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Add optimal stiffness analysis document

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Thomas Dehaeze 2020-04-01 17:19:55 +02:00
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<head>
<!-- 2020-04-01 mer. 16:28 -->
<!-- 2020-04-01 mer. 17:19 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Simscape Model of the Nano-Active-Stabilization-System</title>
@ -246,11 +246,13 @@
<li><a href="#org7af5540">7. Compensating Gravity forces to start simulation at steady state (link)</a></li>
<li><a href="#org4dd191b">8. Disturbances (link)</a></li>
<li><a href="#org8d9280d">9. Simulation of Experiment (link)</a></li>
<li><a href="#orgafa75bf">10. Effect of support&rsquo;s compliance uncertainty on the plant (link)</a></li>
<li><a href="#orga323881">11. Effect of Experimental conditions on the plant dynamics (link)</a></li>
<li><a href="#org14a10e8">12. Active Damping Techniques on the full Simscape Model (link)</a></li>
<li><a href="#orgd818a00">13. Control of the Nano-Active-Stabilization-System (link)</a></li>
<li><a href="#org361f405">14. Useful Matlab Functions (link)</a></li>
<li><a href="#org0605048">10. Effect of support&rsquo;s compliance on the plant dynamics (link)</a></li>
<li><a href="#orge777d0f">11. Effect of the payload&rsquo;s &ldquo;impedance&rdquo; on the plant dynamics (link)</a></li>
<li><a href="#orga323881">12. Effect of Experimental conditions on the plant dynamics (link)</a></li>
<li><a href="#org1adf7f6">13. Optimal Stiffness of the nano-hexapod (link)</a></li>
<li><a href="#org14a10e8">14. Active Damping Techniques on the full Simscape Model (link)</a></li>
<li><a href="#orgd818a00">15. Control of the Nano-Active-Stabilization-System (link)</a></li>
<li><a href="#org361f405">16. Useful Matlab Functions (link)</a></li>
</ul>
</div>
</div>
@ -376,8 +378,8 @@ Experiments are simulated and the results are presented <a href="./experiments.h
</div>
</div>
<div id="outline-container-orgafa75bf" class="outline-2">
<h2 id="orgafa75bf"><span class="section-number-2">10</span> Effect of support&rsquo;s compliance uncertainty on the plant (<a href="uncertainty_support.html">link</a>)</h2>
<div id="outline-container-org0605048" class="outline-2">
<h2 id="org0605048"><span class="section-number-2">10</span> Effect of support&rsquo;s compliance on the plant dynamics (<a href="uncertainty_support.html">link</a>)</h2>
<div class="outline-text-2" id="text-10">
<p>
In this document, is studied how uncertainty on the micro-station compliance will affect the uncertainty of the isolation platform to be designed.
@ -385,19 +387,33 @@ In this document, is studied how uncertainty on the micro-station compliance wil
</div>
</div>
<div id="outline-container-orga323881" class="outline-2">
<h2 id="orga323881"><span class="section-number-2">11</span> Effect of Experimental conditions on the plant dynamics (<a href="uncertainty_experiment.html">link</a>)</h2>
<div id="outline-container-orge777d0f" class="outline-2">
<h2 id="orge777d0f"><span class="section-number-2">11</span> Effect of the payload&rsquo;s &ldquo;impedance&rdquo; on the plant dynamics (<a href="uncertainty_payload.html">link</a>)</h2>
<div class="outline-text-2" id="text-11">
<p>
The payload mass, stiffness and damping properties will influence the dynamics of the isolation platform.
This effect is studied, and conclusions on what characteristics of the isolation platform will lower this effect.
</p>
</div>
</div>
<div id="outline-container-orga323881" class="outline-2">
<h2 id="orga323881"><span class="section-number-2">12</span> Effect of Experimental conditions on the plant dynamics (<a href="uncertainty_experiment.html">link</a>)</h2>
<div class="outline-text-2" id="text-12">
<p>
In this document, the effect of all the experimental conditions (rotation speed, sample mass, &#x2026;) on the plant dynamics are studied.
