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Add stewart platform model size

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Thomas Dehaeze 2020-09-21 13:14:25 +02:00
parent 3972f2f2f6
commit 5256d1f595
2 changed files with 38 additions and 21 deletions
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-09-21 lun. 13:07 -->
<!-- 2020-09-21 lun. 13:14 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>SVD Control</title>
<meta name="generator" content="Org mode" />
@ -27,27 +27,27 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orga7bd74e">1. Simscape Model - Gravimeter</a>
<li><a href="#org09b41c5">1. Simscape Model - Gravimeter</a>
<ul>
<li><a href="#org2acf438">1.1. Simulink</a></li>
<li><a href="#orgaf12c1d">1.1. Simulink</a></li>
</ul>
</li>
<li><a href="#org08c4258">2. Simscape Model - Stewart Platform</a>
<li><a href="#org84efeb7">2. Simscape Model - Stewart Platform</a>
<ul>
<li><a href="#orgb618964">2.1. Jacobian</a></li>
<li><a href="#org5a73bf5">2.2. Simulink</a></li>
<li><a href="#org157458d">2.1. Jacobian</a></li>
<li><a href="#org8947fec">2.2. Simulink</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orga7bd74e" class="outline-2">
<h2 id="orga7bd74e"><span class="section-number-2">1</span> Simscape Model - Gravimeter</h2>
<div id="outline-container-org09b41c5" class="outline-2">
<h2 id="org09b41c5"><span class="section-number-2">1</span> Simscape Model - Gravimeter</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org2acf438" class="outline-3">
<h3 id="org2acf438"><span class="section-number-3">1.1</span> Simulink</h3>
<div id="outline-container-orgaf12c1d" class="outline-3">
<h3 id="orgaf12c1d"><span class="section-number-3">1.1</span> Simulink</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-matlab">open('gravimeter.slx')
@ -89,7 +89,7 @@ State-space model with 4 outputs, 3 inputs, and 6 states.
<div id="orgfba9d15" class="figure">
<div id="org1c9b0ec" class="figure">
<p><img src="figs/open_loop_tf.png" alt="open_loop_tf.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Open Loop Transfer Function from 3 Actuators to 4 Accelerometers</p>
@ -98,12 +98,12 @@ State-space model with 4 outputs, 3 inputs, and 6 states.
</div>
</div>
<div id="outline-container-org08c4258" class="outline-2">
<h2 id="org08c4258"><span class="section-number-2">2</span> Simscape Model - Stewart Platform</h2>
<div id="outline-container-org84efeb7" class="outline-2">
<h2 id="org84efeb7"><span class="section-number-2">2</span> Simscape Model - Stewart Platform</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-orgb618964" class="outline-3">
<h3 id="orgb618964"><span class="section-number-3">2.1</span> Jacobian</h3>
<div id="outline-container-org157458d" class="outline-3">
<h3 id="org157458d"><span class="section-number-3">2.1</span> Jacobian</h3>
<div class="outline-text-3" id="text-2-1">
<p>
First, the position of the &ldquo;joints&rdquo; (points of force application) are estimated and the Jacobian computed.
@ -146,8 +146,8 @@ save('./jacobian.mat', 'Aa', 'Ab', 'As', 'l', 'J');
</div>
</div>
<div id="outline-container-org5a73bf5" class="outline-3">
<h3 id="org5a73bf5"><span class="section-number-3">2.2</span> Simulink</h3>
<div id="outline-container-org8947fec" class="outline-3">
<h3 id="org8947fec"><span class="section-number-3">2.2</span> Simulink</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab">open('stewart_platform/drone_platform.slx');
@ -195,6 +195,16 @@ G.OutputName = {'Ax', 'Ay', 'Az', 'Arx', 'Ary', 'Arz'};
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">size(G)
</pre>
</div>
<pre class="example">
State-space model with 6 outputs, 6 inputs, and 12 states.
</pre>
<p>
Thanks to the Jacobian, we compute the transfer functions in the frame of the legs and in an inertial frame.
</p>
@ -208,21 +218,21 @@ Gl.OutputName = {'A1', 'A2', 'A3', 'A4', 'A5', 'A6'};
</div>
<div id="orgc24d97d" class="figure">
<div id="orgc94fa6a" class="figure">
<p><img src="figs/stewart_platform_translations.png" alt="stewart_platform_translations.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Stewart Platform Plant from forces applied by the legs to the acceleration of the platform</p>
</div>
<div id="orgd85b88a" class="figure">
<div id="org5e7bd8e" class="figure">
<p><img src="figs/stewart_platform_rotations.png" alt="stewart_platform_rotations.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Stewart Platform Plant from torques applied by the legs to the angular acceleration of the platform</p>
</div>
<div id="org85cf2f1" class="figure">
<div id="orgce0e5a7" class="figure">
<p><img src="figs/stewart_platform_legs.png" alt="stewart_platform_legs.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Stewart Platform Plant from forces applied by the legs to displacement of the legs</p>
@ -233,7 +243,7 @@ Gl.OutputName = {'A1', 'A2', 'A3', 'A4', 'A5', 'A6'};
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-09-21 lun. 13:07</p>
<p class="date">Created: 2020-09-21 lun. 13:14</p>
</div>
</body>
</html>

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@ -462,6 +462,13 @@ The dynamics is identified from forces applied by each legs to the measured acce
G.OutputName = {'Ax', 'Ay', 'Az', 'Arx', 'Ary', 'Arz'};
#+end_src
#+begin_src matlab :results output replace
size(G)
#+end_src
#+RESULTS:
: State-space model with 6 outputs, 6 inputs, and 12 states.
Thanks to the Jacobian, we compute the transfer functions in the frame of the legs and in an inertial frame.
#+begin_src matlab
Gx = -G*inv(J');