</li>
</ul>
</li>
-<li><a href="#org3d284c9">3. Dynamical measurements - APA</a>
+<li><a href="#org08deaa5">3. Dynamical measurements - APA</a>
<ul>
-<li><a href="#orga3d3857">3.1. Speedgoat Setup</a>
+<li><a href="#org93b0626">3.1. Speedgoat Setup</a>
<ul>
-<li><a href="#org69156d0">3.1.1. <code>frf_setup.m</code> - Measurement Setup</a></li>
-<li><a href="#orgde5fcc0">3.1.2. <code>frf_save.m</code> - Save Data</a></li>
+<li><a href="#org6d3b33d">3.1.1. <code>frf_setup.m</code> - Measurement Setup</a></li>
+<li><a href="#orgc9ed24e">3.1.2. <code>frf_save.m</code> - Save Data</a></li>
</ul>
</li>
-<li><a href="#org166d825">3.2. Measurements on APA 1</a>
+<li><a href="#org1e81fbd">3.2. Measurements on APA 1</a>
<ul>
-<li><a href="#org384b544">3.2.1. Excitation Signal</a></li>
-<li><a href="#org518a94a">3.2.2. FRF Identification - Setup</a></li>
-<li><a href="#orgc5ede61">3.2.3. FRF Identification - Displacement</a></li>
-<li><a href="#orgd0e0306">3.2.4. FRF Identification - Force Sensor</a></li>
-<li><a href="#org644a07b">3.2.5. Hysteresis</a></li>
-<li><a href="#orga546aea">3.2.6. Estimation of the APA axial stiffness</a></li>
-<li><a href="#org512f70e">3.2.7. Stiffness change due to electrical connections</a></li>
-<li><a href="#org7aac27c">3.2.8. Effect of the resistor on the IFF Plant</a></li>
+<li><a href="#org331c2cc">3.2.1. Excitation Signal</a></li>
+<li><a href="#orgc0d949f">3.2.2. FRF Identification - Setup</a></li>
+<li><a href="#org7b7690e">3.2.3. FRF Identification - Displacement</a></li>
+<li><a href="#orga55f389">3.2.4. FRF Identification - Force Sensor</a></li>
+<li><a href="#org91d57b2">3.2.5. Hysteresis</a></li>
+<li><a href="#org2536a74">3.2.6. Estimation of the APA axial stiffness</a></li>
+<li><a href="#org6ea1fbc">3.2.7. Stiffness change due to electrical connections</a></li>
+<li><a href="#org87f6fad">3.2.8. Effect of the resistor on the IFF Plant</a></li>
</ul>
</li>
-<li><a href="#org20df261">3.3. Comparison of all the APA</a>
+<li><a href="#org799ac62">3.3. Comparison of all the APA</a>
<ul>
-<li><a href="#orgdb73eb0">3.3.1. Axial Stiffnesses - Comparison</a></li>
-<li><a href="#org526932e">3.3.2. FRF Identification - Setup</a></li>
-<li><a href="#orga710d70">3.3.3. FRF Identification - DVF</a></li>
-<li><a href="#orgf160d6e">3.3.4. FRF Identification - IFF</a></li>
+<li><a href="#org6d98582">3.3.1. Axial Stiffnesses - Comparison</a></li>
+<li><a href="#orgf2b5fb3">3.3.2. FRF Identification - Setup</a></li>
+<li><a href="#org96befbe">3.3.3. FRF Identification - DVF</a></li>
+<li><a href="#org0ae36ad">3.3.4. FRF Identification - IFF</a></li>
</ul>
</li>
</ul>
</li>
-<li><a href="#org585297f">4. Dynamical measurements - Struts</a>
+<li><a href="#org86caafb">4. Dynamical measurements - Struts</a>
<ul>
-<li><a href="#org4b7728d">4.1. Measurement on Strut 1</a>
+<li><a href="#org3dad850">4.1. Measurement on Strut 1</a>
<ul>
-<li><a href="#org9a207b3">4.1.1. Without Encoder</a>
+<li><a href="#orgf9bf73b">4.1.1. Without Encoder</a>
<ul>
-<li><a href="#orgec9c46c">4.1.1.1. FRF Identification - Setup</a></li>
-<li><a href="#orge11d516">4.1.1.2. FRF Identification - Displacement</a></li>
-<li><a href="#org62bf3f5">4.1.1.3. FRF Identification - IFF</a></li>
+<li><a href="#org8f88578">4.1.1.1. FRF Identification - Setup</a></li>
+<li><a href="#orgcc08e06">4.1.1.2. FRF Identification - Displacement</a></li>
+<li><a href="#orgfe171f5">4.1.1.3. FRF Identification - IFF</a></li>
</ul>
</li>
-<li><a href="#orgbf66b4f">4.1.2. With Encoder</a>
+<li><a href="#org01cd1e5">4.1.2. With Encoder</a>
<ul>
-<li><a href="#org5ba2d6c">4.1.2.1. Measurement Data</a></li>
-<li><a href="#orgb740ddb">4.1.2.2. FRF Identification - DVF</a></li>
-<li><a href="#orga7f7c45">4.1.2.3. Comparison of the Encoder and Interferometer</a></li>
-<li><a href="#orge2da99d">4.1.2.4. APA Resonances Frequency</a></li>
-<li><a href="#org002bddc">4.1.2.5. Estimated Flexible Joint axial stiffness</a></li>
-<li><a href="#orgb8a11ba">4.1.2.6. FRF Identification - IFF</a></li>
+<li><a href="#org9e75306">4.1.2.1. Measurement Data</a></li>
+<li><a href="#org7c83cc7">4.1.2.2. FRF Identification - DVF</a></li>
+<li><a href="#org259e288">4.1.2.3. Comparison of the Encoder and Interferometer</a></li>
+<li><a href="#org210f2ee">4.1.2.4. APA Resonances Frequency</a></li>
+<li><a href="#org5bba07f">4.1.2.5. Estimated Flexible Joint axial stiffness</a></li>
+<li><a href="#org16c31d9">4.1.2.6. FRF Identification - IFF</a></li>
</ul>
</li>
</ul>
</li>
-<li><a href="#org9fad4b4">4.2. Comparison of all the Struts</a>
+<li><a href="#org2d81875">4.2. Comparison of all the Struts</a>
<ul>
-<li><a href="#org49346d3">4.2.1. FRF Identification - Setup</a></li>
-<li><a href="#orgabceeab">4.2.2. FRF Identification - DVF</a></li>
-<li><a href="#org8cfc7f6">4.2.3. FRF Identification - DVF with interferometer</a></li>
-<li><a href="#org59120b1">4.2.4. FRF Identification - IFF</a></li>
+<li><a href="#orgcbfc374">4.2.1. FRF Identification - Setup</a></li>
+<li><a href="#org17723e2">4.2.2. FRF Identification - DVF</a></li>
+<li><a href="#orga2a2b77">4.2.3. FRF Identification - DVF with interferometer</a></li>
+<li><a href="#orgdc1439d">4.2.4. FRF Identification - IFF</a></li>
</ul>
</li>
</ul>
</li>
-<li><a href="#org5e8cd6b">5. Test Bench APA300ML - Simscape Model</a>
+<li><a href="#orgb0a183d">5. Test Bench APA300ML - Simscape Model</a>
<ul>
-<li><a href="#org987d2cc">5.1. Introduction</a></li>
-<li><a href="#org821abe7">5.2. First Identification</a></li>
-<li><a href="#orgd4e5638">5.3. Identify Sensor/Actuator constants and compare with measured FRF</a>
+<li><a href="#org16cd4a8">5.1. Introduction</a></li>
+<li><a href="#org0d2ccaa">5.2. First Identification</a></li>
+<li><a href="#orgfedb510">5.3. Identify Sensor/Actuator constants and compare with measured FRF</a>
<ul>
-<li><a href="#org0719507">5.3.1. How to identify these constants?</a>
+<li><a href="#org9648429">5.3.1. How to identify these constants?</a>
<ul>
-<li><a href="#orgff68963">5.3.1.1. Piezoelectric Actuator Constant</a></li>
-<li><a href="#orgd78a421">5.3.1.2. Piezoelectric Sensor Constant</a></li>
+<li><a href="#org8aed100">5.3.1.1. Piezoelectric Actuator Constant</a></li>
+<li><a href="#org3873620">5.3.1.2. Piezoelectric Sensor Constant</a></li>
</ul>
</li>
-<li><a href="#orge4b3638">5.3.2. Identification Data</a></li>
-<li><a href="#orgfb42195">5.3.3. 2DoF APA</a>
+<li><a href="#org40d0915">5.3.2. Identification Data</a></li>
+<li><a href="#org968490c">5.3.3. 2DoF APA</a>
<ul>
-<li><a href="#orgaf97374">5.3.3.1. 2DoF APA</a></li>
-<li><a href="#orga1ad011">5.3.3.2. Identification without actuator or sensor constants</a></li>
-<li><a href="#org779ac83">5.3.3.3. Actuator Constant</a></li>
-<li><a href="#org62717da">5.3.3.4. Sensor Constant</a></li>
-<li><a href="#org5cbf2d4">5.3.3.5. Comparison</a></li>
+<li><a href="#org8e3eb76">5.3.3.1. 2DoF APA</a></li>
+<li><a href="#org9053ede">5.3.3.2. Identification without actuator or sensor constants</a></li>
+<li><a href="#org6b815c4">5.3.3.3. Actuator Constant</a></li>
+<li><a href="#org543b981">5.3.3.4. Sensor Constant</a></li>
+<li><a href="#org616188d">5.3.3.5. Comparison</a></li>
</ul>
</li>
-<li><a href="#org6921e6f">5.3.4. Flexible APA</a>
+<li><a href="#org50d4f61">5.3.4. Flexible APA</a>
<ul>
-<li><a href="#org438549b">5.3.4.1. Flexible APA</a></li>
-<li><a href="#org5d0f01f">5.3.4.2. Identification without actuator or sensor constants</a></li>
-<li><a href="#org13e1bb9">5.3.4.3. Actuator Constant</a></li>
-<li><a href="#orgf3eff0f">5.3.4.4. Sensor Constant</a></li>
-<li><a href="#orgf449dc8">5.3.4.5. Comparison</a></li>
+<li><a href="#org04f79fd">5.3.4.1. Flexible APA</a></li>
+<li><a href="#org466fe68">5.3.4.2. Identification without actuator or sensor constants</a></li>
+<li><a href="#org37e23c9">5.3.4.3. Actuator Constant</a></li>
+<li><a href="#org5428c5c">5.3.4.4. Sensor Constant</a></li>
+<li><a href="#org64a0497">5.3.4.5. Comparison</a></li>
</ul>
</li>
</ul>
</li>
-<li><a href="#org0f741d4">5.4. Optimize 2-DoF model to fit the experimental Data</a></li>
+<li><a href="#org360e26d">5.4. Optimize 2-DoF model to fit the experimental Data</a></li>
</ul>
</li>
-<li><a href="#orgac93bd2">6. Test Bench Struts - Simscape Model</a>
+<li><a href="#orgfd4db7c">6. Test Bench Struts - Simscape Model</a>
<ul>
-<li><a href="#orgfd316f9">6.1. Introduction</a></li>
-<li><a href="#orgdbac1a3">6.2. First Identification</a></li>
-<li><a href="#org0e2423b">6.3. Effect of flexible joints</a></li>
-<li><a href="#orgcb59549">6.4. Integral Force Feedback</a>
+<li><a href="#org383b978">6.1. Introduction</a></li>
+<li><a href="#orgec09fa9">6.2. First Identification</a></li>
+<li><a href="#org182d648">6.3. Effect of flexible joints</a></li>
+<li><a href="#org04fdf97">6.4. Integral Force Feedback</a>
<ul>
-<li><a href="#org5f7cf11">6.4.1. Initialize the system</a></li>
-<li><a href="#org3597bbe">6.4.2. Plant Identification</a></li>
-<li><a href="#org77009ac">6.4.3. Root Locus</a></li>
+<li><a href="#org57af20b">6.4.1. Initialize the system</a></li>
+<li><a href="#org804d0f2">6.4.2. Plant Identification</a></li>
+<li><a href="#orgd331b68">6.4.3. Root Locus</a></li>
</ul>
</li>
-<li><a href="#orgf6b7dd9">6.5. Comparison with the experimental Data</a></li>
+<li><a href="#orgf99a81f">6.5. Comparison with the experimental Data</a></li>
</ul>
</li>
-<li><a href="#org1f66afd">7. Function</a>
+<li><a href="#org542c733">7. Function</a>
<ul>
-<li><a href="#org730257f">7.1. <code>initializeBotFlexibleJoint</code> - Initialize Flexible Joint</a>
+<li><a href="#org2002f31">7.1. <code>initializeBotFlexibleJoint</code> - Initialize Flexible Joint</a>
<ul>
-<li><a href="#org64c034e">Function description</a></li>
-<li><a href="#org942e6c2">Optional Parameters</a></li>
-<li><a href="#org58455ca">Initialize the structure</a></li>
-<li><a href="#orgf261788">Set the Joint’s type</a></li>
-<li><a href="#orgede603f">Set parameters</a></li>
+<li><a href="#orgdea7178">Function description</a></li>
+<li><a href="#orgf41e762">Optional Parameters</a></li>
+<li><a href="#orgc438b52">Initialize the structure</a></li>
+<li><a href="#orgd1b0b63">Set the Joint’s type</a></li>
+<li><a href="#org9e43909">Set parameters</a></li>
</ul>
</li>
-<li><a href="#orgef70627">7.2. <code>initializeTopFlexibleJoint</code> - Initialize Flexible Joint</a>
+<li><a href="#org76f54c8">7.2. <code>initializeTopFlexibleJoint</code> - Initialize Flexible Joint</a>
<ul>
-<li><a href="#org091fbd8">Function description</a></li>
-<li><a href="#org1d37383">Optional Parameters</a></li>
-<li><a href="#orgc52ebc0">Initialize the structure</a></li>
-<li><a href="#org0fa0554">Set the Joint’s type</a></li>
-<li><a href="#org5590e46">Set parameters</a></li>
+<li><a href="#org38a994c">Function description</a></li>
+<li><a href="#org7448731">Optional Parameters</a></li>
+<li><a href="#orgbc5e615">Initialize the structure</a></li>
+<li><a href="#org3adeb48">Set the Joint’s type</a></li>
+<li><a href="#org1b36a20">Set parameters</a></li>
</ul>
</li>
-<li><a href="#orgacd4906">7.3. <code>initializeAPA</code> - Initialize APA</a>
+<li><a href="#org01db2f1">7.3. <code>initializeAPA</code> - Initialize APA</a>
<ul>
-<li><a href="#orga698c5e">Function description</a></li>
-<li><a href="#org29dad87">Optional Parameters</a></li>
-<li><a href="#org6eeae8c">Initialize Structure</a></li>
-<li><a href="#org9b8fb4b">Type</a></li>
-<li><a href="#org62c5ed8">Actuator/Sensor Constants</a></li>
-<li><a href="#org0fd8dea">2DoF parameters</a></li>
-<li><a href="#org1d5fd8f">Flexible frame and fully flexible</a></li>
+<li><a href="#orgd230696">Function description</a></li>
+<li><a href="#orgf18780c">Optional Parameters</a></li>
+<li><a href="#orge8497f7">Initialize Structure</a></li>
+<li><a href="#org837d8bb">Type</a></li>
+<li><a href="#orgc23e748">Actuator/Sensor Constants</a></li>
+<li><a href="#orgc803170">2DoF parameters</a></li>
+<li><a href="#orgdbcf682">Flexible frame and fully flexible</a></li>
</ul>
</li>
-<li><a href="#orgbbd63f4">7.4. <code>generateSweepExc</code>: Generate sweep sinus excitation</a>
+<li><a href="#orgc5c4a06">7.4. <code>generateSweepExc</code>: Generate sweep sinus excitation</a>
<ul>
-<li><a href="#org4047364">Function description</a></li>
-<li><a href="#orgdb7f1e4">Optional Parameters</a></li>
-<li><a href="#org46430d0">Sweep Sine part</a></li>
-<li><a href="#org3d78f6c">Smooth Ends</a></li>
-<li><a href="#org63f6cb4">Combine Excitation signals</a></li>
+<li><a href="#org928e990">Function description</a></li>
+<li><a href="#org52f9336">Optional Parameters</a></li>
+<li><a href="#org97f67d4">Sweep Sine part</a></li>
+<li><a href="#org5ecd11d">Smooth Ends</a></li>
+<li><a href="#org81e70f2">Combine Excitation signals</a></li>
</ul>
</li>
-<li><a href="#org9628aeb">7.5. <code>generateShapedNoise</code>: Generate Shaped Noise excitation</a>
+<li><a href="#orgf1900ac">7.5. <code>generateShapedNoise</code>: Generate Shaped Noise excitation</a>
<ul>
-<li><a href="#org526c60c">Function description</a></li>
-<li><a href="#org61cf959">Optional Parameters</a></li>
-<li><a href="#org8ecc3f8">Shaped Noise</a></li>
-<li><a href="#orgebfd6a4">Smooth Ends</a></li>
-<li><a href="#orge82c676">Combine Excitation signals</a></li>
+<li><a href="#org40f50a7">Function description</a></li>
+<li><a href="#orga11d04a">Optional Parameters</a></li>
+<li><a href="#org8d7b46d">Shaped Noise</a></li>
+<li><a href="#orgcd192a4">Smooth Ends</a></li>
+<li><a href="#org2f1448f">Combine Excitation signals</a></li>
</ul>
</li>
-<li><a href="#org5066270">7.6. <code>generateSinIncreasingAmpl</code>: Generate Sinus with increasing amplitude</a>
+<li><a href="#org6799aae">7.6. <code>generateSinIncreasingAmpl</code>: Generate Sinus with increasing amplitude</a>
<ul>
-<li><a href="#org6e1c161">Function description</a></li>
-<li><a href="#orga64324d">Optional Parameters</a></li>
-<li><a href="#orge158235">Sinus excitation</a></li>
-<li><a href="#org2afc938">Smooth Ends</a></li>
-<li><a href="#org1f109d0">Combine Excitation signals</a></li>
+<li><a href="#org784ac8d">Function description</a></li>
+<li><a href="#orgf8a1531">Optional Parameters</a></li>
+<li><a href="#org1316011">Sinus excitation</a></li>
+<li><a href="#org99273a1">Smooth Ends</a></li>
+<li><a href="#orgf3d7f4d">Combine Excitation signals</a></li>
</ul>
</li>
</ul>
@@ -267,21 +267,21 @@ This include:
</ul>
-<div id="orgf295795" class="figure">
+<div id="org9e58473" class="figure">
<p><img src="figs/apa300ML.png" alt="apa300ML.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the APA300ML</p>
</div>
-<div id="outline-container-org4bb4abb" class="outline-2">
-<h2 id="org4bb4abb"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
+<div id="outline-container-org041a21c" class="outline-2">
+<h2 id="org041a21c"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
<div class="outline-text-2" id="text-1">
<p>
-Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#org111f00b">2</a>.
+Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#org36c7af4">2</a>.
</p>
-<div id="org111f00b" class="figure">
+<div id="org36c7af4" class="figure">
<p><img src="figs/apa_model_schematic.png" alt="apa_model_schematic.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Amplified Piezoelectric Actuator Schematic</p>
@@ -306,11 +306,11 @@ We wish here to experimental measure \(g_a\) and \(g_s\).
</p>
<p>
-The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#org33c3146">3</a>.
+The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#orge113690">3</a>.
