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a233fedeac
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b9ba83a46b
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.gitmodules
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3
.gitmodules
vendored
@ -1,3 +0,0 @@
|
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[submodule "nass-simscape"]
|
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path = matlab/nass-simscape
|
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url = https://git.tdehaeze.xyz/tdehaeze/nass-simscape
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@ -1 +0,0 @@
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Subproject commit 6956d39ef86595230b490894a68723fea0042c45
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Binary file not shown.
@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-04-19 lun. 16:33 -->
|
||||
<!-- 2021-04-19 lun. 15:02 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Vibration Table</title>
|
||||
<meta name="author" content="Dehaeze Thomas" />
|
||||
@ -39,42 +39,41 @@
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgd96939c">1. Introduction</a></li>
|
||||
<li><a href="#org8f2a9d3">2. Experimental Setup</a>
|
||||
<li><a href="#orgf5ac764">1. Introduction</a></li>
|
||||
<li><a href="#org5832600">2. Experimental Setup</a>
|
||||
<ul>
|
||||
<li><a href="#orgf60715e">2.1. CAD Model</a></li>
|
||||
<li><a href="#org0740e89">2.2. Instrumentation</a></li>
|
||||
<li><a href="#orgfae411d">2.3. Suspended table</a></li>
|
||||
<li><a href="#org56dc68e">2.4. Inertial Sensors</a></li>
|
||||
<li><a href="#org088c0b5">2.1. CAD Model</a></li>
|
||||
<li><a href="#orge848908">2.2. Instrumentation</a></li>
|
||||
<li><a href="#orgae54ff5">2.3. Suspended table</a></li>
|
||||
<li><a href="#org435fee6">2.4. Inertial Sensors</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org7c42c7b">3. Compute the 6DoF solid body motion from several inertial sensors</a>
|
||||
<li><a href="#orgf366ef9">3. Compute the 6DoF solid body motion from several inertial sensors</a>
|
||||
<ul>
|
||||
<li><a href="#orgb354999">3.1. Define accelerometers positions/orientations</a></li>
|
||||
<li><a href="#org162ae73">3.2. Transformation matrix from motion of the solid body to accelerometer measurements</a></li>
|
||||
<li><a href="#orgb865df3">3.3. Compute the transformation matrix from accelerometer measurement to motion of the solid body</a></li>
|
||||
<li><a href="#orgb03df82">3.1. Define accelerometers positions/orientations</a></li>
|
||||
<li><a href="#orgf872bb6">3.2. Transformation matrix from motion of the solid body to accelerometer measurements</a></li>
|
||||
<li><a href="#orge54a621">3.3. Compute the transformation matrix from accelerometer measurement to motion of the solid body</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgfff4a19">4. Simscape Model</a>
|
||||
<li><a href="#orgae67fb9">4. Simscape Model</a>
|
||||
<ul>
|
||||
<li><a href="#orgd1b8332">4.1. Simscape Sub-systems</a>
|
||||
<li><a href="#org83808e1">4.1. Simscape Sub-systems</a>
|
||||
<ul>
|
||||
<li><a href="#org25263d5">4.1.1. Springs</a></li>
|
||||
<li><a href="#org8fbfccb">4.1.2. Inertial Shaker (IS20)</a></li>
|
||||
<li><a href="#org778a701">4.1.3. 3D accelerometer (356B18)</a></li>
|
||||
<li><a href="#org430fcc4">4.1.1. Springs</a></li>
|
||||
<li><a href="#org741008c">4.1.2. Inertial Shaker (IS20)</a></li>
|
||||
<li><a href="#org5b2f05e">4.1.3. 3D accelerometer (356B18)</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgab1e576">4.2. Identification</a>
|
||||
<li><a href="#org37f2322">4.2. Identification</a>
|
||||
<ul>
|
||||
<li><a href="#org356f48c">4.2.1. Number of states</a></li>
|
||||
<li><a href="#org11eb355">4.2.2. Resonance frequencies and mode shapes</a></li>
|
||||
<li><a href="#org8ef7053">4.2.1. Number of states</a></li>
|
||||
<li><a href="#orgaedd6da">4.2.2. Resonance frequencies and mode shapes</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org337cc72">4.3. Verify transformation</a></li>
|
||||
<li><a href="#org0b133c2">4.3. Verify transformation</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org75a0e2e">5. Nano-Hexapod</a></li>
|
||||
<li><a href="#orge8fad0c">6. Identification of the table’s dynamics</a></li>
|
||||
<li><a href="#org71b8598">5. Identification of the table’s dynamics</a></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
@ -82,33 +81,33 @@
|
||||
<p>This report is also available as a <a href="./vibration-table.pdf">pdf</a>.</p>
|
||||
<hr>
|
||||
|
||||
<div id="outline-container-orgd96939c" class="outline-2">
|
||||
<h2 id="orgd96939c"><span class="section-number-2">1</span> Introduction</h2>
|
||||
<div id="outline-container-orgf5ac764" class="outline-2">
|
||||
<h2 id="orgf5ac764"><span class="section-number-2">1</span> Introduction</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