Conclusion are drawn about what experimental conditions are critical on the variability of the plant dynamics.
</p>
</div>
</div>
<div id="outline-container-org1adf7f6" class="outline-2">
<h2 id="org1adf7f6"><span class="section-number-2">13</span> Optimal Stiffness of the nano-hexapod (<a href="optimal_stiffness.html">link</a>)</h2>
</div>
<div id="outline-container-org14a10e8" class="outline-2">
<h2 id="org14a10e8"><span class="section-number-2">12</span> Active Damping Techniques on the full Simscape Model (<a href="control_active_damping.html">link</a>)</h2>
<div class="outline-text-2" id="text-12">
<h2 id="org14a10e8"><span class="section-number-2">14</span> Active Damping Techniques on the full Simscape Model (<a href="control_active_damping.html">link</a>)</h2>
<div class="outline-text-2" id="text-14">
<p>
Active damping techniques are applied to the full Simscape model.
</p>
@ -405,8 +421,8 @@ Active damping techniques are applied to the full Simscape model.
</div>
<div id="outline-container-orgd818a00" class="outline-2">
<h2 id="orgd818a00"><span class="section-number-2">13</span> Control of the Nano-Active-Stabilization-System (<a href="control.html">link</a>)</h2>
<div class="outline-text-2" id="text-13">
<h2 id="orgd818a00"><span class="section-number-2">15</span> Control of the Nano-Active-Stabilization-System (<a href="control.html">link</a>)</h2>
<div class="outline-text-2" id="text-15">
<p>
In this file are gathered all studies about the control the Nano-Active-Stabilization-System.
</p>
@ -414,8 +430,8 @@ In this file are gathered all studies about the control the Nano-Active-Stabiliz
</div>
<div id="outline-container-org361f405" class="outline-2">
<h2 id="org361f405"><span class="section-number-2">14</span> Useful Matlab Functions (<a href="./functions.html">link</a>)</h2>
<div class="outline-text-2" id="text-14">
<h2 id="org361f405"><span class="section-number-2">16</span> Useful Matlab Functions (<a href="./functions.html">link</a>)</h2>
<div class="outline-text-2" id="text-16">
<p>
Many matlab functions are shared among all the files of the projects.
</p>
@ -428,7 +444,7 @@ These functions are all defined <a href="./functions.html">here</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-01 mer. 16:28</p>
<p class="date">Created: 2020-04-01 mer. 17:19</p>
</div>
</body>
</html>

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</div><div id="content">
<h1 class="title">Determination of the optimal nano-hexapod&rsquo;s stiffness</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org84aa9ce">1. Spindle Rotation Speed</a></li>
<li><a href="#org57a0e57">2. Micro-Station Compliance Effect</a></li>
<li><a href="#orgd6382d8">3. Payload &ldquo;Impedance&rdquo; Effect</a></li>
</ul>
</div>
</div>
<p>
As shown before, many parameters other than the nano-hexapod itself do influence the plant dynamics:
</p>
<ul class="org-ul">
<li>The micro-station compliance (studied <a href="uncertainty_support.html">here</a>)</li>
<li>The payload mass and dynamical properties (studied <a href="uncertainty_payload.html">here</a> and <a href="uncertainty_experiment.html">here</a>)</li>
<li>The experimental conditions, mainly the spindle rotation speed (studied <a href="uncertainty_experiment.html">here</a>)</li>
</ul>
<p>
As seen before, the stiffness of the nano-hexapod greatly influence the effect of such parameters.
