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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"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-09-21 lun. 13:07 --> <!-- 2020-09-21 lun. 13:14 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>SVD Control</title> <title>SVD Control</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -27,27 +27,27 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orga7bd74e">1. Simscape Model - Gravimeter</a> <li><a href="#org09b41c5">1. Simscape Model - Gravimeter</a>
<ul> <ul>
<li><a href="#org2acf438">1.1. Simulink</a></li> <li><a href="#orgaf12c1d">1.1. Simulink</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org08c4258">2. Simscape Model - Stewart Platform</a> <li><a href="#org84efeb7">2. Simscape Model - Stewart Platform</a>
<ul> <ul>
<li><a href="#orgb618964">2.1. Jacobian</a></li> <li><a href="#org157458d">2.1. Jacobian</a></li>
<li><a href="#org5a73bf5">2.2. Simulink</a></li> <li><a href="#org8947fec">2.2. Simulink</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orga7bd74e" class="outline-2"> <div id="outline-container-org09b41c5" class="outline-2">
<h2 id="orga7bd74e"><span class="section-number-2">1</span> Simscape Model - Gravimeter</h2> <h2 id="org09b41c5"><span class="section-number-2">1</span> Simscape Model - Gravimeter</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-org2acf438" class="outline-3"> <div id="outline-container-orgaf12c1d" class="outline-3">
<h3 id="org2acf438"><span class="section-number-3">1.1</span> Simulink</h3> <h3 id="orgaf12c1d"><span class="section-number-3">1.1</span> Simulink</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">open('gravimeter.slx') <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><img src="figs/open_loop_tf.png" alt="open_loop_tf.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Open Loop Transfer Function from 3 Actuators to 4 Accelerometers</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> </div>
<div id="outline-container-org08c4258" class="outline-2"> <div id="outline-container-org84efeb7" class="outline-2">
<h2 id="org08c4258"><span class="section-number-2">2</span> Simscape Model - Stewart Platform</h2> <h2 id="org84efeb7"><span class="section-number-2">2</span> Simscape Model - Stewart Platform</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-orgb618964" class="outline-3"> <div id="outline-container-org157458d" class="outline-3">
<h3 id="orgb618964"><span class="section-number-3">2.1</span> Jacobian</h3> <h3 id="org157458d"><span class="section-number-3">2.1</span> Jacobian</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
First, the position of the &ldquo;joints&rdquo; (points of force application) are estimated and the Jacobian computed. 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> </div>
<div id="outline-container-org5a73bf5" class="outline-3"> <div id="outline-container-org8947fec" class="outline-3">
<h3 id="org5a73bf5"><span class="section-number-3">2.2</span> Simulink</h3> <h3 id="org8947fec"><span class="section-number-3">2.2</span> Simulink</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">open('stewart_platform/drone_platform.slx'); <pre class="src src-matlab">open('stewart_platform/drone_platform.slx');
@ -195,6 +195,16 @@ G.OutputName = {'Ax', 'Ay', 'Az', 'Arx', 'Ary', 'Arz'};
</pre> </pre>
</div> </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> <p>
Thanks to the Jacobian, we compute the transfer functions in the frame of the legs and in an inertial frame. Thanks to the Jacobian, we compute the transfer functions in the frame of the legs and in an inertial frame.
</p> </p>
@ -208,21 +218,21 @@ Gl.OutputName = {'A1', 'A2', 'A3', 'A4', 'A5', 'A6'};
</div> </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><img src="figs/stewart_platform_translations.png" alt="stewart_platform_translations.png" />
</p> </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> <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>
<div id="orgd85b88a" class="figure"> <div id="org5e7bd8e" class="figure">
<p><img src="figs/stewart_platform_rotations.png" alt="stewart_platform_rotations.png" /> <p><img src="figs/stewart_platform_rotations.png" alt="stewart_platform_rotations.png" />
</p> </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> <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>
<div id="org85cf2f1" class="figure"> <div id="orgce0e5a7" class="figure">
<p><img src="figs/stewart_platform_legs.png" alt="stewart_platform_legs.png" /> <p><img src="figs/stewart_platform_legs.png" alt="stewart_platform_legs.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Stewart Platform Plant from forces applied by the legs to displacement of the legs</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>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <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> </div>
</body> </body>
</html> </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'}; G.OutputName = {'Ax', 'Ay', 'Az', 'Arx', 'Ary', 'Arz'};
#+end_src #+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. Thanks to the Jacobian, we compute the transfer functions in the frame of the legs and in an inertial frame.
#+begin_src matlab #+begin_src matlab
Gx = -G*inv(J'); Gx = -G*inv(J');