This document is divided as follows:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Section <a href="#org2abcf65">2</a>: the experimental setup and all the instrumentation are described</li>
|
||||
<li>Section <a href="#orge226c57">3</a>: the mathematics used to compute the 6DoF motion of a solid body from several inertial sensor is derived</li>
|
||||
<li>Section <a href="#orga8d4a3c">4</a>: a Simscape model of the vibration table is developed</li>
|
||||
<li>Section <a href="#org21d6634">6</a>: the table dynamics is identified and compared with the Simscape model</li>
|
||||
<li>Section <a href="#org6a14e7a">2</a>: the experimental setup and all the instrumentation are described</li>
|
||||
<li>Section <a href="#orga0537a2">3</a>: the mathematics used to compute the 6DoF motion of a solid body from several inertial sensor is derived</li>
|
||||
<li>Section <a href="#org2b706f6">4</a>: a Simscape model of the vibration table is developed</li>
|
||||
<li>Section <a href="#org5f4bcf1">5</a>: the table dynamics is identified and compared with the Simscape model</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8f2a9d3" class="outline-2">
|
||||
<h2 id="org8f2a9d3"><span class="section-number-2">2</span> Experimental Setup</h2>
|
||||
<div id="outline-container-org5832600" class="outline-2">
|
||||
<h2 id="org5832600"><span class="section-number-2">2</span> Experimental Setup</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org2abcf65"></a>
|
||||
<a id="org6a14e7a"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgf60715e" class="outline-3">
|
||||
<h3 id="orgf60715e"><span class="section-number-3">2.1</span> CAD Model</h3>
|
||||
<div id="outline-container-org088c0b5" class="outline-3">
|
||||
<h3 id="org088c0b5"><span class="section-number-3">2.1</span> CAD Model</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
|
||||
<div id="org36d3c3b" class="figure">
|
||||
<div id="org8048a79" class="figure">
|
||||
<p><img src="figs/vibration-table-cad-view.png" alt="vibration-table-cad-view.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>CAD View of the vibration table</p>
|
||||
@ -116,10 +115,10 @@ This document is divided as follows:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0740e89" class="outline-3">
|
||||
<h3 id="org0740e89"><span class="section-number-3">2.2</span> Instrumentation</h3>
|
||||
<div id="outline-container-orge848908" class="outline-3">
|
||||
<h3 id="orge848908"><span class="section-number-3">2.2</span> Instrumentation</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<div class="note" id="orga53b0fe">
|
||||
<div class="note" id="orgbb293bd">
|
||||
<p>
|
||||
Here are the documentation of the equipment used for this vibration table:
|
||||
</p>
|
||||
@ -137,8 +136,8 @@ Here are the documentation of the equipment used for this vibration table:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfae411d" class="outline-3">
|
||||
<h3 id="orgfae411d"><span class="section-number-3">2.3</span> Suspended table</h3>
|
||||
<div id="outline-container-orgae54ff5" class="outline-3">
|
||||
<h3 id="orgae54ff5"><span class="section-number-3">2.3</span> Suspended table</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<dl class="org-dl">
|
||||
<dt>Dimensions</dt><dd>450 mm x 450 mm x 60 mm</dd>
|
||||
@ -146,7 +145,7 @@ Here are the documentation of the equipment used for this vibration table:
|
||||
</dl>
|
||||
|
||||
|
||||
<div id="org37d8d17" class="figure">
|
||||
<div id="org5bb879d" class="figure">
|
||||
<p><img src="figs/B4545A_Compliance_inLb-780.png" alt="B4545A_Compliance_inLb-780.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Compliance of the B4545A optical table</p>
|
||||
@ -154,8 +153,8 @@ Here are the documentation of the equipment used for this vibration table:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org56dc68e" class="outline-3">
|
||||
<h3 id="org56dc68e"><span class="section-number-3">2.4</span> Inertial Sensors</h3>
|
||||
<div id="outline-container-org435fee6" class="outline-3">
|
||||
<h3 id="org435fee6"><span class="section-number-3">2.4</span> Inertial Sensors</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
@ -182,18 +181,18 @@ Here are the documentation of the equipment used for this vibration table:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7c42c7b" class="outline-2">
|
||||
<h2 id="org7c42c7b"><span class="section-number-2">3</span> Compute the 6DoF solid body motion from several inertial sensors</h2>
|
||||
<div id="outline-container-orgf366ef9" class="outline-2">
|
||||
<h2 id="orgf366ef9"><span class="section-number-2">3</span> Compute the 6DoF solid body motion from several inertial sensors</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="orge226c57"></a>
|
||||
<a id="orga0537a2"></a>
|
||||
</p>
|
||||
<p>
|
||||
Let’s consider a solid body with several accelerometers attached to it (Figure <a href="#org7cea217">3</a>).