</p>
<p>
We wish here to see if we can determine an optimal stiffness of the nano-hexapod such that:
</p>
<ul class="org-ul">
<li>Section <a href="#org1f375bb">1</a>: the change of its dynamics due to the spindle rotation speed is acceptable</li>
<li>Section <a href="#orgcf5798c">2</a>: the support compliance dynamics is not much present in the nano-hexapod dynamics</li>
<li>Section <a href="#org1a9d09c">3</a>: the change of payload impedance has acceptable effect on the plant dynamics</li>
</ul>
<div id="outline-container-org84aa9ce" class="outline-2">
<h2 id="org84aa9ce"><span class="section-number-2">1</span> Spindle Rotation Speed</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org1f375bb"></a>
</p>
</div>
</div>
<div id="outline-container-org57a0e57" class="outline-2">
<h2 id="org57a0e57"><span class="section-number-2">2</span> Micro-Station Compliance Effect</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgcf5798c"></a>
</p>
<ul class="org-ul">
<li>take the 6dof compliance of the micro-station</li>
<li>simple model + uncertainty</li>
</ul>
</div>
</div>
<div id="outline-container-orgd6382d8" class="outline-2">
<h2 id="orgd6382d8"><span class="section-number-2">3</span> Payload &ldquo;Impedance&rdquo; Effect</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org1a9d09c"></a>
</p>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-01 mer. 17:19</p>
</div>
</body>
</html>

8
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@ -89,13 +89,19 @@ Now that the dynamics of the Model have been tuned and the Disturbances have inc
Experiments are simulated and the results are presented [[./experiments.org][here]].
* Effect of support's compliance uncertainty on the plant ([[file:uncertainty_support.org][link]])
* Effect of support's compliance on the plant dynamics ([[file:uncertainty_support.org][link]])
In this document, is studied how uncertainty on the micro-station compliance will affect the uncertainty of the isolation platform to be designed.
* Effect of the payload's "impedance" on the plant dynamics ([[file:uncertainty_payload.org][link]])
The payload mass, stiffness and damping properties will influence the dynamics of the isolation platform.
This effect is studied, and conclusions on what characteristics of the isolation platform will lower this effect.
* Effect of Experimental conditions on the plant dynamics ([[file:uncertainty_experiment.org][link]])
In this document, the effect of all the experimental conditions (rotation speed, sample mass, ...) on the plant dynamics are studied.
Conclusion are drawn about what experimental conditions are critical on the variability of the plant dynamics.
* Optimal Stiffness of the nano-hexapod ([[file:optimal_stiffness.org][link]])
* Active Damping Techniques on the full Simscape Model ([[file:control_active_damping.org][link]])
Active damping techniques are applied to the full Simscape model.

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@ -0,0 +1,125 @@
#+TITLE: Determination of the optimal nano-hexapod's stiffness
:DRAWER:
#+STARTUP: overview
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas
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:END:
* Introduction :ignore:
As shown before, many parameters other than the nano-hexapod itself do influence the plant dynamics:
- The micro-station compliance (studied [[file:uncertainty_support.org][here]])
- The payload mass and dynamical properties (studied [[file:uncertainty_payload.org][here]] and [[file:uncertainty_experiment.org][here]])
- The experimental conditions, mainly the spindle rotation speed (studied [[file:uncertainty_experiment.org][here]])
As seen before, the stiffness of the nano-hexapod greatly influence the effect of such parameters.
We wish here to see if we can determine an optimal stiffness of the nano-hexapod such that:
- Section [[sec:spindle_rotation_speed]]: the change of its dynamics due to the spindle rotation speed is acceptable
- Section [[sec:micro_station_compliance]]: the support compliance dynamics is not much present in the nano-hexapod dynamics
- Section [[sec:payload_impedance]]: the change of payload impedance has acceptable effect on the plant dynamics
* Spindle Rotation Speed
<<sec:spindle_rotation_speed>>
** Introduction :ignore:
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab :tangle no
simulinkproject('../');
#+end_src
#+begin_src matlab
open('nass_model.slx')
#+end_src
** Conclusion :ignore:
* Micro-Station Compliance Effect
<<sec:micro_station_compliance>>
** Introduction :ignore:
- take the 6dof compliance of the micro-station
- simple model + uncertainty
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab :tangle no
simulinkproject('../');
#+end_src
#+begin_src matlab
open('nass_model.slx')
#+end_src
** Conclusion :ignore:
* Payload "Impedance" Effect
<<sec:payload_impedance>>
** Introduction :ignore:
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab :tangle no
simulinkproject('../');
#+end_src
#+begin_src matlab
open('nass_model.slx')
#+end_src
** Conclusion :ignore: