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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<head>
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<!-- 2019-10-08 mar. 11:13 -->
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<!-- 2020-02-25 mar. 18:08 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Control of the NASS</title>
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<title>Control of the NASS</title>
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@licstart The following is the entire license notice for the
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@licstart The following is the entire license notice for the
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JavaScript code in this tag.
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JavaScript code in this tag.
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Copyright (C) 2012-2019 Free Software Foundation, Inc.
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Copyright (C) 2012-2020 Free Software Foundation, Inc.
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The JavaScript code in this tag is free software: you can
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The JavaScript code in this tag is free software: you can
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redistribute it and/or modify it under the terms of the GNU
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redistribute it and/or modify it under the terms of the GNU
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@ -257,8 +259,7 @@ for the JavaScript code in this tag.
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2019-10-08 mar. 11:13</p>
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<p class="date">Created: 2020-02-25 mar. 18:08</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</div>
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</body>
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</body>
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</html>
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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<head>
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<!-- 2020-02-18 mar. 17:44 -->
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<!-- 2020-02-25 mar. 18:08 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Identification of the disturbances</title>
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<title>Identification of the disturbances</title>
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@ -285,7 +286,7 @@ The goal here is to extract the Power Spectral Density of the sources of perturb
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</p>
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</p>
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<p>
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<p>
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The sources of perturbations are (schematically shown in figure <a href="#org0dbac72">1</a>):
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The sources of perturbations are (schematically shown in figure <a href="#org3b8025c">1</a>):
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</p>
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</p>
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<ul class="org-ul">
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<ul class="org-ul">
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<li>\(D_w\): Ground Motion</li>
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<li>\(D_w\): Ground Motion</li>
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@ -294,12 +295,12 @@ These forces can be due to imperfect guiding for instance.</li>
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</ul>
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</ul>
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<p>
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<p>
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Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure <a href="#org0dbac72">1</a>) and then, using a model, compute the forces that induced such velocity.
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Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure <a href="#org3b8025c">1</a>) and then, using a model, compute the forces that induced such velocity.
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</p>
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</p>
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<div id="org0dbac72" class="figure">
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<div id="org3b8025c" class="figure">
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<p><img src="figs/uniaxial-model-micro-station.png" alt="uniaxial-model-micro-station.png" />
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<p><img src="figs/uniaxial-model-micro-station.png" alt="uniaxial-model-micro-station.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 1: </span>Schematic of the Micro Station and the sources of disturbance</p>
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<p><span class="figure-number">Figure 1: </span>Schematic of the Micro Station and the sources of disturbance</p>
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@ -310,19 +311,19 @@ Because we cannot measure directly the perturbation forces, we have the measure
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This file is divided in the following sections:
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This file is divided in the following sections:
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</p>
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</p>
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<ul class="org-ul">
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<ul class="org-ul">
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<li>Section <a href="#org2c7a8eb">1</a>: the simscape model used here is presented</li>
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<li>Section <a href="#org7cdab70">1</a>: the simscape model used here is presented</li>
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<li>Section <a href="#orgdef3420">2</a>: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup</li>
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<li>Section <a href="#org43ec76b">2</a>: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup</li>
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<li>Section <a href="#org1eb00b2">3</a>: the bode plot of those transfer functions are shown</li>
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<li>Section <a href="#org5636fee">3</a>: the bode plot of those transfer functions are shown</li>
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<li>Section <a href="#orgd955c86">4</a>: the measured PSD of the effect of the disturbances are shown</li>
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<li>Section <a href="#org40a7e4e">4</a>: the measured PSD of the effect of the disturbances are shown</li>
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<li>Section <a href="#org6914212">5</a>: from the model and the measured PSD, the PSD of the disturbance forces are computed</li>
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<li>Section <a href="#orgd113ba5">5</a>: from the model and the measured PSD, the PSD of the disturbance forces are computed</li>
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<li>Section <a href="#orgc51ba08">6</a>: with the computed PSD, the noise budget of the system is done</li>
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<li>Section <a href="#org71da6bd">6</a>: with the computed PSD, the noise budget of the system is done</li>
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</ul>
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</ul>
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<div id="outline-container-Simscape%20Model" class="outline-2">
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<div id="outline-container-orgd6383a2" class="outline-2">
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<h2 id="Simscape-Model"><span class="section-number-2">1</span> Simscape Model</h2>
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<h2 id="Simscape-Model"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-Simscape-Model">
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<div class="outline-text-2" id="text-Simscape-Model">
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<p>
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<p>
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<a id="org2c7a8eb"></a>
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<a id="org7cdab70"></a>
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</p>
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</p>
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<p>
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<p>
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@ -363,11 +364,11 @@ initializeSample(<span class="org-string">'type'</span>, <span class="org-string
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-Identification" class="outline-2">
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<div id="outline-container-orgab57d7a" class="outline-2">
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<h2 id="Identification"><span class="section-number-2">2</span> Identification</h2>
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<h2 id="Identification"><span class="section-number-2">2</span> Identification</h2>
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<div class="outline-text-2" id="text-Identification">
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<div class="outline-text-2" id="text-Identification">
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<p>
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<p>
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<a id="orgdef3420"></a>
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<a id="org43ec76b"></a>
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The transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup with the code below.