|
||||
Let’s consider a solid body with several accelerometers attached to it (Figure <a href="#orgd7a7adf">3</a>).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org7cea217" class="figure">
|
||||
<div id="orgd7a7adf" class="figure">
|
||||
<p><img src="figs/local_to_global_coordinates.png" alt="local_to_global_coordinates.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Schematic of the measured motions of a solid body</p>
|
||||
@ -223,7 +222,7 @@ The measurement of the individual vectors is defined as the vector \(\vec{a}\):
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
From the positions and orientations of the acceleremoters (defined in Section <a href="#orgda5223d">3.1</a>), it is quite straightforward to compute the accelerations measured by the sensors from the acceleration/angular acceleration of the solid body (Section <a href="#org01e9572">3.2</a>).
|
||||
From the positions and orientations of the acceleremoters (defined in Section <a href="#org0125a45">3.1</a>), it is quite straightforward to compute the accelerations measured by the sensors from the acceleration/angular acceleration of the solid body (Section <a href="#orgb9fd993">3.2</a>).
|
||||
From this, we can easily build a transformation matrix \(M\), such that:
|
||||
</p>
|
||||
\begin{equation}
|
||||
@ -231,7 +230,7 @@ From this, we can easily build a transformation matrix \(M\), such that:
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
If the matrix is invertible, we can just take the inverse in order to obtain the transformation matrix giving the 6dof acceleration of the solid body from the accelerometer measurements (Section <a href="#org8cbcf02">3.3</a>):
|
||||
If the matrix is invertible, we can just take the inverse in order to obtain the transformation matrix giving the 6dof acceleration of the solid body from the accelerometer measurements (Section <a href="#orgdaf30e9">3.3</a>):
|
||||
</p>
|
||||
\begin{equation}
|
||||
{}^O\vec{x} = M^{-1} \cdot \vec{a}
|
||||
@ -242,11 +241,11 @@ If it is not invertible, then it means that it is not possible to compute all 6d
|
||||
The solution is then to change the location/orientation of some of the accelerometers.
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgb354999" class="outline-3">
|
||||
<h3 id="orgb354999"><span class="section-number-3">3.1</span> Define accelerometers positions/orientations</h3>
|
||||
<div id="outline-container-orgb03df82" class="outline-3">
|
||||
<h3 id="orgb03df82"><span class="section-number-3">3.1</span> Define accelerometers positions/orientations</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
<a id="orgda5223d"></a>
|
||||
<a id="org0125a45"></a>
|
||||
Let’s first define the position and orientation of all measured accelerations with respect to a defined frame \(\{O\}\).
|
||||
</p>
|
||||
|
||||
@ -261,10 +260,10 @@ Let’s first define the position and orientation of all measured accelerati
|
||||
</div>
|
||||
|
||||
<p>
|
||||
There are summarized in Table <a href="#org9069f15">1</a>.
|
||||
There are summarized in Table <a href="#orgdf64746">1</a>.
|
||||
</p>
|
||||
|
||||
<table id="org9069f15" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orgdf64746" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Positions of the accelerometers fixed to the vibration table with respect to \(\{O\}\)</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -340,10 +339,10 @@ We then define the direction of the measured accelerations (unit vectors):
|
||||
</div>
|
||||
|
||||
<p>
|
||||
They are summarized in Table <a href="#org2f05f69">2</a>.
