2997 lines
134 KiB
HTML
2997 lines
134 KiB
HTML
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="./index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Subsystems used for the Simscape Models</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org6171274">1. Simscape Configuration</a>
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<ul>
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<li><a href="#orgec394e5">Function description</a></li>
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<li><a href="#org84b0cbd">Optional Parameters</a></li>
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<li><a href="#orgf35470d">Structure initialization</a></li>
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<li><a href="#org2939880">Add Type</a></li>
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<li><a href="#org5fe61c6">Save the Structure</a></li>
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</ul>
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</li>
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<li><a href="#orgdda6840">2. Logging Configuration</a>
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<ul>
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<li><a href="#orgf0a9b75">Function description</a></li>
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<li><a href="#org72f1a53">Optional Parameters</a></li>
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<li><a href="#orgc682d61">Structure initialization</a></li>
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<li><a href="#org56212e5">Add Type</a></li>
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<li><a href="#org60d91f1">Sampling Time</a></li>
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<li><a href="#org8542ef9">Save the Structure</a></li>
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</ul>
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</li>
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<li><a href="#org1bf1870">3. Ground</a>
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<ul>
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<li><a href="#orgd8e711f">Simscape Model</a></li>
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<li><a href="#org38347b4">Function description</a></li>
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<li><a href="#org182cb41">Optional Parameters</a></li>
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<li><a href="#org1fca25d">Structure initialization</a></li>
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<li><a href="#org17d2b5b">Add Type</a></li>
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<li><a href="#org4c31ca5">Ground Solid properties</a></li>
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<li><a href="#org542691f">Rotation Point</a></li>
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<li><a href="#orgb4d2559">Save the Structure</a></li>
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</ul>
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</li>
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<li><a href="#orga045749">4. Granite</a>
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<ul>
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<li><a href="#org77d877d">Simscape Model</a></li>
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<li><a href="#org81917d3">Function description</a></li>
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<li><a href="#org483e851">Optional Parameters</a></li>
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<li><a href="#org569af68">Structure initialization</a></li>
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<li><a href="#org413c06d">Add Granite Type</a></li>
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<li><a href="#org63af8a7">Material and Geometry</a></li>
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<li><a href="#org91c540d">Stiffness and Damping properties</a></li>
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<li><a href="#org19876e8">Equilibrium position of the each joint.</a></li>
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<li><a href="#org4222d12">Save the Structure</a></li>
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</ul>
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</li>
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<li><a href="#org6a6adba">5. Translation Stage</a>
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<ul>
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<li><a href="#org669d3ba">Simscape Model</a></li>
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<li><a href="#org4b1d83e">Function description</a></li>
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<li><a href="#orga4cc557">Optional Parameters</a></li>
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<li><a href="#orgaa7c12c">Structure initialization</a></li>
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<li><a href="#org715e876">Add Translation Stage Type</a></li>
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<li><a href="#orgb3a68bf">Material and Geometry</a></li>
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<li><a href="#org4219a53">Stiffness and Damping properties</a></li>
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<li><a href="#orgadbd44c">Equilibrium position of the each joint.</a></li>
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<li><a href="#org1036785">Save the Structure</a></li>
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</ul>
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</li>
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<li><a href="#orgf61cdf3">6. Tilt Stage</a>
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<ul>
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<li><a href="#orgb01cf49">Simscape Model</a></li>
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<li><a href="#org49482e9">Function description</a></li>
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<li><a href="#orgde8a917">Optional Parameters</a></li>
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<li><a href="#orgc0fccee">Structure initialization</a></li>
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<li><a href="#orgea3a7ba">Add Tilt Type</a></li>
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<li><a href="#org54fb975">Material and Geometry</a></li>
|
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<li><a href="#org126e26a">Stiffness and Damping properties</a></li>
|
|
<li><a href="#org6fb4cfd">Equilibrium position of the each joint.</a></li>
|
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<li><a href="#org1ace908">Save the Structure</a></li>
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</ul>
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</li>
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<li><a href="#org3e7754b">7. Spindle</a>
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<ul>
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<li><a href="#orgdd81ea4">Simscape Model</a></li>
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<li><a href="#org1075b26">Function description</a></li>
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|
<li><a href="#org413acbe">Optional Parameters</a></li>
|
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<li><a href="#org3c388fc">Structure initialization</a></li>
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<li><a href="#orge5b17ec">Add Spindle Type</a></li>
|
|
<li><a href="#org6aca787">Material and Geometry</a></li>
|
|
<li><a href="#org58fed09">Stiffness and Damping properties</a></li>
|
|
<li><a href="#orgb89a587">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#orgaf96178">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
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<li><a href="#orgaf1747d">8. Micro Hexapod</a>
|
|
<ul>
|
|
<li><a href="#org345d5ff">Simscape Model</a></li>
|
|
<li><a href="#org65b1d75">Function description</a></li>
|
|
<li><a href="#org5ace3dd">Optional Parameters</a></li>
|
|
<li><a href="#org35fbeff">Function content</a></li>
|
|
<li><a href="#org65a3458">Add Type</a></li>
|
|
<li><a href="#orgac727fa">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orga55d418">9. Center of gravity compensation</a>
|
|
<ul>
|
|
<li><a href="#org672575a">Simscape Model</a></li>
|
|
<li><a href="#orgcc8bfea">Function description</a></li>
|
|
<li><a href="#org50711c3">Optional Parameters</a></li>
|
|
<li><a href="#orge9db3a6">Structure initialization</a></li>
|
|
<li><a href="#orgd3417f4">Add Type</a></li>
|
|
<li><a href="#orgba1c73a">Material and Geometry</a></li>
|
|
<li><a href="#org78460f2">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org7586ab7">10. Mirror</a>
|
|
<ul>
|
|
<li><a href="#orgb5e9e54">Simscape Model</a></li>
|
|
<li><a href="#orgec76fff">Function description</a></li>
|
|
<li><a href="#org8fa0d41">Optional Parameters</a></li>
|
|
<li><a href="#org6cabbe6">Structure initialization</a></li>
|
|
<li><a href="#orgff14824">Add Mirror Type</a></li>
|
|
<li><a href="#orgffcaff5">Material and Geometry</a></li>
|
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<li><a href="#org3a91199">Save the Structure</a></li>
|
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</ul>
|
|
</li>
|
|
<li><a href="#orgd74c144">11. Nano Hexapod</a>
|
|
<ul>
|
|
<li><a href="#orgd5b4fd2">Simscape Model</a></li>
|
|
<li><a href="#org1f5493a">Function description</a></li>
|
|
<li><a href="#orge56e87f">Optional Parameters</a></li>
|
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<li><a href="#orgdee4f19">Function content</a></li>
|
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<li><a href="#org74c9451">Add Type</a></li>
|
|
<li><a href="#org102344d">Save the Structure</a></li>
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</ul>
|
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</li>
|
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<li><a href="#org3d615a1">12. Sample</a>
|
|
<ul>
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<li><a href="#orgef52075">Simscape Model</a></li>
|
|
<li><a href="#orgc7040e2">Function description</a></li>
|
|
<li><a href="#org51cdd59">Optional Parameters</a></li>
|
|
<li><a href="#orge5ac95a">Structure initialization</a></li>
|
|
<li><a href="#org2bb1d24">Add Sample Type</a></li>
|
|
<li><a href="#org022a416">Material and Geometry</a></li>
|
|
<li><a href="#org228453f">Compute the Inertia</a></li>
|
|
<li><a href="#org4343516">Stiffness and Damping properties</a></li>
|
|
<li><a href="#org3ce0863">Equilibrium position of the each joint.</a></li>
|
|
<li><a href="#org6ce7f25">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orge9cbdc9">13. Initialize Controller</a>
|
|
<ul>
|
|
<li><a href="#orgc93deeb">Function Declaration and Documentation</a></li>
|
|
<li><a href="#orgcd36eb6">Optional Parameters</a></li>
|
|
<li><a href="#org31259a8">Structure initialization</a></li>
|
|
<li><a href="#org4207f98">Controller Type</a></li>
|
|
<li><a href="#org75f678f">Save the Structure</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgae5cb57">14. Generate Reference Signals</a>
|
|
<ul>
|
|
<li><a href="#org76f64a8">Function Declaration and Documentation</a></li>
|
|
<li><a href="#orgc92ecb8">Optional Parameters</a></li>
|
|
<li><a href="#orge94c0c2">Initialize Parameters</a></li>
|
|
<li><a href="#orge8640b1">Translation Stage</a></li>
|
|
<li><a href="#org76c7cea">Tilt Stage</a></li>
|
|
<li><a href="#org54ac073">Spindle</a></li>
|
|
<li><a href="#org29dc760">Micro Hexapod</a></li>
|
|
<li><a href="#org04d73dc">Axis Compensation</a></li>
|
|
<li><a href="#org7996dd0">Nano Hexapod</a></li>
|
|
<li><a href="#org4d82b1e">Save</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org544c9dd">15. Initialize Disturbances</a>
|
|
<ul>
|
|
<li><a href="#orge6b4994">Function Declaration and Documentation</a></li>
|
|
<li><a href="#orgb2a6a2a">Optional Parameters</a></li>
|
|
<li><a href="#orgf744aeb">Load Data</a></li>
|
|
<li><a href="#org6c7d666">Parameters</a></li>
|
|
<li><a href="#orgb2108c4">Ground Motion</a></li>
|
|
<li><a href="#orgb70c65e">Translation Stage - X direction</a></li>
|
|
<li><a href="#org070255a">Translation Stage - Z direction</a></li>
|
|
<li><a href="#orgfd5f32b">Spindle - Z direction</a></li>
|
|
<li><a href="#orgba4d479">Direct Forces</a></li>
|
|
<li><a href="#orgf6d2198">Set initial value to zero</a></li>
|
|
<li><a href="#orgb52025f">Save</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgefb8a5e">16. Initialize Position Errors</a>
|
|
<ul>
|
|
<li><a href="#orgcf15571">Function Declaration and Documentation</a></li>
|
|
<li><a href="#orgf25aee2">Optional Parameters</a></li>
|
|
<li><a href="#org75524b1">Structure initialization</a></li>
|
|
<li><a href="#orgc890f7d">Type</a></li>
|
|
<li><a href="#org7d50228">Position Errors</a></li>
|
|
<li><a href="#orgd40e5aa">Save</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgc87e890">17. Z-Axis Geophone</a></li>
|
|
<li><a href="#orgcbddbd1">18. Z-Axis Accelerometer</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<p>
|
|
The full Simscape Model is represented in Figure <a href="#org742ece0">1</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org742ece0" class="figure">
|
|
<p><img src="figs/images/simscape_picture.png" alt="simscape_picture.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Screenshot of the Multi-Body Model representation</p>
|
|
</div>
|
|
|
|
<p>
|
|
This model is divided into multiple subsystems that are independent.
|
|
These subsystems are saved in separate files and imported in the main file using a block balled “subsystem reference”.
|
|
</p>
|
|
|
|
<p>
|
|
Each stage is configured (geometry, mass properties, dynamic properties …) using one function.
|
|
</p>
|
|
|
|
<p>
|
|
These functions are defined below.
|
|
</p>
|
|
|
|
<div id="outline-container-org6171274" class="outline-2">
|
|
<h2 id="org6171274"><span class="section-number-2">1</span> Simscape Configuration</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
<a id="orgb590dcf"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgec394e5" class="outline-3">
|
|
<h3 id="orgec394e5">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgec394e5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeSimscapeConfiguration</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org84b0cbd" class="outline-3">
|
|
<h3 id="org84b0cbd">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org84b0cbd">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.gravity logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf35470d" class="outline-3">
|
|
<h3 id="orgf35470d">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgf35470d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">conf_simscape = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2939880" class="outline-3">
|
|
<h3 id="org2939880">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org2939880">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.gravity
|
|
conf_simscape.type = 1;
|
|
<span class="org-keyword">else</span>
|
|
conf_simscape.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5fe61c6" class="outline-3">
|
|
<h3 id="org5fe61c6">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org5fe61c6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/conf_simscape.mat'</span>, <span class="org-string">'conf_simscape'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdda6840" class="outline-2">
|
|
<h2 id="orgdda6840"><span class="section-number-2">2</span> Logging Configuration</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="org1f9c6ac"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf0a9b75" class="outline-3">
|
|
<h3 id="orgf0a9b75">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgf0a9b75">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeLoggingConfiguration</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org72f1a53" class="outline-3">
|
|
<h3 id="org72f1a53">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org72f1a53">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.log char {mustBeMember(args.log,{<span class="org-string">'none'</span>, <span class="org-string">'all'</span>, <span class="org-string">'forces'</span>})} = <span class="org-string">'none'</span>
|
|
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc682d61" class="outline-3">
|
|
<h3 id="orgc682d61">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgc682d61">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">conf_log = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org56212e5" class="outline-3">
|
|
<h3 id="org56212e5">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org56212e5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.log</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
conf_log.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'all'</span>
|
|
conf_log.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'forces'</span>
|
|
conf_log.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org60d91f1" class="outline-3">
|
|
<h3 id="org60d91f1">Sampling Time</h3>
|
|
<div class="outline-text-3" id="text-org60d91f1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">conf_log.Ts = args.Ts;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8542ef9" class="outline-3">
|
|
<h3 id="org8542ef9">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org8542ef9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/conf_log.mat'</span>, <span class="org-string">'conf_log'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1bf1870" class="outline-2">
|
|
<h2 id="org1bf1870"><span class="section-number-2">3</span> Ground</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="orgbe1f388"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd8e711f" class="outline-3">
|
|
<h3 id="orgd8e711f">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgd8e711f">
|
|
<p>
|
|
The model of the Ground is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>A <b>Cartesian</b> joint that is used to simulation the ground motion</li>
|
|
<li>A solid that represents the ground on which the granite is located</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org31eeec1" class="figure">
|
|
<p><img src="figs/images/simscape_model_ground.png" alt="simscape_model_ground.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Simscape model for the Ground</p>
|
|
</div>
|
|
|
|
|
|
<div id="org342019d" class="figure">
|
|
<p><img src="figs/images/simscape_picture_ground.png" alt="simscape_picture_ground.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Simscape picture for the Ground</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org38347b4" class="outline-3">
|
|
<h3 id="org38347b4">Function description</h3>
|
|
<div class="outline-text-3" id="text-org38347b4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ground]</span> = <span class="org-function-name">initializeGround</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org182cb41" class="outline-3">
|
|
<h3 id="org182cb41">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org182cb41">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>})} = <span class="org-string">'rigid'</span>
|
|
args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) <span class="org-comment">% Rotation point for the ground motion [m]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1fca25d" class="outline-3">
|
|
<h3 id="org1fca25d">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org1fca25d">
|
|
<p>
|
|
First, we initialize the <code>granite</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ground = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org17d2b5b" class="outline-3">
|
|
<h3 id="org17d2b5b">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org17d2b5b">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
ground.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
ground.type = 1;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4c31ca5" class="outline-3">
|
|
<h3 id="org4c31ca5">Ground Solid properties</h3>
|
|
<div class="outline-text-3" id="text-org4c31ca5">
|
|
<p>
|
|
We set the shape and density of the ground solid element.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ground.shape = [2, 2, 0.5]; <span class="org-comment">% [m]</span>
|
|
ground.density = 2800; <span class="org-comment">% [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org542691f" class="outline-3">
|
|
<h3 id="org542691f">Rotation Point</h3>
|
|
<div class="outline-text-3" id="text-org542691f">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ground.rot_point = args.rot_point;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb4d2559" class="outline-3">
|
|
<h3 id="orgb4d2559">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-orgb4d2559">
|
|
<p>
|
|
The <code>ground</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ground'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga045749" class="outline-2">
|
|
<h2 id="orga045749"><span class="section-number-2">4</span> Granite</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org82dc444"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org77d877d" class="outline-3">
|
|
<h3 id="org77d877d">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org77d877d">
|
|
<p>
|
|
The Simscape model of the granite is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>A cartesian joint such that the granite can vibrations along x, y and z axis</li>
|
|
<li>A solid</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The output <code>sample_pos</code> corresponds to the impact point of the X-ray.
|
|
</p>
|
|
|
|
|
|
<div id="org3072cb3" class="figure">
|
|
<p><img src="figs/images/simscape_model_granite.png" alt="simscape_model_granite.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Simscape model for the Granite</p>
|
|
</div>
|
|
|
|
|
|
<div id="org089e7b6" class="figure">
|
|
<p><img src="figs/images/simscape_picture_granite.png" alt="simscape_picture_granite.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Simscape picture for the Granite</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org81917d3" class="outline-3">
|
|
<h3 id="org81917d3">Function description</h3>
|
|
<div class="outline-text-3" id="text-org81917d3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[granite]</span> = <span class="org-function-name">initializeGranite</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org483e851" class="outline-3">
|
|
<h3 id="org483e851">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org483e851">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'none'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 <span class="org-comment">% Density [kg/m3]</span>
|
|
args.x0 (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% Rest position of the Joint in the X direction [m]</span>
|
|
args.y0 (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% Rest position of the Joint in the Y direction [m]</span>
|
|
args.z0 (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% Rest position of the Joint in the Z direction [m]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org569af68" class="outline-3">
|
|
<h3 id="org569af68">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org569af68">
|
|
<p>
|
|
First, we initialize the <code>granite</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org413c06d" class="outline-3">
|
|
<h3 id="org413c06d">Add Granite Type</h3>
|
|
<div class="outline-text-3" id="text-org413c06d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
granite.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
granite.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
granite.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
granite.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
granite.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org63af8a7" class="outline-3">
|
|
<h3 id="org63af8a7">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org63af8a7">
|
|
<p>
|
|
Properties of the Material and link to the geometry of the granite.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite.density = args.density; <span class="org-comment">% [kg/m3]</span>
|
|
granite.STEP = <span class="org-string">'./STEPS/granite/granite.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Z-offset for the initial position of the sample with respect to the granite top surface.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite.sample_pos = 0.8; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org91c540d" class="outline-3">
|
|
<h3 id="org91c540d">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org91c540d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">granite.K = [4e9; 3e8; 8e8]; <span class="org-comment">% [N/m]</span>
|
|
granite.C = [4.0e5; 1.1e5; 9.0e5]; <span class="org-comment">% [N/(m/s)]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org19876e8" class="outline-3">
|
|
<h3 id="org19876e8">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org19876e8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fgm'</span>);
|
|
granite.Deq = <span class="org-type">-</span>Fgm<span class="org-type">'./</span>granite.K;
|
|
<span class="org-keyword">else</span>
|
|
granite.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4222d12" class="outline-3">
|
|
<h3 id="org4222d12">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org4222d12">
|
|
<p>
|
|
The <code>granite</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'granite'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6a6adba" class="outline-2">
|
|
<h2 id="org6a6adba"><span class="section-number-2">5</span> Translation Stage</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="orga6fcdbd"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org669d3ba" class="outline-3">
|
|
<h3 id="org669d3ba">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org669d3ba">
|
|
<p>
|
|
The Simscape model of the Translation stage consist of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One rigid body for the fixed part of the translation stage</li>
|
|
<li>One rigid body for the moving part of the translation stage</li>
|
|
<li>Four 6-DOF Joints that only have some rigidity in the X and Z directions.
|
|
The rigidity in rotation comes from the fact that we use multiple joints that are located at different points</li>
|
|
<li>One 6-DOF joint that represent the Actuator.
|
|
It is used to impose the motion in the Y direction</li>
|
|
<li>One 6-DOF joint to inject force disturbance in the X and Z directions</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgb5e657d" class="figure">
|
|
<p><img src="figs/images/simscape_model_ty.png" alt="simscape_model_ty.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Simscape model for the Translation Stage</p>
|
|
</div>
|
|
|
|
|
|
<div id="org55b7d60" class="figure">
|
|
<p><img src="figs/images/simscape_picture_ty.png" alt="simscape_picture_ty.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Simscape picture for the Translation Stage</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4b1d83e" class="outline-3">
|
|
<h3 id="org4b1d83e">Function description</h3>
|
|
<div class="outline-text-3" id="text-org4b1d83e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ty]</span> = <span class="org-function-name">initializeTy</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga4cc557" class="outline-3">
|
|
<h3 id="orga4cc557">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orga4cc557">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaa7c12c" class="outline-3">
|
|
<h3 id="orgaa7c12c">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgaa7c12c">
|
|
<p>
|
|
First, we initialize the <code>ty</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org715e876" class="outline-3">
|
|
<h3 id="org715e876">Add Translation Stage Type</h3>
|
|
<div class="outline-text-3" id="text-org715e876">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
ty.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
ty.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
ty.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
ty.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
ty.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb3a68bf" class="outline-3">
|
|
<h3 id="orgb3a68bf">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-orgb3a68bf">
|
|
<p>
|
|
Define the density of the materials as well as the geometry (STEP files).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Ty Granite frame</span>
|
|
ty.granite_frame.density = 7800; <span class="org-comment">% [kg/m3] => 43kg</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 = 7800; <span class="org-comment">% [kg/m3] => 76kg</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 = 7800; <span class="org-comment">% [kg/m3]</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 = 7800; <span class="org-comment">% [kg/m3]</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 = 7800; <span class="org-comment">% [kg/m3]</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 = 7800; <span class="org-comment">% [kg/m3]</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 = 7800; <span class="org-comment">% [kg/m3]</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 = 5400; <span class="org-comment">% [kg/m3]</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 = 5400; <span class="org-comment">% [kg/m3]</span>
|
|
ty.rotor.STEP = <span class="org-string">'./STEPS/ty/Ty_Motor_Rotor.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4219a53" class="outline-3">
|
|
<h3 id="org4219a53">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org4219a53">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; <span class="org-comment">% [N/m, N*m/rad]</span>
|
|
ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 2e4]; <span class="org-comment">% [N/(m/s), N*m/(rad/s)]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgadbd44c" class="outline-3">
|
|
<h3 id="orgadbd44c">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-orgadbd44c">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Ftym'</span>);
|
|
ty.Deq = <span class="org-type">-</span>Ftym<span class="org-type">'./</span>ty.K;
|
|
<span class="org-keyword">else</span>
|
|
ty.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1036785" class="outline-3">
|
|
<h3 id="org1036785">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org1036785">
|
|
<p>
|
|
The <code>ty</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ty'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf61cdf3" class="outline-2">
|
|
<h2 id="orgf61cdf3"><span class="section-number-2">6</span> Tilt Stage</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="orga630083"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb01cf49" class="outline-3">
|
|
<h3 id="orgb01cf49">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgb01cf49">
|
|
<p>
|
|
The Simscape model of the Tilt stage is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Two solid bodies for the two part of the stage</li>
|
|
<li><b>Four</b> 6-DOF joints to model the flexibility of the stage.
|
|
These joints are virtually located along the rotation axis and are connecting the two solid bodies.
|
|
These joints have some translation stiffness in the u-v-w directions aligned with the joint.
|
|
The stiffness in rotation between the two solids is due to the fact that the 4 joints are connecting the two solids are different locations</li>
|
|
<li>A Bushing Joint used for the Actuator.
|
|
The Ry motion is imposed by the input.</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgee25bbf" class="figure">
|
|
<p><img src="figs/images/simscape_model_ry.png" alt="simscape_model_ry.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Simscape model for the Tilt Stage</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgcb39e81" class="figure">
|
|
<p><img src="figs/images/simscape_picture_ry.png" alt="simscape_picture_ry.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Simscape picture for the Tilt Stage</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org49482e9" class="outline-3">
|
|
<h3 id="org49482e9">Function description</h3>
|
|
<div class="outline-text-3" id="text-org49482e9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ry]</span> = <span class="org-function-name">initializeRy</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgde8a917" class="outline-3">
|
|
<h3 id="orgde8a917">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgde8a917">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
args.Ry_init (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc0fccee" class="outline-3">
|
|
<h3 id="orgc0fccee">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orgc0fccee">
|
|
<p>
|
|
First, we initialize the <code>ry</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgea3a7ba" class="outline-3">
|
|
<h3 id="orgea3a7ba">Add Tilt Type</h3>
|
|
<div class="outline-text-3" id="text-orgea3a7ba">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
ry.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
ry.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
ry.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
ry.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
ry.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org54fb975" class="outline-3">
|
|
<h3 id="org54fb975">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org54fb975">
|
|
<p>
|
|
Properties of the Material and link to the geometry of the Tilt stage.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Ry - Guide for the tilt stage</span>
|
|
ry.guide.density = 7800; <span class="org-comment">% [kg/m3]</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 = 2400; <span class="org-comment">% [kg/m3]</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 = 3200; <span class="org-comment">% [kg/m3]</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 = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
ry.stage.STEP = <span class="org-string">'./STEPS/ry/Tilt_Stage.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Z-Offset so that the center of rotation matches the sample center;
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry.z_offset = 0.58178; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry.Ry_init = args.Ry_init; <span class="org-comment">% [rad]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org126e26a" class="outline-3">
|
|
<h3 id="org126e26a">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org126e26a">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8];
|
|
ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6fb4cfd" class="outline-3">
|
|
<h3 id="org6fb4cfd">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org6fb4cfd">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fym'</span>);
|
|
ry.Deq = <span class="org-type">-</span>Fym<span class="org-type">'./</span>ry.K;
|
|
<span class="org-keyword">else</span>
|
|
ry.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1ace908" class="outline-3">
|
|
<h3 id="org1ace908">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org1ace908">
|
|
<p>
|
|
The <code>ry</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ry'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3e7754b" class="outline-2">
|
|
<h2 id="org3e7754b"><span class="section-number-2">7</span> Spindle</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<p>
|
|
<a id="org85f7685"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdd81ea4" class="outline-3">
|
|
<h3 id="orgdd81ea4">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgdd81ea4">
|
|
<p>
|
|
The Simscape model of the Spindle is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Two rigid bodies: the stator and the rotor</li>
|
|
<li>A Bushing Joint that is used both as the actuator (the Rz motion is imposed by the input) and as the force perturbation in the Z direction.</li>
|
|
<li>The Bushing joint has some flexibility in the X-Y-Z directions as well as in Rx and Ry rotations</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgf8cd2b8" class="figure">
|
|
<p><img src="figs/images/simscape_model_rz.png" alt="simscape_model_rz.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Simscape model for the Spindle</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8f17d51" class="figure">
|
|
<p><img src="figs/images/simscape_picture_rz.png" alt="simscape_picture_rz.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Simscape picture for the Spindle</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1075b26" class="outline-3">
|
|
<h3 id="org1075b26">Function description</h3>
|
|
<div class="outline-text-3" id="text-org1075b26">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[rz]</span> = <span class="org-function-name">initializeRz</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org413acbe" class="outline-3">
|
|
<h3 id="org413acbe">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org413acbe">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3c388fc" class="outline-3">
|
|
<h3 id="org3c388fc">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org3c388fc">
|
|
<p>
|
|
First, we initialize the <code>rz</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">rz = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge5b17ec" class="outline-3">
|
|
<h3 id="orge5b17ec">Add Spindle Type</h3>
|
|
<div class="outline-text-3" id="text-orge5b17ec">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
rz.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
rz.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
rz.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
rz.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
rz.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6aca787" class="outline-3">
|
|
<h3 id="org6aca787">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org6aca787">
|
|
<p>
|
|
Properties of the Material and link to the geometry of the spindle.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Spindle - Slip Ring</span>
|
|
rz.slipring.density = 7800; <span class="org-comment">% [kg/m3]</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 = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
rz.rotor.STEP = <span class="org-string">'./STEPS/rz/Spindle_Rotor.STEP'</span>;
|
|
|
|
<span class="org-comment">% Spindle - Stator</span>
|
|
rz.stator.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
rz.stator.STEP = <span class="org-string">'./STEPS/rz/Spindle_Stator.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org58fed09" class="outline-3">
|
|
<h3 id="org58fed09">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org58fed09">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7];
|
|
rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb89a587" class="outline-3">
|
|
<h3 id="orgb89a587">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-orgb89a587">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fzm'</span>);
|
|
rz.Deq = <span class="org-type">-</span>Fzm<span class="org-type">'./</span>rz.K;
|
|
<span class="org-keyword">else</span>
|
|
rz.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaf96178" class="outline-3">
|
|
<h3 id="orgaf96178">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-orgaf96178">
|
|
<p>
|
|
The <code>rz</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'rz'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaf1747d" class="outline-2">
|
|
<h2 id="orgaf1747d"><span class="section-number-2">8</span> Micro Hexapod</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<p>
|
|
<a id="org01254ae"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org345d5ff" class="outline-3">
|
|
<h3 id="org345d5ff">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org345d5ff">
|
|
|
|
<div id="org13345ec" class="figure">
|
|
<p><img src="figs/images/simscape_model_micro_hexapod.png" alt="simscape_model_micro_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Simscape model for the Micro-Hexapod</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga63e01a" class="figure">
|
|
<p><img src="figs/images/simscape_picture_micro_hexapod.png" alt="simscape_picture_micro_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Simscape picture for the Micro-Hexapod</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org65b1d75" class="outline-3">
|
|
<h3 id="org65b1d75">Function description</h3>
|
|
<div class="outline-text-3" id="text-org65b1d75">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[micro_hexapod]</span> = <span class="org-function-name">initializeMicroHexapod</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5ace3dd" class="outline-3">
|
|
<h3 id="org5ace3dd">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org5ace3dd">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'modal-analysis'</span>, <span class="org-string">'init'</span>, <span class="org-string">'compliance'</span>})} = <span class="org-string">'flexible'</span>
|
|
<span class="org-comment">% initializeFramesPositions</span>
|
|
args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e<span class="org-type">-</span>3
|
|
args.MO_B (1,1) double {mustBeNumeric} = 270e<span class="org-type">-</span>3
|
|
<span class="org-comment">% generateGeneralConfiguration</span>
|
|
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 50e<span class="org-type">-</span>3
|
|
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 175.5e<span class="org-type">-</span>3
|
|
args.FTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>10, 10, 120<span class="org-type">-</span>10, 120<span class="org-type">+</span>10, 240<span class="org-type">-</span>10, 240<span class="org-type">+</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 45e<span class="org-type">-</span>3
|
|
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 118e<span class="org-type">-</span>3
|
|
args.MTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>60<span class="org-type">+</span>10, 60<span class="org-type">-</span>10, 60<span class="org-type">+</span>10, 180<span class="org-type">-</span>10, 180<span class="org-type">+</span>10, <span class="org-type">-</span>60<span class="org-type">-</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
<span class="org-comment">% initializeStrutDynamics</span>
|
|
args.Ki (6,1) double {mustBeNumeric, mustBeNonnegative} = 2e7<span class="org-type">*</span>ones(6,1)
|
|
args.Ci (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3<span class="org-type">*</span>ones(6,1)
|
|
<span class="org-comment">% initializeCylindricalPlatforms</span>
|
|
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 10
|
|
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 26e<span class="org-type">-</span>3
|
|
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 207.5e<span class="org-type">-</span>3
|
|
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 10
|
|
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 26e<span class="org-type">-</span>3
|
|
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e<span class="org-type">-</span>3
|
|
<span class="org-comment">% initializeCylindricalStruts</span>
|
|
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 25e<span class="org-type">-</span>3
|
|
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 25e<span class="org-type">-</span>3
|
|
<span class="org-comment">% inverseKinematics</span>
|
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
|
<span class="org-comment">% Force that stiffness of each joint should apply at t=0</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org35fbeff" class="outline-3">
|
|
<h3 id="org35fbeff">Function content</h3>
|
|
<div class="outline-text-3" id="text-org35fbeff">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">micro_hexapod = initializeFramesPositions(<span class="org-string">'H'</span>, args.H, <span class="org-string">'MO_B'</span>, args.MO_B);
|
|
micro_hexapod = generateGeneralConfiguration(micro_hexapod, <span class="org-string">'FH'</span>, args.FH, <span class="org-string">'FR'</span>, args.FR, <span class="org-string">'FTh'</span>, args.FTh, <span class="org-string">'MH'</span>, args.MH, <span class="org-string">'MR'</span>, args.MR, <span class="org-string">'MTh'</span>, args.MTh);
|
|
micro_hexapod = computeJointsPose(micro_hexapod);
|
|
micro_hexapod = initializeStrutDynamics(micro_hexapod, <span class="org-string">'Ki'</span>, args.Ki, <span class="org-string">'Ci'</span>, args.Ci);
|
|
micro_hexapod = initializeCylindricalPlatforms(micro_hexapod, <span class="org-string">'Fpm'</span>, args.Fpm, <span class="org-string">'Fph'</span>, args.Fph, <span class="org-string">'Fpr'</span>, args.Fpr, <span class="org-string">'Mpm'</span>, args.Mpm, <span class="org-string">'Mph'</span>, args.Mph, <span class="org-string">'Mpr'</span>, args.Mpr);
|
|
micro_hexapod = initializeCylindricalStruts(micro_hexapod, <span class="org-string">'Fsm'</span>, args.Fsm, <span class="org-string">'Fsh'</span>, args.Fsh, <span class="org-string">'Fsr'</span>, args.Fsr, <span class="org-string">'Msm'</span>, args.Msm, <span class="org-string">'Msh'</span>, args.Msh, <span class="org-string">'Msr'</span>, args.Msr);
|
|
micro_hexapod = computeJacobian(micro_hexapod);
|
|
[Li, dLi] = inverseKinematics(micro_hexapod, <span class="org-string">'AP'</span>, args.AP, <span class="org-string">'ARB'</span>, args.ARB);
|
|
micro_hexapod.Li = Li;
|
|
micro_hexapod.dLi = dLi;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Equilibrium position of the each joint.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fhm'</span>);
|
|
micro_hexapod.dLeq = <span class="org-type">-</span>Fhm<span class="org-type">'./</span>args.Ki;
|
|
<span class="org-keyword">else</span>
|
|
micro_hexapod.dLeq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org65a3458" class="outline-3">
|
|
<h3 id="org65a3458">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org65a3458">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
micro_hexapod.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
micro_hexapod.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
micro_hexapod.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'modal-analysis'</span>
|
|
micro_hexapod.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
micro_hexapod.type = 4;
|
|
<span class="org-keyword">case</span> <span class="org-string">'compliance'</span>
|
|
micro_hexapod.type = 5;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgac727fa" class="outline-3">
|
|
<h3 id="orgac727fa">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-orgac727fa">
|
|
<p>
|
|
The <code>micro_hexapod</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'micro_hexapod'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga55d418" class="outline-2">
|
|
<h2 id="orga55d418"><span class="section-number-2">9</span> Center of gravity compensation</h2>
|
|
<div class="outline-text-2" id="text-9">
|
|
<p>
|
|
<a id="org9989724"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org672575a" class="outline-3">
|
|
<h3 id="org672575a">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-org672575a">
|
|
<p>
|
|
The Simscape model of the Center of gravity compensator is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One main solid that is connected to two other solids (the masses to position of center of mass) through two revolute joints</li>
|
|
<li>The angle of both revolute joints is set by the input</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orge09d585" class="figure">
|
|
<p><img src="figs/images/simscape_model_axisc.png" alt="simscape_model_axisc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Simscape model for the Center of Mass compensation system</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga3d0932" class="figure">
|
|
<p><img src="figs/images/simscape_picture_axisc.png" alt="simscape_picture_axisc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Simscape picture for the Center of Mass compensation system</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcc8bfea" class="outline-3">
|
|
<h3 id="orgcc8bfea">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgcc8bfea">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[axisc]</span> = <span class="org-function-name">initializeAxisc</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org50711c3" class="outline-3">
|
|
<h3 id="org50711c3">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org50711c3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>})} = <span class="org-string">'flexible'</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge9db3a6" class="outline-3">
|
|
<h3 id="orge9db3a6">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orge9db3a6">
|
|
<p>
|
|
First, we initialize the <code>axisc</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">axisc = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd3417f4" class="outline-3">
|
|
<h3 id="orgd3417f4">Add Type</h3>
|
|
<div class="outline-text-3" id="text-orgd3417f4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
axisc.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
axisc.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
axisc.type = 2;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgba1c73a" class="outline-3">
|
|
<h3 id="orgba1c73a">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-orgba1c73a">
|
|
<p>
|
|
Properties of the Material and link to the geometry files.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Structure</span>
|
|
axisc.structure.density = 3400; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.structure.STEP = <span class="org-string">'./STEPS/axisc/axisc_structure.STEP'</span>;
|
|
|
|
<span class="org-comment">% Wheel</span>
|
|
axisc.wheel.density = 2700; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.wheel.STEP = <span class="org-string">'./STEPS/axisc/axisc_wheel.STEP'</span>;
|
|
|
|
<span class="org-comment">% Mass</span>
|
|
axisc.mass.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.mass.STEP = <span class="org-string">'./STEPS/axisc/axisc_mass.STEP'</span>;
|
|
|
|
<span class="org-comment">% Gear</span>
|
|
axisc.gear.density = 7800; <span class="org-comment">% [kg/m3]</span>
|
|
axisc.gear.STEP = <span class="org-string">'./STEPS/axisc/axisc_gear.STEP'</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org78460f2" class="outline-3">
|
|
<h3 id="org78460f2">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org78460f2">
|
|
<p>
|
|
The <code>axisc</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'axisc'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7586ab7" class="outline-2">
|
|
<h2 id="org7586ab7"><span class="section-number-2">10</span> Mirror</h2>
|
|
<div class="outline-text-2" id="text-10">
|
|
<p>
|
|
<a id="org3d670bf"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb5e9e54" class="outline-3">
|
|
<h3 id="orgb5e9e54">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgb5e9e54">
|
|
<p>
|
|
The Simscape Model of the mirror is just a solid body.
|
|
The output <code>mirror_center</code> corresponds to the center of the Sphere and is the point of measurement for the metrology
|
|
</p>
|
|
|
|
|
|
<div id="org281f48a" class="figure">
|
|
<p><img src="figs/images/simscape_model_mirror.png" alt="simscape_model_mirror.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Simscape model for the Mirror</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgf4fa701" class="figure">
|
|
<p><img src="figs/images/simscape_picture_mirror.png" alt="simscape_picture_mirror.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Simscape picture for the Mirror</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgec76fff" class="outline-3">
|
|
<h3 id="orgec76fff">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgec76fff">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeMirror</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8fa0d41" class="outline-3">
|
|
<h3 id="org8fa0d41">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org8fa0d41">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>})} = <span class="org-string">'rigid'</span>
|
|
args.shape char {mustBeMember(args.shape,{<span class="org-string">'spherical'</span>, <span class="org-string">'conical'</span>})} = <span class="org-string">'spherical'</span>
|
|
args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45 <span class="org-comment">% [deg]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6cabbe6" class="outline-3">
|
|
<h3 id="org6cabbe6">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org6cabbe6">
|
|
<p>
|
|
First, we initialize the <code>mirror</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgff14824" class="outline-3">
|
|
<h3 id="orgff14824">Add Mirror Type</h3>
|
|
<div class="outline-text-3" id="text-orgff14824">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
mirror.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
mirror.type = 1;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgffcaff5" class="outline-3">
|
|
<h3 id="orgffcaff5">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-orgffcaff5">
|
|
<p>
|
|
We define the geometrical values.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.h = 0.05; <span class="org-comment">% Height of the mirror [m]</span>
|
|
|
|
mirror.thickness = 0.025; <span class="org-comment">% Thickness of the plate supporting the sample [m]</span>
|
|
|
|
mirror.hole_rad = 0.120; <span class="org-comment">% radius of the hole in the mirror [m]</span>
|
|
|
|
mirror.support_rad = 0.1; <span class="org-comment">% radius of the support plate [m]</span>
|
|
|
|
<span class="org-comment">% point of interest offset in z (above the top surfave) [m]</span>
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
mirror.jacobian = 0.20;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
mirror.jacobian = 0.20 <span class="org-type">-</span> mirror.h;
|
|
<span class="org-keyword">end</span>
|
|
|
|
mirror.rad = 0.180; <span class="org-comment">% radius of the mirror (at the bottom surface) [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.density = 2400; <span class="org-comment">% Density of the material [kg/m3]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.cone_length = mirror.rad<span class="org-type">*</span>tand(args.angle)<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>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Now we define the Shape of the mirror.
|
|
We first start with the internal part.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.shape = [...
|
|
0 mirror.h<span class="org-type">-</span>mirror.thickness
|
|
mirror.hole_rad mirror.h<span class="org-type">-</span>mirror.thickness; ...
|
|
mirror.hole_rad 0; ...
|
|
mirror.rad 0 ...
|
|
];
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then, we define the reflective used part of the mirror.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> strcmp(args.shape, <span class="org-string">'spherical'</span>)
|
|
mirror.sphere_radius = sqrt((mirror.jacobian<span class="org-type">+</span>mirror.h)<span class="org-type">^</span>2<span class="org-type">+</span>mirror.rad<span class="org-type">^</span>2); <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(0, mirror.h, 101)</span>
|
|
mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius<span class="org-type">^</span>2<span class="org-type">-</span>(z<span class="org-type">-</span>mirror.jacobian<span class="org-type">-</span>mirror.h)<span class="org-type">^</span>2) z];
|
|
<span class="org-keyword">end</span>
|
|
<span class="org-keyword">elseif</span> strcmp(args.shape, <span class="org-string">'conical'</span>)
|
|
mirror.shape = [mirror.shape; mirror.rad<span class="org-type">+</span>mirror.h<span class="org-type">/</span>tand(args.angle) mirror.h];
|
|
<span class="org-keyword">else</span>
|
|
error(<span class="org-string">'Shape should be either conical or spherical'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we close the shape.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">mirror.shape = [mirror.shape; 0 mirror.h];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3a91199" class="outline-3">
|
|
<h3 id="org3a91199">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org3a91199">
|
|
<p>
|
|
The <code>mirror</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'mirror'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd74c144" class="outline-2">
|
|
<h2 id="orgd74c144"><span class="section-number-2">11</span> Nano Hexapod</h2>
|
|
<div class="outline-text-2" id="text-11">
|
|
<p>
|
|
<a id="org9a9721e"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd5b4fd2" class="outline-3">
|
|
<h3 id="orgd5b4fd2">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgd5b4fd2">
|
|
|
|
<div id="orga6643fc" class="figure">
|
|
<p><img src="figs/images/simscape_model_nano_hexapod.png" alt="simscape_model_nano_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Simscape model for the Nano Hexapod</p>
|
|
</div>
|
|
|
|
|
|
<div id="org4d9fd08" class="figure">
|
|
<p><img src="figs/images/simscape_picture_nano_hexapod.png" alt="simscape_picture_nano_hexapod.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Simscape picture for the Nano Hexapod</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1f5493a" class="outline-3">
|
|
<h3 id="org1f5493a">Function description</h3>
|
|
<div class="outline-text-3" id="text-org1f5493a">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[nano_hexapod]</span> = <span class="org-function-name">initializeNanoHexapod</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge56e87f" class="outline-3">
|
|
<h3 id="orge56e87f">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orge56e87f">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'none'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
<span class="org-comment">% initializeFramesPositions</span>
|
|
args.H (1,1) double {mustBeNumeric, mustBePositive} = 90e<span class="org-type">-</span>3
|
|
args.MO_B (1,1) double {mustBeNumeric} = 175e<span class="org-type">-</span>3
|
|
<span class="org-comment">% generateGeneralConfiguration</span>
|
|
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e<span class="org-type">-</span>3
|
|
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
args.FTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>10, 10, 120<span class="org-type">-</span>10, 120<span class="org-type">+</span>10, 240<span class="org-type">-</span>10, 240<span class="org-type">+</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e<span class="org-type">-</span>3
|
|
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e<span class="org-type">-</span>3
|
|
args.MTh (6,1) double {mustBeNumeric} = [<span class="org-type">-</span>60<span class="org-type">+</span>10, 60<span class="org-type">-</span>10, 60<span class="org-type">+</span>10, 180<span class="org-type">-</span>10, 180<span class="org-type">+</span>10, <span class="org-type">-</span>60<span class="org-type">-</span>10]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180)
|
|
<span class="org-comment">% initializeStrutDynamics</span>
|
|
args.actuator char {mustBeMember(args.actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
|
|
<span class="org-comment">% initializeCylindricalPlatforms</span>
|
|
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e<span class="org-type">-</span>3
|
|
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e<span class="org-type">-</span>3
|
|
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e<span class="org-type">-</span>3
|
|
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e<span class="org-type">-</span>3
|
|
<span class="org-comment">% initializeCylindricalStruts</span>
|
|
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
|
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e<span class="org-type">-</span>3
|
|
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e<span class="org-type">-</span>3
|
|
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
|
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e<span class="org-type">-</span>3
|
|
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e<span class="org-type">-</span>3
|
|
<span class="org-comment">% inverseKinematics</span>
|
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
|
<span class="org-comment">% Equilibrium position of each leg</span>
|
|
args.dLeq (6,1) double {mustBeNumeric} = zeros(6,1)
|
|
<span class="org-comment">% Force that stiffness of each joint should apply at t=0</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdee4f19" class="outline-3">
|
|
<h3 id="orgdee4f19">Function content</h3>
|
|
<div class="outline-text-3" id="text-orgdee4f19">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">nano_hexapod = initializeFramesPositions(<span class="org-string">'H'</span>, args.H, <span class="org-string">'MO_B'</span>, args.MO_B);
|
|
nano_hexapod = generateGeneralConfiguration(nano_hexapod, <span class="org-string">'FH'</span>, args.FH, <span class="org-string">'FR'</span>, args.FR, <span class="org-string">'FTh'</span>, args.FTh, <span class="org-string">'MH'</span>, args.MH, <span class="org-string">'MR'</span>, args.MR, <span class="org-string">'MTh'</span>, args.MTh);
|
|
nano_hexapod = computeJointsPose(nano_hexapod);
|
|
<span class="org-keyword">if</span> strcmp(args.actuator, <span class="org-string">'piezo'</span>)
|
|
nano_hexapod = initializeStrutDynamics(nano_hexapod, <span class="org-string">'Ki'</span>, 1e7<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
|
<span class="org-keyword">elseif</span> strcmp(args.actuator, <span class="org-string">'lorentz'</span>)
|
|
nano_hexapod = initializeStrutDynamics(nano_hexapod, <span class="org-string">'Ki'</span>, 1e4<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
|
<span class="org-keyword">else</span>
|
|
error(<span class="org-string">'args.actuator should be piezo or lorentz'</span>);
|
|
<span class="org-keyword">end</span>
|
|
nano_hexapod = initializeCylindricalPlatforms(nano_hexapod, <span class="org-string">'Fpm'</span>, args.Fpm, <span class="org-string">'Fph'</span>, args.Fph, <span class="org-string">'Fpr'</span>, args.Fpr, <span class="org-string">'Mpm'</span>, args.Mpm, <span class="org-string">'Mph'</span>, args.Mph, <span class="org-string">'Mpr'</span>, args.Mpr);
|
|
nano_hexapod = initializeCylindricalStruts(nano_hexapod, <span class="org-string">'Fsm'</span>, args.Fsm, <span class="org-string">'Fsh'</span>, args.Fsh, <span class="org-string">'Fsr'</span>, args.Fsr, <span class="org-string">'Msm'</span>, args.Msm, <span class="org-string">'Msh'</span>, args.Msh, <span class="org-string">'Msr'</span>, args.Msr);
|
|
nano_hexapod = computeJacobian(nano_hexapod);
|
|
[Li, dLi] = inverseKinematics(nano_hexapod, <span class="org-string">'AP'</span>, args.AP, <span class="org-string">'ARB'</span>, args.ARB);
|
|
nano_hexapod.Li = Li;
|
|
nano_hexapod.dLi = dLi;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Equilibrium position of the each joint.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">
|
|
<span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fnm'</span>);
|
|
nano_hexapod.dLeq = <span class="org-type">-</span>Fnm<span class="org-type">'./</span>nano_hexapod.Ki;
|
|
<span class="org-keyword">else</span>
|
|
nano_hexapod.dLeq = args.dLeq;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org74c9451" class="outline-3">
|
|
<h3 id="org74c9451">Add Type</h3>
|
|
<div class="outline-text-3" id="text-org74c9451">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
nano_hexapod.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
nano_hexapod.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
nano_hexapod.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
nano_hexapod.type = 4;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org102344d" class="outline-3">
|
|
<h3 id="org102344d">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org102344d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3d615a1" class="outline-2">
|
|
<h2 id="org3d615a1"><span class="section-number-2">12</span> Sample</h2>
|
|
<div class="outline-text-2" id="text-12">
|
|
<p>
|
|
<a id="org9f0d804"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgef52075" class="outline-3">
|
|
<h3 id="orgef52075">Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-orgef52075">
|
|
<p>
|
|
The Simscape model of the sample environment is composed of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>A rigid transform that can be used to translate the sample (position offset)</li>
|
|
<li>A cartesian joint to add some flexibility to the sample environment mount</li>
|
|
<li>A solid that represent the sample</li>
|
|
<li>An input is added to apply some external forces and torques at the center of the sample environment.
|
|
This could be the case for cable forces for instance.</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org4bf20ba" class="figure">
|
|
<p><img src="figs/images/simscape_model_sample.png" alt="simscape_model_sample.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Simscape model for the Sample</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgfaf9137" class="figure">
|
|
<p><img src="figs/images/simscape_picture_sample.png" alt="simscape_picture_sample.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </span>Simscape picture for the Sample</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc7040e2" class="outline-3">
|
|
<h3 id="orgc7040e2">Function description</h3>
|
|
<div class="outline-text-3" id="text-orgc7040e2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[sample]</span> = <span class="org-function-name">initializeSample</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org51cdd59" class="outline-3">
|
|
<h3 id="org51cdd59">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-org51cdd59">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'rigid'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'none'</span>, <span class="org-string">'init'</span>})} = <span class="org-string">'flexible'</span>
|
|
args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 <span class="org-comment">% [m]</span>
|
|
args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 <span class="org-comment">% [m]</span>
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 <span class="org-comment">% [kg]</span>
|
|
args.freq (6,1) double {mustBeNumeric, mustBePositive} = 100<span class="org-type">*</span>ones(6,1) <span class="org-comment">% [Hz]</span>
|
|
args.offset (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
args.Foffset logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge5ac95a" class="outline-3">
|
|
<h3 id="orge5ac95a">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-orge5ac95a">
|
|
<p>
|
|
First, we initialize the <code>sample</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2bb1d24" class="outline-3">
|
|
<h3 id="org2bb1d24">Add Sample Type</h3>
|
|
<div class="outline-text-3" id="text-org2bb1d24">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'none'</span>
|
|
sample.type = 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rigid'</span>
|
|
sample.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'flexible'</span>
|
|
sample.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'init'</span>
|
|
sample.type = 3;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org022a416" class="outline-3">
|
|
<h3 id="org022a416">Material and Geometry</h3>
|
|
<div class="outline-text-3" id="text-org022a416">
|
|
<p>
|
|
We define the geometrical parameters of the sample as well as its mass and position.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.radius = args.radius; <span class="org-comment">% [m]</span>
|
|
sample.height = args.height; <span class="org-comment">% [m]</span>
|
|
sample.mass = args.mass; <span class="org-comment">% [kg]</span>
|
|
sample.offset = args.offset; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org228453f" class="outline-3">
|
|
<h3 id="org228453f">Compute the Inertia</h3>
|
|
<div class="outline-text-3" id="text-org228453f">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.inertia = [1<span class="org-type">/</span>12 <span class="org-type">*</span> sample.mass <span class="org-type">*</span> (3<span class="org-type">*</span>sample.radius<span class="org-type">^</span>2 <span class="org-type">+</span> sample.height<span class="org-type">^</span>2); ...
|
|
1<span class="org-type">/</span>12 <span class="org-type">*</span> sample.mass <span class="org-type">*</span> (3<span class="org-type">*</span>sample.radius<span class="org-type">^</span>2 <span class="org-type">+</span> sample.height<span class="org-type">^</span>2); ...
|
|
1<span class="org-type">/</span>2 <span class="org-type">*</span> sample.mass <span class="org-type">*</span> sample.radius<span class="org-type">^</span>2];
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4343516" class="outline-3">
|
|
<h3 id="org4343516">Stiffness and Damping properties</h3>
|
|
<div class="outline-text-3" id="text-org4343516">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.K = zeros(6, 1);
|
|
sample.C = zeros(6, 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Translation Stiffness and Damping:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.K(1<span class="org-type">:</span>3) = sample.mass <span class="org-type">.*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span> <span class="org-type">*</span> args.freq(1<span class="org-type">:</span>3))<span class="org-type">.^</span>2; <span class="org-comment">% [N/m]</span>
|
|
sample.C(1<span class="org-type">:</span>3) = 0.1 <span class="org-type">*</span> sqrt(sample.K(1<span class="org-type">:</span>3)<span class="org-type">*</span>sample.mass); <span class="org-comment">% [N/(m/s)]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Rotational Stiffness and Damping:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sample.K(4<span class="org-type">:</span>6) = sample.inertia <span class="org-type">.*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span> <span class="org-type">*</span> args.freq(4<span class="org-type">:</span>6))<span class="org-type">.^</span>2; <span class="org-comment">% [N/m]</span>
|
|
sample.C(4<span class="org-type">:</span>6) = 0.1 <span class="org-type">*</span> sqrt(sample.K(4<span class="org-type">:</span>6)<span class="org-type">.*</span>sample.inertia); <span class="org-comment">% [N/(m/s)]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3ce0863" class="outline-3">
|
|
<h3 id="org3ce0863">Equilibrium position of the each joint.</h3>
|
|
<div class="outline-text-3" id="text-org3ce0863">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Foffset <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'none'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'rigid'</span>) <span class="org-type">&&</span> <span class="org-type">~</span>strcmp(args.type, <span class="org-string">'init'</span>)
|
|
load(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fsm'</span>);
|
|
sample.Deq = <span class="org-type">-</span>Fsm<span class="org-type">'./</span>sample.K;
|
|
<span class="org-keyword">else</span>
|
|
sample.Deq = zeros(6,1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6ce7f25" class="outline-3">
|
|
<h3 id="org6ce7f25">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org6ce7f25">
|
|
<p>
|
|
The <code>sample</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'sample'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge9cbdc9" class="outline-2">
|
|
<h2 id="orge9cbdc9"><span class="section-number-2">13</span> Initialize Controller</h2>
|
|
<div class="outline-text-2" id="text-13">
|
|
<p>
|
|
<a id="orgd0062b9"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc93deeb" class="outline-3">
|
|
<h3 id="orgc93deeb">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-orgc93deeb">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeController</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcd36eb6" class="outline-3">
|
|
<h3 id="orgcd36eb6">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgcd36eb6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.type char {mustBeMember(args.type,{<span class="org-string">'open-loop'</span>, <span class="org-string">'iff'</span>, <span class="org-string">'dvf'</span>, <span class="org-string">'hac-dvf'</span>, <span class="org-string">'ref-track-L'</span>, <span class="org-string">'ref-track-iff-L'</span>, <span class="org-string">'cascade-hac-lac'</span>, <span class="org-string">'hac-iff'</span>})} = <span class="org-string">'open-loop'</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org31259a8" class="outline-3">
|
|
<h3 id="org31259a8">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org31259a8">
|
|
<p>
|
|
First, we initialize the <code>controller</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">controller = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4207f98" class="outline-3">
|
|
<h3 id="org4207f98">Controller Type</h3>
|
|
<div class="outline-text-3" id="text-org4207f98">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">switch</span> <span class="org-constant">args.type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'open-loop'</span>
|
|
controller.type = 1;
|
|
<span class="org-keyword">case</span> <span class="org-string">'dvf'</span>
|
|
controller.type = 2;
|
|
<span class="org-keyword">case</span> <span class="org-string">'iff'</span>
|
|
controller.type = 3;
|
|
<span class="org-keyword">case</span> <span class="org-string">'hac-dvf'</span>
|
|
controller.type = 4;
|
|
<span class="org-keyword">case</span> <span class="org-string">'ref-track-L'</span>
|
|
controller.type = 5;
|
|
<span class="org-keyword">case</span> <span class="org-string">'ref-track-iff-L'</span>
|
|
controller.type = 6;
|
|
<span class="org-keyword">case</span> <span class="org-string">'cascade-hac-lac'</span>
|
|
controller.type = 7;
|
|
<span class="org-keyword">case</span> <span class="org-string">'hac-iff'</span>
|
|
controller.type = 8;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org75f678f" class="outline-3">
|
|
<h3 id="org75f678f">Save the Structure</h3>
|
|
<div class="outline-text-3" id="text-org75f678f">
|
|
<p>
|
|
The <code>controller</code> structure is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/controller.mat'</span>, <span class="org-string">'controller'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgae5cb57" class="outline-2">
|
|
<h2 id="orgae5cb57"><span class="section-number-2">14</span> Generate Reference Signals</h2>
|
|
<div class="outline-text-2" id="text-14">
|
|
<p>
|
|
<a id="org5ace526"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org76f64a8" class="outline-3">
|
|
<h3 id="org76f64a8">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-org76f64a8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[ref]</span> = <span class="org-function-name">initializeReferences</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc92ecb8" class="outline-3">
|
|
<h3 id="orgc92ecb8">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgc92ecb8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
<span class="org-comment">% Sampling Frequency [s]</span>
|
|
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3
|
|
<span class="org-comment">% Maximum simulation time [s]</span>
|
|
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
|
|
<span class="org-comment">% Either "constant" / "triangular" / "sinusoidal"</span>
|
|
args.Dy_type char {mustBeMember(args.Dy_type,{<span class="org-string">'constant'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'sinusoidal'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Amplitude of the displacement [m]</span>
|
|
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-comment">% Period of the displacement [s]</span>
|
|
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-comment">% Either "constant" / "triangular" / "sinusoidal"</span>
|
|
args.Ry_type char {mustBeMember(args.Ry_type,{<span class="org-string">'constant'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'sinusoidal'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Amplitude [rad]</span>
|
|
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-comment">% Period of the displacement [s]</span>
|
|
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-comment">% Either "constant" / "rotating"</span>
|
|
args.Rz_type char {mustBeMember(args.Rz_type,{<span class="org-string">'constant'</span>, <span class="org-string">'rotating'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial angle [rad]</span>
|
|
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
|
|
<span class="org-comment">% Period of the rotating [s]</span>
|
|
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-comment">% For now, only constant is implemented</span>
|
|
args.Dh_type char {mustBeMember(args.Dh_type,{<span class="org-string">'constant'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)</span>
|
|
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
|
|
<span class="org-comment">% For now, only constant is implemented</span>
|
|
args.Rm_type char {mustBeMember(args.Rm_type,{<span class="org-string">'constant'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial position of the two masses</span>
|
|
args.Rm_pos (2,1) double {mustBeNumeric} = [0; <span class="org-constant">pi</span>]
|
|
<span class="org-comment">% For now, only constant is implemented</span>
|
|
args.Dn_type char {mustBeMember(args.Dn_type,{<span class="org-string">'constant'</span>})} = <span class="org-string">'constant'</span>
|
|
<span class="org-comment">% Initial position [m,m,m,rad,rad,rad] of the top platform</span>
|
|
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orge94c0c2" class="outline-3">
|
|
<h3 id="orge94c0c2">Initialize Parameters</h3>
|
|
<div class="outline-text-3" id="text-orge94c0c2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Set Sampling Time</span></span>
|
|
Ts = args.Ts;
|
|
Tmax = args.Tmax;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Low Pass Filter to filter out the references</span></span>
|
|
s = zpk(<span class="org-string">'s'</span>);
|
|
w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10;
|
|
xi = 1;
|
|
H_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> 2<span class="org-type">*</span>xi<span class="org-type">/</span>w0<span class="org-type">*</span>s <span class="org-type">+</span> s<span class="org-type">^</span>2<span class="org-type">/</span>w0<span class="org-type">^</span>2);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge8640b1" class="outline-3">
|
|
<h3 id="orge8640b1">Translation Stage</h3>
|
|
<div class="outline-text-3" id="text-orge8640b1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Translation stage - Dy</span></span>
|
|
t = 0<span class="org-type">:</span>Ts<span class="org-type">:</span>Tmax; <span class="org-comment">% Time Vector [s]</span>
|
|
Dy = zeros(length(t), 1);
|
|
Dyd = zeros(length(t), 1);
|
|
Dydd = zeros(length(t), 1);
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Dy_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Dy<span class="org-type">(:) </span>= args.Dy_amplitude;
|
|
Dyd<span class="org-type">(:) </span>= 0;
|
|
Dydd<span class="org-type">(:) </span>= 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
|
|
<span class="org-comment">% This is done to unsure that we start with no displacement</span>
|
|
Dy_raw = args.Dy_amplitude<span class="org-type">*</span>sawtooth(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>t<span class="org-type">/</span>args.Dy_period,1<span class="org-type">/</span>2);
|
|
i0 = find(t<span class="org-type">>=</span>args.Dy_period<span class="org-type">/</span>4,1);
|
|
Dy(1<span class="org-type">:</span>end<span class="org-type">-</span>i0<span class="org-type">+</span>1) = Dy_raw(i0<span class="org-type">:</span>end);
|
|
Dy(end<span class="org-type">-</span>i0<span class="org-type">+</span>2<span class="org-type">:</span>end) = Dy_raw(end); <span class="org-comment">% we fix the last value</span>
|
|
|
|
<span class="org-comment">% The signal is filtered out</span>
|
|
Dy = lsim(H_lpf, Dy, t);
|
|
Dyd = lsim(H_lpf<span class="org-type">*</span>s, Dy, t);
|
|
Dydd = lsim(H_lpf<span class="org-type">*</span>s<span class="org-type">^</span>2, Dy, t);
|
|
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
|
|
Dy<span class="org-type">(:) </span>= args.Dy_amplitude<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>t);
|
|
Dyd = args.Dy_amplitude<span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>cos(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>t);
|
|
Dydd = <span class="org-type">-</span>args.Dy_amplitude<span class="org-type">*</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period)<span class="org-type">^</span>2<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Dy_period<span class="org-type">*</span>t);
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Dy_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Dy = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dy), <span class="org-string">'deriv'</span>, Dyd, <span class="org-string">'dderiv'</span>, Dydd);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org76c7cea" class="outline-3">
|
|
<h3 id="org76c7cea">Tilt Stage</h3>
|
|
<div class="outline-text-3" id="text-org76c7cea">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Tilt Stage - Ry</span></span>
|
|
t = 0<span class="org-type">:</span>Ts<span class="org-type">:</span>Tmax; <span class="org-comment">% Time Vector [s]</span>
|
|
Ry = zeros(length(t), 1);
|
|
Ryd = zeros(length(t), 1);
|
|
Rydd = zeros(length(t), 1);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Ry_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Ry<span class="org-type">(:) </span>= args.Ry_amplitude;
|
|
Ryd<span class="org-type">(:) </span>= 0;
|
|
Rydd<span class="org-type">(:) </span>= 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
|
|
Ry_raw = args.Ry_amplitude<span class="org-type">*</span>sawtooth(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>t<span class="org-type">/</span>args.Ry_period,1<span class="org-type">/</span>2);
|
|
i0 = find(t<span class="org-type">>=</span>args.Ry_period<span class="org-type">/</span>4,1);
|
|
Ry(1<span class="org-type">:</span>end<span class="org-type">-</span>i0<span class="org-type">+</span>1) = Ry_raw(i0<span class="org-type">:</span>end);
|
|
Ry(end<span class="org-type">-</span>i0<span class="org-type">+</span>2<span class="org-type">:</span>end) = Ry_raw(end); <span class="org-comment">% we fix the last value</span>
|
|
|
|
<span class="org-comment">% The signal is filtered out</span>
|
|
Ry = lsim(H_lpf, Ry, t);
|
|
Ryd = lsim(H_lpf<span class="org-type">*</span>s, Ry, t);
|
|
Rydd = lsim(H_lpf<span class="org-type">*</span>s<span class="org-type">^</span>2, Ry, t);
|
|
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
|
|
Ry<span class="org-type">(:) </span>= args.Ry_amplitude<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>t);
|
|
|
|
Ryd = args.Ry_amplitude<span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>cos(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>t);
|
|
Rydd = <span class="org-type">-</span>args.Ry_amplitude<span class="org-type">*</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period)<span class="org-type">^</span>2<span class="org-type">*</span>sin(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Ry_period<span class="org-type">*</span>t);
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Ry_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Ry = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Ry), <span class="org-string">'deriv'</span>, Ryd, <span class="org-string">'dderiv'</span>, Rydd);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org54ac073" class="outline-3">
|
|
<h3 id="org54ac073">Spindle</h3>
|
|
<div class="outline-text-3" id="text-org54ac073">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Spindle - Rz</span></span>
|
|
t = 0<span class="org-type">:</span>Ts<span class="org-type">:</span>Tmax; <span class="org-comment">% Time Vector [s]</span>
|
|
Rz = zeros(length(t), 1);
|
|
Rzd = zeros(length(t), 1);
|
|
Rzdd = zeros(length(t), 1);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Rz_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Rz<span class="org-type">(:) </span>= args.Rz_amplitude;
|
|
Rzd<span class="org-type">(:) </span>= 0;
|
|
Rzdd<span class="org-type">(:) </span>= 0;
|
|
<span class="org-keyword">case</span> <span class="org-string">'rotating'</span>
|
|
Rz<span class="org-type">(:) </span>= 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>args.Rz_period<span class="org-type">*</span>t;
|
|
|
|
<span class="org-comment">% The signal is filtered out</span>
|
|
Rz = lsim(H_lpf, Rz, t);
|
|
Rzd = lsim(H_lpf<span class="org-type">*</span>s, Rz, t);
|
|
Rzdd = lsim(H_lpf<span class="org-type">*</span>s<span class="org-type">^</span>2, Rz, t);
|
|
|
|
<span class="org-comment">% We add the angle offset</span>
|
|
Rz = Rz <span class="org-type">+</span> args.Rz_amplitude;
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Rz_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Rz = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Rz), <span class="org-string">'deriv'</span>, Rzd, <span class="org-string">'dderiv'</span>, Rzdd);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org29dc760" class="outline-3">
|
|
<h3 id="org29dc760">Micro Hexapod</h3>
|
|
<div class="outline-text-3" id="text-org29dc760">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
|
|
t = [0, Ts];
|
|
Dh = zeros(length(t), 6);
|
|
Dhl = zeros(length(t), 6);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Dh_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Dh = [args.Dh_pos, args.Dh_pos];
|
|
|
|
load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'micro_hexapod'</span>);
|
|
|
|
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
|
|
|
|
tx = args.Dh_pos(4);
|
|
ty = args.Dh_pos(5);
|
|
tz = args.Dh_pos(6);
|
|
|
|
ARB = [cos(tz) <span class="org-type">-</span>sin(tz) 0;
|
|
sin(tz) cos(tz) 0;
|
|
0 0 1]<span class="org-type">*</span>...
|
|
[ cos(ty) 0 sin(ty);
|
|
0 1 0;
|
|
<span class="org-type">-</span>sin(ty) 0 cos(ty)]<span class="org-type">*</span>...
|
|
[1 0 0;
|
|
0 cos(tx) <span class="org-type">-</span>sin(tx);
|
|
0 sin(tx) cos(tx)];
|
|
|
|
[<span class="org-type">~</span>, Dhl] = inverseKinematics(micro_hexapod, <span class="org-string">'AP'</span>, AP, <span class="org-string">'ARB'</span>, ARB);
|
|
Dhl = [Dhl, Dhl];
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Dh_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Dh = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dh));
|
|
Dhl = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dhl));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org04d73dc" class="outline-3">
|
|
<h3 id="org04d73dc">Axis Compensation</h3>
|
|
<div class="outline-text-3" id="text-org04d73dc">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Axis Compensation - Rm</span></span>
|
|
t = [0, Ts];
|
|
|
|
Rm = [args.Rm_pos, args.Rm_pos];
|
|
Rm = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Rm));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7996dd0" class="outline-3">
|
|
<h3 id="org7996dd0">Nano Hexapod</h3>
|
|
<div class="outline-text-3" id="text-org7996dd0">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Nano-Hexapod</span></span>
|
|
t = [0, Ts];
|
|
Dn = zeros(length(t), 6);
|
|
|
|
<span class="org-keyword">switch</span> <span class="org-constant">args.Dn_type</span>
|
|
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
|
|
Dn = [args.Dn_pos, args.Dn_pos];
|
|
|
|
load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
|
|
|
|
AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)];
|
|
|
|
tx = args.Dn_pos(4);
|
|
ty = args.Dn_pos(5);
|
|
tz = args.Dn_pos(6);
|
|
|
|
ARB = [cos(tz) <span class="org-type">-</span>sin(tz) 0;
|
|
sin(tz) cos(tz) 0;
|
|
0 0 1]<span class="org-type">*</span>...
|
|
[ cos(ty) 0 sin(ty);
|
|
0 1 0;
|
|
<span class="org-type">-</span>sin(ty) 0 cos(ty)]<span class="org-type">*</span>...
|
|
[1 0 0;
|
|
0 cos(tx) <span class="org-type">-</span>sin(tx);
|
|
0 sin(tx) cos(tx)];
|
|
|
|
[<span class="org-type">~</span>, Dnl] = inverseKinematics(nano_hexapod, <span class="org-string">'AP'</span>, AP, <span class="org-string">'ARB'</span>, ARB);
|
|
Dnl = [Dnl, Dnl];
|
|
<span class="org-keyword">otherwise</span>
|
|
warning(<span class="org-string">'Dn_type is not set correctly'</span>);
|
|
<span class="org-keyword">end</span>
|
|
|
|
Dn = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dn));
|
|
Dnl = struct(<span class="org-string">'time'</span>, t, <span class="org-string">'signals'</span>, struct(<span class="org-string">'values'</span>, Dnl));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4d82b1e" class="outline-3">
|
|
<h3 id="org4d82b1e">Save</h3>
|
|
<div class="outline-text-3" id="text-org4d82b1e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
|
|
save(<span class="org-string">'./mat/nass_references.mat'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>, <span class="org-string">'Dh'</span>, <span class="org-string">'Dhl'</span>, <span class="org-string">'Rm'</span>, <span class="org-string">'Dn'</span>, <span class="org-string">'Dnl'</span>, <span class="org-string">'Ts'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org544c9dd" class="outline-2">
|
|
<h2 id="org544c9dd"><span class="section-number-2">15</span> Initialize Disturbances</h2>
|
|
<div class="outline-text-2" id="text-15">
|
|
<p>
|
|
<a id="org199c5f8"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orge6b4994" class="outline-3">
|
|
<h3 id="orge6b4994">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-orge6b4994">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializeDisturbances</span>(<span class="org-variable-name">args</span>)
|
|
<span class="org-comment">% initializeDisturbances - Initialize the disturbances</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Syntax: [] = initializeDisturbances(args)</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Inputs:</span>
|
|
<span class="org-comment">% - args -</span>
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb2a6a2a" class="outline-3">
|
|
<h3 id="orgb2a6a2a">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgb2a6a2a">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
<span class="org-comment">% Global parameter to enable or disable the disturbances</span>
|
|
args.enable logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Ground Motion - X direction</span>
|
|
args.Dwx logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Ground Motion - Y direction</span>
|
|
args.Dwy logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Ground Motion - Z direction</span>
|
|
args.Dwz logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Translation Stage - X direction</span>
|
|
args.Fty_x logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Translation Stage - Z direction</span>
|
|
args.Fty_z logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-comment">% Spindle - Z direction</span>
|
|
args.Frz_z logical {mustBeNumericOrLogical} = <span class="org-constant">true</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgf744aeb" class="outline-3">
|
|
<h3 id="orgf744aeb">Load Data</h3>
|
|
<div class="outline-text-3" id="text-orgf744aeb">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We remove the first frequency point that usually is very large.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org6c7d666" class="outline-3">
|
|
<h3 id="org6c7d666">Parameters</h3>
|
|
<div class="outline-text-3" id="text-org6c7d666">
|
|
<p>
|
|
We define some parameters that will be used in the algorithm.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Fs = 2<span class="org-type">*</span>dist_f.f(end); <span class="org-comment">% Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]</span>
|
|
N = 2<span class="org-type">*</span>length(dist_f.f); <span class="org-comment">% Number of Samples match the one of the wanted PSD</span>
