1913 lines
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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">Active Damping applied on the Simscape Model</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="#org97abc59">1. Undamped System</a>
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<ul>
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<li><a href="#org7d459a2">1.1. Identification of the dynamics for Active Damping</a>
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<ul>
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<li><a href="#org6a76f18">1.1.1. Initialize the Simulation</a></li>
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<li><a href="#orgceae930">1.1.2. Identification</a></li>
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<li><a href="#org50cac8d">1.1.3. Obtained Plants for Active Damping</a></li>
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</ul>
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</li>
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<li><a href="#orgb30c7fd">1.2. Tomography Experiment</a>
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<ul>
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<li><a href="#orgf71542f">1.2.1. Simulation</a></li>
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<li><a href="#org15546d3">1.2.2. Results</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#org097f664">2. Variability of the system dynamics for Active Damping</a>
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<ul>
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<li><a href="#org39af6f9">2.1. Variation of the Sample Mass</a></li>
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<li><a href="#org229c4c5">2.2. Variation of the Spindle Angle</a></li>
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<li><a href="#org352fc0c">2.3. Variation of the Spindle Rotation Speed</a>
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<ul>
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<li><a href="#orgc6e2b26">2.3.1. Dynamics of the Active Damping plants</a></li>
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<li><a href="#org8aa8182">2.3.2. Variation of the poles and zeros with the Spindle rotation frequency</a></li>
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</ul>
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</li>
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<li><a href="#org0153a58">2.4. Variation of the Tilt Angle</a></li>
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<li><a href="#org4e27559">2.5. Scans of the Translation Stage</a></li>
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<li><a href="#orgb3ee7e4">2.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgf08b709">3. Integral Force Feedback</a>
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<ul>
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<li><a href="#org87395b8">3.1. Control Design</a>
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<ul>
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<li><a href="#org77e4473">3.1.1. Plant</a></li>
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<li><a href="#org1c94029">3.1.2. Control Design</a></li>
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<li><a href="#orga4ebb1c">3.1.3. Diagonal Controller</a></li>
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<li><a href="#orgad90da1">3.1.4. IFF with High Pass Filter</a></li>
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</ul>
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</li>
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<li><a href="#org98b7048">3.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org43bf533">3.2.1. Simulation with IFF Controller</a></li>
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<li><a href="#orge0b6480">3.2.2. Simulation with IFF Controller with added High Pass Filter</a></li>
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<li><a href="#org5f65a86">3.2.3. Compare with Undamped system</a></li>
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</ul>
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</li>
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<li><a href="#org22577cc">3.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org93105e9">4. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#org0181bc6">4.1. Control Design</a>
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<ul>
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<li><a href="#org0baaad9">4.1.1. Plant</a></li>
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<li><a href="#org9d0d598">4.1.2. Control Design</a></li>
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<li><a href="#orgc664cda">4.1.3. Diagonal Controller</a></li>
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</ul>
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</li>
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<li><a href="#org30a47bd">4.2. Tomography Experiment</a>
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<ul>
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<li><a href="#orged4c8ff">4.2.1. Initialize the Simulation</a></li>
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<li><a href="#orgafcf6c3">4.2.2. Simulation</a></li>
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<li><a href="#orgdee965e">4.2.3. Compare with Undamped system</a></li>
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</ul>
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</li>
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<li><a href="#orgc1e250f">4.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orga585807">5. Inertial Control</a>
|
|
<ul>
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|
<li><a href="#orgef3b74a">5.1. Control Design</a>
|
|
<ul>
|
|
<li><a href="#org62bfbc7">5.1.1. Plant</a></li>
|
|
<li><a href="#orgeeec2e5">5.1.2. Control Design</a></li>
|
|
<li><a href="#org240b7fd">5.1.3. Diagonal Controller</a></li>
|
|
</ul>
|
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</li>
|
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<li><a href="#orgea439d2">5.2. Tomography Experiment</a>
|
|
<ul>
|
|
<li><a href="#orgd52597f">5.2.1. Initialize the Simulation</a></li>
|
|
<li><a href="#org2ad0ade">5.2.2. Simulation</a></li>
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<li><a href="#orgfd09099">5.2.3. Compare with Undamped system</a></li>
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</ul>
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</li>
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<li><a href="#org5a63825">5.3. Conclusion</a></li>
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</ul>
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</li>
|
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<li><a href="#org230c9f4">6. Comparison</a>
|
|
<ul>
|
|
<li><a href="#org4baffd6">6.1. Load the plants</a></li>
|
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<li><a href="#orga058c69">6.2. Sensitivity to Disturbance</a></li>
|
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<li><a href="#org7d53c0f">6.3. Damped Plant</a></li>
|
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<li><a href="#org70d41b8">6.4. Tomography Experiment</a>
|
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<ul>
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<li><a href="#org604ad48">6.4.1. Load the Simulation Data</a></li>
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<li><a href="#orgc2877fd">6.4.2. Frequency Domain Analysis</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#orgbe23ba6">7. Useful Functions</a>
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<ul>
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<li><a href="#orge26884f">7.1. prepareTomographyExperiment</a>
|
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<ul>
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<li><a href="#orgbd71c69">Function Description</a></li>
|
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<li><a href="#org79eafae">Optional Parameters</a></li>
|
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<li><a href="#orge7b78fc">Initialize the Simulation</a></li>
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</ul>
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</li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<p>
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First, in section <a href="#orgcd3c1c9">1</a>, we will looked at the undamped system.