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The transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup with the code below.
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</p>
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</p>
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@ -416,15 +417,15 @@ G.OutputName = {<span class="org-string">'Vm'</span>};
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-Sensitivity%20to%20Disturbances" class="outline-2">
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<div id="outline-container-org26913fc" class="outline-2">
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<h2 id="Sensitivity-to-Disturbances"><span class="section-number-2">3</span> Sensitivity to Disturbances</h2>
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<h2 id="Sensitivity-to-Disturbances"><span class="section-number-2">3</span> Sensitivity to Disturbances</h2>
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<div class="outline-text-2" id="text-Sensitivity-to-Disturbances">
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<div class="outline-text-2" id="text-Sensitivity-to-Disturbances">
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<p>
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<p>
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<a id="org1eb00b2"></a>
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<a id="org5636fee"></a>
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</p>
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</p>
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<div id="org40ebd12" class="figure">
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<div id="org7fe296c" class="figure">
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<p><img src="figs/sensitivity_dist_gm.png" alt="sensitivity_dist_gm.png" />
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<p><img src="figs/sensitivity_dist_gm.png" alt="sensitivity_dist_gm.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 2: </span>Sensitivity to Ground Motion (<a href="./figs/sensitivity_dist_gm.png">png</a>, <a href="./figs/sensitivity_dist_gm.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 2: </span>Sensitivity to Ground Motion (<a href="./figs/sensitivity_dist_gm.png">png</a>, <a href="./figs/sensitivity_dist_gm.pdf">pdf</a>)</p>
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@ -432,7 +433,7 @@ G.OutputName = {<span class="org-string">'Vm'</span>};
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<div id="org488da2a" class="figure">
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<div id="orgce9715c" class="figure">
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<p><img src="figs/sensitivity_dist_fty.png" alt="sensitivity_dist_fty.png" />
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<p><img src="figs/sensitivity_dist_fty.png" alt="sensitivity_dist_fty.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 3: </span>Sensitivity to vertical forces applied by the Ty stage (<a href="./figs/sensitivity_dist_fty.png">png</a>, <a href="./figs/sensitivity_dist_fty.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 3: </span>Sensitivity to vertical forces applied by the Ty stage (<a href="./figs/sensitivity_dist_fty.png">png</a>, <a href="./figs/sensitivity_dist_fty.pdf">pdf</a>)</p>
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@ -440,7 +441,7 @@ G.OutputName = {<span class="org-string">'Vm'</span>};
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<div id="org8152b2c" class="figure">
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<div id="orga3e6fbc" class="figure">
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<p><img src="figs/sensitivity_dist_frz.png" alt="sensitivity_dist_frz.png" />
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<p><img src="figs/sensitivity_dist_frz.png" alt="sensitivity_dist_frz.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 4: </span>Sensitivity to vertical forces applied by the Rz stage (<a href="./figs/sensitivity_dist_frz.png">png</a>, <a href="./figs/sensitivity_dist_frz.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 4: </span>Sensitivity to vertical forces applied by the Rz stage (<a href="./figs/sensitivity_dist_frz.png">png</a>, <a href="./figs/sensitivity_dist_frz.pdf">pdf</a>)</p>
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@ -448,11 +449,11 @@ G.OutputName = {<span class="org-string">'Vm'</span>};
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-Power%20Spectral%20Density%20of%20the%20effect%20of%20the%20disturbances" class="outline-2">
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<div id="outline-container-org627e5cf" class="outline-2">
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<h2 id="Power-Spectral-Density-of-the-effect-of-the-disturbances"><span class="section-number-2">4</span> Power Spectral Density of the effect of the disturbances</h2>
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<h2 id="Power-Spectral-Density-of-the-effect-of-the-disturbances"><span class="section-number-2">4</span> Power Spectral Density of the effect of the disturbances</h2>
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<div class="outline-text-2" id="text-Power-Spectral-Density-of-the-effect-of-the-disturbances">
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<div class="outline-text-2" id="text-Power-Spectral-Density-of-the-effect-of-the-disturbances">
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<p>
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<p>
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<a id="orgd955c86"></a>
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<a id="org40a7e4e"></a>
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The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:
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The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:
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</p>
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</p>
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<ul class="org-ul">
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<ul class="org-ul">
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@ -481,15 +482,15 @@ We now compute the relative velocity between the hexapod and the granite due to
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</div>
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</div>
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<p>
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<p>
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The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures <a href="#orga80b694">5</a> and <a href="#org337df44">6</a>.
