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</div><div id="content">
<h1 class="title">Simscape Model of the Nano-Active-Stabilization-System</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org6af5373">1. Simulink project</a></li>
<li><a href="#org2e621fc">2. Simscape Model</a>
<ul>
<li><a href="#orga525a01">2.1. Solid bodies</a></li>
<li><a href="#orgfcbb75d">2.2. Frames</a></li>
<li><a href="#orga9f9a27">2.3. Joints</a></li>
<li><a href="#org09ee778">2.4. Measurements</a></li>
<li><a href="#org318de2c">2.5. Excitation</a></li>
</ul>
</li>
<li><a href="#orgc7f7e1c">3. Notes</a>
<ul>
<li><a href="#orgb12490c">3.1. Simscape files for identification</a></li>
<li><a href="#orgb836c01">3.2. Inputs</a>
<ul>
<li><a href="#orgf1bf5dd">3.2.1. Perturbations</a></li>
<li><a href="#org0810896">3.2.2. Measurement Noise</a></li>
<li><a href="#org5c2d540">3.2.3. Control Inputs</a></li>
</ul>
</li>
<li><a href="#org6e0a79a">3.3. Outputs</a></li>
</ul>
</li>
<li><a href="#orgd49784d">4. Simulink files</a></li>
<li><a href="#orgc98892e">5. Simulink Library</a>
<ul>
<li><a href="#orgb55d4ab">5.1. inputs</a></li>
<li><a href="#org41c1e10">5.2. nass<sub>library</sub></a></li>
<li><a href="#orgded2da1">5.3. pos<sub>error</sub><sub>wrt</sub><sub>nass</sub><sub>base</sub></a></li>
<li><a href="#org7c4f21d">5.4. QuaternionToAngles</a></li>
<li><a href="#org9c713f6">5.5. RotationMatrixToAngle</a></li>
</ul>
</li>
<li><a href="#org3048f9a">6. Scripts</a>
<ul>
<li><a href="#orgff52b6c">6.1. Simulation Initialization</a></li>
</ul>
</li>
<li><a href="#org28ec0bd">7. Functions</a>
<ul>
<li><a href="#org0dfda5a">7.1. computePsdDispl</a></li>
<li><a href="#org553eea9">7.2. computeSetpoint</a></li>
<li><a href="#org786af26">7.3. converErrorBasis</a></li>
<li><a href="#org9ea9883">7.4. generateDiagPidControl</a></li>
<li><a href="#org219d806">7.5. identifyPlant</a></li>
<li><a href="#orgffb2167">7.6. runSimulation</a></li>
</ul>
</li>
<li><a href="#orgcee9dda">8. Initialize Elements</a>
<ul>
<li><a href="#org870f9ac">8.1. Simulation Configuration</a></li>
<li><a href="#orge30fdf8">8.2. Experiment</a></li>
<li><a href="#orgab84833">8.3. Inputs</a></li>
<li><a href="#org103cc41">8.4. Ground</a></li>
<li><a href="#org6619477">8.5. Granite</a></li>
<li><a href="#org77a28f7">8.6. Translation Stage</a></li>
<li><a href="#orge78d8a3">8.7. Tilt Stage</a></li>
<li><a href="#org567c23d">8.8. Spindle</a></li>
<li><a href="#orgc032b1e">8.9. Micro Hexapod</a></li>
<li><a href="#org3b5edf8">8.10. Center of gravity compensation</a></li>
<li><a href="#orgf300722">8.11. Mirror</a></li>
<li><a href="#orgf57d858">8.12. Nano Hexapod</a></li>
<li><a href="#org2e21283">8.13. Sample</a></li>
</ul>
</li>
</ul>
</div>
</div>
<ul class="org-ul">
<li><a href="identification/index.html">Identification of the Micro-Station</a></li>
<li><a href="uniaxial/index.html">Uniaxial Model</a></li>
<li><a href="kinematics/index.html">Kinematics of the station</a></li>
<li><a href="control/index.html">Control</a></li>
<li><a href="active_damping/index.html">Active Damping</a></li>
<li><a href="analysis/index.html">Plant Analysis</a></li>
<li><a href="hac_lac/index.html">HAC LAC</a></li>
<li><a href="kinematics/index.html">Kinematics</a></li>
<li><a href="modal_test/index.html">Modal Analysis</a></li>
<li><a href="cedrat-actuator/index.html">Cedrat Piezo Actuator</a></li>
</ul>
<div id="outline-container-org6af5373" class="outline-2">
<h2 id="org6af5373"><span class="section-number-2">1</span> Simulink project</h2>
<div class="outline-text-2" id="text-1">
<p>
From the <a href="https://mathworks.com/products/simulink/projects.html">Simulink project</a> mathworks page:
</p>
<blockquote>
<p>
Simulink® and Simulink Projects provide a collaborative, scalable environment that enables teams to manage their files and data in one place.
</p>
<p>
With Simulink Projects, you can:
</p>
<ul class="org-ul">
<li><b>Collaborate</b>: Enforce companywide standards such as company tools, libraries, and standard startup and shutdown scripts. Share your work with rich sharing options including MATLAB® toolboxes, email, and archives.</li>
<li><b>Automate</b>: Set up your project environment correctly every time by automating steps such as loading the data, managing the path, and opening the models.</li>
<li><b>Integrate with source control</b>: Enable easy integration with source control and configuration management tools.</li>
</ul>
</blockquote>
<p>
The project can be opened using the <code>simulinkproject</code> function:
</p>
<div class="org-src-container">
<pre class="src src-matlab">simulinkproject<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
When the project opens, a startup script is ran.
The startup script is defined below and is exported to the <code>project_startup.m</code> script.
</p>
<div class="org-src-container">
<pre class="src src-matlab">freqs = logspace<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save_fig = <span class="org-constant">false</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/config.mat'</span>, <span class="org-string">'freqs'</span>, <span class="org-string">'save_fig'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
project = simulinkproject;
projectRoot = project.RootFolder;
myCacheFolder = fullfile<span class="org-rainbow-delimiters-depth-1">(</span>projectRoot, <span class="org-string">'.SimulinkCache'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
myCodeFolder = fullfile<span class="org-rainbow-delimiters-depth-1">(</span>projectRoot, <span class="org-string">'.SimulinkCode'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Simulink.fileGenControl<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'set'</span>,...
<span class="org-string">'CacheFolder'</span>, myCacheFolder,...
<span class="org-string">'CodeGenFolder'</span>, myCodeFolder,...
<span class="org-string">'createDir'</span>, <span class="org-constant">true</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
When the project closes, it runs the <code>project_shutdown.m</code> script defined below.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Simulink.fileGenControl<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'reset'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
The project also permits to automatically add defined folder to the path when the project is opened.
</p>
</div>
</div>
<div id="outline-container-org2e621fc" class="outline-2">
<h2 id="org2e621fc"><span class="section-number-2">2</span> Simscape Model</h2>
<div class="outline-text-2" id="text-2">
<p>
A <a href="https://.mathworks.com/products/simscape.html">simscape</a> model permits to model multi-physics systems.
</p>
<p>
<a href="https://mathworks.com/products/simmechanics.html">Simscape Multibody</a> permits to model multibody systems using blocks representing bodies, joints, constraints, force elements, and sensors.
</p>
</div>
<div id="outline-container-orga525a01" class="outline-3">
<h3 id="orga525a01"><span class="section-number-3">2.1</span> Solid bodies</h3>
<div class="outline-text-3" id="text-2-1">
<p>
Each solid body is represented by a <a href="https://mathworks.com/help/physmod/sm/ref/solid.html">solid block</a>.
The geometry of the solid body can be imported using a <code>step</code> file. The properties of the solid body such as its mass, center of mass and moment of inertia can be derived from its density and its geometry as defined by the <code>step</code> file. They also can be set by hand.
</p>
</div>
</div>
<div id="outline-container-orgfcbb75d" class="outline-3">
<h3 id="orgfcbb75d"><span class="section-number-3">2.2</span> Frames</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made.
</p>
<p>
They can be defined from the solid body geometry, or using the <a href="https://mathworks.com/help/physmod/sm/ref/rigidtransform.html">rigid transform block</a>.
</p>
</div>
</div>
<div id="outline-container-orga9f9a27" class="outline-3">
<h3 id="orga9f9a27"><span class="section-number-3">2.3</span> Joints</h3>
<div class="outline-text-3" id="text-2-3">
<p>
Solid Bodies are connected with joints (between frames of the two solid bodies).
</p>
<p>
There are various types of joints that are all described <a href="https://mathworks.com/help/physmod/sm/ug/joints.html">here</a>.
</p>
<table id="orgbcf1bb7" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Degrees of freedom associated with each joint</caption>
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Joint Block</th>
<th scope="col" class="org-right">Translational DOFs</th>
<th scope="col" class="org-right">Rotational DOFs</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">6-DOF</td>
<td class="org-right">3</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Bearing</td>
<td class="org-right">1</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Bushing</td>
<td class="org-right">3</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Cartesian</td>
<td class="org-right">3</td>
<td class="org-right">0</td>
</tr>
<tr>
<td class="org-left">Constant Velocity</td>
<td class="org-right">0</td>
<td class="org-right">2</td>
</tr>
<tr>
<td class="org-left">Cylindrical</td>
<td class="org-right">1</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Gimbal</td>
<td class="org-right">0</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Leadscrew</td>
<td class="org-right">1 (coupled)</td>
<td class="org-right">1 (coupled)</td>
</tr>
<tr>
<td class="org-left">Pin Slot</td>
<td class="org-right">1</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Planar</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Prismatic</td>
<td class="org-right">1</td>
<td class="org-right">0</td>
</tr>
<tr>
<td class="org-left">Rectangular</td>
<td class="org-right">2</td>
<td class="org-right">0</td>
</tr>
<tr>
<td class="org-left">Revolute</td>
<td class="org-right">0</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Spherical</td>
<td class="org-right">1</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Telescoping</td>
<td class="org-right">1</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Universal</td>
<td class="org-right">0</td>
<td class="org-right">2</td>
</tr>
<tr>
<td class="org-left">Weld</td>
<td class="org-right">0</td>
<td class="org-right">0</td>
</tr>
</tbody>
</table>
<p>
Joint blocks are assortments of joint primitives:
</p>
<ul class="org-ul">
<li><b>Prismatic</b>: allows translation along a single standard axis: <code>Px</code>, <code>Py</code>, <code>Pz</code></li>
<li><b>Revolute</b>: allows rotation about a single standard axis: <code>Rx</code>, <code>Ry</code>, <code>Rz</code></li>
<li><b>Spherical</b>: allow rotation about any 3D axis: <code>S</code></li>
<li><b>Lead Screw</b>: allows coupled rotation and translation on a standard axis: <code>LSz</code></li>
<li><b>Constant Velocity</b>: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: <code>CV</code></li>
</ul>
<table id="orgcdffc88" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Joint primitives for each joint type</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Joint Block</th>
<th scope="col" class="org-left">Px</th>
<th scope="col" class="org-left">Py</th>
<th scope="col" class="org-left">Pz</th>
<th scope="col" class="org-left">Rx</th>
<th scope="col" class="org-left">Ry</th>
<th scope="col" class="org-left">Rz</th>
<th scope="col" class="org-left">S</th>
<th scope="col" class="org-left">CV</th>
<th scope="col" class="org-left">LSz</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">6-DOF</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Bearing</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Bushing</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Cartesian</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Constant Velocity</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Cylindrical</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Gimbal</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Leadscrew</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
</tr>
<tr>
<td class="org-left">Pin Slot</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Planar</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Prismatic</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Rectangular</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Revolute</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Spherical</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Telescoping</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Universal</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">Weld</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
</tbody>
</table>
<p>
For each of the joint primitive, we can specify the dynamical properties:
</p>
<ul class="org-ul">
<li>The <b>spring stiffness</b>: either linear or rotational one</li>
<li>The <b>damping coefficient</b></li>
</ul>
<p>
For the actuation, we can either specify the motion or the force:
</p>
<ul class="org-ul">
<li>the force applied in the corresponding DOF is provided by the input</li>
<li>the motion is provided by the input</li>
</ul>
<p>
A sensor can be added to measure either the position, velocity or acceleration of the joint DOF.
</p>
<p>
Composite Force/Torque sensing:
</p>
<ul class="org-ul">
<li>Constraint force</li>
<li>Total force: gives the sum across all joint primitives over all sources: actuation inputs, internal springs and dampers.</li>
</ul>
</div>
</div>
<div id="outline-container-org09ee778" class="outline-3">
<h3 id="org09ee778"><span class="section-number-3">2.4</span> Measurements</h3>
<div class="outline-text-3" id="text-2-4">
<p>
A transform sensor block measures the spatial relationship between two frames: the base <code>B</code> and the follower <code>F</code>.