</p>
-<div id="org33c3146" class="figure">
+<div id="orge113690" class="figure">
<p><img src="figs/apa-model-simscape-schematic.png" alt="apa-model-simscape-schematic.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Model of the APA with Simscape/Simulink</p>
@@ -318,45 +318,45 @@ The block-diagram model of the piezoelectric actuator is then as shown in Figure
</div>
</div>
-<div id="outline-container-org3cda5e6" class="outline-2">
-<h2 id="org3cda5e6"><span class="section-number-2">2</span> First Basic Measurements</h2>
+<div id="outline-container-org7edef81" class="outline-2">
+<h2 id="org7edef81"><span class="section-number-2">2</span> First Basic Measurements</h2>
<div class="outline-text-2" id="text-2">
<p>
-<a id="org0d66c55"></a>
+<a id="orgf486c15"></a>
</p>
<ul class="org-ul">
-<li>Section <a href="#org272280f">2.1</a>:</li>
-<li>Section <a href="#orgf1a53d7">2.2</a>:</li>
-<li>Section <a href="#orgeeea6f9">2.3</a>:</li>
-<li>Section <a href="#orgdae0410">2.4</a>:</li>
+<li>Section <a href="#org73695e2">2.1</a>:</li>
+<li>Section <a href="#org3125d58">2.2</a>:</li>
+<li>Section <a href="#org5c6e097">2.3</a>:</li>
+<li>Section <a href="#org2f316ce">2.4</a>:</li>
</ul>
</div>
-<div id="outline-container-org01cce7d" class="outline-3">
-<h3 id="org01cce7d"><span class="section-number-3">2.1</span> Geometrical Measurements</h3>
+<div id="outline-container-org65f942e" class="outline-3">
+<h3 id="org65f942e"><span class="section-number-3">2.1</span> Geometrical Measurements</h3>
<div class="outline-text-3" id="text-2-1">
<p>
-<a id="org272280f"></a>
+<a id="org73695e2"></a>
</p>
<p>
-The received APA are shown in Figure <a href="#orgfd3bdf7">4</a>.
+The received APA are shown in Figure <a href="#org8b0ad5f">4</a>.
</p>
-<div id="orgfd3bdf7" class="figure">
+<div id="org8b0ad5f" class="figure">
<p><img src="figs/IMG_20210224_143500.jpg" alt="IMG_20210224_143500.jpg" />
</p>
<p><span class="figure-number">Figure 4: </span>Received APA</p>
</div>
</div>
-<div id="outline-container-org7051010" class="outline-4">
-<h4 id="org7051010"><span class="section-number-4">2.1.1</span> Measurement Setup</h4>
+<div id="outline-container-orgdad2385" class="outline-4">
+<h4 id="orgdad2385"><span class="section-number-4">2.1.1</span> Measurement Setup</h4>
<div class="outline-text-4" id="text-2-1-1">
<p>
-The flatness corresponding to the two interface planes are measured as shown in Figure <a href="#org077b85e">5</a>.
+The flatness corresponding to the two interface planes are measured as shown in Figure <a href="#org371d177">5</a>.
</p>
-<div id="org077b85e" class="figure">
+<div id="org371d177" class="figure">
<p><img src="figs/IMG_20210224_143809.jpg" alt="IMG_20210224_143809.jpg" />
</p>
<p><span class="figure-number">Figure 5: </span>Measurement Setup</p>
@@ -364,8 +364,8 @@ The flatness corresponding to the two interface planes are measured as shown in
</div>
</div>
-<div id="outline-container-org3378d62" class="outline-4">
-<h4 id="org3378d62"><span class="section-number-4">2.1.2</span> Measurement Results</h4>
+<div id="outline-container-org499c0e8" class="outline-4">
+<h4 id="org499c0e8"><span class="section-number-4">2.1.2</span> Measurement Results</h4>
<div class="outline-text-4" id="text-2-1-2">
<p>
The height (Z) measurements at the 8 locations (4 points by plane) are defined below.
@@ -411,10 +411,10 @@ Finally, the flatness is estimated by fitting a plane through the 8 points using
</div>
<p>
-The obtained flatness are shown in Table <a href="#org9b19a2f">1</a>.
+The obtained flatness are shown in Table <a href="#org652d0b1">1</a>.
</p>
-<table id="org9b19a2f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="org652d0b1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Estimated flatness</caption>
<colgroup>
@@ -469,14 +469,14 @@ The obtained flatness are shown in Table <a href="#org9b19a2f">1</a>.
</div>
</div>
-<div id="outline-container-orge5e6d07" class="outline-3">
-<h3 id="orge5e6d07"><span class="section-number-3">2.2</span> Electrical Measurements</h3>
+<div id="outline-container-org8b7b7db" class="outline-3">
+<h3 id="org8b7b7db"><span class="section-number-3">2.2</span> Electrical Measurements</h3>
<div class="outline-text-3" id="text-2-2">
<p>
-<a id="orgf1a53d7"></a>
+<a id="org3125d58"></a>
</p>
-<div class="note" id="org1a23c60">
+<div class="note" id="org3a53976">
<p>
The capacitance of the stacks is measure with the <a href="https://www.gwinstek.com/en-global/products/detail/LCR-800">LCR-800 Meter</a> (<a href="doc/DS_LCR-800_Series_V2_E.pdf">doc</a>)
</p>
@@ -484,7 +484,7 @@ The capacitance of the stacks is measure with the <a href="https://www.gwinstek.
</div>
-<div id="orgdcf55ca" class="figure">
+<div id="orgf033c77" class="figure">
<p><img src="figs/IMG_20210312_120337.jpg" alt="IMG_20210312_120337.jpg" />
</p>
<p><span class="figure-number">Figure 6: </span>LCR Meter used for the measurements</p>
@@ -494,7 +494,7 @@ The capacitance of the stacks is measure with the <a href="https://www.gwinstek.
The excitation frequency is set to be 1kHz.
</p>
-<table id="org88fc0b5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="org37d90be" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Capacitance measured with the LCR meter. The excitation signal is a sinus at 1kHz</caption>
<colgroup>
@@ -556,7 +556,7 @@ The excitation frequency is set to be 1kHz.
</tbody>
</table>
-<div class="warning" id="org43ea88f">
+<div class="warning" id="org7729c5b">
<p>
There is clearly a problem with APA300ML number 3
</p>
@@ -569,25 +569,25 @@ The APA number 3 has ben sent back to Cedrat, and a new APA300ML has been shippe
</div>
</div>
-<div id="outline-container-orgc0b164d" class="outline-3">
-<h3 id="orgc0b164d"><span class="section-number-3">2.3</span> Stroke measurement</h3>
+<div id="outline-container-orgdb9f82c" class="outline-3">
+<h3 id="orgdb9f82c"><span class="section-number-3">2.3</span> Stroke measurement</h3>
<div class="outline-text-3" id="text-2-3">
<p>
-<a id="orgeeea6f9"></a>
+<a id="org5c6e097"></a>
</p>
<p>
We here wish to estimate the stroke of the APA.
</p>
<p>
-To do so, one side of the APA is fixed, and a displacement probe is located on the other side as shown in Figure <a href="#org7f256d0">7</a>.
+To do so, one side of the APA is fixed, and a displacement probe is located on the other side as shown in Figure <a href="#org69aa820">7</a>.
</p>
<p>
Then, a voltage is applied on either one or two stacks using a DAC and a voltage amplifier.
</p>
-<div class="note" id="org974dfc6">
+<div class="note" id="orga6c47b0">
<p>
Here are the documentation of the equipment used for this test bench:
</p>
@@ -600,91 +600,91 @@ Here are the documentation of the equipment used for this test bench:
</div>
-<div id="org7f256d0" class="figure">
+<div id="org69aa820" class="figure">
<p><img src="figs/CE0EF55E-07B7-461B-8CDB-98590F68D15B.jpeg" alt="CE0EF55E-07B7-461B-8CDB-98590F68D15B.jpeg" />
</p>
<p><span class="figure-number">Figure 7: </span>Bench to measured the APA stroke</p>
</div>
</div>
-<div id="outline-container-org72cef74" class="outline-4">
-<h4 id="org72cef74"><span class="section-number-4">2.3.1</span> Voltage applied on one stack</h4>
+<div id="outline-container-org5602516" class="outline-4">
+<h4 id="org5602516"><span class="section-number-4">2.3.1</span> Voltage applied on one stack</h4>
<div class="outline-text-4" id="text-2-3-1">
<p>
Let’s first look at the relation between the voltage applied to <b>one</b> stack to the displacement of the APA as measured by the displacement probe.
</p>
<p>
-The applied voltage is shown in Figure <a href="#org30d2aa8">8</a>.
+The applied voltage is shown in Figure <a href="#org002eea4">8</a>.
</p>
-<div id="org30d2aa8" class="figure">
+<div id="org002eea4" class="figure">
<p><img src="figs/apa_stroke_voltage_time.png" alt="apa_stroke_voltage_time.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Applied voltage as a function of time</p>
</div>
<p>
-The obtained displacement is shown in Figure <a href="#org27c526b">9</a>.
+The obtained displacement is shown in Figure <a href="#org9dfa928">9</a>.
The displacement is set to zero at initial time when the voltage applied is -20V.
</p>
-<div id="org27c526b" class="figure">
+<div id="org9dfa928" class="figure">
<p><img src="figs/apa_stroke_time_1s.png" alt="apa_stroke_time_1s.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Displacement as a function of time for all the APA300ML</p>
</div>
<p>
-Finally, the displacement is shown as a function of the applied voltage in Figure <a href="#orgf5a28c9">10</a>.
+Finally, the displacement is shown as a function of the applied voltage in Figure <a href="#org2dc5b78">10</a>.
We can clearly see that there is a problem with the APA 3.
Also, there is a large hysteresis.
</p>
-<div id="orgf5a28c9" class="figure">
+<div id="org2dc5b78" class="figure">
<p><img src="figs/apa_d_vs_V_1s.png" alt="apa_d_vs_V_1s.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Displacement as a function of the applied voltage</p>
</div>
-<div class="important" id="org7435c41">
+<div class="important" id="org45f090c">
<p>
-We can clearly see from Figure <a href="#orgf5a28c9">10</a> that there is a problem with the APA number 3.
+We can clearly see from Figure <a href="#org2dc5b78">10</a> that there is a problem with the APA number 3.
</p>
</div>
</div>
</div>
-<div id="outline-container-orgedd8b54" class="outline-4">
-<h4 id="orgedd8b54"><span class="section-number-4">2.3.2</span> Voltage applied on two stacks</h4>
+<div id="outline-container-orged80d8a" class="outline-4">
+<h4 id="orged80d8a"><span class="section-number-4">2.3.2</span> Voltage applied on two stacks</h4>
<div class="outline-text-4" id="text-2-3-2">
<p>
Now look at the relation between the voltage applied to the <b>two</b> other stacks to the displacement of the APA as measured by the displacement probe.
</p>
<p>
-The obtained displacement is shown in Figure <a href="#orgedd9abb">11</a>.
+The obtained displacement is shown in Figure <a href="#orgc384dd7">11</a>.
The displacement is set to zero at initial time when the voltage applied is -20V.
</p>
-<div id="orgedd9abb" class="figure">
+<div id="orgc384dd7" class="figure">
<p><img src="figs/apa_stroke_time_2s.png" alt="apa_stroke_time_2s.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Displacement as a function of time for all the APA300ML</p>
</div>
<p>
-Finally, the displacement is shown as a function of the applied voltage in Figure <a href="#orgb20b2b4">12</a>.
+Finally, the displacement is shown as a function of the applied voltage in Figure <a href="#orgf61b850">12</a>.
We can clearly see that there is a problem with the APA 3.
Also, there is a large hysteresis.
</p>
-<div id="orgb20b2b4" class="figure">
+<div id="orgf61b850" class="figure">
<p><img src="figs/apa_d_vs_V_2s.png" alt="apa_d_vs_V_2s.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Displacement as a function of the applied voltage</p>
@@ -692,25 +692,25 @@ Also, there is a large hysteresis.
</div>
</div>
-<div id="outline-container-org21fe09c" class="outline-4">
-<h4 id="org21fe09c"><span class="section-number-4">2.3.3</span> Voltage applied on all three stacks</h4>
+<div id="outline-container-org63e5f31" class="outline-4">
+<h4 id="org63e5f31"><span class="section-number-4">2.3.3</span> Voltage applied on all three stacks</h4>
<div class="outline-text-4" id="text-2-3-3">
<p>
-Finally, we can combine the two measurements to estimate the relation between the displacement and the voltage applied to the <b>three</b> stacks (Figure <a href="#org5eca50d">13</a>).
+Finally, we can combine the two measurements to estimate the relation between the displacement and the voltage applied to the <b>three</b> stacks (Figure <a href="#org194b608">13</a>).
</p>
-<div id="org5eca50d" class="figure">
+<div id="org194b608" class="figure">
<p><img src="figs/apa_d_vs_V_3s.png" alt="apa_d_vs_V_3s.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Displacement as a function of the applied voltage</p>
</div>
<p>
-The obtained maximum stroke for all the APA are summarized in Table <a href="#orgc0373d9">3</a>.
+The obtained maximum stroke for all the APA are summarized in Table <a href="#orgd93cdc9">3</a>.
</p>
-<table id="orgc0373d9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="orgd93cdc9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Measured maximum stroke</caption>
<colgroup>
@@ -765,44 +765,30 @@ The obtained maximum stroke for all the APA are summarized in Table <a href="#or
</div>
</div>
-<div id="outline-container-org9017a4d" class="outline-3">
-<h3 id="org9017a4d"><span class="section-number-3">2.4</span> Spurious resonances</h3>
+<div id="outline-container-org6049f6f" class="outline-3">
+<h3 id="org6049f6f"><span class="section-number-3">2.4</span> Spurious resonances</h3>
<div class="outline-text-3" id="text-2-4">
<p>
-<a id="orgdae0410"></a>
+<a id="org2f316ce"></a>
</p>
</div>
-<div id="outline-container-org471f1fd" class="outline-4">
-<h4 id="org471f1fd"><span class="section-number-4">2.4.1</span> Introduction</h4>
+<div id="outline-container-org9dce8e8" class="outline-4">
+<h4 id="org9dce8e8"><span class="section-number-4">2.4.1</span> Introduction</h4>
<div class="outline-text-4" id="text-2-4-1">
<p>
-Three main resonances are foreseen to be problematic for the control of the APA300ML:
+Three main resonances are foreseen to be problematic for the control of the APA300ML (Figure <a href="#org72982e2">14</a>):
</p>
<ul class="org-ul">
-<li>Mode in X-bending at 189Hz (Figure <a href="#org8ecff8f">14</a>)</li>
-<li>Mode in Y-bending at 285Hz (Figure <a href="#org6068f55">15</a>)</li>
-<li>Mode in Z-torsion at 400Hz (Figure <a href="#orge96dccd">16</a>)</li>
+<li>Mode in X-bending at 189Hz</li>
+<li>Mode in Y-bending at 285Hz</li>
+<li>Mode in Z-torsion at 400Hz</li>
</ul>
-<div id="org8ecff8f" class="figure">
-<p><img src="figs/mode_bending_x.gif" alt="mode_bending_x.gif" />
+<div id="org72982e2" class="figure">
+<p><img src="figs/apa_mode_shapes.gif" alt="apa_mode_shapes.gif" />
</p>
-<p><span class="figure-number">Figure 14: </span>X-bending mode (189Hz)</p>
-</div>
-
-
-<div id="org6068f55" class="figure">
-<p><img src="figs/mode_bending_y.gif" alt="mode_bending_y.gif" />
-</p>
-<p><span class="figure-number">Figure 15: </span>Y-bending mode (285Hz)</p>
-</div>
-
-
-<div id="orge96dccd" class="figure">
-<p><img src="figs/mode_torsion_z.gif" alt="mode_torsion_z.gif" />
-</p>
-<p><span class="figure-number">Figure 16: </span>Z-torsion mode (400Hz)</p>
+<p><span class="figure-number">Figure 14: </span>Spurious resonances. a) X-bending mode at 189Hz. b) Y-bending mode at 285Hz. c) Z-torsion mode at 400Hz</p>
</div>
<p>
@@ -815,16 +801,16 @@ In this section, we try to find the resonance frequency of these modes when one
</div>
</div>
-<div id="outline-container-orgc9ac0dd" class="outline-4">
-<h4 id="orgc9ac0dd"><span class="section-number-4">2.4.2</span> Setup</h4>
+<div id="outline-container-org8dd0475" class="outline-4">
+<h4 id="org8dd0475"><span class="section-number-4">2.4.2</span> Setup</h4>
<div class="outline-text-4" id="text-2-4-2">
<p>
-The measurement setup is shown in Figure <a href="#org3e8b5e2">17</a>.
+The measurement setup is shown in Figure <a href="#orgee02dfa">15</a>.
A Laser vibrometer is measuring the difference of motion of two points.
The APA is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
</p>
-<div class="note" id="orgc028d27">
+<div class="note" id="org10b85da">
<ul class="org-ul">
<li>Laser Doppler Vibrometer Polytec OFV512</li>
<li>Instrumented hammer</li>
@@ -833,28 +819,28 @@ The APA is excited with an instrumented hammer and the transfer function from th
</div>
-<div id="org3e8b5e2" class="figure">
+<div id="orgee02dfa" class="figure">
<p><img src="figs/measurement_setup_torsion.jpg" alt="measurement_setup_torsion.jpg" />
</p>
-<p><span class="figure-number">Figure 17: </span>Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer</p>
+<p><span class="figure-number">Figure 15: </span>Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer</p>
</div>
</div>
</div>
-<div id="outline-container-org814855d" class="outline-4">
-<h4 id="org814855d"><span class="section-number-4">2.4.3</span> Bending - X</h4>
+<div id="outline-container-orge844716" class="outline-4">
+<h4 id="orge844716"><span class="section-number-4">2.4.3</span> Bending - X</h4>
<div class="outline-text-4" id="text-2-4-3">
<p>
-The setup to measure the X-bending motion is shown in Figure <a href="#orgf98ad6e">18</a>.
+The setup to measure the X-bending motion is shown in Figure <a href="#org48e9221">16</a>.
The APA is excited with an instrumented hammer having a solid metallic tip.
The impact point is on the back-side of the APA aligned with the top measurement point.
</p>
-<div id="orgf98ad6e" class="figure">
+<div id="org48e9221" class="figure">
<p><img src="figs/measurement_setup_X_bending.jpg" alt="measurement_setup_X_bending.jpg" />
</p>
-<p><span class="figure-number">Figure 18: </span>X-Bending measurement setup</p>
+<p><span class="figure-number">Figure 16: </span>X-Bending measurement setup</p>
</div>
<p>
@@ -883,26 +869,26 @@ The transfer function from the input force to the output “rotation”
</div>
<p>
-The result is shown in Figure <a href="#org983c576">19</a>.
+The result is shown in Figure <a href="#orgf737fd6">17</a>.
</p>
<p>
The can clearly observe a nice peak at 280Hz, and then peaks at the odd “harmonics” (third “harmonic” at 840Hz, and fifth “harmonic” at 1400Hz).
</p>
-<div id="org983c576" class="figure">
+<div id="orgf737fd6" class="figure">
<p><img src="figs/apa300ml_meas_freq_bending_x.png" alt="apa300ml_meas_freq_bending_x.png" />
</p>
-<p><span class="figure-number">Figure 19: </span>Obtained FRF for the X-bending</p>
+<p><span class="figure-number">Figure 17: </span>Obtained FRF for the X-bending</p>
</div>
</div>
</div>
-<div id="outline-container-org261cde7" class="outline-4">
-<h4 id="org261cde7"><span class="section-number-4">2.4.4</span> Bending - Y</h4>
+<div id="outline-container-orgff619a3" class="outline-4">
+<h4 id="orgff619a3"><span class="section-number-4">2.4.4</span> Bending - Y</h4>
<div class="outline-text-4" id="text-2-4-4">
<p>
-The setup to measure the Y-bending is shown in Figure <a href="#org9224576">20</a>.