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The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures <a href="#orgb815ef2">5</a> and <a href="#org4c2c215">6</a>.
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</p>
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</p>
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<p>
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<p>
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The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#org2f4ee86">7</a>.
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The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#orgaf910f1">7</a>.
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</p>
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</p>
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<div id="orga80b694" class="figure">
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<div id="orgb815ef2" class="figure">
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<p><img src="figs/dist_effect_relative_velocity.png" alt="dist_effect_relative_velocity.png" />
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<p><img src="figs/dist_effect_relative_velocity.png" alt="dist_effect_relative_velocity.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_velocity.png">png</a>, <a href="./figs/dist_effect_relative_velocity.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_velocity.png">png</a>, <a href="./figs/dist_effect_relative_velocity.pdf">pdf</a>)</p>
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@ -497,14 +498,14 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a h
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<div id="org337df44" class="figure">
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<div id="org4c2c215" class="figure">
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<p><img src="figs/dist_effect_relative_motion.png" alt="dist_effect_relative_motion.png" />
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<p><img src="figs/dist_effect_relative_motion.png" alt="dist_effect_relative_motion.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion.png">png</a>, <a href="./figs/dist_effect_relative_motion.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion.png">png</a>, <a href="./figs/dist_effect_relative_motion.pdf">pdf</a>)</p>
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</div>
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</div>
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<div id="org2f4ee86" class="figure">
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<div id="orgaf910f1" class="figure">
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<p><img src="figs/dist_effect_relative_motion_cas.png" alt="dist_effect_relative_motion_cas.png" />
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<p><img src="figs/dist_effect_relative_motion_cas.png" alt="dist_effect_relative_motion_cas.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 7: </span>Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion_cas.png">png</a>, <a href="./figs/dist_effect_relative_motion_cas.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 7: </span>Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion_cas.png">png</a>, <a href="./figs/dist_effect_relative_motion_cas.pdf">pdf</a>)</p>
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@ -512,15 +513,15 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a h
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</div>
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</div>
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</div>
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<div id="outline-container-Compute%20the%20Power%20Spectral%20Density%20of%20the%20disturbance%20force" class="outline-2">
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<div id="outline-container-orge27c71b" class="outline-2">
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<h2 id="Compute-the-Power-Spectral-Density-of-the-disturbance-force"><span class="section-number-2">5</span> Compute the Power Spectral Density of the disturbance force</h2>
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<h2 id="Compute-the-Power-Spectral-Density-of-the-disturbance-force"><span class="section-number-2">5</span> Compute the Power Spectral Density of the disturbance force</h2>
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<div class="outline-text-2" id="text-Compute-the-Power-Spectral-Density-of-the-disturbance-force">
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<div class="outline-text-2" id="text-Compute-the-Power-Spectral-Density-of-the-disturbance-force">
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<p>
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<p>
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<a id="org6914212"></a>
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<a id="orgd113ba5"></a>
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</p>
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</p>
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<p>
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<p>
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||||||
Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#org1eb00b2">3</a>) and from the measured PSD of the relative motion (section <a href="#orgd955c86">4</a>), we can compute the PSD of the disturbance force.
|
Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#org5636fee">3</a>) and from the measured PSD of the relative motion (section <a href="#org40a7e4e">4</a>), we can compute the PSD of the disturbance force.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -530,7 +531,7 @@ tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org9a8bb49" class="figure">
|
<div id="org45cf35c" class="figure">
|
||||||
<p><img src="figs/dist_force_psd.png" alt="dist_force_psd.png" />
|
<p><img src="figs/dist_force_psd.png" alt="dist_force_psd.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the disturbance force (<a href="./figs/dist_force_psd.png">png</a>, <a href="./figs/dist_force_psd.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the disturbance force (<a href="./figs/dist_force_psd.png">png</a>, <a href="./figs/dist_force_psd.pdf">pdf</a>)</p>
|
||||||
@ -538,11 +539,11 @@ tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<
|
|||||||
</div>
|
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|
||||||
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|
||||||
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||||||
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|
<div id="outline-container-org844ca42" class="outline-2">
|
||||||
<h2 id="Noise-Budget"><span class="section-number-2">6</span> Noise Budget</h2>
|
<h2 id="Noise-Budget"><span class="section-number-2">6</span> Noise Budget</h2>
|
||||||
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|
||||||
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|
||||||
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||||||
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|
||||||
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|
||||||
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<p>
|
||||||
@ -551,7 +552,7 @@ We should verify that this is coherent with the measurements.
|
|||||||
</p>
|
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|
||||||
|
|
||||||
|
|
||||||
<div id="orgede2c8c" class="figure">
|
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|
||||||
<p><img src="figs/psd_effect_dist_verif.png" alt="psd_effect_dist_verif.png" />
|
<p><img src="figs/psd_effect_dist_verif.png" alt="psd_effect_dist_verif.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 9: </span>Computed Effect of the disturbances on the relative displacement hexapod/granite (<a href="./figs/psd_effect_dist_verif.png">png</a>, <a href="./figs/psd_effect_dist_verif.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 9: </span>Computed Effect of the disturbances on the relative displacement hexapod/granite (<a href="./figs/psd_effect_dist_verif.png">png</a>, <a href="./figs/psd_effect_dist_verif.pdf">pdf</a>)</p>
|
||||||
@ -559,7 +560,7 @@ We should verify that this is coherent with the measurements.
|
|||||||
|
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||||||
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||||||
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|
||||||
<div id="org4aeb9e5" class="figure">
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|
||||||
<p><img src="figs/cas_computed_relative_displacement.png" alt="cas_computed_relative_displacement.png" />
|
<p><img src="figs/cas_computed_relative_displacement.png" alt="cas_computed_relative_displacement.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 10: </span>CAS of the total Relative Displacement due to all considered sources of perturbation (<a href="./figs/cas_computed_relative_displacement.png">png</a>, <a href="./figs/cas_computed_relative_displacement.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 10: </span>CAS of the total Relative Displacement due to all considered sources of perturbation (<a href="./figs/cas_computed_relative_displacement.png">png</a>, <a href="./figs/cas_computed_relative_displacement.pdf">pdf</a>)</p>
|
||||||
@ -567,7 +568,7 @@ We should verify that this is coherent with the measurements.
|
|||||||
</div>
|
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|
||||||
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|
||||||
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||||||
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|
||||||
<h2 id="Save"><span class="section-number-2">7</span> Save</h2>
|
<h2 id="Save"><span class="section-number-2">7</span> Save</h2>
|
||||||
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|
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|
||||||
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|
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|
||||||
@ -591,7 +592,7 @@ save(<span class="org-string">'./disturbances/mat/dist_psd.mat'</span>, <span cl
|
|||||||
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|
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|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2020-02-18 mar. 17:44</p>
|
<p class="date">Created: 2020-02-25 mar. 18:08</p>
|
||||||
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section 4, provided you include this license notice and a URL
|
||||||
|
through which recipients can access the Corresponding Source.
|
||||||
|
|
||||||
|
|
||||||
|
@licend The above is the entire license notice
|
||||||
|
for the JavaScript code in this tag.