|
|
T0 = N<span class="org-type">/</span>Fs; <span class="org-comment">% Signal Duration [s]</span>
|
|
df = 1<span class="org-type">/</span>T0; <span class="org-comment">% Frequency resolution of the DFT [Hz]</span>
|
|
<span class="org-comment">% Also equal to (dist_f.f(2)-dist_f.f(1))</span>
|
|
t = linspace(0, T0, N<span class="org-type">+</span>1)<span class="org-type">'</span>; <span class="org-comment">% Time Vector [s]</span>
|
|
Ts = 1<span class="org-type">/</span>Fs; <span class="org-comment">% Sampling Time [s]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb2108c4" class="outline-3">
|
|
<h3 id="orgb2108c4">Ground Motion</h3>
|
|
<div class="outline-text-3" id="text-orgb2108c4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">phi = dist_f.psd_gm;
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Dwx <span class="org-type">&&</span> args.enable
|
|
rng<span class="org-type">(111);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
Dwx = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Ground Motion - x direction [m]</span>
|
|
<span class="org-keyword">else</span>
|
|
Dwx = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Dwy <span class="org-type">&&</span> args.enable
|
|
rng<span class="org-type">(112);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
Dwy = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Ground Motion - y direction [m]</span>
|
|
<span class="org-keyword">else</span>
|
|
Dwy = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Dwy <span class="org-type">&&</span> args.enable
|
|
rng<span class="org-type">(113);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
Dwz = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Ground Motion - z direction [m]</span>
|
|
<span class="org-keyword">else</span>
|
|
Dwz = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb70c65e" class="outline-3">
|
|
<h3 id="orgb70c65e">Translation Stage - X direction</h3>
|
|
<div class="outline-text-3" id="text-orgb70c65e">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Fty_x <span class="org-type">&&</span> args.enable
|
|
phi = dist_f.psd_ty; <span class="org-comment">% TODO - we take here the vertical direction which is wrong but approximate</span>
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
rng<span class="org-type">(121);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
u = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Disturbance Force Ty x [N]</span>
|
|
Fty_x = u;
|
|
<span class="org-keyword">else</span>
|
|
Fty_x = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org070255a" class="outline-3">
|
|
<h3 id="org070255a">Translation Stage - Z direction</h3>
|
|
<div class="outline-text-3" id="text-org070255a">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Fty_z <span class="org-type">&&</span> args.enable
|
|
phi = dist_f.psd_ty;
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
rng<span class="org-type">(122);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
u = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Disturbance Force Ty z [N]</span>
|
|
Fty_z = u;
|
|
<span class="org-keyword">else</span>
|
|
Fty_z = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfd5f32b" class="outline-3">
|
|
<h3 id="orgfd5f32b">Spindle - Z direction</h3>
|
|
<div class="outline-text-3" id="text-orgfd5f32b">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.Frz_z <span class="org-type">&&</span> args.enable
|
|
phi = dist_f.psd_rz;
|
|
C = zeros(N<span class="org-type">/</span>2,1);
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:N/2</span>
|
|
C(<span class="org-constant">i</span>) = sqrt(phi(<span class="org-constant">i</span>)<span class="org-type">*</span>df);
|
|
<span class="org-keyword">end</span>
|
|
rng<span class="org-type">(131);</span>
|
|
theta = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>rand(N<span class="org-type">/</span>2,1); <span class="org-comment">% Generate random phase [rad]</span>
|
|
Cx = [0 ; C<span class="org-type">.*</span>complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2<span class="org-type">:</span>end)))];;
|
|
u = N<span class="org-type">/</span>sqrt(2)<span class="org-type">*</span>ifft(Cx); <span class="org-comment">% Disturbance Force Rz z [N]</span>
|
|
Frz_z = u;
|
|
<span class="org-keyword">else</span>
|
|
Frz_z = zeros(length(t), 1);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgba4d479" class="outline-3">
|
|
<h3 id="orgba4d479">Direct Forces</h3>
|
|
<div class="outline-text-3" id="text-orgba4d479">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">u = zeros(length(t), 6);
|
|
Fd = u;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf6d2198" class="outline-3">
|
|
<h3 id="orgf6d2198">Set initial value to zero</h3>
|
|
<div class="outline-text-3" id="text-orgf6d2198">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Dwx = Dwx <span class="org-type">-</span> Dwx(1);
|
|
Dwy = Dwy <span class="org-type">-</span> Dwy(1);
|
|
Dwz = Dwz <span class="org-type">-</span> Dwz(1);
|
|
Fty_x = Fty_x <span class="org-type">-</span> Fty_x(1);
|
|
Fty_z = Fty_z <span class="org-type">-</span> Fty_z(1);
|
|
Frz_z = Frz_z <span class="org-type">-</span> Frz_z(1);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb52025f" class="outline-3">
|
|
<h3 id="orgb52025f">Save</h3>
|
|
<div class="outline-text-3" id="text-orgb52025f">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/nass_disturbances.mat'</span>, <span class="org-string">'Dwx'</span>, <span class="org-string">'Dwy'</span>, <span class="org-string">'Dwz'</span>, <span class="org-string">'Fty_x'</span>, <span class="org-string">'Fty_z'</span>, <span class="org-string">'Frz_z'</span>, <span class="org-string">'Fd'</span>, <span class="org-string">'Ts'</span>, <span class="org-string">'t'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgefb8a5e" class="outline-2">
|
|
<h2 id="orgefb8a5e"><span class="section-number-2">16</span> Initialize Position Errors</h2>
|
|
<div class="outline-text-2" id="text-16">
|
|
<p>
|
|
<a id="orga39c5fc"></a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcf15571" class="outline-3">
|
|
<h3 id="orgcf15571">Function Declaration and Documentation</h3>
|
|
<div class="outline-text-3" id="text-orgcf15571">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">initializePosError</span>(<span class="org-variable-name">args</span>)
|
|
<span class="org-comment">% initializePosError - Initialize the position errors</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Syntax: [] = initializePosError(args)</span>
|
|
<span class="org-comment">%</span>
|
|
<span class="org-comment">% Inputs:</span>
|
|
<span class="org-comment">% - args -</span>
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf25aee2" class="outline-3">
|
|
<h3 id="orgf25aee2">Optional Parameters</h3>
|
|
<div class="outline-text-3" id="text-orgf25aee2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.error logical {mustBeNumericOrLogical} = <span class="org-constant">false</span>
|
|
args.Dy (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
args.Ry (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
args.Rz (1,1) double {mustBeNumeric} = 0 <span class="org-comment">% [m]</span>
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org75524b1" class="outline-3">
|
|
<h3 id="org75524b1">Structure initialization</h3>
|
|
<div class="outline-text-3" id="text-org75524b1">
|
|
<p>
|
|
First, we initialize the <code>pos_error</code> structure.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">pos_error = struct();
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc890f7d" class="outline-3">
|
|
<h3 id="orgc890f7d">Type</h3>
|
|
<div class="outline-text-3" id="text-orgc890f7d">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">if</span> args.error
|
|
pos_error.type = 1;
|
|
<span class="org-keyword">else</span>
|
|
pos_error.type = 0;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7d50228" class="outline-3">
|
|
<h3 id="org7d50228">Position Errors</h3>
|
|
<div class="outline-text-3" id="text-org7d50228">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">pos_error.Dy = args.Dy;
|
|
pos_error.Ry = args.Ry;
|
|
pos_error.Rz = args.Rz;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd40e5aa" class="outline-3">
|
|
<h3 id="orgd40e5aa">Save</h3>
|
|
<div class="outline-text-3" id="text-orgd40e5aa">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/pos_error.mat'</span>, <span class="org-string">'pos_error'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc87e890" class="outline-2">
|
|
<h2 id="orgc87e890"><span class="section-number-2">17</span> Z-Axis Geophone</h2>
|
|
<div class="outline-text-2" id="text-17">
|
|
<p>
|
|
<a id="orgda06de2"></a>
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[geophone]</span> = <span class="org-function-name">initializeZAxisGeophone</span>(<span class="org-variable-name">args</span>)
|
|
arguments
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3 <span class="org-comment">% [kg]</span>
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 1 <span class="org-comment">% [Hz]</span>
|
|
<span class="org-keyword">end</span>
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
|
|
geophone.m = args.mass;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% The Stiffness is set to have the damping resonance frequency</span></span>
|
|
geophone.k = geophone.m <span class="org-type">*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>args.freq)<span class="org-type">^</span>2;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% We set the damping value to have critical damping</span></span>
|
|
geophone.c = 2<span class="org-type">*</span>sqrt(geophone.m <span class="org-type">*</span> geophone.k);
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
|
|
save(<span class="org-string">'./mat/geophone_z_axis.mat'</span>, <span class="org-string">'geophone'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcbddbd1" class="outline-2">
|
|
<h2 id="orgcbddbd1"><span class="section-number-2">18</span> Z-Axis Accelerometer</h2>
|
|
<div class="outline-text-2" id="text-18">
|
|
<p>
|
|
<a id="org071e205"></a>
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[accelerometer]</span> = <span class="org-function-name">initializeZAxisAccelerometer</span>(<span class="org-variable-name">args</span>)
|
|
arguments
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e<span class="org-type">-</span>3 <span class="org-comment">% [kg]</span>
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 5e3 <span class="org-comment">% [Hz]</span>
|
|
<span class="org-keyword">end</span>
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%%</span></span>
|
|
accelerometer.m = args.mass;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% The Stiffness is set to have the damping resonance frequency</span></span>
|
|
accelerometer.k = accelerometer.m <span class="org-type">*</span> (2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>args.freq)<span class="org-type">^</span>2;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% We set the damping value to have critical damping</span></span>
|
|
accelerometer.c = 2<span class="org-type">*</span>sqrt(accelerometer.m <span class="org-type">*</span> accelerometer.k);
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Gain correction of the accelerometer to have a unity gain until the resonance</span></span>
|
|
accelerometer.gain = <span class="org-type">-</span>accelerometer.k<span class="org-type">/</span>accelerometer.m;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Save</span></span>
|
|
save(<span class="org-string">'./mat/accelerometer_z_axis.mat'</span>, <span class="org-string">'accelerometer'</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-04-01 mer. 16:14</p>
|
|
</div>
|
|
</body>
|
|
</html>
|