</p>
<p>
It can give the rotational and translational position, velocity and acceleration.
</p>
<p>
The measurement frame should be specified: it corresponds to the frame in which to resolve the selected spatial measurements. The default is <code>world</code>.
</p>
<p>
If we want to simulate an <b>inertial sensor</b>, we just have to choose <code>B</code> to be the <code>world</code> frame.
</p>
<p>
<b>Force sensors</b> are included in the joints blocks.
</p>
</div>
</div>
<div id="outline-container-org318de2c" class="outline-3">
<h3 id="org318de2c"><span class="section-number-3">2.5</span> Excitation</h3>
<div class="outline-text-3" id="text-2-5">
<p>
We can apply <b>external forces</b> to the model by using an <a href="https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html">external force and torque block</a>.
</p>
<p>
Internal force, acting reciprocally between base and following origins is implemented using the <a href="https://mathworks.com/help/physmod/sm/ref/internalforce.html">internal force block</a> even though it is usually included in one joint block.
</p>
</div>
</div>
</div>
<div id="outline-container-orgc7f7e1c" class="outline-2">
<h2 id="orgc7f7e1c"><span class="section-number-2">3</span> Notes</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-orgb12490c" class="outline-3">
<h3 id="orgb12490c"><span class="section-number-3">3.1</span> Simscape files for identification</h3>
<div class="outline-text-3" id="text-3-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Simscape Name</th>
<th scope="col" class="org-left">Ty</th>
<th scope="col" class="org-left">Ry</th>
<th scope="col" class="org-left">Rz</th>
<th scope="col" class="org-left">Hexa</th>
<th scope="col" class="org-left">NASS</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">id micro station</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
<td class="org-left"> </td>
</tr>
<tr>
<td class="org-left">id nano station stages</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
<td class="org-left">F</td>
</tr>
<tr>
<td class="org-left">id nano station config</td>
<td class="org-left">D</td>
<td class="org-left">D</td>
<td class="org-left">D</td>
<td class="org-left">D</td>
<td class="org-left">F</td>
</tr>
<tr>
<td class="org-left">control nano station</td>
<td class="org-left">D</td>
<td class="org-left">D</td>
<td class="org-left">D</td>
<td class="org-left">D</td>
<td class="org-left">F</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgb836c01" class="outline-3">
<h3 id="orgb836c01"><span class="section-number-3">3.2</span> Inputs</h3>
<div class="outline-text-3" id="text-3-2">
</div>
<div id="outline-container-orgf1bf5dd" class="outline-4">
<h4 id="orgf1bf5dd"><span class="section-number-4">3.2.1</span> Perturbations</h4>
<div class="outline-text-4" id="text-3-2-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Meaning</th>
<th scope="col" class="org-right">Size</th>
<th scope="col" class="org-left">Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>Dw</code></td>
<td class="org-left">Ground motion</td>
<td class="org-right">3</td>
<td class="org-left">[m]</td>
</tr>
<tr>
<td class="org-left"><code>Fg</code></td>
<td class="org-left">External force applied on granite</td>
<td class="org-right">3</td>
<td class="org-left">[N]</td>
</tr>
<tr>
<td class="org-left"><code>Fs</code></td>
<td class="org-left">External force applied on the Sample</td>
<td class="org-right">3</td>
<td class="org-left">[N]</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org0810896" class="outline-4">
<h4 id="org0810896"><span class="section-number-4">3.2.2</span> Measurement Noise</h4>
<div class="outline-text-4" id="text-3-2-2">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Meaning</th>
<th scope="col" class="org-left">Size</th>
<th scope="col" class="org-left">Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left"> </td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org5c2d540" class="outline-4">
<h4 id="org5c2d540"><span class="section-number-4">3.2.3</span> Control Inputs</h4>
<div class="outline-text-4" id="text-3-2-3">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Meaning</th>
<th scope="col" class="org-right">Size</th>
<th scope="col" class="org-left">Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>Fy</code></td>
<td class="org-left">Actuation force for Ty</td>
<td class="org-right">1</td>
<td class="org-left">[N]</td>
</tr>
<tr>
<td class="org-left"><code>Dy</code></td>
<td class="org-left">Imposed displacement for Ty</td>
<td class="org-right">1</td>
<td class="org-left">[m]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>My</code></td>
<td class="org-left">Actuation torque for Ry</td>
<td class="org-right">1</td>
<td class="org-left">[N.m]</td>
</tr>
<tr>
<td class="org-left"><code>Ry</code></td>
<td class="org-left">Imposed rotation for Ry</td>
<td class="org-right">1</td>
<td class="org-left">[rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Mz</code></td>
<td class="org-left">Actuation torque for Rz</td>
<td class="org-right">1</td>
<td class="org-left">[N.m]</td>
</tr>
<tr>
<td class="org-left"><code>Rz</code></td>
<td class="org-left">Imposed rotation for Rz</td>
<td class="org-right">1</td>
<td class="org-left">[rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Fh</code></td>
<td class="org-left">Actuation force/torque for hexapod (cart)</td>
<td class="org-right">6</td>
<td class="org-left">[N, N.m]</td>
</tr>
<tr>
<td class="org-left"><code>Fhl</code></td>
<td class="org-left">Actuation force/torque for hexapod (legs)</td>
<td class="org-right">6</td>
<td class="org-left">[N]</td>
</tr>
<tr>
<td class="org-left"><code>Dh</code></td>
<td class="org-left">Imposed position for hexapod (cart)</td>
<td class="org-right">6</td>
<td class="org-left">[m, rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Rm</code></td>
<td class="org-left">Position of the two masses</td>
<td class="org-right">2</td>
<td class="org-left">[rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Fn</code></td>
<td class="org-left">Actuation force for the NASS (cart)</td>
<td class="org-right">6</td>
<td class="org-left">[N, N.m]</td>
</tr>
<tr>
<td class="org-left"><code>Fnl</code></td>
<td class="org-left">Actuation force for the NASS's legs</td>
<td class="org-right">6</td>
<td class="org-left">[N]</td>
</tr>
<tr>
<td class="org-left"><code>Dn</code></td>
<td class="org-left">Imposed position for the NASS (cart)</td>
<td class="org-right">6</td>
<td class="org-left">[m, rad]</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div id="outline-container-org6e0a79a" class="outline-3">
<h3 id="org6e0a79a"><span class="section-number-3">3.3</span> Outputs</h3>
<div class="outline-text-3" id="text-3-3">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Meaning</th>
<th scope="col" class="org-right">Size</th>
<th scope="col" class="org-left">Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>Dgm</code></td>
<td class="org-left">Absolute displacement of the granite</td>
<td class="org-right">3</td>
<td class="org-left">[m]</td>
</tr>
<tr>
<td class="org-left"><code>Vgm</code></td>
<td class="org-left">Absolute Velocity of the granite</td>
<td class="org-right">3</td>
<td class="org-left">[m/s]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Dym</code></td>
<td class="org-left">Measured displacement of Ty</td>
<td class="org-right">1</td>
<td class="org-left">[m]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Rym</code></td>
<td class="org-left">Measured rotation of Ry</td>
<td class="org-right">1</td>
<td class="org-left">[rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Rzm</code></td>
<td class="org-left">Measured rotation of Rz</td>
<td class="org-right">1</td>
<td class="org-left">[rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Dhm</code></td>
<td class="org-left">Measured position of hexapod (cart)</td>
<td class="org-right">6</td>
<td class="org-left">[m, rad]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Fnlm</code></td>
<td class="org-left">Measured force of NASS's legs</td>
<td class="org-right">6</td>
<td class="org-left">[N]</td>
</tr>
<tr>
<td class="org-left"><code>Dnlm</code></td>
<td class="org-left">Measured elongation of NASS's legs</td>
<td class="org-right">6</td>
<td class="org-left">[m]</td>
</tr>
<tr>
<td class="org-left"><code>Dnm</code></td>
<td class="org-left">Measured position of NASS w.r.t NASS's base</td>
<td class="org-right">6</td>
<td class="org-left">[m, rad]</td>
</tr>
<tr>
<td class="org-left"><code>Vnm</code></td>
<td class="org-left">Measured absolute velocity of NASS platform</td>
<td class="org-right">6</td>
<td class="org-left">[m/s, rad/s]</td>
</tr>
<tr>
<td class="org-left"><code>Vnlm</code></td>
<td class="org-left">Measured absolute velocity of NASS's legs</td>
<td class="org-right">6</td>
<td class="org-left">[m/s]</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><code>Dsm</code></td>
<td class="org-left">Position of Sample w.r.t. granite frame</td>
<td class="org-right">6</td>
<td class="org-left">[m, rad]</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div id="outline-container-orgd49784d" class="outline-2">
<h2 id="orgd49784d"><span class="section-number-2">4</span> Simulink files</h2>
<div class="outline-text-2" id="text-4">
<p>
Few different Simulink files are used:
</p>
<ul class="org-ul">
<li>kinematics</li>
<li>identification - micro station</li>
<li>identification - nano station</li>
<li>control</li>
</ul>
</div>
</div>
<div id="outline-container-orgc98892e" class="outline-2">
<h2 id="orgc98892e"><span class="section-number-2">5</span> Simulink Library</h2>
<div class="outline-text-2" id="text-5">
<p>
A simulink library is developed in order to share elements between the different simulink files.
</p>
</div>
<div id="outline-container-orgb55d4ab" class="outline-3">
<h3 id="orgb55d4ab"><span class="section-number-3">5.1</span> inputs</h3>
</div>
<div id="outline-container-org41c1e10" class="outline-3">
<h3 id="org41c1e10"><span class="section-number-3">5.2</span> nass<sub>library</sub></h3>
</div>
<div id="outline-container-orgded2da1" class="outline-3">
<h3 id="orgded2da1"><span class="section-number-3">5.3</span> pos<sub>error</sub><sub>wrt</sub><sub>nass</sub><sub>base</sub></h3>
</div>
<div id="outline-container-org7c4f21d" class="outline-3">
<h3 id="org7c4f21d"><span class="section-number-3">5.4</span> QuaternionToAngles</h3>
</div>
<div id="outline-container-org9c713f6" class="outline-3">
<h3 id="org9c713f6"><span class="section-number-3">5.5</span> RotationMatrixToAngle</h3>
</div>
</div>
<div id="outline-container-org3048f9a" class="outline-2">
<h2 id="org3048f9a"><span class="section-number-2">6</span> Scripts</h2>
<div class="outline-text-2" id="text-6">
</div>
<div id="outline-container-orgff52b6c" class="outline-3">
<h3 id="orgff52b6c"><span class="section-number-3">6.1</span> Simulation Initialization</h3>
<div class="outline-text-3" id="text-6-1">
<p>
<a id="org1cdf096"></a>
</p>
<p>
This Matlab script is accessible <a href="src/init_simulation.m">here</a>.
</p>
<p>
This script runs just before the simulation is started.
It is used to load the simulation configuration and the controllers used for the simulation.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load all the data used for the simulation</span></span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'sim_conf.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Load Controller</span></span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'controllers.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org28ec0bd" class="outline-2">
<h2 id="org28ec0bd"><span class="section-number-2">7</span> Functions</h2>
<div class="outline-text-2" id="text-7">
</div>
<div id="outline-container-org0dfda5a" class="outline-3">
<h3 id="org0dfda5a"><span class="section-number-3">7.1</span> computePsdDispl</h3>
<div class="outline-text-3" id="text-7-1">
<p>
<a id="orgb5eb383"></a>
</p>
<p>
This Matlab function is accessible <a href="src/computePsdDispl.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">psd_object</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">computePsdDispl</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">sys_data</span>, <span class="org-variable-name">t_init</span>, <span class="org-variable-name">n_av</span><span class="org-rainbow-delimiters-depth-1">)</span>
i_init = find<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.time <span class="org-type">></span> t_init, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
han_win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span>length<span class="org-rainbow-delimiters-depth-3">(</span>sys_data.Dx<span class="org-rainbow-delimiters-depth-4">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">/</span>n_av<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>sys_data.time<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pdx, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.Dx<span class="org-rainbow-delimiters-depth-2">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, han_win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pdy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.Dy<span class="org-rainbow-delimiters-depth-2">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, han_win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pdz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.Dz<span class="org-rainbow-delimiters-depth-2">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, han_win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>prx, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.Rx<span class="org-rainbow-delimiters-depth-2">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, han_win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.Ry<span class="org-rainbow-delimiters-depth-2">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, han_win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>prz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sys_data.Rz<span class="org-rainbow-delimiters-depth-2">(</span>i_init<span class="org-type">:</span>end, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, han_win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
psd_object = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'f'</span>, f, ...
<span class="org-string">'dx'</span>, pdx, ...
<span class="org-string">'dy'</span>, pdy, ...