|
||||||
|
*/
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
function CodeHighlightOn(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(null != target) {
|
||||||
|
elem.cacheClassElem = elem.className;
|
||||||
|
elem.cacheClassTarget = target.className;
|
||||||
|
target.className = "code-highlighted";
|
||||||
|
elem.className = "code-highlighted";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
function CodeHighlightOff(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(elem.cacheClassElem)
|
||||||
|
elem.className = elem.cacheClassElem;
|
||||||
|
if(elem.cacheClassTarget)
|
||||||
|
target.className = elem.cacheClassTarget;
|
||||||
|
}
|
||||||
|
/*]]>*///-->
|
||||||
|
</script>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="org-div-home-and-up">
|
||||||
|
<a accesskey="h" href="../index.html"> UP </a>
|
||||||
|
|
|
||||||
|
<a accesskey="H" href="../index.html"> HOME </a>
|
||||||
|
</div><div id="content">
|
||||||
|
<h1 class="title">Tomography Experiment</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org03b2a76">1. Simscape Model</a></li>
|
||||||
|
<li><a href="#org6ed78a0">2. Tomography Experiment with no disturbances</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orgc1321b7">2.1. Simulation Setup</a></li>
|
||||||
|
<li><a href="#orgebeb6c3">2.2. Analysis</a></li>
|
||||||
|
<li><a href="#orge9a06c9">2.3. Conclusion</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a href="#org16d8e58">3. Tomography Experiment with included perturbations</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orgc6ab502">3.1. Simulation Setup</a></li>
|
||||||
|
<li><a href="#orga551571">3.2. Analysis</a></li>
|
||||||
|
<li><a href="#org3eee8bd">3.3. Conclusion</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a href="#org72f01ab">4. Tomography when the micro-hexapod is not centered</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orga42880e">4.1. Simulation Setup</a></li>
|
||||||
|
<li><a href="#org58e1909">4.2. Analysis</a></li>
|
||||||
|
<li><a href="#org4670aba">4.3. Conclusion</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a href="#org8fa1632">5. Raster Scans with the translation stage</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org5778305">5.1. Simulation Setup</a></li>
|
||||||
|
<li><a href="#org3f73a44">5.2. Analysis</a></li>
|
||||||
|
<li><a href="#org67ff024">5.3. Conclusion</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The goal here is to simulate some scientific experiments with the tuned Simscape model when no control is applied to the nano-hexapod.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
This has several goals:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>Validate the model</li>
|
||||||
|
<li>Estimate the expected error motion for the experiments</li>
|
||||||
|
<li>Estimate the stroke that we may need for the nano-hexapod</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The document in organized as follow:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>In section <a href="#orgfc7d050">1</a> the Simscape model is initialized</li>
|
||||||
|
<li>In section <a href="#org3effbb8">2</a> a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included</li>
|
||||||
|
<li>In section <a href="#org4e7f626">3</a>, the same is done but with disturbance included</li>
|
||||||
|
<li>In section <a href="#orgb31e3fb">4</a> the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included</li>
|
||||||
|
<li>In section <a href="#org6aaeb53">5</a>, scans with the translation stage are simulated with no perturbation included</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
<div id="outline-container-org03b2a76" class="outline-2">
|
||||||
|
<h2 id="org03b2a76"><span class="section-number-2">1</span> Simscape Model</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<p>
|
||||||
|
<a id="orgfc7d050"></a>
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">open(<span class="org-string">'nass_model.slx'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We load the shared simulink configuration and we set the <code>StopTime</code>.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
|
||||||
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'5'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We first initialize all the stages.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeGround();
|
||||||
|
initializeGranite();
|
||||||
|
initializeTy();
|
||||||
|
initializeRy();
|
||||||
|
initializeRz();
|
||||||
|
initializeMicroHexapod();
|
||||||
|
initializeAxisc();
|
||||||
|
initializeMirror();
|
||||||
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
||||||
|
initializeSample(<span class="org-string">'mass'</span>, 1);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We initialize the reference path for all the stages.
|
||||||
|
All stage is set to its zero position except the Spindle which is rotating at 60rpm.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org6ed78a0" class="outline-2">
|
||||||
|
<h2 id="org6ed78a0"><span class="section-number-2">2</span> Tomography Experiment with no disturbances</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<p>
|
||||||
|
<a id="org3effbb8"></a>
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-orgc1321b7" class="outline-3">
|
||||||
|
<h3 id="orgc1321b7"><span class="section-number-3">2.1</span> Simulation Setup</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-1">
|
||||||
|
<p>
|
||||||
|
And we initialize the disturbances to be equal to zero.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeDisturbances(...
