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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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<head>
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<!-- 2019-11-04 lun. 15:46 -->
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<!-- 2019-11-04 lun. 15:53 -->
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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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<title>Simscape Uniaxial Model</title>
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<title>Identification of the disturbances</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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<style type="text/css">
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@ -275,17 +275,17 @@ for the JavaScript code in this tag.
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Simscape Uniaxial Model</h1>
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<h1 class="title">Identification of the disturbances</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orga9da337">1. Identification</a></li>
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<li><a href="#org0c4c66f">2. Sensitivity to Disturbances</a></li>
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<li><a href="#orge0b60ba">3. Power Spectral Density of the effect of the disturbances</a></li>
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<li><a href="#orgf444bc6">4. Compute the Power Spectral Density of the disturbance force</a></li>
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<li><a href="#org9df3e1a">5. Noise Budget</a></li>
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<li><a href="#orgb1f811d">6. Save</a></li>
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<li><a href="#org698f7c0">1. Identification</a></li>
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<li><a href="#orgf877551">2. Sensitivity to Disturbances</a></li>
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<li><a href="#orgb5bd5c7">3. Power Spectral Density of the effect of the disturbances</a></li>
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<li><a href="#org48ef780">4. Compute the Power Spectral Density of the disturbance force</a></li>
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<li><a href="#orge298819">5. Noise Budget</a></li>
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<li><a href="#org38cd52b">6. Save</a></li>
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</ul>
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</div>
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</div>
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@ -307,15 +307,26 @@ These forces can be due to imperfect guiding for instance.</li>
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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) 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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This file is divided in the following sections:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#orge6f61b6">1</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="#org17c8ec0">1</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="#org8df3794">2</a>: the bode plot of those transfer functions are shown</li>
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<li>Section <a href="#org14df12e">3</a>: the measured PSD of the effect of the disturbances are shown</li>
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<li>Section <a href="#orgf7bf807">4</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="#org1fb6fdf">5</a>: with the computed PSD, the noise budget of the system is done</li>
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</ul>
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<div id="outline-container-orga9da337" class="outline-2">
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<h2 id="orga9da337"><span class="section-number-2">1</span> Identification</h2>
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<div id="outline-container-org698f7c0" class="outline-2">
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<h2 id="org698f7c0"><span class="section-number-2">1</span> Identification</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orge6f61b6"></a>
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<a id="org17c8ec0"></a>
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</p>
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<p>
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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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<div class="org-src-container">
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@ -352,14 +363,15 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
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</div>
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</div>
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<div id="outline-container-org0c4c66f" class="outline-2">
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<h2 id="org0c4c66f"><span class="section-number-2">2</span> Sensitivity to Disturbances</h2>
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<div id="outline-container-orgf877551" class="outline-2">
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<h2 id="orgf877551"><span class="section-number-2">2</span> Sensitivity to Disturbances</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org04b950a"></a>
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<a id="org8df3794"></a>
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</p>
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<div id="org3e3443b" class="figure">
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<div id="orgbf23881" class="figure">
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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><span class="figure-number">Figure 1: </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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@ -367,7 +379,7 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
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<div id="orgd9fb712" class="figure">
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<div id="orgbc1a0a8" class="figure">
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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><span class="figure-number">Figure 2: </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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@ -375,7 +387,7 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
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<div id="orgf7d4761" class="figure">
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<div id="org44fd0ad" class="figure">
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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><span class="figure-number">Figure 3: </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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@ -383,11 +395,11 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
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</div>
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</div>
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<div id="outline-container-orge0b60ba" class="outline-2">
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<h2 id="orge0b60ba"><span class="section-number-2">3</span> Power Spectral Density of the effect of the disturbances</h2>
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<div id="outline-container-orgb5bd5c7" class="outline-2">
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<h2 id="orgb5bd5c7"><span class="section-number-2">3</span> Power Spectral Density of the effect of the disturbances</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org7ab0a1d"></a>
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<a id="org14df12e"></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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</p>
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<ul class="org-ul">
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@ -416,15 +428,15 @@ We now compute the relative velocity between the hexapod and the granite due to
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</div>
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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="#org048378a">4</a> and <a href="#orge887351">5</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="#org299c59f">4</a> and <a href="#orgcfcd277">5</a>.
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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="#orge3e2cf9">6</a>.
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The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#org45af273">6</a>.
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</p>
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<div id="org048378a" class="figure">
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<div id="org299c59f" 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>
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<p><span class="figure-number">Figure 4: </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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@ -432,14 +444,14 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a h
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<div id="orge887351" class="figure">
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<div id="orgcfcd277" 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>
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<p><span class="figure-number">Figure 5: </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 id="orge3e2cf9" class="figure">
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<div id="org45af273" 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>
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<p><span class="figure-number">Figure 6: </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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@ -447,15 +459,15 @@ 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 id="outline-container-orgf444bc6" class="outline-2">
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<h2 id="orgf444bc6"><span class="section-number-2">4</span> Compute the Power Spectral Density of the disturbance force</h2>
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<div id="outline-container-org48ef780" class="outline-2">
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<h2 id="org48ef780"><span class="section-number-2">4</span> Compute the Power Spectral Density of the disturbance force</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="orgf3934b5"></a>
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<a id="orgf7bf807"></a>
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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="#org04b950a">2</a>) and from the measured PSD of the relative motion (section <a href="#org7ab0a1d">3</a>), we can compute the PSD of the disturbance force.