<span class="org-string">'dz'</span>, pdz, ...
<span class="org-string">'rx'</span>, prx, ...
<span class="org-string">'ry'</span>, pry, ...
<span class="org-string">'rz'</span>, prz<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org553eea9" class="outline-3">
<h3 id="org553eea9"><span class="section-number-3">7.2</span> computeSetpoint</h3>
<div class="outline-text-3" id="text-7-2">
<p>
<a id="orgd3c6bc1"></a>
</p>
<p>
This Matlab function is accessible <a href="src/computeSetpoint.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">setpoint</span> = <span class="org-function-name">computeSetpoint</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">ty</span>, <span class="org-variable-name">ry</span>, <span class="org-variable-name">rz</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
setpoint = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Ty</span></span>
Ty = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ty ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
% Tyinv = [<span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
% <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-type">-</span>ty ;
% <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
% <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> ];
<span class="org-matlab-cellbreak"><span class="org-comment">%% Ry</span></span>
Ry = <span class="org-rainbow-delimiters-depth-1">[</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% TMry = Ty*Ry*Tyinv;</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Rz</span></span>
Rz = <span class="org-rainbow-delimiters-depth-1">[</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
sin<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% TMrz = Ty*TMry*Rz*TMry'*Tyinv;</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% All stages</span></span>
<span class="org-comment">% </span><span class="org-comment"><span class="org-constant">TM </span></span><span class="org-comment">= TMrz*TMry*Ty;</span>
TM = Ty<span class="org-type">*</span>Ry<span class="org-type">*</span>Rz;
<span class="org-rainbow-delimiters-depth-1">[</span>thetax, thetay, thetaz<span class="org-rainbow-delimiters-depth-1">]</span> = RM2angle<span class="org-rainbow-delimiters-depth-1">(</span>TM<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
setpoint<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = TM<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>;
setpoint<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>thetax, thetay, thetaz<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Custom Functions</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">thetax, thetay, thetaz</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">RM2angle</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">R</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">if</span> abs<span class="org-rainbow-delimiters-depth-1">(</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>R<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">></span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span> % R31 <span class="org-type">!</span>= <span class="org-highlight-numbers-number">1</span> and R31 <span class="org-type">!</span>= <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>
thetay = <span class="org-type">-</span>asin<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
thetax = atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
thetaz = atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
thetaz = <span class="org-highlight-numbers-number">0</span>;
<span class="org-keyword">if</span> abs<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type"><</span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span> % R31 = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>
thetay = <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
thetax = thetaz <span class="org-type">+</span> atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
thetay = <span class="org-type">-</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
thetax = <span class="org-type">-</span>thetaz <span class="org-type">+</span> atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org786af26" class="outline-3">
<h3 id="org786af26"><span class="section-number-3">7.3</span> converErrorBasis</h3>
<div class="outline-text-3" id="text-7-3">
<p>
<a id="orga13b9f1"></a>
</p>
<p>
This Matlab function is accessible <a href="src/converErrorBasis.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">error_nass</span> = <span class="org-function-name">convertErrorBasis</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">pos</span>, <span class="org-variable-name">setpoint</span>, <span class="org-variable-name">ty</span>, <span class="org-variable-name">ry</span>, <span class="org-variable-name">rz</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-comment">% convertErrorBasis -</span>
<span class="org-comment">%</span>
<span class="org-comment">% Syntax: convertErrorBasis(p_error, ty, ry, rz)</span>
<span class="org-comment">%</span>
<span class="org-comment">% Inputs:</span>
<span class="org-comment">% - p_error - Position error of the sample w.r.t. the granite [m, rad]</span>
<span class="org-comment">% - ty - Measured translation of the Ty stage [m]</span>
<span class="org-comment">% - ry - Measured rotation of the Ry stage [rad]</span>
<span class="org-comment">% - rz - Measured rotation of the Rz stage [rad]</span>
<span class="org-comment">%</span>
<span class="org-comment">% Outputs:</span>
<span class="org-comment">% - P_nass - Position error of the sample w.r.t. the NASS base [m]</span>
<span class="org-comment">% - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]</span>
<span class="org-comment">%</span>
<span class="org-comment">% Example:</span>
<span class="org-comment">%</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% If line vector => column vector</span></span>
<span class="org-keyword">if</span> size<span class="org-rainbow-delimiters-depth-1">(</span>pos, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">6</span>
pos = pos<span class="org-type">'</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> size<span class="org-rainbow-delimiters-depth-1">(</span>setpoint, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">6</span>
setpoint = setpoint<span class="org-type">'</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Position of the sample in the frame fixed to the Granite</span></span>
P_granite = <span class="org-rainbow-delimiters-depth-1">[</span>pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>; <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Position [m]</span>
R_granite = <span class="org-rainbow-delimiters-depth-1">[</span>setpoint<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>; <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Reference [m]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Transformation matrices of the stages</span></span>
<span class="org-comment">% T-y</span>
TMty = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ty ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% R-y</span>
TMry = <span class="org-rainbow-delimiters-depth-1">[</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% R-z</span>
TMrz = <span class="org-rainbow-delimiters-depth-1">[</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
sin<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Compute Point coordinates in the new reference fixed to the NASS base</span></span>
<span class="org-comment">% P_nass = TMrz*TMry*TMty*P_granite;</span>
P_nass = TMrz<span class="org-type">\</span>TMry<span class="org-type">\</span>TMty<span class="org-type">\</span>P_granite;
R_nass = TMrz<span class="org-type">\</span>TMry<span class="org-type">\</span>TMty<span class="org-type">\</span>R_granite;
dx = R_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>P_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
dy = R_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>P_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
dz = R_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>P_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Compute new basis vectors linked to the NASS base</span></span>
% ux_nass = TMrz<span class="org-type">*</span>TMry<span class="org-type">*</span>TMty<span class="org-type">*</span>[<span class="org-highlight-numbers-number">1</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>];
% ux_nass = ux_nass(<span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>);
% uy_nass = TMrz<span class="org-type">*</span>TMry<span class="org-type">*</span>TMty<span class="org-type">*</span>[<span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">1</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>];
% uy_nass = uy_nass(<span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>);
% uz_nass = TMrz<span class="org-type">*</span>TMry<span class="org-type">*</span>TMty<span class="org-type">*</span>[<span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">1</span>; <span class="org-highlight-numbers-number">0</span>];
% uz_nass = uz_nass(<span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>);
ux_nass = TMrz<span class="org-type">\</span>TMry<span class="org-type">\</span>TMty<span class="org-type">\</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ux_nass = ux_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
uy_nass = TMrz<span class="org-type">\</span>TMry<span class="org-type">\</span>TMty<span class="org-type">\</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">1</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
uy_nass = uy_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
uz_nass = TMrz<span class="org-type">\</span>TMry<span class="org-type">\</span>TMty<span class="org-type">\</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">0</span>; <span class="org-highlight-numbers-number">1</span>; <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
uz_nass = uz_nass<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Rotations error w.r.t. granite Frame</span></span>
<span class="org-comment">% Rotations error w.r.t. granite Frame</span>
rx_nass = pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ry_nass = pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rz_nass = pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% Rotation matrices of the Sample w.r.t. the Granite</span>
Mrx_error = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> cos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rx_nass<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rx_nass<span class="org-rainbow-delimiters-depth-2">)</span> ;
<span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rx_nass<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rx_nass<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
Mry_error = <span class="org-rainbow-delimiters-depth-1">[</span> cos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>ry_nass<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>ry_nass<span class="org-rainbow-delimiters-depth-2">)</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>ry_nass<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> cos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>ry_nass<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
Mrz_error = <span class="org-rainbow-delimiters-depth-1">[</span>cos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rz_nass<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rz_nass<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
sin<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rz_nass<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">-</span>rz_nass<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% Rotation matrix of the Sample w.r.t. the Granite</span>
Mr_error = Mrz_error<span class="org-type">*</span>Mry_error<span class="org-type">*</span>Mrx_error;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Use matrix to solve</span></span>
R = Mr_error<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">[</span>ux_nass, uy_nass, uz_nass<span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Rotation matrix from NASS base to Sample</span>
<span class="org-rainbow-delimiters-depth-1">[</span>thetax, thetay, thetaz<span class="org-rainbow-delimiters-depth-1">]</span> = RM2angle<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-1">)</span>;
error_nass = <span class="org-rainbow-delimiters-depth-1">[</span>dx; dy; dz; thetax; thetay; thetaz<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Custom Functions</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">thetax, thetay, thetaz</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">RM2angle</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">R</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">if</span> abs<span class="org-rainbow-delimiters-depth-1">(</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>R<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">></span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span> % R31 <span class="org-type">!</span>= <span class="org-highlight-numbers-number">1</span> and R31 <span class="org-type">!</span>= <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>
thetay = <span class="org-type">-</span>asin<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% thetaybis = pi-thetay;</span>
thetax = atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
% thetaxbis = atan2(R(<span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2</span>)<span class="org-type">/</span>cos(thetaybis), R(<span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span>)<span class="org-type">/</span>cos(thetaybis));
thetaz = atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
% thetazbis = atan2(R(<span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>)<span class="org-type">/</span>cos(thetaybis), R(<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>)<span class="org-type">/</span>cos(thetaybis));
<span class="org-keyword">else</span>
thetaz = <span class="org-highlight-numbers-number">0</span>;
<span class="org-keyword">if</span> abs<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type"><</span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span> % R31 = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>
thetay = <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
thetax = thetaz <span class="org-type">+</span> atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
thetay = <span class="org-type">-</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
thetax = <span class="org-type">-</span>thetaz <span class="org-type">+</span> atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org9ea9883" class="outline-3">
<h3 id="org9ea9883"><span class="section-number-3">7.4</span> generateDiagPidControl</h3>
<div class="outline-text-3" id="text-7-4">
<p>
<a id="orgdff51b6"></a>
</p>
<p>
This Matlab function is accessible <a href="src/generateDiagPidControl.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">K</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">generateDiagPidControl</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">G</span>, <span class="org-variable-name">fs</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
pid_opts = pidtuneOptions<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'PhaseMargin'</span>, <span class="org-highlight-numbers-number">50</span>, ...
<span class="org-string">'DesignFocus'</span>, <span class="org-string">'disturbance-rejection'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
K = tf<span class="org-rainbow-delimiters-depth-1">(</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
input_name = G.InputName<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>;
output_name = G.OutputName<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = tf<span class="org-rainbow-delimiters-depth-1">(</span>pidtune<span class="org-rainbow-delimiters-depth-2">(</span>minreal<span class="org-rainbow-delimiters-depth-3">(</span>G<span class="org-rainbow-delimiters-depth-4">(</span>output_name, input_name<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-string">'PIDF'</span>, <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>fs, pid_opts<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
K.InputName = G.OutputName;
K.OutputName = G.InputName;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org219d806" class="outline-3">
<h3 id="org219d806"><span class="section-number-3">7.5</span> identifyPlant</h3>
<div class="outline-text-3" id="text-7-5">
<p>
<a id="org0ed2644"></a>
</p>
<p>
This Matlab function is accessible <a href="src/identifyPlant.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">sys</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">identifyPlant</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
options = linearizeOptions;
options.SampleTime = <span class="org-highlight-numbers-number">0</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'sim_nano_station_id'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fn'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Cartesian forces applied by NASS</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% External forces on the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Forces applied on the NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Es'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Position Error w.r.t. NASS base</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
G.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>, ...
<span class="org-string">'Dgx'</span>, <span class="org-string">'Dgy'</span>, <span class="org-string">'Dgz'</span>, ...
<span class="org-string">'Fsx'</span>, <span class="org-string">'Fsy'</span>, <span class="org-string">'Fsz'</span>, <span class="org-string">'Msx'</span>, <span class="org-string">'Msy'</span>, <span class="org-string">'Msz'</span>, ...
<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>, ...
<span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>, ...
<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, ...
