Add schematic to explain sources of perturbation
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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. 15:53 -->
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<!-- 2019-11-04 lun. 15:56 -->
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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>Identification of the disturbances</title>
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@ -280,12 +280,12 @@ for the JavaScript code in this tag.
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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="#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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<li><a href="#orga5c4454">1. Identification</a></li>
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<li><a href="#org0c8db89">2. Sensitivity to Disturbances</a></li>
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<li><a href="#org000560b">3. Power Spectral Density of the effect of the disturbances</a></li>
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<li><a href="#orgf4292db">4. Compute the Power Spectral Density of the disturbance force</a></li>
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<li><a href="#org40a18b0">5. Noise Budget</a></li>
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<li><a href="#org0562d36">6. Save</a></li>
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</ul>
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</div>
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</div>
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@ -295,34 +295,43 @@ 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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The sources of perturbations are:
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The sources of perturbations are (schematically shown in figure <a href="#org1a5776c">1</a>):
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</p>
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<ul class="org-ul">
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<li>Ground Motion</li>
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<li>Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle.
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<li>\(D_w\): Ground Motion</li>
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<li>Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle (\(F_{rz}\) and \(F_{ty}\)).
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These forces can be due to imperfect guiding for instance.</li>
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</ul>
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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) 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="#org1a5776c">1</a>) and then, using a model, compute the forces that induced such velocity.
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</p>
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<div id="org1a5776c" 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>
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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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</div>
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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="#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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<li>Section <a href="#org6e1c6df">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="#org122fad2">2</a>: the bode plot of those transfer functions are shown</li>
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<li>Section <a href="#org19ee725">3</a>: the measured PSD of the effect of the disturbances are shown</li>
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<li>Section <a href="#org7c3b0b5">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="#org7e2fa27">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-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 id="outline-container-orga5c4454" class="outline-2">
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<h2 id="orga5c4454"><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="org17c8ec0"></a>
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<a id="org6e1c6df"></a>
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</p>
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<p>
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@ -363,43 +372,43 @@ 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-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 id="outline-container-org0c8db89" class="outline-2">
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<h2 id="org0c8db89"><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="org8df3794"></a>
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<a id="org122fad2"></a>
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</p>
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<div id="orgbf23881" class="figure">
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<div id="org8f38398" 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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<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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</div>
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<div id="orgbc1a0a8" class="figure">
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<div id="orga020f23" 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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<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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</div>
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<div id="org44fd0ad" class="figure">
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<div id="org0dea65f" 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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<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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</div>
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</div>
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</div>
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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 id="outline-container-org000560b" class="outline-2">
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<h2 id="org000560b"><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="org14df12e"></a>
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<a id="org19ee725"></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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@ -428,46 +437,46 @@ 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="#org299c59f">4</a> and <a href="#orgcfcd277">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="#orgdd6d206">5</a> and <a href="#org67d7e50">6</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="#org45af273">6</a>.
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The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#orgd8c990c">7</a>.
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</p>
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<div id="org299c59f" class="figure">
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<div id="orgdd6d206" 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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<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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</div>
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<div id="orgcfcd277" class="figure">
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<div id="org67d7e50" 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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<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 id="org45af273" class="figure">
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<div id="orgd8c990c" 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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<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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</div>
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</div>
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</div>
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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 id="outline-container-orgf4292db" class="outline-2">
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<h2 id="orgf4292db"><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="orgf7bf807"></a>
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<a id="org7c3b0b5"></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="#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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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="#org122fad2">2</a>) and from the measured PSD of the relative motion (section <a href="#org19ee725">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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@ -477,19 +486,19 @@ 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="org894deae" class="figure">
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<div id="orgafd3bc8" 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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<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>
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</div>
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</div>
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</div>
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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 id="outline-container-org40a18b0" class="outline-2">
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<h2 id="org40a18b0"><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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<a id="org7e2fa27"></a>
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</p>
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<p>
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@ -498,24 +507,24 @@ We should verify that this is coherent with the measurements.
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</p>
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<div id="orgd8fee5c" class="figure">
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<div id="org3326f40" 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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<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>
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</div>
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<div id="orgc7c290a" class="figure">
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<div id="orgead0a2c" 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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<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>
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</div>
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</div>
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</div>
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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 id="outline-container-org0562d36" class="outline-2">
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<h2 id="org0562d36"><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 (the mat file is accessible <a href="mat/dist_psd.mat">here</a>).
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@ -536,7 +545,7 @@ 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. 15:53</p>
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<p class="date">Created: 2019-11-04 lun. 15:56</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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@ -44,12 +44,124 @@
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* Introduction :ignore:
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The goal here is to extract the Power Spectral Density of the sources of perturbation.
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The sources of perturbations are:
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- Ground Motion
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- Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle.
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The sources of perturbations are (schematically shown in figure [[fig:uniaxial-model-micro-station]]):
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- $D_w$: Ground Motion
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- Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle ($F_{rz}$ and $F_{ty}$).