+The setup to measure the Y-bending is shown in Figure <a href="#orgb92a397">18</a>.
</p>
<p>
@@ -910,10 +896,10 @@ The impact point of the instrumented hammer is located on the back surface of th
</p>
-<div id="org9224576" class="figure">
+<div id="orgb92a397" class="figure">
<p><img src="figs/measurement_setup_Y_bending.jpg" alt="measurement_setup_Y_bending.jpg" />
</p>
-<p><span class="figure-number">Figure 20: </span>Y-Bending measurement setup</p>
+<p><span class="figure-number">Figure 18: </span>Y-Bending measurement setup</p>
</div>
<p>
@@ -926,24 +912,24 @@ The data is loaded, and the transfer function from the force to the measured rot
</div>
<p>
-The results are shown in Figure <a href="#org7c4da10">21</a>.
+The results are shown in Figure <a href="#orgec0653f">19</a>.
The main resonance is at 412Hz, and we also see the third “harmonic” at 1220Hz.
</p>
-<div id="org7c4da10" class="figure">
+<div id="orgec0653f" class="figure">
<p><img src="figs/apa300ml_meas_freq_bending_y.png" alt="apa300ml_meas_freq_bending_y.png" />
</p>
-<p><span class="figure-number">Figure 21: </span>Obtained FRF for the Y-bending</p>
+<p><span class="figure-number">Figure 19: </span>Obtained FRF for the Y-bending</p>
</div>
</div>
</div>
-<div id="outline-container-org4f5c88d" class="outline-4">
-<h4 id="org4f5c88d"><span class="section-number-4">2.4.5</span> Torsion - Z</h4>
+<div id="outline-container-org2083e20" class="outline-4">
+<h4 id="org2083e20"><span class="section-number-4">2.4.5</span> Torsion - Z</h4>
<div class="outline-text-4" id="text-2-4-5">
<p>
-Finally, we measure the Z-torsion resonance as shown in Figure <a href="#orgf38b02c">22</a>.
+Finally, we measure the Z-torsion resonance as shown in Figure <a href="#orgdfdce01">20</a>.
</p>
<p>
@@ -951,10 +937,10 @@ The excitation is shown on the other side of the APA, on the side to excite the
</p>
-<div id="orgf38b02c" class="figure">
+<div id="orgdfdce01" class="figure">
<p><img src="figs/measurement_setup_torsion_bis.jpg" alt="measurement_setup_torsion_bis.jpg" />
</p>
-<p><span class="figure-number">Figure 22: </span>Z-Torsion measurement setup</p>
+<p><span class="figure-number">Figure 20: </span>Z-Torsion measurement setup</p>
</div>
<p>
@@ -967,16 +953,16 @@ The data is loaded, and the transfer function computed.
</div>
<p>
-The results are shown in Figure <a href="#orgc424712">23</a>.
+The results are shown in Figure <a href="#org733b730">21</a>.
We observe a first peak at 267Hz, which corresponds to the X-bending mode that was measured at 280Hz.
And then a second peak at 415Hz, which corresponds to the X-bending mode that was measured at 412Hz.
The mode in pure torsion is probably at higher frequency (peak around 1kHz?).
</p>
-<div id="orgc424712" class="figure">
+<div id="org733b730" class="figure">
<p><img src="figs/apa300ml_meas_freq_torsion_z.png" alt="apa300ml_meas_freq_torsion_z.png" />
</p>
-<p><span class="figure-number">Figure 23: </span>Obtained FRF for the Z-torsion</p>
+<p><span class="figure-number">Figure 21: </span>Obtained FRF for the Z-torsion</p>
</div>
<p>
@@ -989,36 +975,36 @@ In order to verify that, the APA is excited on the top part such that the torsio
</div>
<p>
-The two FRF are compared in Figure <a href="#org60b6c50">24</a>.
+The two FRF are compared in Figure <a href="#org0b6a2cf">22</a>.
It is clear that the first two modes does not correspond to the torsional mode.
Maybe the resonance at 800Hz, or even higher resonances. It is difficult to conclude here.
</p>
-<div id="org60b6c50" class="figure">
+<div id="org0b6a2cf" class="figure">
<p><img src="figs/apa300ml_meas_freq_torsion_z_comp.png" alt="apa300ml_meas_freq_torsion_z_comp.png" />
</p>
-<p><span class="figure-number">Figure 24: </span>Obtained FRF for the Z-torsion</p>
+<p><span class="figure-number">Figure 22: </span>Obtained FRF for the Z-torsion</p>
</div>
</div>
</div>
-<div id="outline-container-org76ae8d0" class="outline-4">
-<h4 id="org76ae8d0"><span class="section-number-4">2.4.6</span> Compare</h4>
+<div id="outline-container-org2c4cad4" class="outline-4">
+<h4 id="org2c4cad4"><span class="section-number-4">2.4.6</span> Compare</h4>
<div class="outline-text-4" id="text-2-4-6">
<p>
-The three measurements are shown in Figure <a href="#org85ca1d4">25</a>.
+The three measurements are shown in Figure <a href="#org0985787">23</a>.
</p>
-<div id="org85ca1d4" class="figure">
+<div id="org0985787" class="figure">
<p><img src="figs/apa300ml_meas_freq_compare.png" alt="apa300ml_meas_freq_compare.png" />
</p>
-<p><span class="figure-number">Figure 25: </span>Obtained FRF - Comparison</p>
+<p><span class="figure-number">Figure 23: </span>Obtained FRF - Comparison</p>
</div>
</div>
</div>
-<div id="outline-container-orge8afc47" class="outline-4">
-<h4 id="orge8afc47"><span class="section-number-4">2.4.7</span> Conclusion</h4>
+<div id="outline-container-org88db94d" class="outline-4">
+<h4 id="org88db94d"><span class="section-number-4">2.4.7</span> Conclusion</h4>
<div class="outline-text-4" id="text-2-4-7">
<p>
When two flexible joints are fixed at each ends of the APA, the APA is mostly in a free/free condition in terms of bending/torsion (the bending/torsional stiffness of the joints being very small).
@@ -1030,7 +1016,7 @@ Therefore, it is quite obvious that we measured higher resonance frequencies tha
It is however quite interesting that there is a factor \(\approx \sqrt{2}\) between the two (increased of the stiffness by a factor 2?).
</p>
-<table id="org88a9ff6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="orgbb14d4c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 4:</span> Measured frequency of the modes</caption>
<colgroup>
@@ -1072,35 +1058,35 @@ It is however quite interesting that there is a factor \(\approx \sqrt{2}\) betw
</div>
</div>
-<div id="outline-container-org3d284c9" class="outline-2">
-<h2 id="org3d284c9"><span class="section-number-2">3</span> Dynamical measurements - APA</h2>
+<div id="outline-container-org08deaa5" class="outline-2">
+<h2 id="org08deaa5"><span class="section-number-2">3</span> Dynamical measurements - APA</h2>
<div class="outline-text-2" id="text-3">
<p>
-<a id="org8962678"></a>
+<a id="org8309884"></a>
</p>
<p>
In this section, a measurement test bench is used to identify the dynamics of the APA.
</p>
<p>
-The bench is shown in Figure <a href="#orge2dba51">26</a>, and a zoom picture on the APA and encoder is shown in Figure <a href="#org4e38bb3">27</a>.
+The bench is shown in Figure <a href="#orgf798837">24</a>, and a zoom picture on the APA and encoder is shown in Figure <a href="#orgc75eb5b">25</a>.
</p>
-<div id="orge2dba51" class="figure">
+<div id="orgf798837" class="figure">
<p><img src="figs/picture_apa_bench.png" alt="picture_apa_bench.png" />
</p>
-<p><span class="figure-number">Figure 26: </span>Picture of the test bench</p>
+<p><span class="figure-number">Figure 24: </span>Picture of the test bench</p>
</div>
-<div id="org4e38bb3" class="figure">
+<div id="orgc75eb5b" class="figure">
<p><img src="figs/picture_apa_bench_encoder.png" alt="picture_apa_bench_encoder.png" />
</p>
-<p><span class="figure-number">Figure 27: </span>Zoom on the APA with the encoder</p>
+<p><span class="figure-number">Figure 25: </span>Zoom on the APA with the encoder</p>
</div>
-<div class="note" id="org7ee7114">
+<div class="note" id="org34124d5">
<p>
Here are the documentation of the equipment used for this test bench:
</p>
@@ -1115,17 +1101,17 @@ Here are the documentation of the equipment used for this test bench:
</div>
<p>
-The bench is schematically shown in Figure <a href="#org8574ae0">28</a> and the signal used are summarized in Table <a href="#org3e9c6ba">5</a>.
+The bench is schematically shown in Figure <a href="#org71617bb">26</a> and the signal used are summarized in Table <a href="#orgf2dfbaf">5</a>.
</p>
-<div id="org8574ae0" class="figure">
+<div id="org71617bb" class="figure">
<p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" />
</p>
-<p><span class="figure-number">Figure 28: </span>Schematic of the Test Bench</p>
+<p><span class="figure-number">Figure 26: </span>Schematic of the Test Bench</p>
</div>
-<table id="org3e9c6ba" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="orgf2dfbaf" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 5:</span> Variables used during the measurements</caption>
<colgroup>
@@ -1187,20 +1173,20 @@ The bench is schematically shown in Figure <a href="#org8574ae0">28</a> and the
This section is structured as follows:
</p>
<ul class="org-ul">
-<li>Section <a href="#orgd658976">3.1</a>: the Speedgoat setup is described (excitation signals, saved signals, etc.)</li>
-<li>Section <a href="#orgae0bb15">3.2</a>: the measurements are first performed on one APA.</li>
-<li>Section <a href="#org1718809">3.3</a>: the same measurements are performed on all the APA and are compared.</li>
+<li>Section <a href="#org299a882">3.1</a>: the Speedgoat setup is described (excitation signals, saved signals, etc.)</li>
+<li>Section <a href="#org334b5e2">3.2</a>: the measurements are first performed on one APA.</li>
+<li>Section <a href="#orgbe4e214">3.3</a>: the same measurements are performed on all the APA and are compared.</li>
</ul>
</div>
-<div id="outline-container-orga3d3857" class="outline-3">
-<h3 id="orga3d3857"><span class="section-number-3">3.1</span> Speedgoat Setup</h3>
+<div id="outline-container-org93b0626" class="outline-3">
+<h3 id="org93b0626"><span class="section-number-3">3.1</span> Speedgoat Setup</h3>
<div class="outline-text-3" id="text-3-1">
<p>
-<a id="orgd658976"></a>
+<a id="org299a882"></a>
</p>
</div>
-<div id="outline-container-org69156d0" class="outline-4">
-<h4 id="org69156d0"><span class="section-number-4">3.1.1</span> <code>frf_setup.m</code> - Measurement Setup</h4>
+<div id="outline-container-org6d3b33d" class="outline-4">
+<h4 id="org6d3b33d"><span class="section-number-4">3.1.1</span> <code>frf_setup.m</code> - Measurement Setup</h4>
<div class="outline-text-4" id="text-3-1-1">
<p>
First is defined the sampling frequency:
@@ -1240,10 +1226,10 @@ V_noise = generateShapedNoise(<span class="org-string">'Ts'</span>, 1<span class
</div>
-<div id="org379d568" class="figure">
+<div id="org44c6c62" class="figure">
<p><img src="figs/frf_meas_noise_excitation.png" alt="frf_meas_noise_excitation.png" />
</p>
-<p><span class="figure-number">Figure 29: </span>Example of Shaped noise excitation signal</p>
+<p><span class="figure-number">Figure 27: </span>Example of Shaped noise excitation signal</p>
</div>
<p>
@@ -1270,14 +1256,14 @@ V_sweep = generateSweepExc(<span class="org-string">'Ts'</span>, Ts, ...
</div>
-<div id="org18470a1" class="figure">
+<div id="org4549b42" class="figure">
<p><img src="figs/frf_meas_sweep_excitation.png" alt="frf_meas_sweep_excitation.png" />
</p>
-<p><span class="figure-number">Figure 30: </span>Example of Sweep Sin excitation signal</p>
+<p><span class="figure-number">Figure 28: </span>Example of Sweep Sin excitation signal</p>
</div>
<p>
-In order to better estimate the high frequency dynamics, a band-limited noise can be used (Figure <a href="#orgc390d1d">31</a>).
+In order to better estimate the high frequency dynamics, a band-limited noise can be used (Figure <a href="#orgf58a5ea">29</a>).
The frequency content of the noise can be precisely controlled.
</p>
<div class="org-src-container">
@@ -1295,10 +1281,10 @@ V_noise_hf = generateShapedNoise(<span class="org-string">'Ts'</span>, 1<span cl
</div>
-<div id="orgc390d1d" class="figure">
+<div id="orgf58a5ea" class="figure">
<p><img src="figs/frf_meas_noise_hf_exc.png" alt="frf_meas_noise_hf_exc.png" />
</p>
-<p><span class="figure-number">Figure 31: </span>Example of band-limited noise excitation signal</p>
+<p><span class="figure-number">Figure 29: </span>Example of band-limited noise excitation signal</p>
</div>
@@ -1318,10 +1304,10 @@ V_sin = generateSinIncreasingAmpl(<span class="org-string">'Ts'</span>, 1<span c
</div>
-<div id="org16790e4" class="figure">
+<div id="org1b6f614" class="figure">
<p><img src="figs/frf_meas_sin_excitation.png" alt="frf_meas_sin_excitation.png" />
</p>
-<p><span class="figure-number">Figure 32: </span>Example of Shaped noise excitation signal</p>
+<p><span class="figure-number">Figure 30: </span>Example of Shaped noise excitation signal</p>
</div>
<p>
@@ -1341,8 +1327,8 @@ save(<span class="org-string">'./frf_data.mat'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-orgde5fcc0" class="outline-4">
-<h4 id="orgde5fcc0"><span class="section-number-4">3.1.2</span> <code>frf_save.m</code> - Save Data</h4>
+<div id="outline-container-orgc9ed24e" class="outline-4">
+<h4 id="orgc9ed24e"><span class="section-number-4">3.1.2</span> <code>frf_save.m</code> - Save Data</h4>
<div class="outline-text-4" id="text-3-1-2">
<p>
First, we get data from the Speedgoat:
@@ -1383,19 +1369,19 @@ save(sprintf(<span class="org-string">'mat/frf_data_%i_huddle.mat'</span>, apa_n
</div>
</div>
-<div id="outline-container-org166d825" class="outline-3">
-<h3 id="org166d825"><span class="section-number-3">3.2</span> Measurements on APA 1</h3>
+<div id="outline-container-org1e81fbd" class="outline-3">
+<h3 id="org1e81fbd"><span class="section-number-3">3.2</span> Measurements on APA 1</h3>
<div class="outline-text-3" id="text-3-2">
<p>
-<a id="orgae0bb15"></a>
+<a id="org334b5e2"></a>
</p>
<p>
Measurements are first performed on only <b>one</b> APA.
Once the measurement procedure is validated, it is performed on all the other APA.
</p>
</div>
-<div id="outline-container-org384b544" class="outline-4">
-<h4 id="org384b544"><span class="section-number-4">3.2.1</span> Excitation Signal</h4>
+<div id="outline-container-org331c2cc" class="outline-4">
+<h4 id="org331c2cc"><span class="section-number-4">3.2.1</span> Excitation Signal</h4>
<div class="outline-text-4" id="text-3-2-1">
<p>
For this first measurement, a basic logarithmic sweep is used between 10Hz and 2kHz.
@@ -1419,20 +1405,20 @@ t = apa_sweep.t <span class="org-type">-</span> apa_sweep.t(1) ; <span class="or
</div>
<p>
-The excitation signal is shown in Figure <a href="#org6ae6845">33</a>.
+The excitation signal is shown in Figure <a href="#org6cadbc4">31</a>.
It is a sweep sine from 10Hz up to 2kHz filtered with a notch centered with the main resonance of the system and a low pass filter.
</p>
-<div id="org6ae6845" class="figure">
+<div id="org6cadbc4" class="figure">
<p><img src="figs/apa_bench_exc_sweep.png" alt="apa_bench_exc_sweep.png" />
</p>
-<p><span class="figure-number">Figure 33: </span>Excitation voltage</p>
+<p><span class="figure-number">Figure 31: </span>Excitation voltage</p>
</div>
</div>
</div>
-<div id="outline-container-org518a94a" class="outline-4">
-<h4 id="org518a94a"><span class="section-number-4">3.2.2</span> FRF Identification - Setup</h4>
+<div id="outline-container-orgc0d949f" class="outline-4">
+<h4 id="orgc0d949f"><span class="section-number-4">3.2.2</span> FRF Identification - Setup</h4>
<div class="outline-text-4" id="text-3-2-2">
<p>
Let’s define the sampling time/frequency.
@@ -1463,15 +1449,15 @@ We get the frequency vector that will be the same for all the frequency domain a
</div>
</div>
-<div id="outline-container-orgc5ede61" class="outline-4">
-<h4 id="orgc5ede61"><span class="section-number-4">3.2.3</span> FRF Identification - Displacement</h4>
+<div id="outline-container-org7b7690e" class="outline-4">
+<h4 id="org7b7690e"><span class="section-number-4">3.2.3</span> FRF Identification - Displacement</h4>
<div class="outline-text-4" id="text-3-2-3">
<p>
In this section, the transfer function from the excitation voltage \(V_a\) to the encoder measured displacement \(d_e\) and interferometer measurement \(d_a\).
</p>
<p>
-The coherence from \(V_a\) to \(d_e\) is computed and shown in Figure <a href="#orga7d946b">34</a>.
+The coherence from \(V_a\) to \(d_e\) is computed and shown in Figure <a href="#orgd5fdfbf">32</a>.
It is quite good from 10Hz up to 500Hz.
</p>
<div class="org-src-container">
@@ -1481,14 +1467,14 @@ It is quite good from 10Hz up to 500Hz.
</div>
-<div id="orga7d946b" class="figure">
+<div id="orgd5fdfbf" class="figure">
<p><img src="figs/apa_1_coh_dvf.png" alt="apa_1_coh_dvf.png" />
</p>
-<p><span class="figure-number">Figure 34: </span>Coherence for the identification from \(V_a\) to \(d_e\)</p>
+<p><span class="figure-number">Figure 32: </span>Coherence for the identification from \(V_a\) to \(d_e\)</p>
</div>
<p>
-The transfer functions are then estimated and shown in Figure <a href="#orgca76a8a">35</a>.
+The transfer functions are then estimated and shown in Figure <a href="#org8082107">33</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% TF - Encoder</span></span>
@@ -1500,13 +1486,13 @@ The transfer functions are then estimated and shown in Figure <a href="#orgca76a
</div>
-<div id="orgca76a8a" class="figure">
+<div id="org8082107" class="figure">
<p><img src="figs/apa_1_frf_dvf.png" alt="apa_1_frf_dvf.png" />
</p>
-<p><span class="figure-number">Figure 35: </span>Obtained transfer functions from \(V_a\) to both \(d_e\) and \(d_a\)</p>
+<p><span class="figure-number">Figure 33: </span>Obtained transfer functions from \(V_a\) to both \(d_e\) and \(d_a\)</p>
</div>
-<div class="important" id="org66a4a2e">
+<div class="important" id="org27ea4c6">
<p>
It seems that using the interferometer, we have a lot more time delay than when using the encoder.
</p>
@@ -1515,15 +1501,15 @@ It seems that using the interferometer, we have a lot more time delay than when
</div>
</div>
-<div id="outline-container-orgd0e0306" class="outline-4">
-<h4 id="orgd0e0306"><span class="section-number-4">3.2.4</span> FRF Identification - Force Sensor</h4>
+<div id="outline-container-orga55f389" class="outline-4">
+<h4 id="orga55f389"><span class="section-number-4">3.2.4</span> FRF Identification - Force Sensor</h4>
<div class="outline-text-4" id="text-3-2-4">
<p>
Now the dynamics from excitation voltage \(V_a\) to the force sensor stack voltage \(V_s\) is identified.
