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Remove few outputs and add missing captions

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Thomas Dehaeze 2020-04-08 12:17:23 +02:00
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2 changed files with 27 additions and 77 deletions
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docs/optimal_stiffness_disturbances.html
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@ -4,7 +4,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-04-08 mer. 12:12 -->
<!-- 2020-04-08 mer. 12:17 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Determination of the optimal nano-hexapod&rsquo;s stiffness for reducing the effect of disturbances</title>
@ -257,7 +257,7 @@
<li><a href="#org78dd34d">2.3. Sensitivity to Stages vibration (Filtering)</a></li>
<li><a href="#orgd4ea2f4">2.4. Effect of Ground motion (Transmissibility).</a></li>
<li><a href="#org0448746">2.5. Direct Forces (Compliance).</a></li>
<li><a href="#orge784867">2.6. Conclusion</a></li>
<li><a href="#org6791692">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org6527e58">3. Effect of granite stiffness</a>
@ -270,7 +270,7 @@
</li>
<li><a href="#org9215f81">3.2. Soft Granite</a></li>
<li><a href="#org8878556">3.3. Effect of the Granite transfer function</a></li>
<li><a href="#org4b4fa39">3.4. Conclusion</a></li>
<li><a href="#orga001da4">3.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8a88fb0">4. Open Loop Budget Error</a>
@ -278,7 +278,7 @@
<li><a href="#org6bd588f">4.1. Noise Budgeting - Theory</a></li>
<li><a href="#orgcc86f59">4.2. Power Spectral Densities</a></li>
<li><a href="#orgef96b89">4.3. Cumulative Amplitude Spectrum</a></li>
<li><a href="#org2b9df24">4.4. Conclusion</a></li>
<li><a href="#org4352c0d">4.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org34c0f38">5. Closed Loop Budget Error</a>
@ -287,7 +287,7 @@
<li><a href="#orgf2d36a1">5.2. Reduction thanks to feedback - Required bandwidth</a></li>
</ul>
</li>
<li><a href="#orgbf0fb63">6. Conclusion</a></li>
<li><a href="#org08f24cd">6. Conclusion</a></li>
</ul>
</div>
</div>
@ -497,8 +497,8 @@ The effect of direct forces/torques applied on the sample (cable forces for inst
</div>
</div>
<div id="outline-container-orge784867" class="outline-3">
<h3 id="orge784867"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-org6791692" class="outline-3">
<h3 id="org6791692"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<p>
@ -678,12 +678,14 @@ From Figures <a href="#orgc4c14fb">11</a> and <a href="#org533cc4b">12</a>, we s
</div>
</div>
<div id="outline-container-org4b4fa39" class="outline-3">
<h3 id="org4b4fa39"><span class="section-number-3">3.4</span> Conclusion</h3>
<div id="outline-container-orga001da4" class="outline-3">
<h3 id="orga001da4"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4">
<div class="important">
<p>
Having a soft granite suspension could greatly improve the sensitivity the ground motion and thus the level of sample vibration if it is found that ground motion is the limiting factor.
Having a soft granite suspension greatly decreases the sensitivity the ground motion.
Also, it does not affect much the sensitivity to stage vibration and direct forces.
Thus the level of sample vibration can be reduced by using a soft granite suspension if it is found that ground motion is the limiting factor.
</p>
</div>
@ -716,7 +718,7 @@ Let&rsquo;s consider Figure <a href="#org7ff50a0">13</a> there \(G_d(s)\) is the
<div id="org7ff50a0" class="figure">
<p><img src="figs/psd_change_tf.png" alt="psd_change_tf.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Figure caption</p>
<p><span class="figure-number">Figure 13: </span>Signal \(d\) going through and LTI transfer function \(G_d(s)\) to give a signal \(y\)</p>
</div>
<p>
@ -742,7 +744,7 @@ Sometimes, we prefer to compute the <b>Amplitude</b> Spectral Density (ASD) whic
<div id="orgc24bdf6" class="figure">
<p><img src="figs/psd_change_tf_multiple_pert.png" alt="psd_change_tf_multiple_pert.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Figure caption</p>
<p><span class="figure-number">Figure 14: </span>Block diagram showing and output \(y\) resulting from the addition of multiple perturbations \(d_i\)</p>
</div>
<p>
@ -823,24 +825,6 @@ Similarly, the Cumulative Amplitude Spectrum of the sample vibrations are shown:
The black dashed line corresponds to the performance objective of a sample vibration equal to \(10\ nm [rms]\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">freqs = dist_f.f;
<span class="org-type">figure</span>;
hold on;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Ks)</span>
plot(freqs, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(freqs), flip(dist_f.psd_gm<span class="org-type">.*</span>abs(squeeze(freqresp(Gd{<span class="org-constant">i</span>}(<span class="org-string">'Ez'</span>, <span class="org-string">'Dwz'</span>), freqs, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2)))), <span class="org-string">'-'</span>, ...