<span class="org-string">'Edx'</span>, <span class="org-string">'Rdy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Create the sub transfer functions</span></span>
<span class="org-comment">% From forces applied in the cartesian frame to displacement of the sample in the cartesian frame</span>
sys.G_cart = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span><span class="org-rainbow-delimiters-depth-3">}</span>, <span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% From ground motion to Sample displacement</span>
sys.G_gm = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span><span class="org-rainbow-delimiters-depth-3">}</span>, <span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dgx'</span>, <span class="org-string">'Dgy'</span>, <span class="org-string">'Dgz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% From direct forces applied on the sample to displacement of the sample</span>
sys.G_fs = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span><span class="org-rainbow-delimiters-depth-3">}</span>, <span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Fsx'</span>, <span class="org-string">'Fsy'</span>, <span class="org-string">'Fsz'</span>, <span class="org-string">'Msx'</span>, <span class="org-string">'Msy'</span>, <span class="org-string">'Msz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% From forces applied on NASS's legs to force sensor in each leg</span>
sys.G_iff = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span><span class="org-rainbow-delimiters-depth-3">}</span>, <span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% From forces applied on NASS's legs to displacement of each leg</span>
sys.G_dleg = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span><span class="org-rainbow-delimiters-depth-3">}</span>, <span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% From forces applied on NASS's legs to displacement of each leg</span>
sys.G_plant = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Edx'</span>, <span class="org-string">'Rdy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span><span class="org-rainbow-delimiters-depth-3">}</span>, <span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgffb2167" class="outline-3">
<h3 id="orgffb2167"><span class="section-number-3">7.6</span> runSimulation</h3>
<div class="outline-text-3" id="text-7-6">
<p>
<a id="orge0cdc60"></a>
</p>
<p>
This Matlab function is accessible <a href="src/runSimulation.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[]</span></span> = <span class="org-function-name">runSimulation</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">sys_name</span>, <span class="org-variable-name">sys_mass</span>, <span class="org-variable-name">ctrl_type</span>, <span class="org-variable-name">act_damp</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Load the controller and save it for the simulation</span></span>
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>ctrl_type, <span class="org-string">'cl'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>act_damp, <span class="org-string">'none'</span><span class="org-rainbow-delimiters-depth-1">)</span>
K_obj = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/K_fb.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K = K_obj.<span class="org-rainbow-delimiters-depth-1">(</span>sprintf<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'K_%s_%s'</span>, sys_mass, sys_name)); <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
save<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span><span class="org-rainbow-delimiters-depth-3">)</span>;
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-3">(</span>ctrl_type, <span class="org-string">'cl'</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">&&</span> strcmp<span class="org-rainbow-delimiters-depth-3">(</span>act_damp, <span class="org-string">'iff'</span><span class="org-rainbow-delimiters-depth-3">)</span>
K_obj = load<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-string">'./mat/K_fb_iff.mat'</span><span class="org-rainbow-delimiters-depth-3">)</span>;
K = K_obj.<span class="org-rainbow-delimiters-depth-3">(</span>sprintf<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-string">'K_%s_%s_iff'</span>, sys_mass, sys_name)); <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
save<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span><span class="org-rainbow-delimiters-depth-5">)</span>;
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-5">(</span>ctrl_type, <span class="org-string">'ol'</span><span class="org-rainbow-delimiters-depth-5">)</span>
K = tf<span class="org-rainbow-delimiters-depth-5">(</span>zeros<span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-6">)</span><span class="org-rainbow-delimiters-depth-5">)</span>; <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
save<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span><span class="org-rainbow-delimiters-depth-5">)</span>;
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-string">'ctrl_type should be cl or ol'</span><span class="org-rainbow-delimiters-depth-5">)</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Active Damping</span></span>
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-5">(</span>act_damp, <span class="org-string">'iff'</span><span class="org-rainbow-delimiters-depth-5">)</span>
K_iff_crit = load<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-string">'./mat/K_iff_crit.mat'</span><span class="org-rainbow-delimiters-depth-5">)</span>;
K_iff = K_iff_crit.<span class="org-rainbow-delimiters-depth-5">(</span>sprintf<span class="org-rainbow-delimiters-depth-6">(</span><span class="org-string">'K_iff_%s_%s'</span>, sys_mass, sys_name)); <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
save<span class="org-rainbow-delimiters-depth-7">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-7">(</span>act_damp, <span class="org-string">'none'</span><span class="org-rainbow-delimiters-depth-7">)</span>
K_iff = tf<span class="org-rainbow-delimiters-depth-7">(</span>zeros<span class="org-rainbow-delimiters-depth-8">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-8">)</span><span class="org-rainbow-delimiters-depth-7">)</span>; <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
save<span class="org-rainbow-delimiters-depth-7">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-7">(</span>sys_name, <span class="org-string">'pz'</span><span class="org-rainbow-delimiters-depth-7">)</span>
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-7">(</span>struct<span class="org-rainbow-delimiters-depth-8">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-8">)</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-7">(</span>sys_name, <span class="org-string">'vc'</span><span class="org-rainbow-delimiters-depth-7">)</span>
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-7">(</span>struct<span class="org-rainbow-delimiters-depth-8">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'lorentz'</span><span class="org-rainbow-delimiters-depth-8">)</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-7">(</span><span class="org-string">'sys_name should be pz or vc'</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-7">(</span>sys_mass, <span class="org-string">'light'</span><span class="org-rainbow-delimiters-depth-7">)</span>
initializeSample<span class="org-rainbow-delimiters-depth-7">(</span>struct<span class="org-rainbow-delimiters-depth-8">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-8">)</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-7">(</span>sys_mass, <span class="org-string">'heavy'</span><span class="org-rainbow-delimiters-depth-7">)</span>
initializeSample<span class="org-rainbow-delimiters-depth-7">(</span>struct<span class="org-rainbow-delimiters-depth-8">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-8">)</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-7">(</span><span class="org-string">'sys_mass should be light or heavy'</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the simulation</span></span>
<span class="org-matlab-simulink-keyword">sim</span><span class="org-rainbow-delimiters-depth-7">(</span><span class="org-string">'sim_nano_station_ctrl.slx'</span><span class="org-rainbow-delimiters-depth-7">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Split the Dsample matrix into vectors</span></span>
<span class="org-rainbow-delimiters-depth-7">[</span>Dx, Dy, Dz, Rx, Ry, Rz<span class="org-rainbow-delimiters-depth-7">]</span> = matSplit<span class="org-rainbow-delimiters-depth-7">(</span>Es.Data, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-7">)</span>; <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
time = Dsample.Time; <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save the result</span></span>
filename = sprintf<span class="org-rainbow-delimiters-depth-7">(</span><span class="org-string">'sim_%s_%s_%s_%s'</span>, sys_mass, sys_name, ctrl_type, act_damp);
save<span class="org-rainbow-delimiters-depth-8">(</span>sprintf<span class="org-rainbow-delimiters-depth-9">(</span><span class="org-string">'./mat/%s.mat'</span>, filename), ...
<span class="org-string">'time'</span>, <span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>, <span class="org-string">'K'</span><span class="org-rainbow-delimiters-depth-9">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgcee9dda" class="outline-2">
<h2 id="orgcee9dda"><span class="section-number-2">8</span> Initialize Elements</h2>
<div class="outline-text-2" id="text-8">
</div>
<div id="outline-container-org870f9ac" class="outline-3">
<h3 id="org870f9ac"><span class="section-number-3">8.1</span> Simulation Configuration</h3>
<div class="outline-text-3" id="text-8-1">
<p>
<a id="org0e8d931"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeSimConf.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[]</span></span> = <span class="org-function-name">initializeSimConf</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Ts'</span>, <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">4</span>, ...<span class="org-comment"> % Sampling time [s]</span>
<span class="org-string">'Tsim'</span>, <span class="org-highlight-numbers-number">10</span>, ...<span class="org-comment"> % Simulation time [s]</span>
<span class="org-string">'cl_time'</span>, <span class="org-highlight-numbers-number">0</span>, ...<span class="org-comment"> % Close Loop time [s]</span>
<span class="org-string">'gravity'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Gravity along the z axis</span>
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
sim_conf = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
sim_conf.Ts = opts.Ts;
sim_conf.Tsim = opts.Tsim;
sim_conf.cl_time = opts.cl_time;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Gravity</span></span>
<span class="org-keyword">if</span> opts.gravity
sim_conf.g = <span class="org-type">-</span><span class="org-highlight-numbers-number">9</span>.<span class="org-highlight-numbers-number">8</span>; <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
<span class="org-keyword">else</span>
sim_conf.g = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">%#</span><span class="org-comment"><span class="org-bold">ok</span></span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/sim_conf.mat'</span>, <span class="org-string">'sim_conf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orge30fdf8" class="outline-3">
<h3 id="orge30fdf8"><span class="section-number-3">8.2</span> Experiment</h3>
<div class="outline-text-3" id="text-8-2">
<p>
<a id="org27259e7"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeExperiment.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[]</span></span> = <span class="org-function-name">initializeExperiment</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">exp_name</span>, <span class="org-variable-name">sys_mass</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>exp_name, <span class="org-string">'tomography'</span><span class="org-rainbow-delimiters-depth-1">)</span>
opts_sim = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'Tsim'</span>, <span class="org-highlight-numbers-number">5</span>, ...
<span class="org-string">'cl_time'</span>, <span class="org-highlight-numbers-number">5</span> ...
<span class="org-rainbow-delimiters-depth-1">)</span>;
initializeSimConf<span class="org-rainbow-delimiters-depth-1">(</span>opts_sim<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>sys_mass, <span class="org-string">'light'</span><span class="org-rainbow-delimiters-depth-1">)</span>
opts_inputs = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'Dw'</span>, <span class="org-constant">true</span>, ...
<span class="org-string">'Rz'</span>, <span class="org-highlight-numbers-number">60</span> ...<span class="org-comment"> % rpm</span>
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> strcpm<span class="org-rainbow-delimiters-depth-1">(</span>sys_mass, <span class="org-string">'heavy'</span><span class="org-rainbow-delimiters-depth-1">)</span>
opts_inputs = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'Dw'</span>, <span class="org-constant">true</span>, ...
<span class="org-string">'Rz'</span>, <span class="org-highlight-numbers-number">1</span> ...<span class="org-comment"> % rpm</span>
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'sys_mass should be light or heavy'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
initializeInputs<span class="org-rainbow-delimiters-depth-1">(</span>opts_inputs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'exp_name is only configured for tomography'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgab84833" class="outline-3">
<h3 id="orgab84833"><span class="section-number-3">8.3</span> Inputs</h3>
<div class="outline-text-3" id="text-8-3">
<p>
<a id="org9834d3d"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeInputs.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">inputs</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeInputs</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span> ...
<span class="org-string">'Dw'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'Dy'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'Ry'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'Rz'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'Dh'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'Rm'</span>, <span class="org-constant">false</span>, ...
<span class="org-string">'Dn'</span>, <span class="org-constant">false</span> ...
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Load Sampling Time and Simulation Time</span></span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/sim_conf.mat'</span>, <span class="org-string">'sim_conf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Define the time vector</span></span>
t = <span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>sim_conf.Ts<span class="org-type">:</span>sim_conf.Tsim;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Ground motion - Dw</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dw<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dw <span class="org-type">==</span> <span class="org-constant">true</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/perturbations.mat'</span>, <span class="org-string">'Wxg'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Dw = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">100</span><span class="org-type">*</span>random<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'norm'</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Dw<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = lsim<span class="org-rainbow-delimiters-depth-1">(</span>Wxg, Dw<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, t<span class="org-rainbow-delimiters-depth-1">)</span>;
Dw<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = lsim<span class="org-rainbow-delimiters-depth-1">(</span>Wxg, Dw<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, t<span class="org-rainbow-delimiters-depth-1">)</span>;
Dw<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = lsim<span class="org-rainbow-delimiters-depth-1">(</span>Wxg, Dw<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, t<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dw<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dw <span class="org-type">==</span> <span class="org-constant">false</span>
Dw = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
Dw = opts.Dw;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Translation stage - Dy</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dy<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dy <span class="org-type">==</span> <span class="org-constant">true</span>
Dy = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dy<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dy <span class="org-type">==</span> <span class="org-constant">false</span>
Dy = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
Dy = opts.Dy;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Tilt Stage - Ry</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Ry<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Ry <span class="org-type">==</span> <span class="org-constant">true</span>
Ry = <span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>t<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Ry<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Ry <span class="org-type">==</span> <span class="org-constant">false</span>
Ry = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> isnumeric<span class="org-rainbow-delimiters-depth-1">(</span>opts.Ry<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> length<span class="org-rainbow-delimiters-depth-1">(</span>opts.Ry<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">1</span>
Ry = opts.Ry<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>ones<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
Ry = opts.Ry;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Spindle - Rz</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Rz<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Rz <span class="org-type">==</span> <span class="org-constant">true</span>
Rz = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">*</span>t;
<span class="org-keyword">elseif</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Rz<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Rz <span class="org-type">==</span> <span class="org-constant">false</span>
Rz = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> isnumeric<span class="org-rainbow-delimiters-depth-1">(</span>opts.Rz<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> length<span class="org-rainbow-delimiters-depth-1">(</span>opts.Rz<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">1</span>
Rz = opts.Rz<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">60</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>t;
<span class="org-keyword">else</span>
Rz = opts.Rz;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Micro Hexapod - Dh</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dh<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dh <span class="org-type">==</span> <span class="org-constant">true</span>
Dh = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dh<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dh <span class="org-type">==</span> <span class="org-constant">false</span>
Dh = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
Dh = opts.Dh;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Axis Compensation - Rm</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Rm<span class="org-rainbow-delimiters-depth-1">)</span>
Rm = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Rm<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-constant">pi</span><span class="org-type">*</span>ones<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
Rm = opts.Rm;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Nano Hexapod - Dn</span></span>
<span class="org-keyword">if</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dn<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dn <span class="org-type">==</span> <span class="org-constant">true</span>
Dn = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">elseif</span> islogical<span class="org-rainbow-delimiters-depth-1">(</span>opts.Dn<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">&&</span> opts.Dn <span class="org-type">==</span> <span class="org-constant">false</span>
Dn = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
Dn = opts.Dn;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Setpoint - Ds</span></span>
Ds = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">t</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
Ds<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = computeSetpoint<span class="org-rainbow-delimiters-depth-1">(</span>Dy<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">)</span>, Ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">)</span>, Rz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% External Forces applied on the Granite</span></span>
Fg = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% External Forces applied on the Sample</span></span>
Fs = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>t<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Create the input Structure that will contain all the inputs</span></span>
inputs = struct<span class="org-rainbow-delimiters-depth-1">(</span> ...
<span class="org-string">'Ts'</span>, sim_conf.Ts, ...
<span class="org-string">'Dw'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Dw, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Dy'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Dy, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Ry'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Ry, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Rz'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Rz, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Dh'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Dh, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Rm'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Rm, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Dn'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Dn, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Ds'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Ds, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Fg'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Fg, t<span class="org-rainbow-delimiters-depth-2">)</span>, ...
<span class="org-string">'Fs'</span>, timeseries<span class="org-rainbow-delimiters-depth-2">(</span>Fs, t<span class="org-rainbow-delimiters-depth-2">)</span> ...
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/inputs.mat'</span>, <span class="org-string">'inputs'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Custom Functions</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name">setpoint</span> = <span class="org-function-name">computeSetpoint</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">ty</span>, <span class="org-variable-name">ry</span>, <span class="org-variable-name">rz</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
setpoint = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Ty</span></span>
TMTy = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ty ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Ry</span></span>
TMRy = <span class="org-rainbow-delimiters-depth-1">[</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> sin<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>ry<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Rz</span></span>
TMRz = <span class="org-rainbow-delimiters-depth-1">[</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
sin<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> cos<span class="org-rainbow-delimiters-depth-2">(</span>rz<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> ;
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span> <span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% All stages</span></span>
TM = TMTy<span class="org-type">*</span>TMRy<span class="org-type">*</span>TMRz;
<span class="org-rainbow-delimiters-depth-1">[</span>thetax, thetay, thetaz<span class="org-rainbow-delimiters-depth-1">]</span> = RM2angle<span class="org-rainbow-delimiters-depth-1">(</span>TM<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
setpoint<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = TM<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>;
setpoint<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>thetax, thetay, thetaz<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Custom Functions</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">thetax, thetay, thetaz</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">RM2angle</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">R</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">if</span> abs<span class="org-rainbow-delimiters-depth-1">(</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>R<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">></span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span> % R31 <span class="org-type">!</span>= <span class="org-highlight-numbers-number">1</span> and R31 <span class="org-type">!</span>= <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>
thetay = <span class="org-type">-</span>asin<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
thetax = atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
thetaz = atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>thetay<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
thetaz = <span class="org-highlight-numbers-number">0</span>;
<span class="org-keyword">if</span> abs<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type"><</span> <span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span> % R31 = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>
thetay = <span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
thetax = thetaz <span class="org-type">+</span> atan2<span class="org-rainbow-delimiters-depth-1">(</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">else</span>
thetay = <span class="org-type">-</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
thetax = <span class="org-type">-</span>thetaz <span class="org-type">+</span> atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>R<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org103cc41" class="outline-3">
<h3 id="org103cc41"><span class="section-number-3">8.4</span> Ground</h3>
<div class="outline-text-3" id="text-8-4">
<p>
<a id="orga991e31"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeGround.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">ground</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeGround</span><span class="org-rainbow-delimiters-depth-1">()</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
ground = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
ground.shape = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [m]</span>
ground.density = <span class="org-highlight-numbers-number">2800</span>; <span class="org-comment">% [kg/m3]</span>
ground.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ground'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org6619477" class="outline-3">
<h3 id="org6619477"><span class="section-number-3">8.5</span> Granite</h3>
<div class="outline-text-3" id="text-8-5">
<p>
<a id="org15c259d"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeGranite.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">granite</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeGranite</span><span class="org-rainbow-delimiters-depth-1">()</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
granite = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Static Properties</span></span>
granite.density = <span class="org-highlight-numbers-number">2800</span>; <span class="org-comment">% [kg/m3]</span>
granite.volume = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">72</span>; <span class="org-comment">% [m3] TODO - should</span>
granite.mass = granite.density<span class="org-type">*</span>granite.volume; <span class="org-comment">% [kg]</span>
granite.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
granite.STEP = <span class="org-string">'./STEPS/granite/granite.STEP'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Dynamical Properties</span></span>
granite.k.x = <span class="org-highlight-numbers-number">1e8</span>; <span class="org-comment">% [N/m]</span>
granite.c.x = <span class="org-highlight-numbers-number">1e4</span>; <span class="org-comment">% [N/(m/s)]</span>
granite.k.y = <span class="org-highlight-numbers-number">1e8</span>; <span class="org-comment">% [N/m]</span>
granite.c.y = <span class="org-highlight-numbers-number">1e4</span>; <span class="org-comment">% [N/(m/s)]</span>
granite.k.z = <span class="org-highlight-numbers-number">1e8</span>; <span class="org-comment">% [N/m]</span>
granite.c.z = <span class="org-highlight-numbers-number">1e4</span>; <span class="org-comment">% [N/(m/s)]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Positioning parameters</span></span>
granite.sample_pos = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">8</span>; <span class="org-comment">% Z-offset for the initial position of the sample [m]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'granite'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org77a28f7" class="outline-3">
<h3 id="org77a28f7"><span class="section-number-3">8.6</span> Translation Stage</h3>
<div class="outline-text-3" id="text-8-6">
<p>
<a id="org98bfb5b"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeTy.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">ty</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeTy</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rigid'</span>, <span class="org-constant">false</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
ty = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Y-Translation - Static Properties</span></span>
<span class="org-comment">% Ty Granite frame</span>
ty.granite_frame.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.granite_frame.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">753</span> <span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">753</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.granite_frame.STEP = <span class="org-string">'./STEPS/Ty/Ty_Granite_Frame.STEP'</span>;
<span class="org-comment">% Guide Translation Ty</span>
ty.guide.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.guide.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.guide.STEP = <span class="org-string">'./STEPS/ty/Ty_Guide.STEP'</span>;
<span class="org-comment">% Ty - Guide_Translation12</span>
ty.guide12.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.guide12.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.guide12.STEP = <span class="org-string">'./STEPS/Ty/Ty_Guide_12.STEP'</span>;
<span class="org-comment">% Ty - Guide_Translation11</span>
ty.guide11.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.guide11.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.guide11.STEP = <span class="org-string">'./STEPS/ty/Ty_Guide_11.STEP'</span>;
<span class="org-comment">% Ty - Guide_Translation22</span>
ty.guide22.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.guide22.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.guide22.STEP = <span class="org-string">'./STEPS/ty/Ty_Guide_22.STEP'</span>;
<span class="org-comment">% Ty - Guide_Translation21</span>
ty.guide21.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.guide21.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.guide21.STEP = <span class="org-string">'./STEPS/Ty/Ty_Guide_21.STEP'</span>;
<span class="org-comment">% Ty - Plateau translation</span>
ty.frame.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ty.frame.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.frame.STEP = <span class="org-string">'./STEPS/ty/Ty_Stage.STEP'</span>;
<span class="org-comment">% Ty Stator Part</span>
ty.stator.density = <span class="org-highlight-numbers-number">5400</span>; <span class="org-comment">% [kg/m3]</span>
ty.stator.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.stator.STEP = <span class="org-string">'./STEPS/ty/Ty_Motor_Stator.STEP'</span>;
<span class="org-comment">% Ty Rotor Part</span>
ty.rotor.density = <span class="org-highlight-numbers-number">5400</span>; <span class="org-comment">% [kg/m3]</span>
ty.rotor.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ty.rotor.STEP = <span class="org-string">'./STEPS/ty/Ty_Motor_Rotor.STEP'</span>;
ty.m = <span class="org-highlight-numbers-number">250</span>; <span class="org-comment">% TODO [kg]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Y-Translation - Dynamicals Properties</span></span>
<span class="org-keyword">if</span> opts.rigid
ty.k.ax = <span class="org-highlight-numbers-number">1e10</span>; % Axial Stiffness <span class="org-keyword">for</span> each of the <span class="org-highlight-numbers-number">4</span> guidance (y) [N<span class="org-type">/</span>m]
<span class="org-keyword">else</span>
ty.k.ax = <span class="org-highlight-numbers-number">1e7</span><span class="org-type">/</span><span class="org-highlight-numbers-number">4</span>; % Axial Stiffness <span class="org-keyword">for</span> each of the <span class="org-highlight-numbers-number">4</span> guidance (y) [N<span class="org-type">/</span>m]
<span class="org-keyword">end</span>
ty.k.rad = <span class="org-highlight-numbers-number">9e9</span><span class="org-type">/</span><span class="org-highlight-numbers-number">4</span>; % Radial Stiffness <span class="org-keyword">for</span> each of the <span class="org-highlight-numbers-number">4</span> guidance (x<span class="org-type">-</span>z) [N<span class="org-type">/</span>m]
ty.c.ax = <span class="org-highlight-numbers-number">100</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>ty.k.ax<span class="org-type">/</span>ty.m<span class="org-rainbow-delimiters-depth-1">)</span>;
ty.c.rad = <span class="org-highlight-numbers-number">100</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>ty.k.rad<span class="org-type">/</span>ty.m<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ty'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orge78d8a3" class="outline-3">
<h3 id="orge78d8a3"><span class="section-number-3">8.7</span> Tilt Stage</h3>
<div class="outline-text-3" id="text-8-7">
<p>
<a id="org87f3ecd"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeRy.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">ry</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeRy</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rigid'</span>, <span class="org-constant">false</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
ry = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Tilt Stage - Static Properties</span></span>
<span class="org-comment">% Ry - Guide for the tilt stage</span>
ry.guide.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ry.guide.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ry.guide.STEP = <span class="org-string">'./STEPS/ry/Tilt_Guide.STEP'</span>;
<span class="org-comment">% Ry - Rotor of the motor</span>
ry.rotor.density = <span class="org-highlight-numbers-number">2400</span>; <span class="org-comment">% [kg/m3]</span>
ry.rotor.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ry.rotor.STEP = <span class="org-string">'./STEPS/ry/Tilt_Motor_Axis.STEP'</span>;
<span class="org-comment">% Ry - Motor</span>
ry.motor.density = <span class="org-highlight-numbers-number">3200</span>; <span class="org-comment">% [kg/m3]</span>
ry.motor.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ry.motor.STEP = <span class="org-string">'./STEPS/ry/Tilt_Motor.STEP'</span>;
<span class="org-comment">% Ry - Plateau Tilt</span>
ry.stage.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
ry.stage.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
ry.stage.STEP = <span class="org-string">'./STEPS/ry/Tilt_Stage.STEP'</span>;
ry.m = <span class="org-highlight-numbers-number">200</span>; <span class="org-comment">% TODO [kg]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Tilt Stage - Dynamical Properties</span></span>
<span class="org-keyword">if</span> opts.rigid
ry.k.tilt = <span class="org-highlight-numbers-number">1e10</span>; <span class="org-comment">% Rotation stiffness around y [N*m/deg]</span>
<span class="org-keyword">else</span>
ry.k.tilt = <span class="org-highlight-numbers-number">1e4</span>; <span class="org-comment">% Rotation stiffness around y [N*m/deg]</span>
<span class="org-keyword">end</span>
ry.k.h = <span class="org-highlight-numbers-number">357e6</span><span class="org-type">/</span><span class="org-highlight-numbers-number">4</span>; <span class="org-comment">% Stiffness in the direction of the guidance [N/m]</span>
ry.k.rad = <span class="org-highlight-numbers-number">555e6</span><span class="org-type">/</span><span class="org-highlight-numbers-number">4</span>; <span class="org-comment">% Stiffness in the top direction [N/m]</span>
ry.k.rrad = <span class="org-highlight-numbers-number">238e6</span><span class="org-type">/</span><span class="org-highlight-numbers-number">4</span>; <span class="org-comment">% Stiffness in the side direction [N/m]</span>
ry.c.h = <span class="org-highlight-numbers-number">10</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>ry.k.h<span class="org-type">/</span>ry.m<span class="org-rainbow-delimiters-depth-1">)</span>;
ry.c.rad = <span class="org-highlight-numbers-number">10</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>ry.k.rad<span class="org-type">/</span>ry.m<span class="org-rainbow-delimiters-depth-1">)</span>;
ry.c.rrad = <span class="org-highlight-numbers-number">10</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>ry.k.rrad<span class="org-type">/</span>ry.m<span class="org-rainbow-delimiters-depth-1">)</span>;
ry.c.tilt = <span class="org-highlight-numbers-number">10</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>ry.k.tilt<span class="org-type">/</span>ry.m<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Positioning parameters</span></span>
ry.z_offset = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">58178</span>; <span class="org-comment">% Z-Offset so that the center of rotation matches the sample center [m]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ry'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org567c23d" class="outline-3">
<h3 id="org567c23d"><span class="section-number-3">8.8</span> Spindle</h3>
<div class="outline-text-3" id="text-8-8">
<p>