</p>
<p>
-The coherence is computed and shown in Figure <a href="#org1dc8c20">36</a> and found very good from 10Hz up to 2kHz.
+The coherence is computed and shown in Figure <a href="#orgda492cb">34</a> and found very good from 10Hz up to 2kHz.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% TF - Encoder</span></span>
@@ -1532,14 +1518,14 @@ The coherence is computed and shown in Figure <a href="#org1dc8c20">36</a> and f
</div>
-<div id="org1dc8c20" class="figure">
+<div id="orgda492cb" class="figure">
<p><img src="figs/apa_1_coh_iff.png" alt="apa_1_coh_iff.png" />
</p>
-<p><span class="figure-number">Figure 36: </span>Coherence for the identification from \(V_a\) to \(V_s\)</p>
+<p><span class="figure-number">Figure 34: </span>Coherence for the identification from \(V_a\) to \(V_s\)</p>
</div>
<p>
-The transfer function is estimated and shown in Figure <a href="#orgdb5b84c">37</a>.
+The transfer function is estimated and shown in Figure <a href="#orgba32bec">35</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Transfer function estimation</span></span>
@@ -1548,16 +1534,16 @@ The transfer function is estimated and shown in Figure <a href="#orgdb5b84c">37<
</div>
-<div id="orgdb5b84c" class="figure">
+<div id="orgba32bec" class="figure">
<p><img src="figs/apa_1_frf_iff.png" alt="apa_1_frf_iff.png" />
</p>
-<p><span class="figure-number">Figure 37: </span>Obtained transfer functions from \(V_a\) to \(V_s\)</p>
+<p><span class="figure-number">Figure 35: </span>Obtained transfer functions from \(V_a\) to \(V_s\)</p>
</div>
</div>
</div>
-<div id="outline-container-org644a07b" class="outline-4">
-<h4 id="org644a07b"><span class="section-number-4">3.2.5</span> Hysteresis</h4>
+<div id="outline-container-org91d57b2" class="outline-4">
+<h4 id="org91d57b2"><span class="section-number-4">3.2.5</span> Hysteresis</h4>
<div class="outline-text-4" id="text-3-2-5">
<p>
We here wish to visually see the amount of hysteresis present in the APA.
@@ -1580,14 +1566,14 @@ Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
</p>
<p>
-We expect to obtained something like the hysteresis shown in Figure <a href="#orgbc00382">38</a>.
+We expect to obtained something like the hysteresis shown in Figure <a href="#org7b100c3">36</a>.
</p>
-<div id="orgbc00382" class="figure">
+<div id="org7b100c3" class="figure">
<p><img src="figs/expected_hysteresis.png" alt="expected_hysteresis.png" />
</p>
-<p><span class="figure-number">Figure 38: </span>Expected Hysteresis <a class='org-ref-reference' href="#poel10_explor_activ_hard_mount_vibrat">poel10_explor_activ_hard_mount_vibrat</a></p>
+<p><span class="figure-number">Figure 36: </span>Expected Hysteresis <a class='org-ref-reference' href="#poel10_explor_activ_hard_mount_vibrat">poel10_explor_activ_hard_mount_vibrat</a></p>
</div>
<p>
@@ -1609,13 +1595,13 @@ The excitation voltage amplitudes are:
</div>
<p>
-The excitation voltage and the measured displacement are shown in Figure <a href="#orgc67612a">39</a>.
+The excitation voltage and the measured displacement are shown in Figure <a href="#org3f7cfe4">37</a>.
</p>
-<div id="orgc67612a" class="figure">
+<div id="org3f7cfe4" class="figure">
<p><img src="figs/hyst_exc_signal_time.png" alt="hyst_exc_signal_time.png" />
</p>
-<p><span class="figure-number">Figure 39: </span>Excitation voltage and measured displacement</p>
+<p><span class="figure-number">Figure 37: </span>Excitation voltage and measured displacement</p>
</div>
<p>
@@ -1624,16 +1610,16 @@ Also, it is centered on zero.
</p>
<p>
-The measured displacement at a function of the output voltage are shown in Figure <a href="#orgb5679c6">40</a>.
+The measured displacement at a function of the output voltage are shown in Figure <a href="#org412c209">38</a>.
</p>
-<div id="orgb5679c6" class="figure">
+<div id="org412c209" class="figure">
<p><img src="figs/hyst_results_multi_ampl.png" alt="hyst_results_multi_ampl.png" />
</p>
-<p><span class="figure-number">Figure 40: </span>Obtained hysteresis for multiple excitation amplitudes</p>
+<p><span class="figure-number">Figure 38: </span>Obtained hysteresis for multiple excitation amplitudes</p>
</div>
-<div class="important" id="org0084c0d">
+<div class="important" id="org949aa58">
<p>
It is quite clear that hysteresis is increasing with the excitation amplitude.
</p>
@@ -1646,8 +1632,8 @@ Also, no hysteresis is found on the sensor stack voltage.
</div>
</div>
-<div id="outline-container-orga546aea" class="outline-4">
-<h4 id="orga546aea"><span class="section-number-4">3.2.6</span> Estimation of the APA axial stiffness</h4>
+<div id="outline-container-org2536a74" class="outline-4">
+<h4 id="org2536a74"><span class="section-number-4">3.2.6</span> Estimation of the APA axial stiffness</h4>
<div class="outline-text-4" id="text-3-2-6">
<p>
In order to estimate the stiffness of the APA, a weight with known mass \(m_a\) is added on top of the suspended granite and the deflection \(d_e\) is measured using the encoder.
@@ -1666,7 +1652,7 @@ Here, a mass of 6.4 kg is used:
</div>
<p>
-The data is loaded, and the measured displacement is shown in Figure <a href="#orgf8bb36a">41</a>.
+The data is loaded, and the measured displacement is shown in Figure <a href="#org7e40f37">39</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">apa_mass = load(sprintf(<span class="org-string">'frf_data_%i_add_mass_closed_circuit.mat'</span>, 1), <span class="org-string">'t'</span>, <span class="org-string">'de'</span>);
@@ -1675,10 +1661,10 @@ apa_mass.de = apa_mass.de <span class="org-type">-</span> mean(apa_mass.de(apa_m
</div>
-<div id="orgf8bb36a" class="figure">
+<div id="org7e40f37" class="figure">
<p><img src="figs/apa_1_meas_stiffness.png" alt="apa_1_meas_stiffness.png" />
</p>
-<p><span class="figure-number">Figure 41: </span>Measured displacement when adding the mass and removing the mass</p>
+<p><span class="figure-number">Figure 39: </span>Measured displacement when adding the mass and removing the mass</p>
</div>
<p>
@@ -1702,8 +1688,8 @@ k = 1.68 [N/um]
</div>
</div>
-<div id="outline-container-org512f70e" class="outline-4">
-<h4 id="org512f70e"><span class="section-number-4">3.2.7</span> Stiffness change due to electrical connections</h4>
+<div id="outline-container-org6ea1fbc" class="outline-4">
+<h4 id="org6ea1fbc"><span class="section-number-4">3.2.7</span> Stiffness change due to electrical connections</h4>
<div class="outline-text-4" id="text-3-2-7">
<p>
We wish here to see if the stiffness changes when the actuator stacks are not connected to the amplifier and the sensor stacks are not connected to the ADC.
@@ -1732,19 +1718,19 @@ add_mass_cc.de = add_mass_cc.de <span class="org-type">-</span> mean(add_mass_cc
</div>
<p>
-The measured displacements are shown in Figure <a href="#orgff1f9c2">42</a>.
+The measured displacements are shown in Figure <a href="#orga7d044e">40</a>.
</p>
-<div id="orgff1f9c2" class="figure">
+<div id="orga7d044e" class="figure">
<p><img src="figs/apa_meas_k_time_oc_cc.png" alt="apa_meas_k_time_oc_cc.png" />
</p>
-<p><span class="figure-number">Figure 42: </span>Measured displacement</p>
+<p><span class="figure-number">Figure 40: </span>Measured displacement</p>
</div>
<p>
And the stiffness is estimated in both case.
-The results are shown in Table <a href="#org01bcadd">6</a>.
+The results are shown in Table <a href="#orgc5cfd42">6</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">apa_k_oc = 9.8 <span class="org-type">*</span> added_mass <span class="org-type">/</span> (mean(add_mass_oc.de(add_mass_oc.t <span class="org-type">></span> 12 <span class="org-type">&</span> add_mass_oc.t <span class="org-type"><</span> 12.5)) <span class="org-type">-</span> mean(add_mass_oc.de(add_mass_oc.t <span class="org-type">></span> 20 <span class="org-type">&</span> add_mass_oc.t <span class="org-type"><</span> 20.5)));
@@ -1752,7 +1738,7 @@ apa_k_cc = 9.8 <span class="org-type">*</span> added_mass <span class="org-type"
</pre>
</div>
-<table id="org01bcadd" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="orgc5cfd42" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 6:</span> Measured stiffnesses on “open” and “closed” circuits</caption>
<colgroup>
@@ -1779,7 +1765,7 @@ apa_k_cc = 9.8 <span class="org-type">*</span> added_mass <span class="org-type"
</tbody>
</table>
-<div class="important" id="orgcf9c2cb">
+<div class="important" id="orgd5404f0">
<p>
Clearly, connecting the actuator stacks to the amplified (basically equivalent as to short circuiting them) lowers the stiffness.
</p>
@@ -1788,8 +1774,8 @@ Clearly, connecting the actuator stacks to the amplified (basically equivalent a
</div>
</div>
-<div id="outline-container-org7aac27c" class="outline-4">
-<h4 id="org7aac27c"><span class="section-number-4">3.2.8</span> Effect of the resistor on the IFF Plant</h4>
+<div id="outline-container-org87f6fad" class="outline-4">
+<h4 id="org87f6fad"><span class="section-number-4">3.2.8</span> Effect of the resistor on the IFF Plant</h4>
<div class="outline-text-4" id="text-3-2-8">
<p>
A resistor \(R \approx 80.6\,k\Omega\) is added in parallel with the sensor stack.
@@ -1851,16 +1837,16 @@ The transfer function of the corresponding high pass filter is:
</div>
<p>
-Let’s compare the transfer function from actuator stack to sensor stack with and without the added resistor in Figure <a href="#orgecd15bb">43</a>.
+Let’s compare the transfer function from actuator stack to sensor stack with and without the added resistor in Figure <a href="#org5d5164b">41</a>.
</p>
-<div id="orgecd15bb" class="figure">
+<div id="org5d5164b" class="figure">
<p><img src="figs/frf_iff_effect_R.png" alt="frf_iff_effect_R.png" />
</p>
-<p><span class="figure-number">Figure 43: </span>Transfer function from \(V_a\) to \(V_s\) with and without the resistor \(k\)</p>
+<p><span class="figure-number">Figure 41: </span>Transfer function from \(V_a\) to \(V_s\) with and without the resistor \(k\)</p>
</div>
-<div class="important" id="org537c1bd">
+<div class="important" id="org2f328cd">
<p>
The added resistor has indeed the expected effect.
</p>
@@ -1870,18 +1856,18 @@ The added resistor has indeed the expected effect.
</div>
</div>
-<div id="outline-container-org20df261" class="outline-3">
-<h3 id="org20df261"><span class="section-number-3">3.3</span> Comparison of all the APA</h3>
+<div id="outline-container-org799ac62" class="outline-3">
+<h3 id="org799ac62"><span class="section-number-3">3.3</span> Comparison of all the APA</h3>
<div class="outline-text-3" id="text-3-3">
<p>
-<a id="org1718809"></a>
+<a id="orgbe4e214"></a>
</p>
<p>
-The same measurements that was performed in Section <a href="#orgae0bb15">3.2</a> are now performed on all the APA and then compared.
+The same measurements that was performed in Section <a href="#org334b5e2">3.2</a> are now performed on all the APA and then compared.
</p>
</div>
-<div id="outline-container-orgdb73eb0" class="outline-4">
-<h4 id="orgdb73eb0"><span class="section-number-4">3.3.1</span> Axial Stiffnesses - Comparison</h4>
+<div id="outline-container-org6d98582" class="outline-4">
+<h4 id="org6d98582"><span class="section-number-4">3.3.1</span> Axial Stiffnesses - Comparison</h4>
<div class="outline-text-4" id="text-3-3-1">
<p>
Let’s first compare the APA axial stiffnesses.
@@ -1917,11 +1903,11 @@ The data are loaded.
</div>
<p>
-The raw measurements are shown in Figure <a href="#orgf00e3d3">44</a>.
+The raw measurements are shown in Figure <a href="#org001b5cb">42</a>.
All the APA seems to have similar stiffness except the APA 7 which should have an higher stiffness.
</p>
-<div class="question" id="org98acbd4">
+<div class="question" id="orga6bbf36">
<p>
It is however strange that the displacement \(d_e\) when the mass is removed is higher for the APA 7 than for the other APA.
What could cause that?
@@ -1930,17 +1916,17 @@ What could cause that?
</div>
-<div id="orgf00e3d3" class="figure">
+<div id="org001b5cb" class="figure">
<p><img src="figs/apa_meas_k_time.png" alt="apa_meas_k_time.png" />
</p>
-<p><span class="figure-number">Figure 44: </span>Raw measurements for all the APA. A mass of 6.4kg is added at arround 15s and removed at arround 22s</p>
+<p><span class="figure-number">Figure 42: </span>Raw measurements for all the APA. A mass of 6.4kg is added at arround 15s and removed at arround 22s</p>
</div>
<p>
-The stiffnesses are computed for all the APA and are summarized in Table <a href="#org54e6502">7</a>.
+The stiffnesses are computed for all the APA and are summarized in Table <a href="#org0a39324">7</a>.
</p>
-<table id="org54e6502" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+<table id="org0a39324" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 7:</span> Measured stiffnesses</caption>
<colgroup>
@@ -1992,7 +1978,7 @@ The stiffnesses are computed for all the APA and are summarized in Table <a href
</tbody>
</table>
-<div class="important" id="orgad2d1ae">
+<div class="important" id="org5899605">
<p>
The APA300ML manual specifies the nominal stiffness to be \(1.8\,[N/\mu m]\) which is very close to what have been measured.
Only the APA number 7 is a little bit off.
@@ -2002,8 +1988,8 @@ Only the APA number 7 is a little bit off.
</div>
</div>
-<div id="outline-container-org526932e" class="outline-4">
-<h4 id="org526932e"><span class="section-number-4">3.3.2</span> FRF Identification - Setup</h4>
+<div id="outline-container-orgf2b5fb3" class="outline-4">
+<h4 id="orgf2b5fb3"><span class="section-number-4">3.3.2</span> FRF Identification - Setup</h4>
<div class="outline-text-4" id="text-3-3-2">
<p>
The identification is performed in three steps:
@@ -2079,8 +2065,8 @@ We get the frequency vector that will be the same for all the frequency domain a
</div>
</div>
-<div id="outline-container-orga710d70" class="outline-4">
-<h4 id="orga710d70"><span class="section-number-4">3.3.3</span> FRF Identification - DVF</h4>
+<div id="outline-container-org96befbe" class="outline-4">
+<h4 id="org96befbe"><span class="section-number-4">3.3.3</span> FRF Identification - DVF</h4>
<div class="outline-text-4" id="text-3-3-3">
<p>
In this section, the dynamics from excitation voltage \(V_a\) to encoder measured displacement \(d_e\) is identified.
@@ -2106,15 +2092,15 @@ coh_noise_hf = zeros(length(f), length(apa_nums));
</div>
<p>
-The coherence is shown in Figure <a href="#orgeb0f903">45</a>.
+The coherence is shown in Figure <a href="#org3c831ab">43</a>.
It is clear that the Sweep sine gives good coherence up to 400Hz and that the high frequency noise excitation signal helps increasing a little bit the coherence at high frequency.
</p>
-<div id="orgeb0f903" class="figure">
+<div id="org3c831ab" class="figure">
<p><img src="figs/apa_frf_dvf_plant_coh.png" alt="apa_frf_dvf_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 45: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
+<p><span class="figure-number">Figure 43: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
</div>
@@ -2138,11 +2124,11 @@ dvf_noise_hf = zeros(length(f), length(apa_nums));
</div>
<p>
-The obtained transfer functions are shown in Figure <a href="#org064f81f">46</a>.
+The obtained transfer functions are shown in Figure <a href="#org492d862">44</a>.
They are all superimposed except for the APA7.
</p>
-<div class="question" id="org3fcc26d">
+<div class="question" id="org1479f37">
<p>
Why is the APA7 off?
We could think that the APA7 is stiffer, but also the mass line is off.
@@ -2157,14 +2143,14 @@ Maybe it could be due to the amplifier?
</div>
-<div id="org064f81f" class="figure">
+<div id="org492d862" class="figure">
<p><img src="figs/apa_frf_dvf_plant_tf.png" alt="apa_frf_dvf_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 46: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
+<p><span class="figure-number">Figure 44: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
</div>
<p>
-A zoom on the main resonance is shown in Figure <a href="#org1df513c">47</a>.
+A zoom on the main resonance is shown in Figure <a href="#org84284ef">45</a>.
It is clear that expect for the APA 7, the response around the resonances are well matching for all the APA.
</p>
@@ -2172,7 +2158,7 @@ It is clear that expect for the APA 7, the response around the resonances are we
It is also clear that there is not a single resonance but two resonances, a first one at 95Hz and a second one at 105Hz.
</p>
-<div class="question" id="org47afc56">
+<div class="question" id="orgc20eee1">
<p>
Why is there a double resonance at around 94Hz?
</p>
@@ -2180,23 +2166,23 @@ Why is there a double resonance at around 94Hz?
</div>
-<div id="org1df513c" class="figure">
+<div id="org84284ef" class="figure">
<p><img src="figs/apa_frf_dvf_zoom_res_plant_tf.png" alt="apa_frf_dvf_zoom_res_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 47: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\)) - Zoom on the main resonance</p>
+<p><span class="figure-number">Figure 45: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\)) - Zoom on the main resonance</p>
</div>
</div>
</div>
-<div id="outline-container-orgf160d6e" class="outline-4">
-<h4 id="orgf160d6e"><span class="section-number-4">3.3.4</span> FRF Identification - IFF</h4>
+<div id="outline-container-org0ae36ad" class="outline-4">
+<h4 id="org0ae36ad"><span class="section-number-4">3.3.4</span> FRF Identification - IFF</h4>
<div class="outline-text-4" id="text-3-3-4">
<p>
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
</p>
<p>
-First the coherence is computed and shown in Figure <a href="#orge7875f9">48</a>.
+First the coherence is computed and shown in Figure <a href="#org10c2b80">46</a>.
The coherence is very nice from 10Hz to 2kHz.
It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
</p>
@@ -2218,14 +2204,14 @@ coh_noise_hf = zeros(length(f), length(apa_nums));
</div>
-<div id="orge7875f9" class="figure">
+<div id="org10c2b80" class="figure">
<p><img src="figs/apa_frf_iff_plant_coh.png" alt="apa_frf_iff_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 48: </span>Obtained coherence for the IFF plant</p>
+<p><span class="figure-number">Figure 46: </span>Obtained coherence for the IFF plant</p>
</div>
<p>
-Then the FRF are estimated and shown in Figure <a href="#orgabf3b03">49</a>
+Then the FRF are estimated and shown in Figure <a href="#org2efd37b">47</a>
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% FRF estimation of the transfer function from Va to Vs</span></span>
@@ -2244,57 +2230,57 @@ iff_noise_hf = zeros(length(f), length(apa_nums));
</div>
-<div id="orgabf3b03" class="figure">
+<div id="org2efd37b" class="figure">
<p><img src="figs/apa_frf_iff_plant_tf.png" alt="apa_frf_iff_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 49: </span>Identified IFF Plant</p>
+<p><span class="figure-number">Figure 47: </span>Identified IFF Plant</p>
</div>
</div>
</div>
</div>
</div>
-<div id="outline-container-org585297f" class="outline-2">
-<h2 id="org585297f"><span class="section-number-2">4</span> Dynamical measurements - Struts</h2>
+<div id="outline-container-org86caafb" class="outline-2">
+<h2 id="org86caafb"><span class="section-number-2">4</span> Dynamical measurements - Struts</h2>
<div class="outline-text-2" id="text-4">
<p>
-<a id="orgf722be9"></a>
+<a id="org6000d1d"></a>
</p>
<p>
-The same bench used in Section <a href="#org8962678">3</a> is here used with the strut instead of only the APA.
+The same bench used in Section <a href="#org8309884">3</a> is here used with the strut instead of only the APA.
</p>
<p>
-The bench is shown in Figure <a href="#orgc59eac8">50</a>.
-Measurements are performed either when no encoder is fixed to the strut (Figure <a href="#org67e87c0">51</a>) or when one encoder is fixed to the strut (Figure <a href="#orgc59eac8">50</a>).
+The bench is shown in Figure <a href="#orgb5fdd80">48</a>.
+Measurements are performed either when no encoder is fixed to the strut (Figure <a href="#orge0ba236">49</a>) or when one encoder is fixed to the strut (Figure <a href="#orgb5fdd80">48</a>).
</p>
-<div id="orgc59eac8" class="figure">
+<div id="orgb5fdd80" class="figure">
<p><img src="figs/test_bench_leg_overview.png" alt="test_bench_leg_overview.png" />
</p>
-<p><span class="figure-number">Figure 50: </span>Test Bench with Strut - Overview</p>
+<p><span class="figure-number">Figure 48: </span>Test Bench with Strut - Overview</p>
</div>
-<div id="org67e87c0" class="figure">
+<div id="orge0ba236" class="figure">
<p><img src="figs/test_bench_leg_front.png" alt="test_bench_leg_front.png" />
</p>
-<p><span class="figure-number">Figure 51: </span>Test Bench with Strut - Zoom on the strut</p>
+<p><span class="figure-number">Figure 49: </span>Test Bench with Strut - Zoom on the strut</p>
</div>
-<div id="org96d29f4" class="figure">
+<div id="org0146e6e" class="figure">
<p><img src="figs/test_bench_leg_coder.png" alt="test_bench_leg_coder.png" />
</p>
-<p><span class="figure-number">Figure 52: </span>Test Bench with Strut - Zoom on the strut with the encoder</p>
+<p><span class="figure-number">Figure 50: </span>Test Bench with Strut - Zoom on the strut with the encoder</p>
</div>
</div>
-<div id="outline-container-org4b7728d" class="outline-3">
-<h3 id="org4b7728d"><span class="section-number-3">4.1</span> Measurement on Strut 1</h3>
+<div id="outline-container-org3dad850" class="outline-3">
+<h3 id="org3dad850"><span class="section-number-3">4.1</span> Measurement on Strut 1</h3>
<div class="outline-text-3" id="text-4-1">
<p>
-<a id="org6f9d0f2"></a>
+<a id="org1a96191"></a>
</p>
<p>
Measurements are first performed on the strut 1 that contains:
@@ -2304,15 +2290,15 @@ Measurements are first performed on the strut 1 that contains:
<li>flex 1 and flex 2</li>
</ul>
</div>
-<div id="outline-container-org9a207b3" class="outline-4">
-<h4 id="org9a207b3"><span class="section-number-4">4.1.1</span> Without Encoder</h4>
+<div id="outline-container-orgf9bf73b" class="outline-4">
+<h4 id="orgf9bf73b"><span class="section-number-4">4.1.1</span> Without Encoder</h4>
<div class="outline-text-4" id="text-4-1-1">
<p>
-<a id="orgad44262"></a>
+<a id="orga147709"></a>
</p>
</div>
-<div id="outline-container-orgec9c46c" class="outline-5">
-<h5 id="orgec9c46c"><span class="section-number-5">4.1.1.1</span> FRF Identification - Setup</h5>
+<div id="outline-container-org8f88578" class="outline-5">
+<h5 id="org8f88578"><span class="section-number-5">4.1.1.1</span> FRF Identification - Setup</h5>
<div class="outline-text-5" id="text-4-1-1-1">
<p>
The identification is performed in three steps:
@@ -2368,8 +2354,8 @@ We get the frequency vector that will be the same for all the frequency domain a
</div>
</div>
-<div id="outline-container-orge11d516" class="outline-5">
-<h5 id="orge11d516"><span class="section-number-5">4.1.1.2</span> FRF Identification - Displacement</h5>
+<div id="outline-container-orgcc08e06" class="outline-5">
+<h5 id="orgcc08e06"><span class="section-number-5">4.1.1.2</span> FRF Identification - Displacement</h5>
<div class="outline-text-5" id="text-4-1-1-2">
<p>
In this section, the dynamics from the excitation voltage \(V_a\) to the interferometer \(d_a\) is identified.
@@ -2385,14 +2371,14 @@ We compute the coherence for 2nd and 3rd identification:
</div>
-<div id="orgd2bca9c" class="figure">
+<div id="orgb889abd" class="figure">
<p><img src="figs/strut_1_frf_dvf_plant_coh.png" alt="strut_1_frf_dvf_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 53: </span>Obtained coherence for the plant from \(V_a\) to \(d_a\)</p>
+<p><span class="figure-number">Figure 51: </span>Obtained coherence for the plant from \(V_a\) to \(d_a\)</p>
</div>
<p>
-The transfer function from \(V_a\) to the interferometer measured displacement \(d_a\) is estimated and shown in Figure <a href="#org1de07bf">54</a>.
+The transfer function from \(V_a\) to the interferometer measured displacement \(d_a\) is estimated and shown in Figure <a href="#org0bd6a34">52</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">[dvf_sweep, <span class="org-type">~</span>] = tfestimate(leg_sweep.Va, leg_sweep.da, win, [], [], 1<span class="org-type">/</span>Ts);
@@ -2401,23 +2387,23 @@ The transfer function from \(V_a\) to the interferometer measured displacement \
</div>
-<div id="org1de07bf" class="figure">
+<div id="org0bd6a34" class="figure">
<p><img src="figs/strut_1_frf_dvf_plant_tf.png" alt="strut_1_frf_dvf_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 54: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the interferometer \(d_a\))</p>
+<p><span class="figure-number">Figure 52: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the interferometer \(d_a\))</p>
</div>
</div>
</div>
-<div id="outline-container-org62bf3f5" class="outline-5">
-<h5 id="org62bf3f5"><span class="section-number-5">4.1.1.3</span> FRF Identification - IFF</h5>
+<div id="outline-container-orgfe171f5" class="outline-5">
+<h5 id="orgfe171f5"><span class="section-number-5">4.1.1.3</span> FRF Identification - IFF</h5>
<div class="outline-text-5" id="text-4-1-1-3">
<p>
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
</p>
<p>
-First the coherence is computed and shown in Figure <a href="#orgd931694">55</a>.
+First the coherence is computed and shown in Figure <a href="#org70c4e77">53</a>.
The coherence is very nice from 10Hz to 2kHz.
It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
</p>
@@ -2429,14 +2415,14 @@ It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the ex
</div>
-<div id="orgd931694" class="figure">
+<div id="org70c4e77" class="figure">
<p><img src="figs/strut_1_frf_iff_plant_coh.png" alt="strut_1_frf_iff_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 55: </span>Obtained coherence for the IFF plant</p>
+<p><span class="figure-number">Figure 53: </span>Obtained coherence for the IFF plant</p>
</div>
<p>
-Then the FRF are estimated and shown in Figure <a href="#org7795584">56</a>
+Then the FRF are estimated and shown in Figure <a href="#org0cca0c4">54</a>
</p>
<div class="org-src-container">
<pre class="src src-matlab">[iff_sweep, <span class="org-type">~</span>] = tfestimate(leg_sweep.Va, leg_sweep.Vs, win, [], [], 1<span class="org-type">/</span>Ts);
@@ -2445,24 +2431,24 @@ Then the FRF are estimated and shown in Figure <a href="#org7795584">56</a>
</div>
-<div id="org7795584" class="figure">
+<div id="org0cca0c4" class="figure">
<p><img src="figs/strut_1_frf_iff_plant_tf.png" alt="strut_1_frf_iff_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 56: </span>Identified IFF Plant for the Strut 1</p>
+<p><span class="figure-number">Figure 54: </span>Identified IFF Plant for the Strut 1</p>
</div>
</div>
</div>
</div>
-<div id="outline-container-orgbf66b4f" class="outline-4">
-<h4 id="orgbf66b4f"><span class="section-number-4">4.1.2</span> With Encoder</h4>
+<div id="outline-container-org01cd1e5" class="outline-4">
+<h4 id="org01cd1e5"><span class="section-number-4">4.1.2</span> With Encoder</h4>
<div class="outline-text-4" id="text-4-1-2">
<p>
-<a id="org6a4e5ba"></a>
+<a id="org1371835"></a>
</p>
</div>
-<div id="outline-container-org5ba2d6c" class="outline-5">
-<h5 id="org5ba2d6c"><span class="section-number-5">4.1.2.1</span> Measurement Data</h5>
+<div id="outline-container-org9e75306" class="outline-5">
+<h5 id="org9e75306"><span class="section-number-5">4.1.2.1</span> Measurement Data</h5>
<div class="outline-text-5" id="text-4-1-2-1">
<div class="org-src-container">
<pre class="src src-matlab">leg_enc_sweep = load(sprintf(<span class="org-string">'frf_data_leg_coder_badly_align_%i_noise.mat'</span>, 1), <span class="org-string">'t'</span>, <span class="org-string">'Va'</span>, <span class="org-string">'Vs'</span>, <span class="org-string">'de'</span>, <span class="org-string">'da'</span>);
@@ -2472,8 +2458,8 @@ leg_enc_noise_hf = load(sprintf(<span class="org-string">'frf_data_leg_coder_bad
</div>
</div>
-<div id="outline-container-orgb740ddb" class="outline-5">
-<h5 id="orgb740ddb"><span class="section-number-5">4.1.2.2</span> FRF Identification - DVF</h5>
+<div id="outline-container-org7c83cc7" class="outline-5">
+<h5 id="org7c83cc7"><span class="section-number-5">4.1.2.2</span> FRF Identification - DVF</h5>
<div class="outline-text-5" id="text-4-1-2-2">
<p>
In this section, the dynamics from \(V_a\) to \(d_e\) is identified.
@@ -2489,10 +2475,10 @@ We compute the coherence for 2nd and 3rd identification:
</div>
-<div id="org8b37f45" class="figure">
+<div id="org273bef4" class="figure">
<p><img src="figs/strut_1_enc_frf_dvf_plant_coh.png" alt="strut_1_enc_frf_dvf_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 57: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
+<p><span class="figure-number">Figure 55: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
</div>
<div class="org-src-container">
@@ -2508,14 +2494,14 @@ We compute the coherence for 2nd and 3rd identification:
</div>
<p>
-The obtained transfer functions are shown in Figure <a href="#orga926797">58</a>.
+The obtained transfer functions are shown in Figure <a href="#org69ba801">56</a>.
</p>
<p>
They are all superimposed except for the APA7.
</p>
-<div class="question" id="orged0b724">
+<div class="question" id="org7c20681">
<p>
Why is the APA7 off?
We could think that the APA7 is stiffer, but also the mass line is off.
@@ -2529,7 +2515,7 @@ Maybe it could be due to the amplifier?
</div>
-<div class="question" id="org110dae7">
+<div class="question" id="orgd1f0500">
<p>
Why is there a double resonance at around 94Hz?
</p>
@@ -2537,33 +2523,33 @@ Why is there a double resonance at around 94Hz?
</div>
-<div id="orga926797" class="figure">
+<div id="org69ba801" class="figure">
<p><img src="figs/strut_1_enc_frf_dvf_plant_tf.png" alt="strut_1_enc_frf_dvf_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 58: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
+<p><span class="figure-number">Figure 56: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
</div>
</div>
</div>
-<div id="outline-container-orga7f7c45" class="outline-5">
-<h5 id="orga7f7c45"><span class="section-number-5">4.1.2.3</span> Comparison of the Encoder and Interferometer</h5>
+<div id="outline-container-org259e288" class="outline-5">
+<h5 id="org259e288"><span class="section-number-5">4.1.2.3</span> Comparison of the Encoder and Interferometer</h5>
<div class="outline-text-5" id="text-4-1-2-3">
<p>
The interferometer could here represent the case where the encoders are fixed to the plates and not the APA.
</p>
<p>
-The dynamics from \(V_a\) to \(d_e\) and from \(V_a\) to \(d_a\) are compared in Figure <a href="#orgd0e6bdf">59</a>.
+The dynamics from \(V_a\) to \(d_e\) and from \(V_a\) to \(d_a\) are compared in Figure <a href="#org18d0387">57</a>.
</p>
-<div id="orgd0e6bdf" class="figure">
+<div id="org18d0387" class="figure">
<p><img src="figs/strut_1_comp_enc_int.png" alt="strut_1_comp_enc_int.png" />
</p>
-<p><span class="figure-number">Figure 59: </span>Comparison of the transfer functions from excitation voltage \(V_a\) to either the encoder \(d_e\) or the interferometer \(d_a\)</p>
+<p><span class="figure-number">Figure 57: </span>Comparison of the transfer functions from excitation voltage \(V_a\) to either the encoder \(d_e\) or the interferometer \(d_a\)</p>
</div>
-<div class="important" id="org23f91c4">
+<div class="important" id="org07576f8">
<p>
It will clearly be difficult to do something (except some low frequency positioning) with the encoders fixed to the APA.
</p>
@@ -2572,53 +2558,39 @@ It will clearly be difficult to do something (except some low frequency position
</div>
</div>
-<div id="outline-container-orge2da99d" class="outline-5">
-<h5 id="orge2da99d"><span class="section-number-5">4.1.2.4</span> APA Resonances Frequency</h5>
+<div id="outline-container-org210f2ee" class="outline-5">
+<h5 id="org210f2ee"><span class="section-number-5">4.1.2.4</span> APA Resonances Frequency</h5>
<div class="outline-text-5" id="text-4-1-2-4">
<p>
-As shown in Figure <a href="#orgccd81a5">60</a>, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
+As shown in Figure <a href="#orgfbdbf1a">58</a>, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
</p>
-<div id="orgccd81a5" class="figure">
+<div id="orgfbdbf1a" class="figure">
<p><img src="figs/strut_1_spurious_resonances.png" alt="strut_1_spurious_resonances.png" />
</p>
-<p><span class="figure-number">Figure 60: </span>Magnitude of the transfer function from excitation voltage \(V_a\) to encoder measurement \(d_e\). The frequency of the resonances are noted.</p>
+<p><span class="figure-number">Figure 58: </span>Magnitude of the transfer function from excitation voltage \(V_a\) to encoder measurement \(d_e\). The frequency of the resonances are noted.</p>
</div>
<p>
These resonances correspond to parasitic resonances of the APA itself.
-They are very close to what was estimated using the FEM:
+They are very close to what was estimated using the FEM (Figure <a href="#orgf7a6fae">59</a>):
</p>
<ul class="org-ul">
-<li>X-bending mode at around 190Hz (Figure <a href="#org56987c2">61</a>)</li>
-<li>Y-bending mode at around 290Hz (Figure <a href="#org9c2488f">62</a>)</li>
-<li>Z-torsion mode at around 400Hz (Figure <a href="#orgb46438c">63</a>)</li>
+<li>Mode in X-bending at 189Hz</li>
+<li>Mode in Y-bending at 285Hz</li>
+<li>Mode in Z-torsion at 400Hz</li>
</ul>
-<div id="org56987c2" class="figure">
-<p><img src="figs/mode_bending_x.gif" alt="mode_bending_x.gif" />
+<div id="orgf7a6fae" class="figure">
+<p><img src="figs/apa_mode_shapes.gif" alt="apa_mode_shapes.gif" />
</p>
-<p><span class="figure-number">Figure 61: </span>X-bending mode (189Hz)</p>
+<p><span class="figure-number">Figure 59: </span>Spurious resonances. a) X-bending mode at 189Hz. b) Y-bending mode at 285Hz. c) Z-torsion mode at 400Hz</p>
</div>
-
-<div id="org9c2488f" class="figure">
-<p><img src="figs/mode_bending_y.gif" alt="mode_bending_y.gif" />
-</p>
-<p><span class="figure-number">Figure 62: </span>Y-bending mode (285Hz)</p>
-</div>
-
-
-<div id="orgb46438c" class="figure">
-<p><img src="figs/mode_torsion_z.gif" alt="mode_torsion_z.gif" />
-</p>
-<p><span class="figure-number">Figure 63: </span>Z-torsion mode (400Hz)</p>
-</div>
-
-<div class="important" id="org8781db1">
+<div class="important" id="orgd7ba304">
<p>
The resonances are indeed due to limited stiffness of the APA.
</p>
@@ -2627,8 +2599,8 @@ The resonances are indeed due to limited stiffness of the APA.
</div>
</div>
-<div id="outline-container-org002bddc" class="outline-5">
-<h5 id="org002bddc"><span class="section-number-5">4.1.2.5</span> Estimated Flexible Joint axial stiffness</h5>
+<div id="outline-container-org5bba07f" class="outline-5">
+<h5 id="org5bba07f"><span class="section-number-5">4.1.2.5</span> Estimated Flexible Joint axial stiffness</h5>
<div class="outline-text-5" id="text-4-1-2-5">
<div class="org-src-container">
<pre class="src src-matlab">load(sprintf(<span class="org-string">'frf_data_leg_coder_%i_add_mass_closed_circuit.mat'</span>, 1), <span class="org-string">'t'</span>, <span class="org-string">'Va'</span>, <span class="org-string">'Vs'</span>, <span class="org-string">'de'</span>, <span class="org-string">'da'</span>);
@@ -2682,7 +2654,7 @@ hold off;
</pre>
</div>
-<div class="question" id="org4d0dcfa">
+<div class="question" id="org6350fd1">
<p>
What is strange is that the encoder is measuring a larger displacement than the interferometer.
That should be the opposite.
@@ -2693,15 +2665,15 @@ Maybe is is caused by the fact that the APA is experiencing some bending and the
</div>
</div>
-<div id="outline-container-orgb8a11ba" class="outline-5">
-<h5 id="orgb8a11ba"><span class="section-number-5">4.1.2.6</span> FRF Identification - IFF</h5>
+<div id="outline-container-org16c31d9" class="outline-5">
+<h5 id="org16c31d9"><span class="section-number-5">4.1.2.6</span> FRF Identification - IFF</h5>
<div class="outline-text-5" id="text-4-1-2-6">
<p>
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
</p>
<p>
-First the coherence is computed and shown in Figure <a href="#orgd931694">55</a>.
+First the coherence is computed and shown in Figure <a href="#org70c4e77">53</a>.
The coherence is very nice from 10Hz to 2kHz.