|
||||||
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
||||||
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
||||||
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
||||||
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
||||||
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
||||||
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
||||||
|
);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We simulate the model.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we save the obtained data.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">tomo_align_no_dist = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
||||||
|
save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>, <span class="org-string">'-append'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgebeb6c3" class="outline-3">
|
||||||
|
<h3 id="orgebeb6c3"><span class="section-number-3">2.2</span> Analysis</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
|
||||||
|
t = tomo_align_no_dist.t;
|
||||||
|
MTr = tomo_align_no_dist.MTr;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
||||||
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
||||||
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
||||||
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
||||||
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
||||||
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org47272c3" class="figure">
|
||||||
|
<p><img src="figs/exp_tomo_without_dist_trans.png" alt="exp_tomo_without_dist_trans.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 1: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist_trans.png">png</a>, <a href="./figs/exp_tomo_without_dist_trans.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org72f4825" class="figure">
|
||||||
|
<p><img src="figs/exp_tomo_without_dist_rot.png" alt="exp_tomo_without_dist_rot.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 2: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist_rot.png">png</a>, <a href="./figs/exp_tomo_without_dist_rot.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orge9a06c9" class="outline-3">
|
||||||
|
<h3 id="orge9a06c9"><span class="section-number-3">2.3</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-3">
|
||||||
|
<div class="important">
|
||||||
|
<p>
|
||||||
|
When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included.
|
||||||
|
This residual error motion probably comes from a small misalignment somewhere.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org16d8e58" class="outline-2">
|
||||||
|
<h2 id="org16d8e58"><span class="section-number-2">3</span> Tomography Experiment with included perturbations</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<p>
|
||||||
|
<a id="org4e7f626"></a>
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-orgc6ab502" class="outline-3">
|
||||||
|
<h3 id="orgc6ab502"><span class="section-number-3">3.1</span> Simulation Setup</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-1">
|
||||||
|
<p>
|
||||||
|
We now activate the disturbances.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeDisturbances(...
|
||||||
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
||||||
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
||||||
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
||||||
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
||||||
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
||||||
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
||||||
|
);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We simulate the model.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we save the obtained data.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">tomo_align_dist = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
||||||
|
save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'-append'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orga551571" class="outline-3">
|
||||||
|
<h3 id="orga551571"><span class="section-number-3">3.2</span> Analysis</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
|
||||||
|
t = tomo_align_dist.t;
|
||||||
|
MTr = tomo_align_dist.MTr;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
||||||
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
||||||
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
||||||
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
||||||
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
||||||
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org5b3411f" class="figure">
|
||||||
|
<p><img src="figs/exp_tomo_dist_trans.png" alt="exp_tomo_dist_trans.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 3: </span>X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist_trans.png">png</a>, <a href="./figs/exp_tomo_dist_trans.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org7934376" class="figure">
|
||||||
|
<p><img src="figs/exp_tomo_dist_rot.png" alt="exp_tomo_dist_rot.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 4: </span>X-Y-Z rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist_rot.png">png</a>, <a href="./figs/exp_tomo_dist_rot.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org3eee8bd" class="outline-3">
|
||||||
|
<h3 id="org3eee8bd"><span class="section-number-3">3.3</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-3">
|
||||||
|
<div class="important">
|
||||||
|
<p>
|
||||||
|
Error motion is what expected from the disturbance measurements.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org72f01ab" class="outline-2">
|
||||||
|
<h2 id="org72f01ab"><span class="section-number-2">4</span> Tomography when the micro-hexapod is not centered</h2>
|
||||||
|
<div class="outline-text-2" id="text-4">
|
||||||
|
<p>
|
||||||
|
<a id="orgb31e3fb"></a>
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-orga42880e" class="outline-3">
|
||||||
|
<h3 id="orga42880e"><span class="section-number-3">4.1</span> Simulation Setup</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-1">
|
||||||
|
<p>
|
||||||
|
We first set the wanted translation of the Micro Hexapod.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">P_micro_hexapod = [0.01; 0; 0]; <span class="org-comment">% [m]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We initialize the reference path.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Dh_pos'</span>, [P_micro_hexapod; 0; 0; 0], <span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We initialize the stages.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeMicroHexapod(<span class="org-string">'AP'</span>, P_micro_hexapod);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we initialize the disturbances to zero.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeDisturbances(...