|
||||
They are summarized in Table <a href="#org13c9bf3">2</a>.
|
||||
</p>
|
||||
|
||||
<table id="org2f05f69" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org13c9bf3" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 2:</span> Orientations of the accelerometers fixed to the vibration table expressed in \(\{O\}\)</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -407,11 +406,11 @@ They are summarized in Table <a href="#org2f05f69">2</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org162ae73" class="outline-3">
|
||||
<h3 id="org162ae73"><span class="section-number-3">3.2</span> Transformation matrix from motion of the solid body to accelerometer measurements</h3>
|
||||
<div id="outline-container-orgf872bb6" class="outline-3">
|
||||
<h3 id="orgf872bb6"><span class="section-number-3">3.2</span> Transformation matrix from motion of the solid body to accelerometer measurements</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
<a id="org01e9572"></a>
|
||||
<a id="orgb9fd993"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -476,7 +475,7 @@ a_i = \begin{bmatrix}
|
||||
And finally we can combine the 6 (line) vectors for the 6 accelerometers to write that in a matrix form.
|
||||
We obtain Eq. \eqref{eq:M_matrix}.
|
||||
</p>
|
||||
<div class="important" id="org9083ed5">
|
||||
<div class="important" id="org1f576e5">
|
||||
<p>
|
||||
The transformation from solid body acceleration \({}^O\vec{x}\) from sensor measured acceleration \(\vec{a}\) is:
|
||||
</p>
|
||||
@ -511,10 +510,10 @@ Let’s define such matrix using matlab:
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained matrix is shown in Table <a href="#org7dd170d">3</a>.
|
||||
The obtained matrix is shown in Table <a href="#orgb7789db">3</a>.
|
||||
</p>
|
||||
|
||||
<table id="org7dd170d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orgb7789db" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 3:</span> Effect of a displacement/rotation on the 6 measurements</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -608,11 +607,11 @@ The obtained matrix is shown in Table <a href="#org7dd170d">3</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb865df3" class="outline-3">
|
||||
<h3 id="orgb865df3"><span class="section-number-3">3.3</span> Compute the transformation matrix from accelerometer measurement to motion of the solid body</h3>
|
||||
<div id="outline-container-orge54a621" class="outline-3">
|
||||
<h3 id="orge54a621"><span class="section-number-3">3.3</span> Compute the transformation matrix from accelerometer measurement to motion of the solid body</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
<a id="org8cbcf02"></a>
|
||||
<a id="orgdaf30e9"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -631,10 +630,10 @@ We therefore need the determinant of \(M\) to be non zero:
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained inverse of the matrix is shown in Table <a href="#org8a443b4">4</a>.
|
||||
The obtained inverse of the matrix is shown in Table <a href="#orgb3868cf">4</a>.
|
||||
</p>
|
||||
|
||||
<table id="org8a443b4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orgb3868cf" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 4:</span> Compute the displacement/rotation from the 6 measurements</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -729,28 +728,28 @@ The obtained inverse of the matrix is shown in Table <a href="#org8a443b4">4</a>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfff4a19" class="outline-2">
|
||||
<h2 id="orgfff4a19"><span class="section-number-2">4</span> Simscape Model</h2>
|
||||
<div id="outline-container-orgae67fb9" class="outline-2">
|
||||
<h2 id="orgae67fb9"><span class="section-number-2">4</span> Simscape Model</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orga8d4a3c"></a>
|
||||
<a id="org2b706f6"></a>
|
||||
</p>
|
||||
<p>
|
||||
In this section, the Simscape model of the vibration table is described.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org2ecfaca" class="figure">
|
||||
<div id="org79ee770" class="figure">
|
||||
<p><img src="figs/simscape_vibration_table.png" alt="simscape_vibration_table.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>3D representation of the simscape model</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgd1b8332" class="outline-3">
|
||||
<h3 id="orgd1b8332"><span class="section-number-3">4.1</span> Simscape Sub-systems</h3>
|
||||
<div id="outline-container-org83808e1" class="outline-3">
|
||||
<h3 id="org83808e1"><span class="section-number-3">4.1</span> Simscape Sub-systems</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
<a id="org39306c3"></a>
|
||||