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</p>
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<p>
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Then, we will compare three active damping techniques:
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</p>
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<ul class="org-ul">
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<li>In section <a href="#org81e3ebf">3</a>: the integral force feedback is used</li>
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<li>In section <a href="#org5349d23">4</a>: the direct velocity feedback is used</li>
|
|
<li>In section <a href="#org6300794">5</a>: inertial control is used</li>
|
|
</ul>
|
|
|
|
<p>
|
|
For each of the active damping technique, we will:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Look at the damped plant</li>
|
|
<li>Simulate tomography experiments</li>
|
|
<li>Compare the sensitivity from disturbances</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The disturbances are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Ground motion</li>
|
|
<li>Motion errors of all the stages</li>
|
|
</ul>
|
|
|
|
<div id="outline-container-org97abc59" class="outline-2">
|
|
<h2 id="org97abc59"><span class="section-number-2">1</span> Undamped System</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
<a id="orgcd3c1c9"></a>
|
|
</p>
|
|
<p>
|
|
We first look at the undamped system.
|
|
The performance of this undamped system will be compared with the damped system using various techniques.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org7d459a2" class="outline-3">
|
|
<h3 id="org7d459a2"><span class="section-number-3">1.1</span> Identification of the dynamics for Active Damping</h3>
|
|
<div class="outline-text-3" id="text-1-1">
|
|
</div>
|
|
<div id="outline-container-org6a76f18" class="outline-4">
|
|
<h4 id="org6a76f18"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4>
|
|
<div class="outline-text-4" id="text-1-1-1">
|
|
<p>
|
|
We initialize all the stages with the default parameters.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the references to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences();
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And all the controllers are set to 0.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_ine = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_ine'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgceae930" class="outline-4">
|
|
<h4 id="orgceae930"><span class="section-number-4">1.1.2</span> Identification</h4>
|
|
<div class="outline-text-4" id="text-1-1-2">
|
|
<p>
|
|
First, we identify the dynamics of the system using the <code>linearize</code> function.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nass_active_damping'</span>;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
clear io; io_i = 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Dnlm'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Vlm'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G = linearize(mdl, io, 0.5, options);
|
|
G.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
|
|
G.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-string">'Dnlm2'</span>, <span class="org-string">'Dnlm3'</span>, <span class="org-string">'Dnlm4'</span>, <span class="org-string">'Dnlm5'</span>, <span class="org-string">'Dnlm6'</span>, ...
|
|
<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>, ...
|
|
<span class="org-string">'Vnlm1'</span>, <span class="org-string">'Vnlm2'</span>, <span class="org-string">'Vnlm3'</span>, <span class="org-string">'Vnlm4'</span>, <span class="org-string">'Vnlm5'</span>, <span class="org-string">'Vnlm6'</span>};
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We then create transfer functions corresponding to the active damping plants.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">G_iff = minreal(G({<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>}, {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>}));
|
|
G_dvf = minreal(G({<span class="org-string">'Dnlm1'</span>, <span class="org-string">'Dnlm2'</span>, <span class="org-string">'Dnlm3'</span>, <span class="org-string">'Dnlm4'</span>, <span class="org-string">'Dnlm5'</span>, <span class="org-string">'Dnlm6'</span>}, {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>}));
|
|
G_ine = minreal(G({<span class="org-string">'Vnlm1'</span>, <span class="org-string">'Vnlm2'</span>, <span class="org-string">'Vnlm3'</span>, <span class="org-string">'Vnlm4'</span>, <span class="org-string">'Vnlm5'</span>, <span class="org-string">'Vnlm6'</span>}, {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>}));
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save them for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./active_damping/mat/undamped_plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'G_ine'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org50cac8d" class="outline-4">
|
|
<h4 id="org50cac8d"><span class="section-number-4">1.1.3</span> Obtained Plants for Active Damping</h4>
|
|
<div class="outline-text-4" id="text-1-1-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/undamped_plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'G_ine'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgae07e00" class="figure">
|
|
<p><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span><code>G_iff</code>: IFF Plant (<a href="./figs/nass_active_damping_iff_plant.png">png</a>, <a href="./figs/nass_active_damping_iff_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org54ba9ab" class="figure">
|
|
<p><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span><code>G_dvf</code>: Plant for Direct Velocity Feedback (<a href="./figs/nass_active_damping_dvf_plant.png">png</a>, <a href="./figs/nass_active_damping_dvf_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8d04315" class="figure">
|
|
<p><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span><code>G_ine</code>: Inertial Feedback Plant (<a href="./figs/nass_active_damping_inertial_plant.png">png</a>, <a href="./figs/nass_active_damping_inertial_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb30c7fd" class="outline-3">
|
|
<h3 id="orgb30c7fd"><span class="section-number-3">1.2</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
</div>
|
|
<div id="outline-container-orgf71542f" class="outline-4">
|
|
<h4 id="orgf71542f"><span class="section-number-4">1.2.1</span> Simulation</h4>
|
|
<div class="outline-text-4" id="text-1-2-1">
|
|
<p>
|
|
We initialize elements for the tomography experiment.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">prepareTomographyExperiment();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We change the simulation stop time.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'3'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we simulate the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'sim_nass_active_damping'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we save the simulation results for further analysis
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'Eg'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org15546d3" class="outline-4">
|
|
<h4 id="org15546d3"><span class="section-number-4">1.2.2</span> Results</h4>
|
|
<div class="outline-text-4" id="text-1-2-2">
|
|
<p>
|
|
We load the results of tomography experiments.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>);
|
|
t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orga9eaa7e" class="figure">
|
|
<p><img src="figs/nass_act_damp_undamped_sim_tomo_trans.png" alt="nass_act_damp_undamped_sim_tomo_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_undamped_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_undamped_sim_tomo_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orge6dfe03" class="figure">
|
|
<p><img src="figs/nass_act_damp_undamped_sim_tomo_rot.png" alt="nass_act_damp_undamped_sim_tomo_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_undamped_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_undamped_sim_tomo_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org097f664" class="outline-2">
|
|
<h2 id="org097f664"><span class="section-number-2">2</span> Variability of the system dynamics for Active Damping</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="org2ff3e99"></a>
|
|
</p>
|
|
<p>
|
|
The goal of this section is to study how the dynamics of the Active Damping plants are changing with the experimental conditions.
|
|
These experimental conditions are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>The mass of the sample (section <a href="#orgf4c0294">2.1</a>)</li>
|
|
<li>The spindle angle with a null rotating speed (section <a href="#org103d069">2.2</a>)</li>
|
|
<li>The spindle rotation speed (section <a href="#org329a267">2.3</a>)</li>
|
|
<li>The tilt angle (section <a href="#org3f724e4">2.4</a>)</li>
|
|
<li>The scans of the translation stage (section <a href="#org6499091">2.5</a>)</li>
|
|
</ul>
|
|
|
|
<p>
|
|
For the identification of the dynamics, the system is simulation for \(\approx 0.5s\) before the linearization is performed.
|
|
This is done in order for the transient phase to be over.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org39af6f9" class="outline-3">
|
|
<h3 id="org39af6f9"><span class="section-number-3">2.1</span> Variation of the Sample Mass</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
<a id="orgf4c0294"></a>
|
|
</p>
|
|
<p>
|
|
For all the identifications, the disturbances are disabled and no controller are used.
|
|
</p>
|
|
<p>
|
|
We identify the dynamics for the following sample mass.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">masses = [1, 10, 50]; <span class="org-comment">% [kg]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div id="org568a9b1" class="figure">
|
|
<p><img src="figs/act_damp_variability_iff_sample_mass.png" alt="act_damp_variability_iff_sample_mass.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Variability of the IFF plant with the Sample Mass (<a href="./figs/act_damp_variability_iff_sample_mass.png">png</a>, <a href="./figs/act_damp_variability_iff_sample_mass.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgb99e55d" class="figure">
|
|
<p><img src="figs/act_damp_variability_dvf_sample_mass.png" alt="act_damp_variability_dvf_sample_mass.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Variability of the DVF plant with the Sample Mass (<a href="./figs/act_damp_variability_dvf_sample_mass.png">png</a>, <a href="./figs/act_damp_variability_dvf_sample_mass.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org34d5224" class="figure">
|
|
<p><img src="figs/act_damp_variability_ine_sample_mass.png" alt="act_damp_variability_ine_sample_mass.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Variability of the Inertial plant with the Sample Mass (<a href="./figs/act_damp_variability_ine_sample_mass.png">png</a>, <a href="./figs/act_damp_variability_ine_sample_mass.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org229c4c5" class="outline-3">
|
|
<h3 id="org229c4c5"><span class="section-number-3">2.2</span> Variation of the Spindle Angle</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
<a id="org103d069"></a>
|
|
</p>
|
|
<p>
|
|
We identify the dynamics for the following Spindle angles.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Rz_amplitudes = [0, <span class="org-constant">pi</span><span class="org-type">/</span>4, <span class="org-constant">pi</span><span class="org-type">/</span>2, <span class="org-constant">pi</span>]; <span class="org-comment">% [rad]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div id="orgd4b2f43" class="figure">
|
|
<p><img src="figs/act_damp_variability_iff_spindle_angle.png" alt="act_damp_variability_iff_spindle_angle.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Variability of the IFF plant with the Spindle Angle (<a href="./figs/act_damp_variability_iff_spindle_angle.png">png</a>, <a href="./figs/act_damp_variability_iff_spindle_angle.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org83b65c2" class="figure">
|
|
<p><img src="figs/act_damp_variability_dvf_spindle_angle.png" alt="act_damp_variability_dvf_spindle_angle.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Variability of the DVF plant with the Spindle Angle (<a href="./figs/act_damp_variability_dvf_spindle_angle.png">png</a>, <a href="./figs/act_damp_variability_dvf_spindle_angle.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org9d12465" class="figure">
|
|
<p><img src="figs/act_damp_variability_ine_spindle_angle.png" alt="act_damp_variability_ine_spindle_angle.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Variability of the Inertial plant with the Spindle Angle (<a href="./figs/act_damp_variability_ine_spindle_angle.png">png</a>, <a href="./figs/act_damp_variability_ine_spindle_angle.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org352fc0c" class="outline-3">
|
|
<h3 id="org352fc0c"><span class="section-number-3">2.3</span> Variation of the Spindle Rotation Speed</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
<a id="org329a267"></a>
|
|
</p>
|
|
<p>
|
|
We identify the dynamics for the following Spindle rotation periods.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Rz_periods = [60, 6, 2, 1]; <span class="org-comment">% [s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The identification of the dynamics is done at the same Spindle angle position.
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-orgc6e2b26" class="outline-4">
|
|
<h4 id="orgc6e2b26"><span class="section-number-4">2.3.1</span> Dynamics of the Active Damping plants</h4>
|
|
<div class="outline-text-4" id="text-2-3-1">
|
|
|
|
<div id="org3436e1a" class="figure">
|
|
<p><img src="figs/act_damp_variability_iff_spindle_speed.png" alt="act_damp_variability_iff_spindle_speed.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Variability of the IFF plant with the Spindle rotation speed (<a href="./figs/act_damp_variability_iff_spindle_speed.png">png</a>, <a href="./figs/act_damp_variability_iff_spindle_speed.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga1a9583" class="figure">
|
|
<p><img src="figs/act_damp_variability_iff_spindle_speed_zoom.png" alt="act_damp_variability_iff_spindle_speed_zoom.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Variability of the IFF plant with the Spindle rotation speed (<a href="./figs/act_damp_variability_iff_spindle_speed_zoom.png">png</a>, <a href="./figs/act_damp_variability_iff_spindle_speed_zoom.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org06821ac" class="figure">
|
|
<p><img src="figs/act_damp_variability_dvf_spindle_speed.png" alt="act_damp_variability_dvf_spindle_speed.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Variability of the DVF plant with the Spindle rotation speed (<a href="./figs/act_damp_variability_dvf_spindle_speed.png">png</a>, <a href="./figs/act_damp_variability_dvf_spindle_speed.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org0c492f1" class="figure">
|
|
<p><img src="figs/act_damp_variability_dvf_spindle_speed_zoom.png" alt="act_damp_variability_dvf_spindle_speed_zoom.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Variability of the DVF plant with the Spindle rotation speed (<a href="./figs/act_damp_variability_dvf_spindle_speed_zoom.png">png</a>, <a href="./figs/act_damp_variability_dvf_spindle_speed_zoom.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org61474a1" class="figure">
|
|
<p><img src="figs/act_damp_variability_ine_spindle_speed.png" alt="act_damp_variability_ine_spindle_speed.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Variability of the Inertial plant with the Spindle rotation speed (<a href="./figs/act_damp_variability_ine_spindle_speed.png">png</a>, <a href="./figs/act_damp_variability_ine_spindle_speed.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgf54e8be" class="figure">
|
|
<p><img src="figs/act_damp_variability_ine_spindle_speed_zoom.png" alt="act_damp_variability_ine_spindle_speed_zoom.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Variability of the Inertial plant with the Spindle rotation speed (<a href="./figs/act_damp_variability_ine_spindle_speed_zoom.png">png</a>, <a href="./figs/act_damp_variability_ine_spindle_speed_zoom.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8aa8182" class="outline-4">
|
|
<h4 id="org8aa8182"><span class="section-number-4">2.3.2</span> Variation of the poles and zeros with the Spindle rotation frequency</h4>
|
|
<div class="outline-text-4" id="text-2-3-2">
|
|
|
|
<div id="org88e0700" class="figure">
|
|
<p><img src="figs/campbell_diagram_spindle_rotation.png" alt="campbell_diagram_spindle_rotation.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Evolution of the pole with respect to the spindle rotation speed (<a href="./figs/campbell_diagram_spindle_rotation.png">png</a>, <a href="./figs/campbell_diagram_spindle_rotation.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgb70444b" class="figure">
|
|
<p><img src="figs/variation_zeros_active_damping_plants.png" alt="variation_zeros_active_damping_plants.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Evolution of the zero with respect to the spindle rotation speed (<a href="./figs/variation_zeros_active_damping_plants.png">png</a>, <a href="./figs/variation_zeros_active_damping_plants.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0153a58" class="outline-3">
|
|
<h3 id="org0153a58"><span class="section-number-3">2.4</span> Variation of the Tilt Angle</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
<a id="org3f724e4"></a>
|
|
</p>
|
|
<p>
|
|
We identify the dynamics for the following Tilt stage angles.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Ry_amplitudes = [<span class="org-type">-</span>3<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>180, 3<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>180]; <span class="org-comment">% [rad]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div id="org3b6edaa" class="figure">
|
|
<p><img src="figs/act_damp_variability_iff_tilt_angle.png" alt="act_damp_variability_iff_tilt_angle.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Variability of the IFF plant with the Tilt stage Angle (<a href="./figs/act_damp_variability_iff_tilt_angle.png">png</a>, <a href="./figs/act_damp_variability_iff_tilt_angle.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org07994f6" class="figure">
|
|
<p><img src="figs/act_damp_variability_dvf_tilt_angle.png" alt="act_damp_variability_dvf_tilt_angle.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </span>Variability of the DVF plant with the Tilt Angle (<a href="./figs/act_damp_variability_dvf_tilt_angle.png">png</a>, <a href="./figs/act_damp_variability_dvf_tilt_angle.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8d15388" class="figure">
|
|
<p><img src="figs/act_damp_variability_ine_tilt_angle.png" alt="act_damp_variability_ine_tilt_angle.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 22: </span>Variability of the Inertial plant with the Tilt Angle (<a href="./figs/act_damp_variability_ine_tilt_angle.png">png</a>, <a href="./figs/act_damp_variability_ine_tilt_angle.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4e27559" class="outline-3">
|
|
<h3 id="org4e27559"><span class="section-number-3">2.5</span> Scans of the Translation Stage</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<p>
|
|
<a id="org6499091"></a>
|
|
</p>
|
|
<p>
|
|
We want here to verify if the dynamics used for Active damping is varying when using the translation stage for scans.
|
|
</p>
|
|
<p>
|
|
We initialize the translation stage reference to be a sinus with an amplitude of 5mm and a period of 1s (Figure <a href="#orgcd997d7">23</a>).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Dy_type'</span>, <span class="org-string">'sinusoidal'</span>, ...
|
|
<span class="org-string">'Dy_amplitude'</span>, 5e<span class="org-type">-</span>3, ...<span class="org-comment"> % [m]</span>
|
|
<span class="org-string">'Dy_period'</span>, 1); <span class="org-comment">% [s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgcd997d7" class="figure">
|
|
<p><img src="figs/ty_scanning_reference_sinus.png" alt="ty_scanning_reference_sinus.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 23: </span>Reference path for the translation stage (<a href="./figs/ty_scanning_reference_sinus.png">png</a>, <a href="./figs/ty_scanning_reference_sinus.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
We identify the dynamics at different positions (times) when scanning with the Translation stage.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">t_lin = [0.5, 0.75, 1, 1.25];
|
|
</pre>
|
|
</div>
|
|
|
|
<div id="orgd5f0d49" class="figure">
|
|
<p><img src="figs/act_damp_variability_iff_ty_scans.png" alt="act_damp_variability_iff_ty_scans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 24: </span>Variability of the IFF plant at different Ty scan positions (<a href="./figs/act_damp_variability_iff_ty_scans.png">png</a>, <a href="./figs/act_damp_variability_iff_ty_scans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgf38c00d" class="figure">
|
|
<p><img src="figs/act_damp_variability_dvf_ty_scans.png" alt="act_damp_variability_dvf_ty_scans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 25: </span>Variability of the DVF plant at different Ty scan positions (<a href="./figs/act_damp_variability_dvf_ty_scans.png">png</a>, <a href="./figs/act_damp_variability_dvf_ty_scans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga10665d" class="figure">
|
|
<p><img src="figs/act_damp_variability_ine_ty_scans.png" alt="act_damp_variability_ine_ty_scans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 26: </span>Variability of the Inertial plant at different Ty scan positions (<a href="./figs/act_damp_variability_ine_ty_scans.png">png</a>, <a href="./figs/act_damp_variability_ine_ty_scans.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb3ee7e4" class="outline-3">
|
|
<h3 id="orgb3ee7e4"><span class="section-number-3">2.6</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
<table id="orgf5b86c1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 1:</span> Conclusion on the variability of the system dynamics for active damping</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-center" />
|
|
|
|
<col class="org-center" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-center"> </th>
|
|
<th scope="col" class="org-center"><b>Change of Dynamics</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-center"><b>Sample Mass</b></td>
|
|
<td class="org-center">Large</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-center"><b>Spindle Angle</b></td>
|
|
<td class="org-center">Small</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-center"><b>Spindle Rotation Speed</b></td>
|
|
<td class="org-center">First resonance is split in two resonances</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-center"><b>Tilt Angle</b></td>
|
|
<td class="org-center">Negligible</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-center"><b>Translation Stage scans</b></td>
|
|
<td class="org-center">Negligible</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Also, for the Inertial Sensor, a RHP zero may appear when the spindle is rotating fast.
|
|
</p>
|
|
|
|
<div class="important">
|
|
<p>
|
|
When using either a force sensor or a relative motion sensor for active damping, the only “parameter” that induce a large change for the dynamics to be controlled is the <b>sample mass</b>.
|
|
Thus, the developed damping techniques should be robust to variations of the sample mass.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf08b709" class="outline-2">
|
|
<h2 id="orgf08b709"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="org81e3ebf"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/iff.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
<p>
|
|
Integral Force Feedback is applied on the simscape model.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org87395b8" class="outline-3">
|
|
<h3 id="org87395b8"><span class="section-number-3">3.1</span> Control Design</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
</div>
|
|
<div id="outline-container-org77e4473" class="outline-4">
|
|
<h4 id="org77e4473"><span class="section-number-4">3.1.1</span> Plant</h4>
|
|
<div class="outline-text-4" id="text-3-1-1">
|
|
<p>
|
|
Let’s load the previously indentified undamped plant:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/undamped_plants.mat'</span>, <span class="org-string">'G_iff'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Let’s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure <a href="#org3a42d2a">27</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org3a42d2a" class="figure">
|
|
<p><img src="figs/iff_plant.png" alt="iff_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 27: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/iff_plant.png">png</a>, <a href="./figs/iff_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1c94029" class="outline-4">
|
|
<h4 id="org1c94029"><span class="section-number-4">3.1.2</span> Control Design</h4>
|
|
<div class="outline-text-4" id="text-3-1-2">
|
|
<p>
|
|
The controller for each pair of actuator/sensor is:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_iff = 1000<span class="org-type">/</span>s;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The corresponding loop gains are shown in figure <a href="#org0308d43">28</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org0308d43" class="figure">
|
|
<p><img src="figs/iff_open_loop.png" alt="iff_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 28: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/iff_open_loop.png">png</a>, <a href="./figs/iff_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga4ebb1c" class="outline-4">
|
|
<h4 id="orga4ebb1c"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4>
|
|
<div class="outline-text-4" id="text-3-1-3">
|
|
<p>
|
|
We create the diagonal controller and we add a minus sign as we have a positive
|
|
feedback architecture.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>K_iff<span class="org-type">*</span>eye(6);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We save the controller for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./active_damping/mat/K_iff.mat'</span>, <span class="org-string">'K_iff'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgad90da1" class="outline-4">
|
|
<h4 id="orgad90da1"><span class="section-number-4">3.1.4</span> IFF with High Pass Filter</h4>
|
|
<div class="outline-text-4" id="text-3-1-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">w_hpf = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10; <span class="org-comment">% Cut-off frequency for the high pass filter [rad/s]</span>
|
|
|
|
K_iff = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>200<span class="org-type">/</span>s <span class="org-type">*</span> (s<span class="org-type">/</span>w_hpf)<span class="org-type">/</span>(s<span class="org-type">/</span>w_hpf <span class="org-type">+</span> 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The corresponding loop gains are shown in figure <a href="#orgf71e7d4">29</a>.
|
|
</p>
|
|
|
|
<div id="orgf71e7d4" class="figure">
|
|
<p><img src="figs/iff_hpf_open_loop.png" alt="iff_hpf_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 29: </span>Loop Gain for the Integral Force Feedback with an High pass filter (<a href="./figs/iff_hpf_open_loop.png">png</a>, <a href="./figs/iff_hpf_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
We create the diagonal controller and we add a minus sign as we have a positive
|
|
feedback architecture.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>K_iff<span class="org-type">*</span>eye(6);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We save the controller for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./active_damping/mat/K_iff_hpf.mat'</span>, <span class="org-string">'K_iff'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org98b7048" class="outline-3">
|
|
<h3 id="org98b7048"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
</div>
|
|
<div id="outline-container-org43bf533" class="outline-4">
|
|
<h4 id="org43bf533"><span class="section-number-4">3.2.1</span> Simulation with IFF Controller</h4>
|
|
<div class="outline-text-4" id="text-3-2-1">
|
|
<p>
|
|
We initialize elements for the tomography experiment.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">prepareTomographyExperiment();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the IFF controller.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/K_iff.mat'</span>, <span class="org-string">'K_iff'</span>);
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We change the simulation stop time.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'3'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we simulate the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'sim_nass_active_damping'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we save the simulation results for further analysis
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">En_iff = En;
|
|
Eg_iff = Eg;
|
|
save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En_iff'</span>, <span class="org-string">'Eg_iff'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge0b6480" class="outline-4">
|
|
<h4 id="orge0b6480"><span class="section-number-4">3.2.2</span> Simulation with IFF Controller with added High Pass Filter</h4>
|
|
<div class="outline-text-4" id="text-3-2-2">
|
|
<p>
|
|
We initialize elements for the tomography experiment.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">prepareTomographyExperiment();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the IFF controller with the High Pass Filter.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/K_iff_hpf.mat'</span>, <span class="org-string">'K_iff'</span>);
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We change the simulation stop time.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'3'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we simulate the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'sim_nass_active_damping'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we save the simulation results for further analysis
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">En_iff_hpf = En;
|
|
Eg_iff_hpf = Eg;
|
|
save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En_iff_hpf'</span>, <span class="org-string">'Eg_iff_hpf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5f65a86" class="outline-4">
|
|
<h4 id="org5f65a86"><span class="section-number-4">3.2.3</span> Compare with Undamped system</h4>
|
|
<div class="outline-text-4" id="text-3-2-3">
|
|
<p>
|
|
We load the results of tomography experiments.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'En_iff'</span>, <span class="org-string">'En_iff_hpf'</span>);
|
|
t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org623648a" class="figure">
|
|
<p><img src="figs/nass_act_damp_iff_sim_tomo_xy.png" alt="nass_act_damp_iff_sim_tomo_xy.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 30: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_iff_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_xy.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgfa2a7a6" class="figure">
|
|
<p><img src="figs/nass_act_damp_iff_sim_tomo_trans.png" alt="nass_act_damp_iff_sim_tomo_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 31: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_iff_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org016ac9d" class="figure">
|
|
<p><img src="figs/nass_act_damp_iff_sim_tomo_rot.png" alt="nass_act_damp_iff_sim_tomo_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 32: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_iff_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org22577cc" class="outline-3">
|
|
<h3 id="org22577cc"><span class="section-number-3">3.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="important">
|
|
<p>
|
|
Integral Force Feedback:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Robust (guaranteed stability)</li>
|
|
<li>Acceptable Damping</li>
|
|
<li>Increase the sensitivity to disturbances at low frequencies</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org93105e9" class="outline-2">
|
|
<h2 id="org93105e9"><span class="section-number-2">4</span> Direct Velocity Feedback</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org5349d23"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/dvf.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
<p>
|
|
In the Direct Velocity Feedback (DVF), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
|
|
The actuator displacement can be measured with a capacitive sensor for instance.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org0181bc6" class="outline-3">
|
|
<h3 id="org0181bc6"><span class="section-number-3">4.1</span> Control Design</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
</div>
|
|
<div id="outline-container-org0baaad9" class="outline-4">
|
|
<h4 id="org0baaad9"><span class="section-number-4">4.1.1</span> Plant</h4>
|
|
<div class="outline-text-4" id="text-4-1-1">
|
|
<p>
|
|
Let’s load the undamped plant:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/undamped_plants.mat'</span>, <span class="org-string">'G_dvf'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure <a href="#orgb6f6883">33</a>).
|
|
</p>
|
|
|
|
|
|
<div id="orgb6f6883" class="figure">
|
|
<p><img src="figs/dvf_plant.png" alt="dvf_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 33: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/dvf_plant.png">png</a>, <a href="./figs/dvf_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9d0d598" class="outline-4">
|
|
<h4 id="org9d0d598"><span class="section-number-4">4.1.2</span> Control Design</h4>
|
|
<div class="outline-text-4" id="text-4-1-2">
|
|
<p>
|
|
The Direct Velocity Feedback is defined below.