|
||||||
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
||||||
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
||||||
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
||||||
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
||||||
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
||||||
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
||||||
|
);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We simulate the model.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we save the obtained data.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">tomo_not_align = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
||||||
|
save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'-append'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org58e1909" class="outline-3">
|
||||||
|
<h3 id="org58e1909"><span class="section-number-3">4.2</span> Analysis</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_not_align'</span>);
|
||||||
|
t = tomo_not_align.t;
|
||||||
|
MTr = tomo_not_align.MTr;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
||||||
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
||||||
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
||||||
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
||||||
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
||||||
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org40355c3" class="figure">
|
||||||
|
<p><img src="figs/exp_tomo_offset_trans.png" alt="exp_tomo_offset_trans.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 5: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset_trans.png">png</a>, <a href="./figs/exp_tomo_offset_trans.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org3f64362" class="figure">
|
||||||
|
<p><img src="figs/exp_tomo_offset_rot.png" alt="exp_tomo_offset_rot.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 6: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset_rot.png">png</a>, <a href="./figs/exp_tomo_offset_rot.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4670aba" class="outline-3">
|
||||||
|
<h3 id="org4670aba"><span class="section-number-3">4.3</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-3">
|
||||||
|
<div class="important">
|
||||||
|
<p>
|
||||||
|
The main motions are translations in the X direction of the mobile platform (corresponds to the eccentricity of the micro-hexapod) and rotations along the rotating Y axis.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org8fa1632" class="outline-2">
|
||||||
|
<h2 id="org8fa1632"><span class="section-number-2">5</span> Raster Scans with the translation stage</h2>
|
||||||
|
<div class="outline-text-2" id="text-5">
|
||||||
|
<p>
|
||||||
|
<a id="org6aaeb53"></a>
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org5778305" class="outline-3">
|
||||||
|
<h3 id="org5778305"><span class="section-number-3">5.1</span> Simulation Setup</h3>
|
||||||
|
<div class="outline-text-3" id="text-5-1">
|
||||||
|
<p>
|
||||||
|
We set the reference path.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Dy_type'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'Dy_amplitude'</span>, 10e<span class="org-type">-</span>3, <span class="org-string">'Dy_period'</span>, 1);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We initialize the stages.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeGround();
|
||||||
|
initializeGranite();
|
||||||
|
initializeTy();
|
||||||
|
initializeRy();
|
||||||
|
initializeRz();
|
||||||
|
initializeMicroHexapod();
|
||||||
|
initializeAxisc();
|
||||||
|
initializeMirror();
|
||||||
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
||||||
|
initializeSample(<span class="org-string">'mass'</span>, 1);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we initialize the disturbances to zero.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeDisturbances(...
|
||||||
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
||||||
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
||||||
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
||||||
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
||||||
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
||||||
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
||||||
|
);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We simulate the model.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we save the obtained data.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">ty_scan = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
||||||
|
save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'ty_scan'</span>, <span class="org-string">'-append'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org3f73a44" class="outline-3">
|
||||||
|
<h3 id="org3f73a44"><span class="section-number-3">5.2</span> Analysis</h3>
|
||||||
|
<div class="outline-text-3" id="text-5-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'ty_scan'</span>);
|
||||||
|
t = ty_scan.t;
|
||||||
|
MTr = ty_scan.MTr;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
||||||
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
||||||
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
||||||
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
||||||
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
||||||
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org042610c" class="figure">
|
||||||
|
<p><img src="figs/exp_ty_scan_trans.png" alt="exp_ty_scan_trans.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 7: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan_trans.png">png</a>, <a href="./figs/exp_ty_scan_trans.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org26a730c" class="figure">
|
||||||
|
<p><img src="figs/exp_ty_scan_rot.png" alt="exp_ty_scan_rot.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 8: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan_rot.png">png</a>, <a href="./figs/exp_ty_scan_rot.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org67ff024" class="outline-3">
|
||||||
|
<h3 id="org67ff024"><span class="section-number-3">5.3</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-5-3">
|
||||||
|
<div class="important">
|
||||||
|
<p>
|
||||||
|
This is logic that the main error moving is translation along the Y axis and rotation along the X axis.
|
||||||
|
In order to reduce the errors, we can make a smoother reference path for the translation stage.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-02-25 mar. 18:08</p>
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</div>
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</body>
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</html>
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