It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
</p>
@@ -2713,14 +2685,14 @@ It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the ex
</div>
-<div id="orgd5159f7" class="figure">
+<div id="org898e622" class="figure">
<p><img src="figs/strut_1_frf_iff_plant_coh.png" alt="strut_1_frf_iff_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 64: </span>Obtained coherence for the IFF plant</p>
+<p><span class="figure-number">Figure 60: </span>Obtained coherence for the IFF plant</p>
</div>
<p>
-Then the FRF are estimated and shown in Figure <a href="#orga2d0bf7">65</a>
+Then the FRF are estimated and shown in Figure <a href="#orged16314">61</a>
</p>
<div class="org-src-container">
<pre class="src src-matlab">[iff_enc_sweep, <span class="org-type">~</span>] = tfestimate(leg_enc_sweep.Va, leg_enc_sweep.Vs, win, [], [], 1<span class="org-type">/</span>Ts);
@@ -2729,23 +2701,23 @@ Then the FRF are estimated and shown in Figure <a href="#orga2d0bf7">65</a>
</div>
-<div id="orga2d0bf7" class="figure">
+<div id="orged16314" class="figure">
<p><img src="figs/strut_1_enc_frf_iff_plant_tf.png" alt="strut_1_enc_frf_iff_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 65: </span>Identified IFF Plant</p>
+<p><span class="figure-number">Figure 61: </span>Identified IFF Plant</p>
</div>
<p>
-Let’s now compare the IFF plants whether the encoders are fixed to the APA or not (Figure <a href="#orgb9b5b0a">66</a>).
+Let’s now compare the IFF plants whether the encoders are fixed to the APA or not (Figure <a href="#orgc11bb52">62</a>).
</p>
-<div id="orgb9b5b0a" class="figure">
+<div id="orgc11bb52" class="figure">
<p><img src="figs/strut_1_frf_iff_effect_enc.png" alt="strut_1_frf_iff_effect_enc.png" />
</p>
-<p><span class="figure-number">Figure 66: </span>Effect of the encoder on the IFF plant</p>
+<p><span class="figure-number">Figure 62: </span>Effect of the encoder on the IFF plant</p>
</div>
-<div class="important" id="orgdf8aa6d">
+<div class="important" id="org589d9fb">
<p>
We can see that the IFF does not change whether of not the encoder are fixed to the struts.
</p>
@@ -2756,18 +2728,18 @@ We can see that the IFF does not change whether of not the encoder are fixed to
</div>
</div>
-<div id="outline-container-org9fad4b4" class="outline-3">
-<h3 id="org9fad4b4"><span class="section-number-3">4.2</span> Comparison of all the Struts</h3>
+<div id="outline-container-org2d81875" class="outline-3">
+<h3 id="org2d81875"><span class="section-number-3">4.2</span> Comparison of all the Struts</h3>
<div class="outline-text-3" id="text-4-2">
<p>
-<a id="orgfd53ceb"></a>
+<a id="orgf5f3d28"></a>
</p>
<p>
Now all struts are measured using the same procedure and test bench.
</p>
</div>
-<div id="outline-container-org49346d3" class="outline-4">
-<h4 id="org49346d3"><span class="section-number-4">4.2.1</span> FRF Identification - Setup</h4>
+<div id="outline-container-orgcbfc374" class="outline-4">
+<h4 id="orgcbfc374"><span class="section-number-4">4.2.1</span> FRF Identification - Setup</h4>
<div class="outline-text-4" id="text-4-2-1">
<p>
The identification is performed in two steps:
@@ -2841,8 +2813,8 @@ We get the frequency vector that will be the same for all the frequency domain a
</div>
</div>
-<div id="outline-container-orgabceeab" class="outline-4">
-<h4 id="orgabceeab"><span class="section-number-4">4.2.2</span> FRF Identification - DVF</h4>
+<div id="outline-container-org17723e2" class="outline-4">
+<h4 id="org17723e2"><span class="section-number-4">4.2.2</span> FRF Identification - DVF</h4>
<div class="outline-text-4" id="text-4-2-2">
<p>
In this section, the dynamics from \(V_a\) to \(d_e\) is identified.
@@ -2868,15 +2840,15 @@ coh_noise_hf = zeros(length(f), length(leg_nums));
</div>
<p>
-The coherence is shown in Figure <a href="#orgd8721f1">67</a>.
+The coherence is shown in Figure <a href="#org2625e5d">63</a>.
It is clear that the Noise sine gives good coherence up to 400Hz and that the high frequency noise excitation signal helps increasing a little bit the coherence at high frequency.
</p>
-<div id="orgd8721f1" class="figure">
+<div id="org2625e5d" class="figure">
<p><img src="figs/struts_frf_dvf_plant_coh.png" alt="struts_frf_dvf_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 67: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
+<p><span class="figure-number">Figure 63: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
</div>
@@ -2900,22 +2872,22 @@ dvf_noise_hf = zeros(length(f), length(leg_nums));
</div>
<p>
-The obtained transfer functions are shown in Figure <a href="#orgc7fc6eb">68</a>.
+The obtained transfer functions are shown in Figure <a href="#org504c20e">64</a>.
</p>
<p>
They are all superimposed except for the LEG7.
</p>
-<div id="orgc7fc6eb" class="figure">
+<div id="org504c20e" class="figure">
<p><img src="figs/struts_frf_dvf_plant_tf.png" alt="struts_frf_dvf_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 68: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
+<p><span class="figure-number">Figure 64: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
</div>
-<div class="important" id="org71921be">
+<div class="important" id="org492bd35">
<p>
-Depending on how the APA are mounted with the flexible joints, the dynamics can change a lot as shown in Figure <a href="#orgc7fc6eb">68</a>.
+Depending on how the APA are mounted with the flexible joints, the dynamics can change a lot as shown in Figure <a href="#org504c20e">64</a>.
In the future, a “pin” will be used to better align the APA with the flexible joints.
We can expect the amplitude of the spurious resonances to decrease.
</p>
@@ -2924,8 +2896,8 @@ We can expect the amplitude of the spurious resonances to decrease.
</div>
</div>
-<div id="outline-container-org8cfc7f6" class="outline-4">
-<h4 id="org8cfc7f6"><span class="section-number-4">4.2.3</span> FRF Identification - DVF with interferometer</h4>
+<div id="outline-container-orga2a2b77" class="outline-4">
+<h4 id="orga2a2b77"><span class="section-number-4">4.2.3</span> FRF Identification - DVF with interferometer</h4>
<div class="outline-text-4" id="text-4-2-3">
<p>
In this section, the dynamics from \(V_a\) to \(d_a\) is identified.
@@ -2951,14 +2923,14 @@ coh_noise_hf = zeros(length(f), length(leg_nums));
</div>
<p>
-The coherence is shown in Figure <a href="#org3c70e90">69</a>.
+The coherence is shown in Figure <a href="#orga17ddf2">65</a>.
It is clear that the Noise sine gives good coherence up to 400Hz and that the high frequency noise excitation signal helps increasing a little bit the coherence at high frequency.
</p>
-<div id="org3c70e90" class="figure">
+<div id="orga17ddf2" class="figure">
<p><img src="figs/struts_frf_int_plant_coh.png" alt="struts_frf_int_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 69: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
+<p><span class="figure-number">Figure 65: </span>Obtained coherence for the plant from \(V_a\) to \(d_e\)</p>
</div>
<p>
@@ -2981,7 +2953,7 @@ dvf_a_noise_hf = zeros(length(f), length(leg_nums));
</div>
<p>
-The obtained transfer functions are shown in Figure <a href="#org5becb4c">70</a>.
+The obtained transfer functions are shown in Figure <a href="#orgd0b1c97">66</a>.
</p>
<p>
@@ -2989,23 +2961,23 @@ They are all superimposed except for the LEG7.
</p>
-<div id="org5becb4c" class="figure">
+<div id="orgd0b1c97" class="figure">
<p><img src="figs/struts_frf_int_plant_tf.png" alt="struts_frf_int_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 70: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
+<p><span class="figure-number">Figure 66: </span>Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))</p>
</div>
</div>
</div>
-<div id="outline-container-org59120b1" class="outline-4">
-<h4 id="org59120b1"><span class="section-number-4">4.2.4</span> FRF Identification - IFF</h4>
+<div id="outline-container-orgdc1439d" class="outline-4">
+<h4 id="orgdc1439d"><span class="section-number-4">4.2.4</span> FRF Identification - IFF</h4>
<div class="outline-text-4" id="text-4-2-4">
<p>
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
</p>
<p>
-First the coherence is computed and shown in Figure <a href="#org951f8b9">71</a>.
+First the coherence is computed and shown in Figure <a href="#org8794331">67</a>.
The coherence is very nice from 10Hz to 2kHz.
It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
</p>
@@ -3027,14 +2999,14 @@ coh_noise_hf = zeros(length(f), length(leg_nums));
</div>
-<div id="org951f8b9" class="figure">
+<div id="org8794331" class="figure">
<p><img src="figs/struts_frf_iff_plant_coh.png" alt="struts_frf_iff_plant_coh.png" />
</p>
-<p><span class="figure-number">Figure 71: </span>Obtained coherence for the IFF plant</p>
+<p><span class="figure-number">Figure 67: </span>Obtained coherence for the IFF plant</p>
</div>
<p>
-Then the FRF are estimated and shown in Figure <a href="#org23d673a">72</a>
+Then the FRF are estimated and shown in Figure <a href="#org262cea1">68</a>
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% FRF estimation of the transfer function from Va to Vs</span></span>
@@ -3053,38 +3025,38 @@ iff_noise_hf = zeros(length(f), length(leg_nums));
</div>
-<div id="org23d673a" class="figure">
+<div id="org262cea1" class="figure">
<p><img src="figs/struts_frf_iff_plant_tf.png" alt="struts_frf_iff_plant_tf.png" />
</p>
-<p><span class="figure-number">Figure 72: </span>Identified IFF Plant</p>
+<p><span class="figure-number">Figure 68: </span>Identified IFF Plant</p>
</div>
</div>
</div>
</div>
</div>
-<div id="outline-container-org5e8cd6b" class="outline-2">
-<h2 id="org5e8cd6b"><span class="section-number-2">5</span> Test Bench APA300ML - Simscape Model</h2>
+<div id="outline-container-orgb0a183d" class="outline-2">
+<h2 id="orgb0a183d"><span class="section-number-2">5</span> Test Bench APA300ML - Simscape Model</h2>
<div class="outline-text-2" id="text-5">
</div>
-<div id="outline-container-org987d2cc" class="outline-3">
-<h3 id="org987d2cc"><span class="section-number-3">5.1</span> Introduction</h3>
+<div id="outline-container-org16cd4a8" class="outline-3">
+<h3 id="org16cd4a8"><span class="section-number-3">5.1</span> Introduction</h3>
<div class="outline-text-3" id="text-5-1">
<p>
-A simscape model (Figure <a href="#orgeb9f27b">73</a>) of the measurement bench is used.
+A simscape model (Figure <a href="#org12742ab">69</a>) of the measurement bench is used.
</p>
-<div id="orgeb9f27b" class="figure">
+<div id="org12742ab" class="figure">
<p><img src="figs/model_bench_apa.png" alt="model_bench_apa.png" />
</p>
-<p><span class="figure-number">Figure 73: </span>Screenshot of the Simscape model</p>
+<p><span class="figure-number">Figure 69: </span>Screenshot of the Simscape model</p>
</div>
</div>
</div>
-<div id="outline-container-org821abe7" class="outline-3">
-<h3 id="org821abe7"><span class="section-number-3">5.2</span> First Identification</h3>
+<div id="outline-container-org0d2ccaa" class="outline-3">
+<h3 id="org0d2ccaa"><span class="section-number-3">5.2</span> First Identification</h3>
<div class="outline-text-3" id="text-5-2">
<p>
The APA is first initialized with default parameters and the transfer function from excitation voltage \(V_a\) (before the amplification of 20 due to the PD200 amplifier) to the sensor stack voltage \(V_s\), encoder \(d_L\) and interferometer \(z\) is identified.
@@ -3112,35 +3084,35 @@ Ga.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
<p>
-The obtain dynamics are shown in Figure <a href="#org7b2bd95">74</a> and <a href="#orgbff346f">75</a>.
+The obtain dynamics are shown in Figure <a href="#orgfacd83f">70</a> and <a href="#org7c5ff30">71</a>.
</p>
-<div id="org7b2bd95" class="figure">
+<div id="orgfacd83f" class="figure">
<p><img src="figs/apa_model_bench_bode_vs.png" alt="apa_model_bench_bode_vs.png" />
</p>
-<p><span class="figure-number">Figure 74: </span>Bode plot of the transfer function from \(V_a\) to \(V_s\)</p>
+<p><span class="figure-number">Figure 70: </span>Bode plot of the transfer function from \(V_a\) to \(V_s\)</p>
</div>
-<div id="orgbff346f" class="figure">
+<div id="org7c5ff30" class="figure">
<p><img src="figs/apa_model_bench_bode_dl_z.png" alt="apa_model_bench_bode_dl_z.png" />
</p>
-<p><span class="figure-number">Figure 75: </span>Bode plot of the transfer function from \(V_a\) to \(d_L\) and to \(z\)</p>
+<p><span class="figure-number">Figure 71: </span>Bode plot of the transfer function from \(V_a\) to \(d_L\) and to \(z\)</p>
</div>
</div>
</div>
-<div id="outline-container-orgd4e5638" class="outline-3">
-<h3 id="orgd4e5638"><span class="section-number-3">5.3</span> Identify Sensor/Actuator constants and compare with measured FRF</h3>
+<div id="outline-container-orgfedb510" class="outline-3">
+<h3 id="orgfedb510"><span class="section-number-3">5.3</span> Identify Sensor/Actuator constants and compare with measured FRF</h3>
<div class="outline-text-3" id="text-5-3">
</div>
-<div id="outline-container-org0719507" class="outline-4">
-<h4 id="org0719507"><span class="section-number-4">5.3.1</span> How to identify these constants?</h4>
+<div id="outline-container-org9648429" class="outline-4">
+<h4 id="org9648429"><span class="section-number-4">5.3.1</span> How to identify these constants?</h4>
<div class="outline-text-4" id="text-5-3-1">
</div>
-<div id="outline-container-orgff68963" class="outline-5">
-<h5 id="orgff68963"><span class="section-number-5">5.3.1.1</span> Piezoelectric Actuator Constant</h5>
+<div id="outline-container-org8aed100" class="outline-5">
+<h5 id="org8aed100"><span class="section-number-5">5.3.1.1</span> Piezoelectric Actuator Constant</h5>
<div class="outline-text-5" id="text-5-3-1-1">
<p>
Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\).
@@ -3165,8 +3137,8 @@ From the two gains, it is then easy to determine \(g_a\):
</div>
</div>
-<div id="outline-container-orgd78a421" class="outline-5">
-<h5 id="orgd78a421"><span class="section-number-5">5.3.1.2</span> Piezoelectric Sensor Constant</h5>
+<div id="outline-container-org3873620" class="outline-5">
+<h5 id="org3873620"><span class="section-number-5">5.3.1.2</span> Piezoelectric Sensor Constant</h5>
<div class="outline-text-5" id="text-5-3-1-2">
<p>
Similarly, it is easy to determine the gain from the excitation voltage \(V_a\) to the voltage generated by the sensor stack \(V_s\):
@@ -3200,8 +3172,8 @@ Then, the “sensor” constant is:
</div>
</div>
-<div id="outline-container-orge4b3638" class="outline-4">
-<h4 id="orge4b3638"><span class="section-number-4">5.3.2</span> Identification Data</h4>
+<div id="outline-container-org40d0915" class="outline-4">
+<h4 id="org40d0915"><span class="section-number-4">5.3.2</span> Identification Data</h4>
<div class="outline-text-4" id="text-5-3-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load the identification Data</span></span>
@@ -3257,12 +3229,12 @@ We get the frequency vector that will be the same for all the frequency domain a
</div>
</div>
-<div id="outline-container-orgfb42195" class="outline-4">
-<h4 id="orgfb42195"><span class="section-number-4">5.3.3</span> 2DoF APA</h4>
+<div id="outline-container-org968490c" class="outline-4">
+<h4 id="org968490c"><span class="section-number-4">5.3.3</span> 2DoF APA</h4>
<div class="outline-text-4" id="text-5-3-3">
</div>
-<div id="outline-container-orgaf97374" class="outline-5">
-<h5 id="orgaf97374"><span class="section-number-5">5.3.3.1</span> 2DoF APA</h5>
+<div id="outline-container-org8e3eb76" class="outline-5">
+<h5 id="org8e3eb76"><span class="section-number-5">5.3.3.1</span> 2DoF APA</h5>
<div class="outline-text-5" id="text-5-3-3-1">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Initialize a 2DoF APA with Ga=Gs=1</span></span>
@@ -3272,8 +3244,8 @@ n_hexapod.actuator = initializeAPA(<span class="org-string">'type'</span>, <span
</div>
</div>
-<div id="outline-container-orga1ad011" class="outline-5">
-<h5 id="orga1ad011"><span class="section-number-5">5.3.3.2</span> Identification without actuator or sensor constants</h5>
+<div id="outline-container-org9053ede" class="outline-5">
+<h5 id="org9053ede"><span class="section-number-5">5.3.3.2</span> Identification without actuator or sensor constants</h5>
<div class="outline-text-5" id="text-5-3-3-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
@@ -3292,8 +3264,8 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-org779ac83" class="outline-5">
-<h5 id="org779ac83"><span class="section-number-5">5.3.3.3</span> Actuator Constant</h5>
+<div id="outline-container-org6b815c4" class="outline-5">
+<h5 id="org6b815c4"><span class="section-number-5">5.3.3.3</span> Actuator Constant</h5>
<div class="outline-text-5" id="text-5-3-3-3">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Estimated Actuator Constant</span></span>
@@ -3313,8 +3285,8 @@ ga = -32.1 [N/V]
</div>
</div>
-<div id="outline-container-org62717da" class="outline-5">
-<h5 id="org62717da"><span class="section-number-5">5.3.3.4</span> Sensor Constant</h5>
+<div id="outline-container-org543b981" class="outline-5">
+<h5 id="org543b981"><span class="section-number-5">5.3.3.4</span> Sensor Constant</h5>
<div class="outline-text-5" id="text-5-3-3-4">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Estimated Sensor Constant</span></span>
@@ -3334,8 +3306,8 @@ gs = 0.085 [V/m]
</div>
</div>
-<div id="outline-container-org5cbf2d4" class="outline-5">
-<h5 id="org5cbf2d4"><span class="section-number-5">5.3.3.5</span> Comparison</h5>
+<div id="outline-container-org616188d" class="outline-5">
+<h5 id="org616188d"><span class="section-number-5">5.3.3.5</span> Comparison</h5>
<div class="outline-text-5" id="text-5-3-3-5">
<p>
Identify the dynamics with included constants.