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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="#org8df3794">2</a>) and from the measured PSD of the relative motion (section <a href="#org14df12e">3</a>), we can compute the PSD of the disturbance force.
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</p>
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<div class="org-src-container">
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@ -465,7 +477,7 @@ tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs<span class="org-rain
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</div>
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<div id="orgfc0e496" class="figure">
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<div id="org894deae" class="figure">
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<p><img src="figs/dist_force_psd.png" alt="dist_force_psd.png" />
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</p>
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<p><span class="figure-number">Figure 7: </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>
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@ -473,16 +485,20 @@ tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs<span class="org-rain
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</div>
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</div>
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<div id="outline-container-org9df3e1a" class="outline-2">
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<h2 id="org9df3e1a"><span class="section-number-2">5</span> Noise Budget</h2>
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<div id="outline-container-orge298819" class="outline-2">
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<h2 id="orge298819"><span class="section-number-2">5</span> Noise Budget</h2>
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<div class="outline-text-2" id="text-5">
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<p>
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<a id="org1fb6fdf"></a>
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</p>
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<p>
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Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.
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We should verify that this is coherent with the measurements.
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</p>
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<div id="org8995b51" class="figure">
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<div id="orgd8fee5c" class="figure">
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<p><img src="figs/psd_effect_dist_verif.png" alt="psd_effect_dist_verif.png" />
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</p>
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<p><span class="figure-number">Figure 8: </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>
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@ -490,7 +506,7 @@ We should verify that this is coherent with the measurements.
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<div id="org4921ccd" class="figure">
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<div id="orgc7c290a" class="figure">
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<p><img src="figs/cas_computed_relative_displacement.png" alt="cas_computed_relative_displacement.png" />
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</p>
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<p><span class="figure-number">Figure 9: </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>
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@ -498,11 +514,11 @@ We should verify that this is coherent with the measurements.
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</div>
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</div>
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<div id="outline-container-orgb1f811d" class="outline-2">
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<h2 id="orgb1f811d"><span class="section-number-2">6</span> Save</h2>
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<div id="outline-container-org38cd52b" class="outline-2">
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<h2 id="org38cd52b"><span class="section-number-2">6</span> Save</h2>
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<div class="outline-text-2" id="text-6">
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<p>
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The PSD of the disturbance force are now saved for further noise budgeting when control is applied.
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The PSD of the disturbance force are now saved for further noise budgeting when control is applied (the mat file is accessible <a href="mat/dist_psd.mat">here</a>).
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</p>
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<div class="org-src-container">
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@ -512,7 +528,7 @@ dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m<span
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dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz]
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dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz]
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save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/disturbance-forces.mat'</span>, <span class="org-string">'dist_f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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</div>
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@ -520,7 +536,7 @@ save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string
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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: 2019-11-04 lun. 15:46</p>
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<p class="date">Created: 2019-11-04 lun. 15:53</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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</body>
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@ -1,4 +1,4 @@
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#+TITLE: Simscape Uniaxial Model
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#+TITLE: Identification of the disturbances
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:DRAWER:
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#+STARTUP: overview
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@ -51,7 +51,12 @@ The sources of perturbations are:
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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) and then, using a model, compute the forces that induced such velocity.
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This file is divided in the following sections:
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- Section [[sec:identification]]: 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
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- Section [[sec:sensitivity_disturbances]]: the bode plot of those transfer functions are shown
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- Section [[sec:psd_dist]]: the measured PSD of the effect of the disturbances are shown
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- Section [[sec:psd_force_dist]]: from the model and the measured PSD, the PSD of the disturbance forces are computed
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- Section [[sec:noise_budget]]: with the computed PSD, the noise budget of the system is done
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* Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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@ -73,6 +78,8 @@ Because we cannot measure directly the perturbation forces, we have the measure
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* Identification
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<<sec:identification>>
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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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#+begin_src matlab
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%% Options for Linearized
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options = linearizeOptions;
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@ -104,6 +111,7 @@ G.OutputName = {'Dgm', 'Dhm', 'Vm'};
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* Sensitivity to Disturbances
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<<sec:sensitivity_disturbances>>
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#+begin_src matlab :exports none
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freqs = logspace(0, 3, 1000);
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@ -308,6 +316,8 @@ Now, from the extracted transfer functions from the disturbance force to the rel
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[[file:figs/dist_force_psd.png]]
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* Noise Budget
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<<sec:noise_budget>>
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Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.
|
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We should verify that this is coherent with the measurements.
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@ -366,7 +376,7 @@ We should verify that this is coherent with the measurements.
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[[file:figs/cas_computed_relative_displacement.png]]
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* Save
|
||||
The PSD of the disturbance force are now saved for further noise budgeting when control is applied.
|
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The PSD of the disturbance force are now saved for further noise budgeting when control is applied (the mat file is accessible [[file:mat/dist_psd.mat][here]]).
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#+begin_src matlab
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dist_f = struct();
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@ -375,5 +385,5 @@ The PSD of the disturbance force are now saved for further noise budgeting when
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dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]
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dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]
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||||
save('./disturbances/mat/disturbance-forces.mat', 'dist_f');
|
||||
save('./disturbances/mat/dist_psd.mat', 'dist_f');
|
||||
#+end_src
|
||||
|
||||
Loading…
Reference in New Issue
Block a user