<a id="orga6d2fea"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeRz.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">rz</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeRz</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rigid'</span>, <span class="org-constant">false</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
rz = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Spindle - Static Properties</span></span>
<span class="org-comment">% Spindle - Slip Ring</span>
rz.slipring.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
rz.slipring.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
rz.slipring.STEP = <span class="org-string">'./STEPS/rz/Spindle_Slip_Ring.STEP'</span>;
<span class="org-comment">% Spindle - Rotor</span>
rz.rotor.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
rz.rotor.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
rz.rotor.STEP = <span class="org-string">'./STEPS/rz/Spindle_Rotor.STEP'</span>;
<span class="org-comment">% Spindle - Stator</span>
rz.stator.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
rz.stator.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
rz.stator.STEP = <span class="org-string">'./STEPS/rz/Spindle_Stator.STEP'</span>;
<span class="org-comment">% Estimated mass of the mooving part</span>
rz.m = <span class="org-highlight-numbers-number">250</span>; <span class="org-comment">% [kg]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Spindle - Dynamical Properties</span></span>
<span class="org-comment">% Estimated stiffnesses</span>
rz.k.ax = <span class="org-highlight-numbers-number">2e9</span>; <span class="org-comment">% Axial Stiffness [N/m]</span>
rz.k.rad = <span class="org-highlight-numbers-number">7e8</span>; <span class="org-comment">% Radial Stiffness [N/m]</span>
rz.k.rot = <span class="org-highlight-numbers-number">100e6</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">360</span>; <span class="org-comment">% Rotational Stiffness [N*m/deg]</span>
<span class="org-keyword">if</span> opts.rigid
rz.k.tilt = <span class="org-highlight-numbers-number">1e10</span>; <span class="org-comment">% Vertical Rotational Stiffness [N*m/deg]</span>
<span class="org-keyword">else</span>
rz.k.tilt = <span class="org-highlight-numbers-number">1e2</span>; <span class="org-comment">% TODO what value should I put? [N*m/deg]</span>
<span class="org-keyword">end</span>
<span class="org-comment">% TODO</span>
rz.c.ax = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>rz.k.ax<span class="org-type">/</span>rz.m<span class="org-rainbow-delimiters-depth-1">)</span>;
rz.c.rad = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>rz.k.rad<span class="org-type">/</span>rz.m<span class="org-rainbow-delimiters-depth-1">)</span>;
rz.c.tilt = <span class="org-highlight-numbers-number">100</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>rz.k.tilt<span class="org-type">/</span>rz.m<span class="org-rainbow-delimiters-depth-1">)</span>;
rz.c.rot = <span class="org-highlight-numbers-number">100</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>rz.k.rot<span class="org-type">/</span>rz.m<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'rz'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgc032b1e" class="outline-3">
<h3 id="orgc032b1e"><span class="section-number-3">8.9</span> Micro Hexapod</h3>
<div class="outline-text-3" id="text-8-9">
<p>
<a id="orgbd011a3"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeMicroHexapod.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">micro_hexapod</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeMicroHexapod</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Stewart Object</span></span>
micro_hexapod = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
micro_hexapod.h = <span class="org-highlight-numbers-number">350</span>; <span class="org-comment">% Total height of the platform [mm]</span>
% micro_hexapod.jacobian = <span class="org-highlight-numbers-number">269</span>.<span class="org-highlight-numbers-number">26</span>; % Distance from the top platform to the Jacobian point [mm]
micro_hexapod.jacobian = <span class="org-highlight-numbers-number">270</span>; <span class="org-comment">% Distance from the top platform to the Jacobian point [mm]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Bottom Plate - Mechanical Design</span></span>
BP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
BP.rad.int = <span class="org-highlight-numbers-number">110</span>; <span class="org-comment">% Internal Radius [mm]</span>
BP.rad.ext = <span class="org-highlight-numbers-number">207</span>.<span class="org-highlight-numbers-number">5</span>; <span class="org-comment">% External Radius [mm]</span>
BP.thickness = <span class="org-highlight-numbers-number">26</span>; <span class="org-comment">% Thickness [mm]</span>
BP.leg.rad = <span class="org-highlight-numbers-number">175</span>.<span class="org-highlight-numbers-number">5</span>; <span class="org-comment">% Radius where the legs articulations are positionned [mm]</span>
BP.leg.ang = <span class="org-highlight-numbers-number">9</span>.<span class="org-highlight-numbers-number">5</span>; <span class="org-comment">% Angle Offset [deg]</span>
BP.density = <span class="org-highlight-numbers-number">8000</span>; % Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
BP.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
BP.shape = <span class="org-rainbow-delimiters-depth-1">[</span>BP.rad.int BP.thickness; BP.rad.int <span class="org-highlight-numbers-number">0</span>; BP.rad.ext <span class="org-highlight-numbers-number">0</span>; BP.rad.ext BP.thickness<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Top Plate - Mechanical Design</span></span>
TP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
TP.rad.int = <span class="org-highlight-numbers-number">82</span>; <span class="org-comment">% Internal Radius [mm]</span>
TP.rad.ext = <span class="org-highlight-numbers-number">150</span>; <span class="org-comment">% Internal Radius [mm]</span>
TP.thickness = <span class="org-highlight-numbers-number">26</span>; <span class="org-comment">% Thickness [mm]</span>
TP.leg.rad = <span class="org-highlight-numbers-number">118</span>; <span class="org-comment">% Radius where the legs articulations are positionned [mm]</span>
TP.leg.ang = <span class="org-highlight-numbers-number">12</span>.<span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Angle Offset [deg]</span>
TP.density = <span class="org-highlight-numbers-number">8000</span>; % Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
TP.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
TP.shape = <span class="org-rainbow-delimiters-depth-1">[</span>TP.rad.int TP.thickness; TP.rad.int <span class="org-highlight-numbers-number">0</span>; TP.rad.ext <span class="org-highlight-numbers-number">0</span>; TP.rad.ext TP.thickness<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Struts</span></span>
Leg = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
Leg.stroke = <span class="org-highlight-numbers-number">10e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span>; <span class="org-comment">% Maximum Stroke of each leg [m]</span>
Leg.k.ax = <span class="org-highlight-numbers-number">5e7</span>; <span class="org-comment">% Stiffness of each leg [N/m]</span>
Leg.ksi.ax = <span class="org-highlight-numbers-number">3</span>; <span class="org-comment">% Maximum amplification at resonance []</span>
Leg.rad.bottom = <span class="org-highlight-numbers-number">25</span>; <span class="org-comment">% Radius of the cylinder of the bottom part [mm]</span>
Leg.rad.top = <span class="org-highlight-numbers-number">17</span>; <span class="org-comment">% Radius of the cylinder of the top part [mm]</span>
Leg.density = <span class="org-highlight-numbers-number">8000</span>; % Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
Leg.color.bottom = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
Leg.color.top = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
Leg.sphere.bottom = Leg.rad.bottom; <span class="org-comment">% Size of the sphere at the end of the leg [mm]</span>
Leg.sphere.top = Leg.rad.top; <span class="org-comment">% Size of the sphere at the end of the leg [mm]</span>
Leg.m = TP.density<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-3">(</span>TP.rad.ext<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>TP.thickness<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-3">(</span>TP.rad.int<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>TP.thickness<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>; <span class="org-comment">% TODO [kg]</span>
Leg = updateDamping<span class="org-rainbow-delimiters-depth-1">(</span>Leg<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Sphere</span></span>
SP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
SP.height.bottom = <span class="org-highlight-numbers-number">27</span>; <span class="org-comment">% [mm]</span>
SP.height.top = <span class="org-highlight-numbers-number">27</span>; <span class="org-comment">% [mm]</span>
SP.density.bottom = <span class="org-highlight-numbers-number">8000</span>; % [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
SP.density.top = <span class="org-highlight-numbers-number">8000</span>; % [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
SP.color.bottom = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [rgb]</span>
SP.color.top = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [rgb]</span>
SP.k.ax = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% [N*m/deg]</span>
SP.ksi.ax = <span class="org-highlight-numbers-number">10</span>;
SP.thickness.bottom = SP.height.bottom<span class="org-type">-</span>Leg.sphere.bottom; <span class="org-comment">% [mm]</span>
SP.thickness.top = SP.height.top<span class="org-type">-</span>Leg.sphere.top; <span class="org-comment">% [mm]</span>
SP.rad.bottom = Leg.sphere.bottom; <span class="org-comment">% [mm]</span>
SP.rad.top = Leg.sphere.top; <span class="org-comment">% [mm]</span>
SP.m = SP.density.bottom<span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>SP.rad.bottom<span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>SP.height.bottom<span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% TODO [kg]</span>
SP = updateDamping<span class="org-rainbow-delimiters-depth-1">(</span>SP<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
Leg.support.bottom = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> SP.thickness.bottom; <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>; SP.rad.bottom <span class="org-highlight-numbers-number">0</span>; SP.rad.bottom SP.height.bottom<span class="org-rainbow-delimiters-depth-1">]</span>;
Leg.support.top = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> SP.thickness.top; <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>; SP.rad.top <span class="org-highlight-numbers-number">0</span>; SP.rad.top SP.height.top<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
micro_hexapod.BP = BP;
micro_hexapod.TP = TP;
micro_hexapod.Leg = Leg;
micro_hexapod.SP = SP;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
micro_hexapod = initializeParameters<span class="org-rainbow-delimiters-depth-1">(</span>micro_hexapod<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'micro_hexapod'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">element</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">updateDamping</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">element</span><span class="org-rainbow-delimiters-depth-1">)</span>
field = fieldnames<span class="org-rainbow-delimiters-depth-1">(</span>element.k<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">field</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
element.c.<span class="org-rainbow-delimiters-depth-1">(</span>field<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>element.ksi.<span class="org-rainbow-delimiters-depth-1">(</span>field<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>element.k.<span class="org-rainbow-delimiters-depth-2">(</span>field<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>element.m<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">stewart</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeParameters</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">stewart</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Connection points on base and top plate w.r.t. World frame at the center of the base plate</span></span>
stewart.pos_base = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
stewart.pos_top = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
alpha_b = stewart.BP.leg.ang<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span>; % angle de décalage par rapport à <span class="org-highlight-numbers-number">120</span> deg (pour positionner les supports bases)
alpha_t = stewart.TP.leg.ang<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span>; % <span class="org-type">+-</span> offset angle from <span class="org-highlight-numbers-number">120</span> degree spacing on top
height = <span class="org-rainbow-delimiters-depth-1">(</span>stewart.h<span class="org-type">-</span>stewart.BP.thickness<span class="org-type">-</span>stewart.TP.thickness<span class="org-type">-</span>stewart.Leg.sphere.bottom<span class="org-type">-</span>stewart.Leg.sphere.top<span class="org-type">-</span>stewart.SP.thickness.bottom<span class="org-type">-</span>stewart.SP.thickness.top<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% TODO</span>
radius_b = stewart.BP.leg.rad<span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% rayon emplacement support base</span>
radius_t = stewart.TP.leg.rad<span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% top radius in meters</span>
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">3</span></span>
<span class="org-comment">% base points</span>
angle_m_b = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> alpha_b;
angle_p_b = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> alpha_b;
stewart.pos_base<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_b<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_b<span class="org-rainbow-delimiters-depth-2">)</span>, radius_b<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_b<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.pos_base<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_b<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_b<span class="org-rainbow-delimiters-depth-2">)</span>, radius_b<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_b<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% top points</span>
% Top points are <span class="org-highlight-numbers-number">60</span> degrees offset
angle_m_t = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> alpha_t <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>;
angle_p_t = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> alpha_t <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>;
stewart.pos_top<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_t<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_t<span class="org-rainbow-delimiters-depth-2">)</span>, radius_t<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_t<span class="org-rainbow-delimiters-depth-2">)</span>, height<span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.pos_top<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_t<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_t<span class="org-rainbow-delimiters-depth-2">)</span>, radius_t<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_t<span class="org-rainbow-delimiters-depth-2">)</span>, height<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">end</span>
<span class="org-comment">% permute pos_top points so that legs are end points of base and top points</span>
stewart.pos_top = <span class="org-rainbow-delimiters-depth-1">[</span>stewart.pos_top<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>; stewart.pos_top<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">5</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>; %<span class="org-highlight-numbers-number">6th</span> point on top connects to <span class="org-highlight-numbers-number">1st</span> on bottom
stewart.pos_top_tranform = stewart.pos_top <span class="org-type">-</span> height<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,ones<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% leg vectors</span></span>
legs = stewart.pos_top <span class="org-type">-</span> stewart.pos_base;
leg_length = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
leg_vectors = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
leg_length<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = norm<span class="org-rainbow-delimiters-depth-1">(</span>legs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
leg_vectors<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">/</span> leg_length<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
stewart.Leg.lenght = <span class="org-highlight-numbers-number">1000</span><span class="org-type">*</span>leg_length<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1</span>.<span class="org-highlight-numbers-number">5</span>;
stewart.Leg.shape.bot = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>; ...
stewart.Leg.rad.bottom <span class="org-highlight-numbers-number">0</span>; ...
stewart.Leg.rad.bottom stewart.Leg.lenght; ...
stewart.Leg.rad.top stewart.Leg.lenght; ...
stewart.Leg.rad.top <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>stewart.Leg.lenght; ...