@@ -3350,28 +3322,28 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
-<div id="orgbdd0057" class="figure">
+<div id="org6c97d49" class="figure">
<p><img src="figs/apa_act_constant_comp.png" alt="apa_act_constant_comp.png" />
</p>
-<p><span class="figure-number">Figure 76: </span>Comparison of the experimental data and Simscape model (\(u\) to \(d\mathcal{L}_m\))</p>
+<p><span class="figure-number">Figure 72: </span>Comparison of the experimental data and Simscape model (\(u\) to \(d\mathcal{L}_m\))</p>
</div>
-<div id="org694acfd" class="figure">
+<div id="orgc7e607c" class="figure">
<p><img src="figs/apa_sens_constant_comp.png" alt="apa_sens_constant_comp.png" />
</p>
-<p><span class="figure-number">Figure 77: </span>Comparison of the experimental data and Simscape model (\(V_a\) to \(V_s\))</p>
+<p><span class="figure-number">Figure 73: </span>Comparison of the experimental data and Simscape model (\(V_a\) to \(V_s\))</p>
</div>
</div>
</div>
</div>
-<div id="outline-container-org6921e6f" class="outline-4">
-<h4 id="org6921e6f"><span class="section-number-4">5.3.4</span> Flexible APA</h4>
+<div id="outline-container-org50d4f61" class="outline-4">
+<h4 id="org50d4f61"><span class="section-number-4">5.3.4</span> Flexible APA</h4>
<div class="outline-text-4" id="text-5-3-4">
</div>
-<div id="outline-container-org438549b" class="outline-5">
-<h5 id="org438549b"><span class="section-number-5">5.3.4.1</span> Flexible APA</h5>
+<div id="outline-container-org04f79fd" class="outline-5">
+<h5 id="org04f79fd"><span class="section-number-5">5.3.4.1</span> Flexible APA</h5>
<div class="outline-text-5" id="text-5-3-4-1">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Initialize the APA as a flexible body</span></span>
@@ -3381,8 +3353,8 @@ n_hexapod.actuator = initializeAPA(<span class="org-string">'type'</span>, <span
</div>
</div>
-<div id="outline-container-org5d0f01f" class="outline-5">
-<h5 id="org5d0f01f"><span class="section-number-5">5.3.4.2</span> Identification without actuator or sensor constants</h5>
+<div id="outline-container-org466fe68" class="outline-5">
+<h5 id="org466fe68"><span class="section-number-5">5.3.4.2</span> Identification without actuator or sensor constants</h5>
<div class="outline-text-5" id="text-5-3-4-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Identify the dynamics</span></span>
@@ -3394,8 +3366,8 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-org13e1bb9" class="outline-5">
-<h5 id="org13e1bb9"><span class="section-number-5">5.3.4.3</span> Actuator Constant</h5>
+<div id="outline-container-org37e23c9" class="outline-5">
+<h5 id="org37e23c9"><span class="section-number-5">5.3.4.3</span> Actuator Constant</h5>
<div class="outline-text-5" id="text-5-3-4-3">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Actuator Constant</span></span>
@@ -3415,8 +3387,8 @@ ga = 23.4 [N/V]
</div>
</div>
-<div id="outline-container-orgf3eff0f" class="outline-5">
-<h5 id="orgf3eff0f"><span class="section-number-5">5.3.4.4</span> Sensor Constant</h5>
+<div id="outline-container-org5428c5c" class="outline-5">
+<h5 id="org5428c5c"><span class="section-number-5">5.3.4.4</span> Sensor Constant</h5>
<div class="outline-text-5" id="text-5-3-4-4">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Sensor Constant</span></span>
@@ -3436,8 +3408,8 @@ gs = -4674826.805 [V/m]
</div>
</div>
-<div id="outline-container-orgf449dc8" class="outline-5">
-<h5 id="orgf449dc8"><span class="section-number-5">5.3.4.5</span> Comparison</h5>
+<div id="outline-container-org64a0497" class="outline-5">
+<h5 id="org64a0497"><span class="section-number-5">5.3.4.5</span> Comparison</h5>
<div class="outline-text-5" id="text-5-3-4-5">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Identify with updated constants</span></span>
@@ -3449,25 +3421,25 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
-<div id="org80d7dac" class="figure">
+<div id="orgac961ae" class="figure">
<p><img src="figs/apa_act_constant_comp_flex.png" alt="apa_act_constant_comp_flex.png" />
</p>
-<p><span class="figure-number">Figure 78: </span>Comparison of the experimental data and Simscape model (\(u\) to \(d\mathcal{L}_m\))</p>
+<p><span class="figure-number">Figure 74: </span>Comparison of the experimental data and Simscape model (\(u\) to \(d\mathcal{L}_m\))</p>
</div>
-<div id="org7164f3c" class="figure">
+<div id="org352e0bd" class="figure">
<p><img src="figs/apa_sens_constant_comp_flex.png" alt="apa_sens_constant_comp_flex.png" />
</p>
-<p><span class="figure-number">Figure 79: </span>Comparison of the experimental data and Simscape model (\(u\) to \(\tau_m\))</p>
+<p><span class="figure-number">Figure 75: </span>Comparison of the experimental data and Simscape model (\(u\) to \(\tau_m\))</p>
</div>
</div>
</div>
</div>
</div>
-<div id="outline-container-org0f741d4" class="outline-3">
-<h3 id="org0f741d4"><span class="section-number-3">5.4</span> Optimize 2-DoF model to fit the experimental Data</h3>
+<div id="outline-container-org360e26d" class="outline-3">
+<h3 id="org360e26d"><span class="section-number-3">5.4</span> Optimize 2-DoF model to fit the experimental Data</h3>
<div class="outline-text-3" id="text-5-4">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Optimized parameters</span></span>
@@ -3485,24 +3457,24 @@ n_hexapod.actuator = initializeAPA(<span class="org-string">'type'</span>, <span
</div>
-<div id="org16a6208" class="figure">
+<div id="org67484e7" class="figure">
<p><img src="figs/comp_apa_plant_after_opt.png" alt="comp_apa_plant_after_opt.png" />
</p>
-<p><span class="figure-number">Figure 80: </span>Comparison of the measured FRF and the optimized model</p>
+<p><span class="figure-number">Figure 76: </span>Comparison of the measured FRF and the optimized model</p>
</div>
</div>
</div>
</div>
-<div id="outline-container-orgac93bd2" class="outline-2">
-<h2 id="orgac93bd2"><span class="section-number-2">6</span> Test Bench Struts - Simscape Model</h2>
+<div id="outline-container-orgfd4db7c" class="outline-2">
+<h2 id="orgfd4db7c"><span class="section-number-2">6</span> Test Bench Struts - Simscape Model</h2>
<div class="outline-text-2" id="text-6">
</div>
-<div id="outline-container-orgfd316f9" class="outline-3">
-<h3 id="orgfd316f9"><span class="section-number-3">6.1</span> Introduction</h3>
+<div id="outline-container-org383b978" class="outline-3">
+<h3 id="org383b978"><span class="section-number-3">6.1</span> Introduction</h3>
</div>
-<div id="outline-container-orgdbac1a3" class="outline-3">
-<h3 id="orgdbac1a3"><span class="section-number-3">6.2</span> First Identification</h3>
+<div id="outline-container-orgec09fa9" class="outline-3">
+<h3 id="orgec09fa9"><span class="section-number-3">6.2</span> First Identification</h3>
<div class="outline-text-3" id="text-6-2">
<p>
The object containing all the data is created.
@@ -3535,23 +3507,23 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
-<div id="orgdb26805" class="figure">
+<div id="org77e7685" class="figure">
<p><img src="figs/strut_bench_model_iff_bode.png" alt="strut_bench_model_iff_bode.png" />
</p>
-<p><span class="figure-number">Figure 81: </span>Identified transfer function from \(V_a\) to \(V_s\)</p>
+<p><span class="figure-number">Figure 77: </span>Identified transfer function from \(V_a\) to \(V_s\)</p>
</div>
-<div id="org87fb3ea" class="figure">
+<div id="org1ce8a6b" class="figure">
<p><img src="figs/strut_bench_model_dvf_bode.png" alt="strut_bench_model_dvf_bode.png" />
</p>
-<p><span class="figure-number">Figure 82: </span>Identified transfer function from \(V_a\) to \(d_L\)</p>
+<p><span class="figure-number">Figure 78: </span>Identified transfer function from \(V_a\) to \(d_L\)</p>
</div>
</div>
</div>
-<div id="outline-container-org0e2423b" class="outline-3">
-<h3 id="org0e2423b"><span class="section-number-3">6.3</span> Effect of flexible joints</h3>
+<div id="outline-container-org182d648" class="outline-3">
+<h3 id="org182d648"><span class="section-number-3">6.3</span> Effect of flexible joints</h3>
<div class="outline-text-3" id="text-6-3">
<p>
Perfect
@@ -3610,31 +3582,31 @@ Gf.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
<p>
-Comparison in Figures <a href="#org60d3eda">83</a>, <a href="#orgef3b4bc">84</a> and <a href="#org33a89eb">85</a>.
+Comparison in Figures <a href="#org5aa8898">79</a>, <a href="#orga81b823">80</a> and <a href="#orgf4fad65">81</a>.
</p>
-<div id="org60d3eda" class="figure">
+<div id="org5aa8898" class="figure">
<p><img src="figs/strut_effect_joint_comp_vs.png" alt="strut_effect_joint_comp_vs.png" />
</p>
-<p><span class="figure-number">Figure 83: </span>Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(V_s\)</p>
+<p><span class="figure-number">Figure 79: </span>Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(V_s\)</p>
</div>
-<div id="orgef3b4bc" class="figure">
+<div id="orga81b823" class="figure">
<p><img src="figs/strut_effect_joint_comp_dl.png" alt="strut_effect_joint_comp_dl.png" />
</p>
-<p><span class="figure-number">Figure 84: </span>Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(d_L\) (encoder)</p>
+<p><span class="figure-number">Figure 80: </span>Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(d_L\) (encoder)</p>
</div>
-<div id="org33a89eb" class="figure">
+<div id="orgf4fad65" class="figure">
<p><img src="figs/strut_effect_joint_comp_z.png" alt="strut_effect_joint_comp_z.png" />
</p>
-<p><span class="figure-number">Figure 85: </span>Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(z\) (interferometer)</p>
+<p><span class="figure-number">Figure 81: </span>Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(z\) (interferometer)</p>
</div>
-<div class="important" id="orgd64eacd">
+<div class="important" id="orga9f8f1a">
<p>
Imperfection of the flexible joints has the largest impact on the transfer function from \(V_a\) to \(d_L\).
However, it has relatively small impact on the transfer functions from \(V_a\) to \(V_s\) and to \(z\).
@@ -3644,12 +3616,12 @@ However, it has relatively small impact on the transfer functions from \(V_a\) t
</div>
</div>
-<div id="outline-container-orgcb59549" class="outline-3">
-<h3 id="orgcb59549"><span class="section-number-3">6.4</span> Integral Force Feedback</h3>
+<div id="outline-container-org04fdf97" class="outline-3">
+<h3 id="org04fdf97"><span class="section-number-3">6.4</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-6-4">
</div>
-<div id="outline-container-org5f7cf11" class="outline-4">
-<h4 id="org5f7cf11"><span class="section-number-4">6.4.1</span> Initialize the system</h4>
+<div id="outline-container-org57af20b" class="outline-4">
+<h4 id="org57af20b"><span class="section-number-4">6.4.1</span> Initialize the system</h4>
<div class="outline-text-4" id="text-6-4-1">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Initialize typical system</span></span>
@@ -3662,8 +3634,8 @@ n_hexapod.actuator = initializeAPA(<span class="org-string">'type'</span>, <span
</div>
</div>
-<div id="outline-container-org3597bbe" class="outline-4">
-<h4 id="org3597bbe"><span class="section-number-4">6.4.2</span> Plant Identification</h4>
+<div id="outline-container-org804d0f2" class="outline-4">
+<h4 id="org804d0f2"><span class="section-number-4">6.4.2</span> Plant Identification</h4>
<div class="outline-text-4" id="text-6-4-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Identify th edynamics</span></span>
@@ -3681,8 +3653,8 @@ Giff = G(<span class="org-string">'Vs'</span>, <span class="org-string">'Va'</sp
</div>
</div>
-<div id="outline-container-org77009ac" class="outline-4">
-<h4 id="org77009ac"><span class="section-number-4">6.4.3</span> Root Locus</h4>
+<div id="outline-container-orgd331b68" class="outline-4">
+<h4 id="orgd331b68"><span class="section-number-4">6.4.3</span> Root Locus</h4>
<div class="outline-text-4" id="text-6-4-3">
\begin{equation}
K_{\text{IFF}} = \frac{g}{s + \omega_c}
@@ -3697,8 +3669,8 @@ wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span c
</div>
</div>
-<div id="outline-container-orgf6b7dd9" class="outline-3">
-<h3 id="orgf6b7dd9"><span class="section-number-3">6.5</span> Comparison with the experimental Data</h3>
+<div id="outline-container-orgf99a81f" class="outline-3">
+<h3 id="orgf99a81f"><span class="section-number-3">6.5</span> Comparison with the experimental Data</h3>
<div class="outline-text-3" id="text-6-5">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Initialize Simscape data</span></span>
@@ -3723,30 +3695,30 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
-<div id="org27cc567" class="figure">
+<div id="orgceb78d7" class="figure">
<p><img src="figs/comp_strut_plant_after_opt.png" alt="comp_strut_plant_after_opt.png" />
</p>
-<p><span class="figure-number">Figure 86: </span>Comparison of the measured FRF and the optimized model</p>
+<p><span class="figure-number">Figure 82: </span>Comparison of the measured FRF and the optimized model</p>
</div>
</div>
</div>
</div>
-<div id="outline-container-org1f66afd" class="outline-2">
-<h2 id="org1f66afd"><span class="section-number-2">7</span> Function</h2>
+<div id="outline-container-org542c733" class="outline-2">
+<h2 id="org542c733"><span class="section-number-2">7</span> Function</h2>
<div class="outline-text-2" id="text-7">
</div>
-<div id="outline-container-org730257f" class="outline-3">
-<h3 id="org730257f"><span class="section-number-3">7.1</span> <code>initializeBotFlexibleJoint</code> - Initialize Flexible Joint</h3>
+<div id="outline-container-org2002f31" class="outline-3">
+<h3 id="org2002f31"><span class="section-number-3">7.1</span> <code>initializeBotFlexibleJoint</code> - Initialize Flexible Joint</h3>
<div class="outline-text-3" id="text-7-1">
<p>
-<a id="orgfb366ac"></a>
+<a id="org2819983"></a>
</p>
</div>
-<div id="outline-container-org64c034e" class="outline-4">
-<h4 id="org64c034e">Function description</h4>
-<div class="outline-text-4" id="text-org64c034e">
+<div id="outline-container-orgdea7178" class="outline-4">
+<h4 id="orgdea7178">Function description</h4>
+<div class="outline-text-4" id="text-orgdea7178">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[flex_bot]</span> = <span class="org-function-name">initializeBotFlexibleJoint</span>(<span class="org-variable-name">args</span>)
<span class="org-comment">% initializeBotFlexibleJoint -</span>
@@ -3763,9 +3735,9 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-org942e6c2" class="outline-4">
-<h4 id="org942e6c2">Optional Parameters</h4>
-<div class="outline-text-4" id="text-org942e6c2">
+<div id="outline-container-orgf41e762" class="outline-4">
+<h4 id="orgf41e762">Optional Parameters</h4>
+<div class="outline-text-4" id="text-orgf41e762">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'2dof'</span>, <span class="org-string">'3dof'</span>, <span class="org-string">'4dof'</span>})} = <span class="org-string">'2dof'</span>
@@ -3785,9 +3757,9 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-org58455ca" class="outline-4">
-<h4 id="org58455ca">Initialize the structure</h4>
-<div class="outline-text-4" id="text-org58455ca">
+<div id="outline-container-orgc438b52" class="outline-4">
+<h4 id="orgc438b52">Initialize the structure</h4>
+<div class="outline-text-4" id="text-orgc438b52">
<div class="org-src-container">
<pre class="src src-matlab">flex_bot = struct();
</pre>
@@ -3795,9 +3767,9 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-orgf261788" class="outline-4">
-<h4 id="orgf261788">Set the Joint’s type</h4>
-<div class="outline-text-4" id="text-orgf261788">
+<div id="outline-container-orgd1b0b63" class="outline-4">
+<h4 id="orgd1b0b63">Set the Joint’s type</h4>
+<div class="outline-text-4" id="text-orgd1b0b63">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
<span class="org-keyword">case</span> <span class="org-string">'2dof'</span>
@@ -3812,9 +3784,9 @@ Gs.OutputName = {<span class="org-string">'Vs'</span>, <span class="org-string">
</div>
</div>
-<div id="outline-container-orgede603f" class="outline-4">
-<h4 id="orgede603f">Set parameters</h4>
-<div class="outline-text-4" id="text-orgede603f">
+<div id="outline-container-org9e43909" class="outline-4">
+<h4 id="org9e43909">Set parameters</h4>
+<div class="outline-text-4" id="text-org9e43909">
<div class="org-src-container">
<pre class="src src-matlab">flex_bot.kRx = args.kRx;
flex_bot.kRy = args.kRy;
@@ -3834,17 +3806,17 @@ flex_bot.cz = args.cz;
</div>
</div>
-<div id="outline-container-orgef70627" class="outline-3">
-<h3 id="orgef70627"><span class="section-number-3">7.2</span> <code>initializeTopFlexibleJoint</code> - Initialize Flexible Joint</h3>
+<div id="outline-container-org76f54c8" class="outline-3">
+<h3 id="org76f54c8"><span class="section-number-3">7.2</span> <code>initializeTopFlexibleJoint</code> - Initialize Flexible Joint</h3>
<div class="outline-text-3" id="text-7-2">
<p>
-<a id="org0c42a5d"></a>
+<a id="orgcf68506"></a>
</p>
</div>
-<div id="outline-container-org091fbd8" class="outline-4">
-<h4 id="org091fbd8">Function description</h4>
-<div class="outline-text-4" id="text-org091fbd8">
+<div id="outline-container-org38a994c" class="outline-4">
+<h4 id="org38a994c">Function description</h4>
+<div class="outline-text-4" id="text-org38a994c">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[flex_top]</span> = <span class="org-function-name">initializeTopFlexibleJoint</span>(<span class="org-variable-name">args</span>)
<span class="org-comment">% initializeTopFlexibleJoint -</span>
@@ -3861,9 +3833,9 @@ flex_bot.cz = args.cz;
</div>
</div>
-<div id="outline-container-org1d37383" class="outline-4">
-<h4 id="org1d37383">Optional Parameters</h4>
-<div class="outline-text-4" id="text-org1d37383">
+<div id="outline-container-org7448731" class="outline-4">
+<h4 id="org7448731">Optional Parameters</h4>
+<div class="outline-text-4" id="text-org7448731">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'2dof'</span>, <span class="org-string">'3dof'</span>, <span class="org-string">'4dof'</span>})} = <span class="org-string">'2dof'</span>
@@ -3883,9 +3855,9 @@ flex_bot.cz = args.cz;
</div>
</div>
-<div id="outline-container-orgc52ebc0" class="outline-4">
-<h4 id="orgc52ebc0">Initialize the structure</h4>
-<div class="outline-text-4" id="text-orgc52ebc0">
+<div id="outline-container-orgbc5e615" class="outline-4">
+<h4 id="orgbc5e615">Initialize the structure</h4>
+<div class="outline-text-4" id="text-orgbc5e615">
<div class="org-src-container">
<pre class="src src-matlab">flex_top = struct();
</pre>
@@ -3893,9 +3865,9 @@ flex_bot.cz = args.cz;
</div>
</div>
-<div id="outline-container-org0fa0554" class="outline-4">
-<h4 id="org0fa0554">Set the Joint’s type</h4>
-<div class="outline-text-4" id="text-org0fa0554">