<span class="org-string">'DisplayName'</span>, sprintf(<span class="org-string">'$k = %.0g$ [N/m]'</span>, Ks(<span class="org-constant">i</span>)));
<span class="org-keyword">end</span>
plot([freqs(1) freqs(end)], [10e<span class="org-type">-</span>9 10e<span class="org-type">-</span>9], <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'CAS $E_y$ $[m]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim([1, 500]); ylim([1e<span class="org-type">-</span>10 1e<span class="org-type">-</span>6]);
</pre>
</div>
<div id="org488d65f" class="figure">
<p><img src="figs/opt_stiff_cas_dz_gm.png" alt="opt_stiff_cas_dz_gm.png" />
@ -848,24 +832,6 @@ xlim([1, 500]); ylim([1e<span class="org-type">-</span>10 1e<span class="org-typ
<p><span class="figure-number">Figure 18: </span>Cumulative Amplitude Spectrum of the Sample vertical position error due to Ground motion for multiple nano-hexapod stiffnesses (<a href="./figs/opt_stiff_cas_dz_gm.png">png</a>, <a href="./figs/opt_stiff_cas_dz_gm.pdf">pdf</a>)</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">freqs = dist_f.f;
<span class="org-type">figure</span>;
hold on;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Ks)</span>
plot(freqs, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(freqs), flip(dist_f.psd_rz<span class="org-type">.*</span>abs(squeeze(freqresp(Gd{<span class="org-constant">i</span>}(<span class="org-string">'Ez'</span>, <span class="org-string">'Frz_z'</span>), freqs, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2)))), <span class="org-string">'-'</span>, ...
<span class="org-string">'DisplayName'</span>, sprintf(<span class="org-string">'$k = %.0g$ [N/m]'</span>, Ks(<span class="org-constant">i</span>)));
<span class="org-keyword">end</span>
plot([freqs(1) freqs(end)], [10e<span class="org-type">-</span>9 10e<span class="org-type">-</span>9], <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'CAS $[m]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([1, 500]); ylim([1e<span class="org-type">-</span>10 1e<span class="org-type">-</span>6]);
</pre>
</div>
<div id="orge5458c6" class="figure">
<p><img src="figs/opt_stiff_cas_dz_rz.png" alt="opt_stiff_cas_dz_rz.png" />
@ -873,24 +839,6 @@ xlim([1, 500]); ylim([1e<span class="org-type">-</span>10 1e<span class="org-typ
<p><span class="figure-number">Figure 19: </span>Cumulative Amplitude Spectrum of the Sample vertical position error due to Vertical vibration of the Spindle for multiple nano-hexapod stiffnesses (<a href="./figs/opt_stiff_cas_dz_rz.png">png</a>, <a href="./figs/opt_stiff_cas_dz_rz.pdf">pdf</a>)</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">freqs = dist_f.f;
<span class="org-type">figure</span>;
hold on;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Ks)</span>
plot(freqs, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(freqs), flip(psd_tot(<span class="org-type">:</span>,<span class="org-constant">i</span>))))), <span class="org-string">'-'</span>, ...
<span class="org-string">'DisplayName'</span>, sprintf(<span class="org-string">'$k = %.0g$ [N/m]'</span>, Ks(<span class="org-constant">i</span>)));
<span class="org-keyword">end</span>
plot([freqs(1) freqs(end)], [10e<span class="org-type">-</span>9 10e<span class="org-type">-</span>9], <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'CAS $E_z$ $[m]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim([1, 500]); ylim([1e<span class="org-type">-</span>10 1e<span class="org-type">-</span>6]);
</pre>
</div>
<div id="orgf6888f0" class="figure">
<p><img src="figs/opt_stiff_cas_dz_tot.png" alt="opt_stiff_cas_dz_tot.png" />
@ -900,8 +848,8 @@ xlim([1, 500]); ylim([1e<span class="org-type">-</span>10 1e<span class="org-typ
</div>
</div>
<div id="outline-container-org2b9df24" class="outline-3">
<h3 id="org2b9df24"><span class="section-number-3">4.4</span> Conclusion</h3>
<div id="outline-container-org4352c0d" class="outline-3">
<h3 id="org4352c0d"><span class="section-number-3">4.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-4">
<div class="important">
<p>
@ -1064,8 +1012,8 @@ The obtained required bandwidth (approximate upper and lower bounds) to obtained
</div>
</div>
<div id="outline-container-orgbf0fb63" class="outline-2">
<h2 id="orgbf0fb63"><span class="section-number-2">6</span> Conclusion</h2>
<div id="outline-container-org08f24cd" class="outline-2">
<h2 id="org08f24cd"><span class="section-number-2">6</span> Conclusion</h2>
<div class="outline-text-2" id="text-6">
<div class="important">
<p>
@ -1083,7 +1031,7 @@ From Figure <a href="#orgd677910">23</a> and Table <a href="#org5ab4860">1</a>,
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-08 mer. 12:12</p>
<p class="date">Created: 2020-04-08 mer. 12:17</p>
</div>
</body>
</html>

14
org/optimal_stiffness_disturbances.org
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@ -693,7 +693,9 @@ From Figures [[fig:opt_stiff_soft_granite_Frz]] and [[fig:opt_stiff_soft_granite
** Conclusion
#+begin_important
Having a soft granite suspension could greatly improve the sensitivity the ground motion and thus the level of sample vibration if it is found that ground motion is the limiting factor.
Having a soft granite suspension greatly decreases the sensitivity the ground motion.
Also, it does not affect much the sensitivity to stage vibration and direct forces.
Thus the level of sample vibration can be reduced by using a soft granite suspension if it is found that ground motion is the limiting factor.
#+end_important
* Open Loop Budget Error
@ -729,7 +731,7 @@ Let's consider Figure [[fig:psd_change_tf]] there $G_d(s)$ is the transfer funct
#+end_src
#+name: fig:psd_change_tf
#+caption: Figure caption
#+caption: Signal $d$ going through and LTI transfer function $G_d(s)$ to give a signal $y$
#+RESULTS:
[[file:figs/psd_change_tf.png]]
@ -768,7 +770,7 @@ Sometimes, we prefer to compute the *Amplitude* Spectral Density (ASD) which is
#+end_src
#+name: fig:psd_change_tf_multiple_pert
#+caption: Figure caption
#+caption: Block diagram showing and output $y$ resulting from the addition of multiple perturbations $d_i$
#+RESULTS:
[[file:figs/psd_change_tf_multiple_pert.png]]
@ -892,7 +894,7 @@ Similarly, the Cumulative Amplitude Spectrum of the sample vibrations are shown:
The black dashed line corresponds to the performance objective of a sample vibration equal to $10\ nm [rms]$.
#+begin_src matlab
#+begin_src matlab :exports none
freqs = dist_f.f;
figure;
@ -918,7 +920,7 @@ The black dashed line corresponds to the performance objective of a sample vibra
#+caption: Cumulative Amplitude Spectrum of the Sample vertical position error due to Ground motion for multiple nano-hexapod stiffnesses ([[./figs/opt_stiff_cas_dz_gm.png][png]], [[./figs/opt_stiff_cas_dz_gm.pdf][pdf]])
[[file:figs/opt_stiff_cas_dz_gm.png]]
#+begin_src matlab
#+begin_src matlab :exports none
freqs = dist_f.f;
figure;
@ -944,7 +946,7 @@ The black dashed line corresponds to the performance objective of a sample vibra
#+caption: Cumulative Amplitude Spectrum of the Sample vertical position error due to Vertical vibration of the Spindle for multiple nano-hexapod stiffnesses ([[./figs/opt_stiff_cas_dz_rz.png][png]], [[./figs/opt_stiff_cas_dz_rz.pdf][pdf]])
[[file:figs/opt_stiff_cas_dz_rz.png]]
#+begin_src matlab
#+begin_src matlab :exports none
freqs = dist_f.f;
figure;