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>stewart.Leg.lenght<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Calculate revolute and cylindrical axes</span></span>
rev1 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev2 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
cyl1 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
rev1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = cross<span class="org-rainbow-delimiters-depth-1">(</span>leg_vectors<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = rev1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">/</span> norm<span class="org-rainbow-delimiters-depth-1">(</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span> cross<span class="org-rainbow-delimiters-depth-1">(</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, leg_vectors<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = rev2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">/</span> norm<span class="org-rainbow-delimiters-depth-1">(</span>rev2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
cyl1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = leg_vectors<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Coordinate systems</span></span>
stewart.lower_leg = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rotation'</span>, eye<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
stewart.upper_leg = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rotation'</span>, eye<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
stewart.lower_leg<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>.rotation = <span class="org-rainbow-delimiters-depth-1">[</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, rev2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, cyl1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.upper_leg<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>.rotation = <span class="org-rainbow-delimiters-depth-1">[</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, rev2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, cyl1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Position Matrix</span></span>
stewart.M_pos_base = stewart.pos_base <span class="org-type">+</span> <span class="org-rainbow-delimiters-depth-1">(</span>height<span class="org-type">+</span><span class="org-rainbow-delimiters-depth-2">(</span>stewart.TP.thickness<span class="org-type">+</span>stewart.Leg.sphere.top<span class="org-type">+</span>stewart.SP.thickness.top<span class="org-type">+</span>stewart.jacobian<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,ones<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Compute Jacobian Matrix</span></span>
aa = stewart.pos_top_tranform <span class="org-type">+</span> <span class="org-rainbow-delimiters-depth-1">(</span>stewart.jacobian <span class="org-type">-</span> stewart.TP.thickness <span class="org-type">-</span> stewart.SP.height.top<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,ones<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.J = getJacobianMatrix<span class="org-rainbow-delimiters-depth-1">(</span>leg_vectors<span class="org-type">'</span>, aa<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">function</span> <span class="org-variable-name">J</span> = <span class="org-function-name">getJacobianMatrix</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">RM</span>,<span class="org-variable-name">M_pos_base</span><span class="org-rainbow-delimiters-depth-1">)</span>
% RM<span class="org-type">:</span> [<span class="org-highlight-numbers-number">3x6</span>] unit vector of each leg in the fixed frame
% M_pos_base<span class="org-type">:</span> [<span class="org-highlight-numbers-number">3x6</span>] vector of the leg connection at the top platform location in the fixed frame
J = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
J<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = RM<span class="org-type">'</span>;
J<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = cross<span class="org-rainbow-delimiters-depth-1">(</span>M_pos_base, RM<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org3b5edf8" class="outline-3">
<h3 id="org3b5edf8"><span class="section-number-3">8.10</span> Center of gravity compensation</h3>
<div class="outline-text-3" id="text-8-10">
<p>
<a id="org908ebcf"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeAxisc.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">axisc</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeAxisc</span><span class="org-rainbow-delimiters-depth-1">()</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
axisc = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Axis Compensator - Static Properties</span></span>
<span class="org-comment">% Structure</span>
axisc.structure.density = <span class="org-highlight-numbers-number">3400</span>; <span class="org-comment">% [kg/m3]</span>
axisc.structure.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
axisc.structure.STEP = <span class="org-string">'./STEPS/axisc/axisc_structure.STEP'</span>;
<span class="org-comment">% Wheel</span>
axisc.wheel.density = <span class="org-highlight-numbers-number">2700</span>; <span class="org-comment">% [kg/m3]</span>
axisc.wheel.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">753</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">753</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">753</span><span class="org-rainbow-delimiters-depth-1">]</span>;
axisc.wheel.STEP = <span class="org-string">'./STEPS/axisc/axisc_wheel.STEP'</span>;
<span class="org-comment">% Mass</span>
axisc.mass.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
axisc.mass.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
axisc.mass.STEP = <span class="org-string">'./STEPS/axisc/axisc_mass.STEP'</span>;
<span class="org-comment">% Gear</span>
axisc.gear.density = <span class="org-highlight-numbers-number">7800</span>; <span class="org-comment">% [kg/m3]</span>
axisc.gear.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">792</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">820</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">933</span><span class="org-rainbow-delimiters-depth-1">]</span>;
axisc.gear.STEP = <span class="org-string">'./STEPS/axisc/axisc_gear.STEP'</span>;
axisc.m = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% TODO [kg]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Axis Compensator - Dynamical Properties</span></span>
axisc.k.ax = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% TODO [N*m/deg)]</span>
axisc.c.ax = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>axisc.k.ax<span class="org-type">/</span>axisc.m<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'axisc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf300722" class="outline-3">
<h3 id="orgf300722"><span class="section-number-3">8.11</span> Mirror</h3>
<div class="outline-text-3" id="text-8-11">
<p>
<a id="orgb5894e5"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeMirror.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[]</span></span> = <span class="org-function-name">initializeMirror</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
<span class="org-string">'shape'</span>, <span class="org-string">'spherical'</span>, ...<span class="org-comment"> % spherical or conical</span>
<span class="org-string">'angle'</span>, <span class="org-highlight-numbers-number">45</span> ...
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
mirror = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
mirror.h = <span class="org-highlight-numbers-number">50</span>; <span class="org-comment">% height of the mirror [mm]</span>
mirror.thickness = <span class="org-highlight-numbers-number">25</span>; <span class="org-comment">% Thickness of the plate supporting the sample [mm]</span>
mirror.hole_rad = <span class="org-highlight-numbers-number">120</span>; <span class="org-comment">% radius of the hole in the mirror [mm]</span>
mirror.support_rad = <span class="org-highlight-numbers-number">100</span>; <span class="org-comment">% radius of the support plate [mm]</span>
mirror.jacobian = <span class="org-highlight-numbers-number">150</span>; <span class="org-comment">% point of interest offset in z (above the top surfave) [mm]</span>
mirror.rad = <span class="org-highlight-numbers-number">180</span>; <span class="org-comment">% radius of the mirror (at the bottom surface) [mm]</span>
mirror.density = <span class="org-highlight-numbers-number">2400</span>; <span class="org-comment">% Density of the mirror [kg/m3]</span>
mirror.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">4</span> <span class="org-highlight-numbers-number">1</span>.<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span>.<span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color of the mirror</span>
mirror.cone_length = mirror.rad<span class="org-type">*</span>tand<span class="org-rainbow-delimiters-depth-1">(</span>opts.angle<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">+</span>mirror.h<span class="org-type">+</span>mirror.jacobian; <span class="org-comment">% Distance from Apex point of the cone to jacobian point</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Shape</span></span>
mirror.shape = <span class="org-rainbow-delimiters-depth-1">[</span>...
<span class="org-highlight-numbers-number">0</span> mirror.h<span class="org-type">-</span>mirror.thickness
mirror.hole_rad mirror.h<span class="org-type">-</span>mirror.thickness; ...
mirror.hole_rad <span class="org-highlight-numbers-number">0</span>; ...
mirror.rad <span class="org-highlight-numbers-number">0</span> ...
<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>opts.shape, <span class="org-string">'spherical'</span><span class="org-rainbow-delimiters-depth-1">)</span>
mirror.sphere_radius = sqrt<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>mirror.jacobian<span class="org-type">+</span>mirror.h<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">+</span>mirror.rad<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Radius of the sphere [mm]</span>
<span class="org-keyword">for</span> <span class="org-variable-name">z</span> = <span class="org-constant">linspace</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant"><span class="org-highlight-numbers-number">0</span></span><span class="org-constant">, mirror.h, </span><span class="org-constant"><span class="org-highlight-numbers-number">101</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
mirror.shape = <span class="org-rainbow-delimiters-depth-1">[</span>mirror.shape; sqrt<span class="org-rainbow-delimiters-depth-2">(</span>mirror.sphere_radius<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">-</span><span class="org-rainbow-delimiters-depth-3">(</span>z<span class="org-type">-</span>mirror.jacobian<span class="org-type">-</span>mirror.h<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span> z<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>opts.shape, <span class="org-string">'conical'</span><span class="org-rainbow-delimiters-depth-1">)</span>
mirror.shape = <span class="org-rainbow-delimiters-depth-1">[</span>mirror.shape; mirror.rad<span class="org-type">+</span>mirror.h<span class="org-type">/</span>tand<span class="org-rainbow-delimiters-depth-2">(</span>opts.angle<span class="org-rainbow-delimiters-depth-2">)</span> mirror.h<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Shape should be either conical or spherical'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
mirror.shape = <span class="org-rainbow-delimiters-depth-1">[</span>mirror.shape; <span class="org-highlight-numbers-number">0</span> mirror.h<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'mirror'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf57d858" class="outline-3">
<h3 id="orgf57d858"><span class="section-number-3">8.12</span> Nano Hexapod</h3>
<div class="outline-text-3" id="text-8-12">
<p>
<a id="org9b0c46a"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeNanoHexapod.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">nano_hexapod</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeNanoHexapod</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Stewart Object</span></span>
nano_hexapod = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
nano_hexapod.h = <span class="org-highlight-numbers-number">90</span>; <span class="org-comment">% Total height of the platform [mm]</span>
nano_hexapod.jacobian = <span class="org-highlight-numbers-number">175</span>; <span class="org-comment">% Point where the Jacobian is computed => Center of rotation [mm]</span>
% nano_hexapod.jacobian = <span class="org-highlight-numbers-number">174</span>.<span class="org-highlight-numbers-number">26</span>; % Point where the Jacobian is computed =<span class="org-type">></span> Center of rotation [mm]
<span class="org-matlab-cellbreak"><span class="org-comment">%% Bottom Plate</span></span>
BP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
BP.rad.int = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Internal Radius [mm]</span>
BP.rad.ext = <span class="org-highlight-numbers-number">150</span>; <span class="org-comment">% External Radius [mm]</span>
BP.thickness = <span class="org-highlight-numbers-number">10</span>; <span class="org-comment">% Thickness [mm]</span>
BP.leg.rad = <span class="org-highlight-numbers-number">100</span>; <span class="org-comment">% Radius where the legs articulations are positionned [mm]</span>
BP.leg.ang = <span class="org-highlight-numbers-number">5</span>; <span class="org-comment">% Angle Offset [deg]</span>
BP.density = <span class="org-highlight-numbers-number">8000</span>;% Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
BP.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
BP.shape = <span class="org-rainbow-delimiters-depth-1">[</span>BP.rad.int BP.thickness; BP.rad.int <span class="org-highlight-numbers-number">0</span>; BP.rad.ext <span class="org-highlight-numbers-number">0</span>; BP.rad.ext BP.thickness<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Top Plate</span></span>
TP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
TP.rad.int = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Internal Radius [mm]</span>
TP.rad.ext = <span class="org-highlight-numbers-number">100</span>; <span class="org-comment">% Internal Radius [mm]</span>
TP.thickness = <span class="org-highlight-numbers-number">10</span>; <span class="org-comment">% Thickness [mm]</span>
TP.leg.rad = <span class="org-highlight-numbers-number">90</span>; <span class="org-comment">% Radius where the legs articulations are positionned [mm]</span>
TP.leg.ang = <span class="org-highlight-numbers-number">5</span>; <span class="org-comment">% Angle Offset [deg]</span>
TP.density = <span class="org-highlight-numbers-number">8000</span>;% Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
TP.color = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
TP.shape = <span class="org-rainbow-delimiters-depth-1">[</span>TP.rad.int TP.thickness; TP.rad.int <span class="org-highlight-numbers-number">0</span>; TP.rad.ext <span class="org-highlight-numbers-number">0</span>; TP.rad.ext TP.thickness<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Leg</span></span>
Leg = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
Leg.stroke = <span class="org-highlight-numbers-number">80e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span>; <span class="org-comment">% Maximum Stroke of each leg [m]</span>
<span class="org-keyword">if</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>opts.actuator, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-1">)</span>
Leg.k.ax = <span class="org-highlight-numbers-number">1e7</span>; <span class="org-comment">% Stiffness of each leg [N/m]</span>
<span class="org-keyword">elseif</span> strcmp<span class="org-rainbow-delimiters-depth-1">(</span>opts.actuator, <span class="org-string">'lorentz'</span><span class="org-rainbow-delimiters-depth-1">)</span>
Leg.k.ax = <span class="org-highlight-numbers-number">1e4</span>; <span class="org-comment">% Stiffness of each leg [N/m]</span>
<span class="org-keyword">else</span>
error<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts.actuator should be piezo or lorentz'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
Leg.ksi.ax = <span class="org-highlight-numbers-number">10</span>; <span class="org-comment">% Maximum amplification at resonance []</span>
Leg.rad.bottom = <span class="org-highlight-numbers-number">12</span>; <span class="org-comment">% Radius of the cylinder of the bottom part [mm]</span>