+<div id="outline-container-org3adeb48" class="outline-4">
+<h4 id="org3adeb48">Set the Joint’s type</h4>
+<div class="outline-text-4" id="text-org3adeb48">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
<span class="org-keyword">case</span> <span class="org-string">'2dof'</span>
@@ -3910,9 +3882,9 @@ flex_bot.cz = args.cz;
</div>
</div>
-<div id="outline-container-org5590e46" class="outline-4">
-<h4 id="org5590e46">Set parameters</h4>
-<div class="outline-text-4" id="text-org5590e46">
+<div id="outline-container-org1b36a20" class="outline-4">
+<h4 id="org1b36a20">Set parameters</h4>
+<div class="outline-text-4" id="text-org1b36a20">
<div class="org-src-container">
<pre class="src src-matlab">flex_top.kRx = args.kRx;
flex_top.kRy = args.kRy;
@@ -3932,17 +3904,17 @@ flex_top.cz = args.cz;
</div>
</div>
-<div id="outline-container-orgacd4906" class="outline-3">
-<h3 id="orgacd4906"><span class="section-number-3">7.3</span> <code>initializeAPA</code> - Initialize APA</h3>
+<div id="outline-container-org01db2f1" class="outline-3">
+<h3 id="org01db2f1"><span class="section-number-3">7.3</span> <code>initializeAPA</code> - Initialize APA</h3>
<div class="outline-text-3" id="text-7-3">
<p>
-<a id="org1e9c7e6"></a>
+<a id="org1d86fc4"></a>
</p>
</div>
-<div id="outline-container-orga698c5e" class="outline-4">
-<h4 id="orga698c5e">Function description</h4>
-<div class="outline-text-4" id="text-orga698c5e">
+<div id="outline-container-orgd230696" class="outline-4">
+<h4 id="orgd230696">Function description</h4>
+<div class="outline-text-4" id="text-orgd230696">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[actuator]</span> = <span class="org-function-name">initializeAPA</span>(<span class="org-variable-name">args</span>)
<span class="org-comment">% initializeAPA -</span>
@@ -3959,9 +3931,9 @@ flex_top.cz = args.cz;
</div>
</div>
-<div id="outline-container-org29dad87" class="outline-4">
-<h4 id="org29dad87">Optional Parameters</h4>
-<div class="outline-text-4" id="text-org29dad87">
+<div id="outline-container-orgf18780c" class="outline-4">
+<h4 id="orgf18780c">Optional Parameters</h4>
+<div class="outline-text-4" id="text-orgf18780c">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
<span class="org-variable-name">args</span>.type char {mustBeMember(args.type,{<span class="org-string">'2dof'</span>, <span class="org-string">'flexible frame'</span>, <span class="org-string">'flexible'</span>})} = <span class="org-string">'2dof'</span>
@@ -3992,9 +3964,9 @@ flex_top.cz = args.cz;
</div>
</div>
-<div id="outline-container-org6eeae8c" class="outline-4">
-<h4 id="org6eeae8c">Initialize Structure</h4>
-<div class="outline-text-4" id="text-org6eeae8c">
+<div id="outline-container-orge8497f7" class="outline-4">
+<h4 id="orge8497f7">Initialize Structure</h4>
+<div class="outline-text-4" id="text-orge8497f7">
<div class="org-src-container">
<pre class="src src-matlab">actuator = struct();
</pre>
@@ -4002,9 +3974,9 @@ flex_top.cz = args.cz;
</div>
</div>
-<div id="outline-container-org9b8fb4b" class="outline-4">
-<h4 id="org9b8fb4b">Type</h4>
-<div class="outline-text-4" id="text-org9b8fb4b">
+<div id="outline-container-org837d8bb" class="outline-4">
+<h4 id="org837d8bb">Type</h4>
+<div class="outline-text-4" id="text-org837d8bb">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
<span class="org-keyword">case</span> <span class="org-string">'2dof'</span>
@@ -4019,9 +3991,9 @@ flex_top.cz = args.cz;
</div>
</div>
-<div id="outline-container-org62c5ed8" class="outline-4">
-<h4 id="org62c5ed8">Actuator/Sensor Constants</h4>
-<div class="outline-text-4" id="text-org62c5ed8">
+<div id="outline-container-orgc23e748" class="outline-4">
+<h4 id="orgc23e748">Actuator/Sensor Constants</h4>
+<div class="outline-text-4" id="text-orgc23e748">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Ga <span class="org-type">==</span> 0
<span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
@@ -4056,9 +4028,9 @@ flex_top.cz = args.cz;
</div>
</div>
-<div id="outline-container-org0fd8dea" class="outline-4">
-<h4 id="org0fd8dea">2DoF parameters</h4>
-<div class="outline-text-4" id="text-org0fd8dea">
+<div id="outline-container-orgc803170" class="outline-4">
+<h4 id="orgc803170">2DoF parameters</h4>
+<div class="outline-text-4" id="text-orgc803170">
<div class="org-src-container">
<pre class="src src-matlab">actuator.k = args.k; <span class="org-comment">% [N/m]</span>
actuator.ke = args.ke; <span class="org-comment">% [N/m]</span>
@@ -4074,9 +4046,9 @@ actuator.Leq = args.Leq; <span class="org-comment">% [m]</span>
</div>
</div>
-<div id="outline-container-org1d5fd8f" class="outline-4">
-<h4 id="org1d5fd8f">Flexible frame and fully flexible</h4>
-<div class="outline-text-4" id="text-org1d5fd8f">
+<div id="outline-container-orgdbcf682" class="outline-4">
+<h4 id="orgdbcf682">Flexible frame and fully flexible</h4>
+<div class="outline-text-4" id="text-orgdbcf682">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
<span class="org-keyword">case</span> <span class="org-string">'flexible frame'</span>
@@ -4099,17 +4071,17 @@ actuator.cs = args.cs; <span class="org-comment">% Damping of one stack [N/m]</s
</div>
</div>
-<div id="outline-container-orgbbd63f4" class="outline-3">
-<h3 id="orgbbd63f4"><span class="section-number-3">7.4</span> <code>generateSweepExc</code>: Generate sweep sinus excitation</h3>
+<div id="outline-container-orgc5c4a06" class="outline-3">
+<h3 id="orgc5c4a06"><span class="section-number-3">7.4</span> <code>generateSweepExc</code>: Generate sweep sinus excitation</h3>
<div class="outline-text-3" id="text-7-4">
<p>
-<a id="org54e0cd1"></a>
+<a id="org001f2cb"></a>
</p>
</div>
-<div id="outline-container-org4047364" class="outline-4">
-<h4 id="org4047364">Function description</h4>
-<div class="outline-text-4" id="text-org4047364">
+<div id="outline-container-org928e990" class="outline-4">
+<h4 id="org928e990">Function description</h4>
+<div class="outline-text-4" id="text-org928e990">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[U_exc]</span> = <span class="org-function-name">generateSweepExc</span>(<span class="org-variable-name">args</span>)
<span class="org-comment">% generateSweepExc - Generate a Sweep Sine excitation signal</span>
@@ -4132,9 +4104,9 @@ actuator.cs = args.cs; <span class="org-comment">% Damping of one stack [N/m]</s
</div>
</div>
-<div id="outline-container-orgdb7f1e4" class="outline-4">
-<h4 id="orgdb7f1e4">Optional Parameters</h4>
-<div class="outline-text-4" id="text-orgdb7f1e4">
+<div id="outline-container-org52f9336" class="outline-4">
+<h4 id="org52f9336">Optional Parameters</h4>
+<div class="outline-text-4" id="text-org52f9336">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
<span class="org-variable-name">args</span>.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>4
@@ -4152,9 +4124,9 @@ actuator.cs = args.cs; <span class="org-comment">% Damping of one stack [N/m]</s
</div>
</div>
-<div id="outline-container-org46430d0" class="outline-4">
-<h4 id="org46430d0">Sweep Sine part</h4>
-<div class="outline-text-4" id="text-org46430d0">
+<div id="outline-container-org97f67d4" class="outline-4">
+<h4 id="org97f67d4">Sweep Sine part</h4>
+<div class="outline-text-4" id="text-org97f67d4">
<div class="org-src-container">
<pre class="src src-matlab">t_sweep = 0<span class="org-type">:</span>args.Ts<span class="org-type">:</span>args.exc_duration;
@@ -4183,9 +4155,9 @@ actuator.cs = args.cs; <span class="org-comment">% Damping of one stack [N/m]</s
</div>
</div>
-<div id="outline-container-org3d78f6c" class="outline-4">
-<h4 id="org3d78f6c">Smooth Ends</h4>
-<div class="outline-text-4" id="text-org3d78f6c">
+<div id="outline-container-org5ecd11d" class="outline-4">
+<h4 id="org5ecd11d">Smooth Ends</h4>
+<div class="outline-text-4" id="text-org5ecd11d">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">if</span> args.t_start <span class="org-type">></span> 0
t_smooth_start = args.Ts<span class="org-type">:</span>args.Ts<span class="org-type">:</span>args.t_start;
@@ -4214,9 +4186,9 @@ actuator.cs = args.cs; <span class="org-comment">% Damping of one stack [N/m]</s
</div>
</div>
-<div id="outline-container-org63f6cb4" class="outline-4">
-<h4 id="org63f6cb4">Combine Excitation signals</h4>
-<div class="outline-text-4" id="text-org63f6cb4">
+<div id="outline-container-org81e70f2" class="outline-4">
+<h4 id="org81e70f2">Combine Excitation signals</h4>
+<div class="outline-text-4" id="text-org81e70f2">
<div class="org-src-container">
<pre class="src src-matlab">V_exc = [V_smooth_start, V_sweep, V_smooth_end];
t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1<span class="org-type">:</span>length(V_exc)<span class="org-type">-</span>1];
@@ -4231,17 +4203,17 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-org9628aeb" class="outline-3">
-<h3 id="org9628aeb"><span class="section-number-3">7.5</span> <code>generateShapedNoise</code>: Generate Shaped Noise excitation</h3>
+<div id="outline-container-orgf1900ac" class="outline-3">
+<h3 id="orgf1900ac"><span class="section-number-3">7.5</span> <code>generateShapedNoise</code>: Generate Shaped Noise excitation</h3>
<div class="outline-text-3" id="text-7-5">
<p>
-<a id="org2cc91b1"></a>
+<a id="org0aa0340"></a>
</p>
</div>
-<div id="outline-container-org526c60c" class="outline-4">
-<h4 id="org526c60c">Function description</h4>
-<div class="outline-text-4" id="text-org526c60c">
+<div id="outline-container-org40f50a7" class="outline-4">
+<h4 id="org40f50a7">Function description</h4>
+<div class="outline-text-4" id="text-org40f50a7">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[U_exc]</span> = <span class="org-function-name">generateShapedNoise</span>(<span class="org-variable-name">args</span>)
<span class="org-comment">% generateShapedNoise - Generate a Shaped Noise excitation signal</span>
@@ -4261,9 +4233,9 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-org61cf959" class="outline-4">
-<h4 id="org61cf959">Optional Parameters</h4>
-<div class="outline-text-4" id="text-org61cf959">
+<div id="outline-container-orga11d04a" class="outline-4">
+<h4 id="orga11d04a">Optional Parameters</h4>
+<div class="outline-text-4" id="text-orga11d04a">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
<span class="org-variable-name">args</span>.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>4
@@ -4278,9 +4250,9 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-org8ecc3f8" class="outline-4">
-<h4 id="org8ecc3f8">Shaped Noise</h4>
-<div class="outline-text-4" id="text-org8ecc3f8">
+<div id="outline-container-org8d7b46d" class="outline-4">
+<h4 id="org8d7b46d">Shaped Noise</h4>
+<div class="outline-text-4" id="text-org8d7b46d">
<div class="org-src-container">
<pre class="src src-matlab">t_noise = 0<span class="org-type">:</span>args.Ts<span class="org-type">:</span>args.exc_duration;
@@ -4298,9 +4270,9 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-orgebfd6a4" class="outline-4">
-<h4 id="orgebfd6a4">Smooth Ends</h4>
-<div class="outline-text-4" id="text-orgebfd6a4">
+<div id="outline-container-orgcd192a4" class="outline-4">
+<h4 id="orgcd192a4">Smooth Ends</h4>
+<div class="outline-text-4" id="text-orgcd192a4">
<div class="org-src-container">
<pre class="src src-matlab">t_smooth_start = args.Ts<span class="org-type">:</span>args.Ts<span class="org-type">:</span>args.t_start;
@@ -4324,9 +4296,9 @@ V_smooth_end = zeros(size(t_smooth_start));
</div>
</div>
-<div id="outline-container-orge82c676" class="outline-4">
-<h4 id="orge82c676">Combine Excitation signals</h4>
-<div class="outline-text-4" id="text-orge82c676">
+<div id="outline-container-org2f1448f" class="outline-4">
+<h4 id="org2f1448f">Combine Excitation signals</h4>
+<div class="outline-text-4" id="text-org2f1448f">
<div class="org-src-container">
<pre class="src src-matlab">V_exc = [V_smooth_start, V_noise, V_smooth_end];
t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1<span class="org-type">:</span>length(V_exc)<span class="org-type">-</span>1];
@@ -4341,17 +4313,17 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-org5066270" class="outline-3">
-<h3 id="org5066270"><span class="section-number-3">7.6</span> <code>generateSinIncreasingAmpl</code>: Generate Sinus with increasing amplitude</h3>
+<div id="outline-container-org6799aae" class="outline-3">
+<h3 id="org6799aae"><span class="section-number-3">7.6</span> <code>generateSinIncreasingAmpl</code>: Generate Sinus with increasing amplitude</h3>
<div class="outline-text-3" id="text-7-6">
<p>
-<a id="orgc13a81a"></a>
+<a id="org6d08cff"></a>
</p>
</div>
-<div id="outline-container-org6e1c161" class="outline-4">
-<h4 id="org6e1c161">Function description</h4>
-<div class="outline-text-4" id="text-org6e1c161">
+<div id="outline-container-org784ac8d" class="outline-4">
+<h4 id="org784ac8d">Function description</h4>
+<div class="outline-text-4" id="text-org784ac8d">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[U_exc]</span> = <span class="org-function-name">generateSinIncreasingAmpl</span>(<span class="org-variable-name">args</span>)
<span class="org-comment">% generateSinIncreasingAmpl - Generate Sinus with increasing amplitude</span>
@@ -4372,9 +4344,9 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-orga64324d" class="outline-4">
-<h4 id="orga64324d">Optional Parameters</h4>
-<div class="outline-text-4" id="text-orga64324d">
+<div id="outline-container-orgf8a1531" class="outline-4">
+<h4 id="orgf8a1531">Optional Parameters</h4>
+<div class="outline-text-4" id="text-orgf8a1531">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">arguments</span>
<span class="org-variable-name">args</span>.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>4
@@ -4390,9 +4362,9 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
</div>
-<div id="outline-container-orge158235" class="outline-4">
-<h4 id="orge158235">Sinus excitation</h4>
-<div class="outline-text-4" id="text-orge158235">
+<div id="outline-container-org1316011" class="outline-4">
+<h4 id="org1316011">Sinus excitation</h4>
+<div class="outline-text-4" id="text-org1316011">
<div class="org-src-container">
<pre class="src src-matlab">t_noise = 0<span class="org-type">:</span>args.Ts<span class="org-type">:</span>args.sin_period<span class="org-type">*</span>args.sin_num;
sin_exc = [];
@@ -4408,9 +4380,9 @@ sin_exc = [];
</div>
</div>
-<div id="outline-container-org2afc938" class="outline-4">
-<h4 id="org2afc938">Smooth Ends</h4>
-<div class="outline-text-4" id="text-org2afc938">
+<div id="outline-container-org99273a1" class="outline-4">
+<h4 id="org99273a1">Smooth Ends</h4>
+<div class="outline-text-4" id="text-org99273a1">
<div class="org-src-container">
<pre class="src src-matlab">t_smooth_start = args.Ts<span class="org-type">:</span>args.Ts<span class="org-type">:</span>args.t_start;
@@ -4434,9 +4406,9 @@ V_smooth_end = zeros(size(t_smooth_start));
</div>
</div>
-<div id="outline-container-org1f109d0" class="outline-4">
-<h4 id="org1f109d0">Combine Excitation signals</h4>
-<div class="outline-text-4" id="text-org1f109d0">
+<div id="outline-container-orgf3d7f4d" class="outline-4">
+<h4 id="orgf3d7f4d">Combine Excitation signals</h4>
+<div class="outline-text-4" id="text-orgf3d7f4d">
<div class="org-src-container">
<pre class="src src-matlab">V_exc = [V_smooth_start, sin_exc, V_smooth_end];
t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1<span class="org-type">:</span>length(V_exc)<span class="org-type">-</span>1];
@@ -4459,7 +4431,7 @@ t_exc = args.Ts<span class="org-type">*</span>[0<span class="org-type">:</span>1
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2021-06-09 mer. 19:01</p>
+<p class="date">Created: 2021-06-14 lun. 23:20</p>
</div>
</body>
</html>
diff --git a/test-bench-apa300ml.org b/test-bench-apa300ml.org
index 0ab6a97..45f49fb 100644
--- a/test-bench-apa300ml.org
+++ b/test-bench-apa300ml.org
@@ -520,25 +520,15 @@ data2orgtable(1e6*apa300ml_stroke', {'APA 1', 'APA 2', 'APA 3', 'APA 4', 'APA 5'
<<sec:spurious_resonances>>
*** Introduction
-Three main resonances are foreseen to be problematic for the control of the APA300ML:
-- Mode in X-bending at 189Hz (Figure [[fig:mode_bending_x]])
-- Mode in Y-bending at 285Hz (Figure [[fig:mode_bending_y]])
-- Mode in Z-torsion at 400Hz (Figure [[fig:mode_torsion_z]])
+Three main resonances are foreseen to be problematic for the control of the APA300ML (Figure [[fig:apa_mode_shapes]]):
+- Mode in X-bending at 189Hz
+- Mode in Y-bending at 285Hz
+- Mode in Z-torsion at 400Hz
-#+name: fig:mode_bending_x
-#+caption: X-bending mode (189Hz)
-#+attr_latex: :width 0.9\linewidth
-[[file:figs/mode_bending_x.gif]]
-
-#+name: fig:mode_bending_y
-#+caption: Y-bending mode (285Hz)
-#+attr_latex: :width 0.9\linewidth
-[[file:figs/mode_bending_y.gif]]
-
-#+name: fig:mode_torsion_z
-#+caption: Z-torsion mode (400Hz)
-#+attr_latex: :width 0.9\linewidth
-[[file:figs/mode_torsion_z.gif]]
+#+name: fig:apa_mode_shapes
+#+caption: Spurious resonances. a) X-bending mode at 189Hz. b) Y-bending mode at 285Hz. c) Z-torsion mode at 400Hz
+#+attr_latex: :width \linewidth
+[[file:figs/apa_mode_shapes.gif]]
These modes are present when flexible joints are fixed to the ends of the APA300ML.
@@ -2532,25 +2522,15 @@ exportFig('figs/strut_1_spurious_resonances.pdf', 'width', 'wide', 'height', 'ta
These resonances correspond to parasitic resonances of the APA itself.
-They are very close to what was estimated using the FEM:
-- X-bending mode at around 190Hz (Figure [[fig:mode_bending_x_bis]])
-- Y-bending mode at around 290Hz (Figure [[fig:mode_bending_y_bis]])
-- Z-torsion mode at around 400Hz (Figure [[fig:mode_torsion_z_bis]])
+They are very close to what was estimated using the FEM (Figure [[fig:apa_mode_shapes_bis]]):
+- Mode in X-bending at 189Hz
+- Mode in Y-bending at 285Hz
+- Mode in Z-torsion at 400Hz
-#+name: fig:mode_bending_x_bis
-#+caption: X-bending mode (189Hz)
-#+attr_latex: :width 0.9\linewidth
-[[file:figs/mode_bending_x.gif]]
-
-#+name: fig:mode_bending_y_bis
-#+caption: Y-bending mode (285Hz)
-#+attr_latex: :width 0.9\linewidth
-[[file:figs/mode_bending_y.gif]]
-
-#+name: fig:mode_torsion_z_bis
-#+caption: Z-torsion mode (400Hz)
-#+attr_latex: :width 0.9\linewidth
-[[file:figs/mode_torsion_z.gif]]
+#+name: fig:apa_mode_shapes_bis
+#+caption: Spurious resonances. a) X-bending mode at 189Hz. b) Y-bending mode at 285Hz. c) Z-torsion mode at 400Hz
+#+attr_latex: :width \linewidth
+[[file:figs/apa_mode_shapes.gif]]
#+begin_important
The resonances are indeed due to limited stiffness of the APA.
diff --git a/test-bench-apa300ml.pdf b/test-bench-apa300ml.pdf
index 781917c..b7111b5 100644
Binary files a/test-bench-apa300ml.pdf and b/test-bench-apa300ml.pdf differ