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These forces can be due to imperfect guiding for instance.
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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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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 [[fig:uniaxial-model-micro-station]]) and then, using a model, compute the forces that induced such velocity.
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#+begin_src latex :file uniaxial-model-micro-station.pdf :post pdf2svg(file=*this*, ext="png") :exports results
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\begin{tikzpicture}
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% ====================
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% Parameters
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% ====================
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\def\massw{2.2} % Width of the masses
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\def\massh{0.8} % Height of the masses
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\def\spaceh{1.2} % Height of the springs/dampers
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\def\dispw{0.4} % Width of the dashed line for the displacement
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\def\disph{0.3} % Height of the arrow for the displacements
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\def\bracs{0.05} % Brace spacing vertically
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\def\brach{-12pt} % Brace shift horizontaly
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\def\fsensh{0.2} % Height of the force sensor
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\def\velsize{0.2} % Size of the velocity sensor
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% ====================
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% ====================
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% Ground
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% ====================
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\draw (-0.5*\massw, 0) -- (0.5*\massw, 0);
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\draw[dashed] (0.5*\massw, 0) -- ++(1, 0);
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\draw[->, dasehd] (0.5*\massw+0.8, 0) -- ++(0, 0.5) node[right]{$D_{w}$};
|
||||
% ====================
|
||||
|
||||
|
||||
% ====================
|
||||
% Marble
|
||||
\begin{scope}[shift={(0, 0)}]
|
||||
% Mass
|
||||
\draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{m}$};
|
||||
|
||||
% Spring, Damper, and Actuator
|
||||
\draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{m}$};
|
||||
\draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{m}$};
|
||||
|
||||
% Legend
|
||||
\draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
|
||||
(-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Marble};
|
||||
|
||||
% Displacements
|
||||
\draw[dashed] (0.5*\massw, \spaceh+\massh) -- ++(2*\dispw, 0) coordinate(xm) -- ++(2.2*\dispw, 0) coordinate(dbot);
|
||||
\end{scope}
|
||||
% ====================
|
||||
|
||||
|
||||
% ====================
|
||||
% Ty
|
||||
\begin{scope}[shift={(0, \spaceh+\massh)}]
|
||||
% Mass
|
||||
\draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{t}$};
|
||||
|
||||
% Spring, Damper, and Actuator
|
||||
\draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{t}$};
|
||||
\draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{t}$};
|
||||
\draw[actuator={0.45}{0.2}] ( 0.4*\massw, 0) -- ( 0.4*\massw, \spaceh) node[midway, right=0.1](ft){$F_{ty}$};
|
||||
|
||||
% Legend
|
||||
\draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
|
||||
(-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Ty};
|
||||
\end{scope}
|
||||
% ====================
|
||||
|
||||
|
||||
% ====================
|
||||
% Rz
|
||||
\begin{scope}[shift={(0, 2*(\spaceh+\massh))}]
|
||||
% Mass
|
||||
\draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{z}$};
|
||||
|
||||
% Spring, Damper, and Actuator
|
||||
\draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{z}$};
|
||||
\draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{z}$};
|
||||
\draw[actuator] ( 0.4*\massw, 0) -- ( 0.4*\massw, \spaceh) node[midway, right=0.1](F){$F_{rz}$};
|
||||
|
||||
% Legend
|
||||
\draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
|
||||
(-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Rz};
|
||||
\end{scope}
|
||||
% ====================
|
||||
|
||||
|
||||
% ====================
|
||||
% Hexapod
|
||||
\begin{scope}[shift={(0, 3*(\spaceh+\massh))}]
|
||||
% Mass
|
||||
\draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m_{h}$};
|
||||
|
||||
% Spring, Damper, and Actuator
|
||||
\draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k_{h}$};
|
||||
\draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c_{h}$};
|
||||
|
||||
% Displacements
|
||||
\draw[dashed] (0.5*\massw, \spaceh+\massh) -- ++(2*\dispw, 0) coordinate(xs) -- ++(2.2*\dispw, 0) coordinate(dtop);
|
||||
|
||||
% Legend
|
||||
\draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
|
||||
(-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) node[midway,rotate=90,anchor=south,yshift=10pt]{Hexapod};
|
||||
\end{scope}
|
||||
% ====================
|
||||
|
||||
\draw[<->] ($(dbot)+(-0.3,0)$) --node[midway, right]{$D$} ($(dtop)+(-0.3,0)$);
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+name: fig:uniaxial-model-micro-station
|
||||
#+caption: Schematic of the Micro Station and the sources of disturbance
|
||||
#+RESULTS:
|
||||
[[file:figs/uniaxial-model-micro-station.png]]
|
||||
|
||||
|
||||
This file is divided in the following sections:
|
||||
- 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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figs/uniaxial-model-micro-station.png
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figs/uniaxial-model-micro-station.png
Normal file
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After Width: | Height: | Size: 20 KiB |
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Reference in New Issue
Block a user