Leg.rad.top = <span class="org-highlight-numbers-number">10</span>; <span class="org-comment">% Radius of the cylinder of the top part [mm]</span>
Leg.density = <span class="org-highlight-numbers-number">8000</span>; % Density of the material [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
Leg.color.bottom = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
Leg.color.top = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% Color [rgb]</span>
Leg.sphere.bottom = Leg.rad.bottom; <span class="org-comment">% Size of the sphere at the end of the leg [mm]</span>
Leg.sphere.top = Leg.rad.top; <span class="org-comment">% Size of the sphere at the end of the leg [mm]</span>
Leg.m = TP.density<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-3">(</span>TP.rad.ext<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>TP.thickness<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-3">(</span>TP.rad.int<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>TP.thickness<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>; <span class="org-comment">% TODO [kg]</span>
Leg = updateDamping<span class="org-rainbow-delimiters-depth-1">(</span>Leg<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Sphere</span></span>
SP = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
SP.height.bottom = <span class="org-highlight-numbers-number">15</span>; <span class="org-comment">% [mm]</span>
SP.height.top = <span class="org-highlight-numbers-number">15</span>; <span class="org-comment">% [mm]</span>
SP.density.bottom = <span class="org-highlight-numbers-number">8000</span>; % [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
SP.density.top = <span class="org-highlight-numbers-number">8000</span>; % [kg<span class="org-type">/</span>m<span class="org-type">^</span><span class="org-highlight-numbers-number">3</span>]
SP.color.bottom = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [rgb]</span>
SP.color.top = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [rgb]</span>
SP.k.ax = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% [N*m/deg]</span>
SP.ksi.ax = <span class="org-highlight-numbers-number">3</span>;
SP.thickness.bottom = SP.height.bottom<span class="org-type">-</span>Leg.sphere.bottom; <span class="org-comment">% [mm]</span>
SP.thickness.top = SP.height.top<span class="org-type">-</span>Leg.sphere.top; <span class="org-comment">% [mm]</span>
SP.rad.bottom = Leg.sphere.bottom; <span class="org-comment">% [mm]</span>
SP.rad.top = Leg.sphere.top; <span class="org-comment">% [mm]</span>
SP.m = SP.density.bottom<span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>SP.rad.bottom<span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>SP.height.bottom<span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% TODO [kg]</span>
SP = updateDamping<span class="org-rainbow-delimiters-depth-1">(</span>SP<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
Leg.support.bottom = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> SP.thickness.bottom; <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>; SP.rad.bottom <span class="org-highlight-numbers-number">0</span>; SP.rad.bottom SP.height.bottom<span class="org-rainbow-delimiters-depth-1">]</span>;
Leg.support.top = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> SP.thickness.top; <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>; SP.rad.top <span class="org-highlight-numbers-number">0</span>; SP.rad.top SP.height.top<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
nano_hexapod.BP = BP;
nano_hexapod.TP = TP;
nano_hexapod.Leg = Leg;
nano_hexapod.SP = SP;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
nano_hexapod = initializeParameters<span class="org-rainbow-delimiters-depth-1">(</span>nano_hexapod<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">element</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">updateDamping</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">element</span><span class="org-rainbow-delimiters-depth-1">)</span>
field = fieldnames<span class="org-rainbow-delimiters-depth-1">(</span>element.k<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">field</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
element.c.<span class="org-rainbow-delimiters-depth-1">(</span>field<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>element.ksi.<span class="org-rainbow-delimiters-depth-1">(</span>field<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>element.k.<span class="org-rainbow-delimiters-depth-2">(</span>field<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span>element.m<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
<span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">stewart</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeParameters</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">stewart</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Connection points on base and top plate w.r.t. World frame at the center of the base plate</span></span>
stewart.pos_base = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
stewart.pos_top = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
alpha_b = stewart.BP.leg.ang<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span>; % angle de décalage par rapport à <span class="org-highlight-numbers-number">120</span> deg (pour positionner les supports bases)
alpha_t = stewart.TP.leg.ang<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">180</span>; % <span class="org-type">+-</span> offset angle from <span class="org-highlight-numbers-number">120</span> degree spacing on top
height = <span class="org-rainbow-delimiters-depth-1">(</span>stewart.h<span class="org-type">-</span>stewart.BP.thickness<span class="org-type">-</span>stewart.TP.thickness<span class="org-type">-</span>stewart.Leg.sphere.bottom<span class="org-type">-</span>stewart.Leg.sphere.top<span class="org-type">-</span>stewart.SP.thickness.bottom<span class="org-type">-</span>stewart.SP.thickness.top<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% TODO</span>
radius_b = stewart.BP.leg.rad<span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% rayon emplacement support base</span>
radius_t = stewart.TP.leg.rad<span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% top radius in meters</span>
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">3</span></span>
<span class="org-comment">% base points</span>
angle_m_b = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> alpha_b;
angle_p_b = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> alpha_b;
stewart.pos_base<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_b<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_b<span class="org-rainbow-delimiters-depth-2">)</span>, radius_b<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_b<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.pos_base<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_b<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_b<span class="org-rainbow-delimiters-depth-2">)</span>, radius_b<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_b<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-comment">% top points</span>
% Top points are <span class="org-highlight-numbers-number">60</span> degrees offset
angle_m_t = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> alpha_t <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>;
angle_p_t = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span> <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> alpha_t <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>;
stewart.pos_top<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_t<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_t<span class="org-rainbow-delimiters-depth-2">)</span>, radius_t<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_m_t<span class="org-rainbow-delimiters-depth-2">)</span>, height<span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.pos_top<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span>radius_t<span class="org-type">*</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_t<span class="org-rainbow-delimiters-depth-2">)</span>, radius_t<span class="org-type">*</span>sin<span class="org-rainbow-delimiters-depth-2">(</span>angle_p_t<span class="org-rainbow-delimiters-depth-2">)</span>, height<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">end</span>
<span class="org-comment">% permute pos_top points so that legs are end points of base and top points</span>
stewart.pos_top = <span class="org-rainbow-delimiters-depth-1">[</span>stewart.pos_top<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>; stewart.pos_top<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">5</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>; %<span class="org-highlight-numbers-number">6th</span> point on top connects to <span class="org-highlight-numbers-number">1st</span> on bottom
stewart.pos_top_tranform = stewart.pos_top <span class="org-type">-</span> height<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,ones<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% leg vectors</span></span>
legs = stewart.pos_top <span class="org-type">-</span> stewart.pos_base;
leg_length = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
leg_vectors = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
leg_length<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = norm<span class="org-rainbow-delimiters-depth-1">(</span>legs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
leg_vectors<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">/</span> leg_length<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
stewart.Leg.lenght = <span class="org-highlight-numbers-number">1000</span><span class="org-type">*</span>leg_length<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1</span>.<span class="org-highlight-numbers-number">5</span>;
stewart.Leg.shape.bot = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>; ...
stewart.Leg.rad.bottom <span class="org-highlight-numbers-number">0</span>; ...
stewart.Leg.rad.bottom stewart.Leg.lenght; ...
stewart.Leg.rad.top stewart.Leg.lenght; ...
stewart.Leg.rad.top <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>stewart.Leg.lenght; ...
<span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>stewart.Leg.lenght<span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Calculate revolute and cylindrical axes</span></span>
rev1 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev2 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
cyl1 = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
rev1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = cross<span class="org-rainbow-delimiters-depth-1">(</span>leg_vectors<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = rev1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">/</span> norm<span class="org-rainbow-delimiters-depth-1">(</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span> cross<span class="org-rainbow-delimiters-depth-1">(</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, leg_vectors<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
rev2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = rev2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">/</span> norm<span class="org-rainbow-delimiters-depth-1">(</span>rev2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
cyl1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = leg_vectors<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Coordinate systems</span></span>
stewart.lower_leg = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rotation'</span>, eye<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
stewart.upper_leg = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'rotation'</span>, eye<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
stewart.lower_leg<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>.rotation = <span class="org-rainbow-delimiters-depth-1">[</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, rev2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, cyl1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.upper_leg<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>.rotation = <span class="org-rainbow-delimiters-depth-1">[</span>rev1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, rev2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span>, cyl1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>,<span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Position Matrix</span></span>
stewart.M_pos_base = stewart.pos_base <span class="org-type">+</span> <span class="org-rainbow-delimiters-depth-1">(</span>height<span class="org-type">+</span><span class="org-rainbow-delimiters-depth-2">(</span>stewart.TP.thickness<span class="org-type">+</span>stewart.Leg.sphere.top<span class="org-type">+</span>stewart.SP.thickness.top<span class="org-type">+</span>stewart.jacobian<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,ones<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Compute Jacobian Matrix</span></span>
aa = stewart.pos_top_tranform <span class="org-type">+</span> <span class="org-rainbow-delimiters-depth-1">(</span>stewart.jacobian <span class="org-type">-</span> stewart.TP.thickness <span class="org-type">-</span> stewart.SP.height.top<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,ones<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
stewart.J = getJacobianMatrix<span class="org-rainbow-delimiters-depth-1">(</span>leg_vectors<span class="org-type">'</span>, aa<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">function</span> <span class="org-variable-name">J</span> = <span class="org-function-name">getJacobianMatrix</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">RM</span>,<span class="org-variable-name">M_pos_base</span><span class="org-rainbow-delimiters-depth-1">)</span>
% RM<span class="org-type">:</span> [<span class="org-highlight-numbers-number">3x6</span>] unit vector of each leg in the fixed frame
% M_pos_base<span class="org-type">:</span> [<span class="org-highlight-numbers-number">3x6</span>] vector of the leg connection at the top platform location in the fixed frame
J = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>;
J<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = RM<span class="org-type">'</span>;
J<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = cross<span class="org-rainbow-delimiters-depth-1">(</span>M_pos_base, RM<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org2e21283" class="outline-3">
<h3 id="org2e21283"><span class="section-number-3">8.13</span> Sample</h3>
<div class="outline-text-3" id="text-8-13">
<p>
<a id="org0a4b50f"></a>
</p>
<p>
This Matlab function is accessible <a href="src/initializeSample.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">sample</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeSample</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
sample = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'radius'</span>, <span class="org-highlight-numbers-number">100</span>, ...
<span class="org-string">'height'</span>, <span class="org-highlight-numbers-number">300</span>, ...
<span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span>, ...
<span class="org-string">'offset'</span>, <span class="org-highlight-numbers-number">0</span>, ...
<span class="org-string">'color'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">45</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">45</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">45</span><span class="org-rainbow-delimiters-depth-2">]</span> ...
<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
sample.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
sample.k.x = <span class="org-highlight-numbers-number">1e8</span>;
sample.c.x = sqrt<span class="org-rainbow-delimiters-depth-1">(</span>sample.k.x<span class="org-type">*</span>sample.mass<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">10</span>;
sample.k.y = <span class="org-highlight-numbers-number">1e8</span>;
sample.c.y = sqrt<span class="org-rainbow-delimiters-depth-1">(</span>sample.k.y<span class="org-type">*</span>sample.mass<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">10</span>;
sample.k.z = <span class="org-highlight-numbers-number">1e8</span>;
sample.c.z = sqrt<span class="org-rainbow-delimiters-depth-1">(</span>sample.k.y<span class="org-type">*</span>sample.mass<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">10</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'sample'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-29 mar. 10:52</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>