<a id="orgc93c68c"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -758,11 +757,11 @@ Parameters for sub-components of the simscape model are defined below.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org25263d5" class="outline-4">
|
||||
<h4 id="org25263d5"><span class="section-number-4">4.1.1</span> Springs</h4>
|
||||
<div id="outline-container-org430fcc4" class="outline-4">
|
||||
<h4 id="org430fcc4"><span class="section-number-4">4.1.1</span> Springs</h4>
|
||||
<div class="outline-text-4" id="text-4-1-1">
|
||||
<p>
|
||||
<a id="orgee18182"></a>
|
||||
<a id="org4ce6c6c"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -793,11 +792,11 @@ And we can increase the “equilibrium position” of the vertical sprin
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8fbfccb" class="outline-4">
|
||||
<h4 id="org8fbfccb"><span class="section-number-4">4.1.2</span> Inertial Shaker (IS20)</h4>
|
||||
<div id="outline-container-org741008c" class="outline-4">
|
||||
<h4 id="org741008c"><span class="section-number-4">4.1.2</span> Inertial Shaker (IS20)</h4>
|
||||
<div class="outline-text-4" id="text-4-1-2">
|
||||
<p>
|
||||
<a id="org4592c5e"></a>
|
||||
<a id="org65750ec"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -813,7 +812,7 @@ The inertial mass is guided inside the housing and an actuator (coil and magnet)
|
||||
The “reacting” force on the support is then used as an excitation.
|
||||
</p>
|
||||
|
||||
<table id="orgec31de6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orgbcb82ac" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 5:</span> Summary of the IS20 datasheet</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -851,7 +850,7 @@ The “reacting” force on the support is then used as an excitation.
|
||||
</table>
|
||||
|
||||
<p>
|
||||
From the datasheet in Table <a href="#orgec31de6">5</a>, we can estimate the parameters of the physical shaker.
|
||||
From the datasheet in Table <a href="#orgbcb82ac">5</a>, we can estimate the parameters of the physical shaker.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -868,11 +867,11 @@ shaker.c = 0.2<span class="org-type">*</span>sqrt(shaker.k<span class="org-type"
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org778a701" class="outline-4">
|
||||
<h4 id="org778a701"><span class="section-number-4">4.1.3</span> 3D accelerometer (356B18)</h4>
|
||||
<div id="outline-container-org5b2f05e" class="outline-4">
|
||||
<h4 id="org5b2f05e"><span class="section-number-4">4.1.3</span> 3D accelerometer (356B18)</h4>
|
||||
<div class="outline-text-4" id="text-4-1-3">
|
||||
<p>
|
||||
<a id="orgdc35834"></a>
|
||||
<a id="org23e3d96"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -887,7 +886,7 @@ An accelerometer consists of 2 solids:
|
||||
The relative motion between the housing and the inertial mass gives a measurement of the acceleration of the measured body (up to the suspension mode of the inertial mass).
|
||||
</p>
|
||||
|
||||
<table id="org64105ec" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org60e803f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 6:</span> Summary of the 356B18 datasheet</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -991,16 +990,16 @@ The accelerometer model can be chosen by setting the <code>type</code> property:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgab1e576" class="outline-3">
|
||||
<h3 id="orgab1e576"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div id="outline-container-org37f2322" class="outline-3">
|
||||
<h3 id="org37f2322"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
<a id="org350a100"></a>
|
||||
<a id="org5252ce8"></a>
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org356f48c" class="outline-4">
|
||||
<h4 id="org356f48c"><span class="section-number-4">4.2.1</span> Number of states</h4>
|
||||
<div id="outline-container-org8ef7053" class="outline-4">
|
||||
<h4 id="org8ef7053"><span class="section-number-4">4.2.1</span> Number of states</h4>
|
||||
<div class="outline-text-4" id="text-4-2-1">
|
||||
<p>
|
||||
Let’s first use perfect 3d accelerometers:
|
||||
@ -1076,8 +1075,8 @@ This corresponds to 6 states for each triaxial accelerometers.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org11eb355" class="outline-4">
|
||||
<h4 id="org11eb355"><span class="section-number-4">4.2.2</span> Resonance frequencies and mode shapes</h4>
|
||||
<div id="outline-container-orgaedd6da" class="outline-4">
|
||||
<h4 id="orgaedd6da"><span class="section-number-4">4.2.2</span> Resonance frequencies and mode shapes</h4>
|
||||
<div class="outline-text-4" id="text-4-2-2">
|
||||
<p>
|
||||
Let’s now identify the resonance frequency and mode shapes associated with the suspension modes of the optical table.
|
||||
@ -1124,11 +1123,11 @@ And the associated response of the optical table
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The results are shown in Table <a href="#org909caf2">7</a>.
|
||||
The results are shown in Table <a href="#org7e240b1">7</a>.
|
||||
The motion associated to the mode shapes are just indicative.
|
||||
</p>
|
||||
|
||||
<table id="org909caf2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org7e240b1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 7:</span> Resonance frequency and approximation of the mode shapes</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -1223,8 +1222,8 @@ The motion associated to the mode shapes are just indicative.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org337cc72" class="outline-3">
|
||||
<h3 id="org337cc72"><span class="section-number-3">4.3</span> Verify transformation</h3>
|
||||
<div id="outline-container-org0b133c2" class="outline-3">
|
||||
<h3 id="org0b133c2"><span class="section-number-3">4.3</span> Verify transformation</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
@ -1267,41 +1266,18 @@ bodeFig({G_acc(6), G_id(6)})
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org75a0e2e" class="outline-2">
|
||||
<h2 id="org75a0e2e"><span class="section-number-2">5</span> Nano-Hexapod</h2>
|
||||
<div id="outline-container-org71b8598" class="outline-2">
|
||||
<h2 id="org71b8598"><span class="section-number-2">5</span> Identification of the table’s dynamics</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<p>
|
||||
<a id="orga1006b8"></a>
|
||||
</p>
|
||||
<p>
|
||||
A configuration is added to be able to put the nano-hexapod on top of the vibration table as shown in Figure <a href="#org2ecfaca">4</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org4d16b70" class="figure">
|
||||
<p><img src="figs/vibration_table_nano_hexapod_simscape.png" alt="vibration_table_nano_hexapod_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>3D representation of the simscape model with the nano-hexapod</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The nano-hexapod’s simscape model is taken from another <a href="https://git.tdehaeze.xyz/tdehaeze/nass-simscape">git repository</a>.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge8fad0c" class="outline-2">
|
||||
<h2 id="orge8fad0c"><span class="section-number-2">6</span> Identification of the table’s dynamics</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<p>
|
||||
<a id="org21d6634"></a>
|
||||
<a id="org5f4bcf1"></a>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-04-19 lun. 16:33</p>
|
||||
<p class="date">Created: 2021-04-19 lun. 15:02</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -714,53 +714,6 @@ bodeFig({G_acc(5), G_id(5)})
|
||||
bodeFig({G_acc(6), G_id(6)})
|
||||
#+end_src
|
||||
|
||||
* Nano-Hexapod
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/nano_hexapod.m
|
||||
:END:
|
||||
<<sec:nano_hexapod>>
|
||||
** Introduction :ignore:
|
||||
|
||||
A configuration is added to be able to put the nano-hexapod on top of the vibration table as shown in Figure [[fig:simscape_vibration_table]].
|
||||
|
||||
#+name: fig:simscape_vibration_table
|
||||
#+caption: 3D representation of the simscape model with the nano-hexapod
|
||||
#+attr_latex: :width 0.8\linewidth
|
||||
[[file:figs/vibration_table_nano_hexapod_simscape.png]]
|
||||
|
||||
The nano-hexapod's simscape model is taken from another [[https://git.tdehaeze.xyz/tdehaeze/nass-simscape][git repository]].
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('matlab/')
|
||||
addpath('matlab/nass-simscape/matlab/nano_hexapod/')
|
||||
addpath('matlab/nass-simscape/STEPS/nano_hexapod/')
|
||||
addpath('matlab/nass-simscape/STEPS/png/')
|
||||
addpath('matlab/nass-simscape/src/')
|
||||
addpath('matlab/nass-simscape/mat/')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('nass-simscape/matlab/nano_hexapod/')
|
||||
addpath('nass-simscape/STEPS/nano_hexapod/')
|
||||
addpath('nass-simscape/STEPS/png/')
|
||||
addpath('nass-simscape/src/')
|
||||
addpath('nass-simscape/mat/')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
% Open the Simulink File
|
||||
open('vibration_table')
|
||||
#+end_src
|
||||
|
||||
* Identification of the table's dynamics
|
||||
<<sec:table_dynamics>>
|
||||
** Matlab Init :noexport:ignore:
|
||||
|
||||
Loading…
Reference in New Issue
Block a user