|
|
A Low pass Filter is added to make the controller transfer function proper.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_dvf = s<span class="org-type">*</span>20000<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10000);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained loop gains are shown in figure <a href="#org684052f">34</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org684052f" class="figure">
|
|
<p><img src="figs/dvf_open_loop.png" alt="dvf_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 34: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/dvf_open_loop.png">png</a>, <a href="./figs/dvf_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc664cda" class="outline-4">
|
|
<h4 id="orgc664cda"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4>
|
|
<div class="outline-text-4" id="text-4-1-3">
|
|
<p>
|
|
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_dvf = <span class="org-type">-</span>K_dvf<span class="org-type">*</span>eye(6);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We save the controller for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./active_damping/mat/K_dvf.mat'</span>, <span class="org-string">'K_dvf'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org30a47bd" class="outline-3">
|
|
<h3 id="org30a47bd"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
</div>
|
|
<div id="outline-container-orged4c8ff" class="outline-4">
|
|
<h4 id="orged4c8ff"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4>
|
|
<div class="outline-text-4" id="text-4-2-1">
|
|
<p>
|
|
We initialize elements for the tomography experiment.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">prepareTomographyExperiment();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the DVF controller.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/K_dvf.mat'</span>, <span class="org-string">'K_dvf'</span>);
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgafcf6c3" class="outline-4">
|
|
<h4 id="orgafcf6c3"><span class="section-number-4">4.2.2</span> Simulation</h4>
|
|
<div class="outline-text-4" id="text-4-2-2">
|
|
<p>
|
|
We change the simulation stop time.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'3'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we simulate the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'sim_nass_active_damping'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we save the simulation results for further analysis
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">En_dvf = En;
|
|
Eg_dvf = Eg;
|
|
save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En_dvf'</span>, <span class="org-string">'Eg_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdee965e" class="outline-4">
|
|
<h4 id="orgdee965e"><span class="section-number-4">4.2.3</span> Compare with Undamped system</h4>
|
|
<div class="outline-text-4" id="text-4-2-3">
|
|
<p>
|
|
We load the results of tomography experiments.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'En_dvf'</span>);
|
|
t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org36b30ec" class="figure">
|
|
<p><img src="figs/nass_act_damp_dvf_sim_tomo_xy.png" alt="nass_act_damp_dvf_sim_tomo_xy.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 35: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_dvf_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_xy.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org4df3961" class="figure">
|
|
<p><img src="figs/nass_act_damp_dvf_sim_tomo_trans.png" alt="nass_act_damp_dvf_sim_tomo_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 36: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_dvf_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org259181f" class="figure">
|
|
<p><img src="figs/nass_act_damp_dvf_sim_tomo_rot.png" alt="nass_act_damp_dvf_sim_tomo_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 37: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_dvf_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc1e250f" class="outline-3">
|
|
<h3 id="orgc1e250f"><span class="section-number-3">4.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<div class="important">
|
|
<p>
|
|
Direct Velocity Feedback:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li></li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga585807" class="outline-2">
|
|
<h2 id="orga585807"><span class="section-number-2">5</span> Inertial Control</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org6300794"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/ine.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
<p>
|
|
In Inertial Control, a feedback is applied between the measured <b>absolute</b> motion (velocity or acceleration) of the platform to the actuator force input.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgef3b74a" class="outline-3">
|
|
<h3 id="orgef3b74a"><span class="section-number-3">5.1</span> Control Design</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
</div>
|
|
<div id="outline-container-org62bfbc7" class="outline-4">
|
|
<h4 id="org62bfbc7"><span class="section-number-4">5.1.1</span> Plant</h4>
|
|
<div class="outline-text-4" id="text-5-1-1">
|
|
<p>
|
|
Let’s load the undamped plant:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/undamped_plants.mat'</span>, <span class="org-string">'G_ine'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure <a href="#org4952d1e">38</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org4952d1e" class="figure">
|
|
<p><img src="figs/ine_plant.png" alt="ine_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 38: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/ine_plant.png">png</a>, <a href="./figs/ine_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgeeec2e5" class="outline-4">
|
|
<h4 id="orgeeec2e5"><span class="section-number-4">5.1.2</span> Control Design</h4>
|
|
<div class="outline-text-4" id="text-5-1-2">
|
|
<p>
|
|
The controller is defined below and the obtained loop gain is shown in figure <a href="#org7db3cd8">39</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_ine = 1e4<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org7db3cd8" class="figure">
|
|
<p><img src="figs/ine_open_loop_gain.png" alt="ine_open_loop_gain.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 39: </span>Loop Gain for Inertial Control (<a href="./figs/ine_open_loop_gain.png">png</a>, <a href="./figs/ine_open_loop_gain.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org240b7fd" class="outline-4">
|
|
<h4 id="org240b7fd"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4>
|
|
<div class="outline-text-4" id="text-5-1-3">
|
|
<p>
|
|
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_ine = <span class="org-type">-</span>K_ine<span class="org-type">*</span>eye(6);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We save the controller for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./active_damping/mat/K_ine.mat'</span>, <span class="org-string">'K_ine'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgea439d2" class="outline-3">
|
|
<h3 id="orgea439d2"><span class="section-number-3">5.2</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
</div>
|
|
<div id="outline-container-orgd52597f" class="outline-4">
|
|
<h4 id="orgd52597f"><span class="section-number-4">5.2.1</span> Initialize the Simulation</h4>
|
|
<div class="outline-text-4" id="text-5-2-1">
|
|
<p>
|
|
We initialize elements for the tomography experiment.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">prepareTomographyExperiment();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the Inertial controller.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/K_ine.mat'</span>, <span class="org-string">'K_ine'</span>);
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_ine'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2ad0ade" class="outline-4">
|
|
<h4 id="org2ad0ade"><span class="section-number-4">5.2.2</span> Simulation</h4>
|
|
<div class="outline-text-4" id="text-5-2-2">
|
|
<p>
|
|
We change the simulation stop time.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'3'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we simulate the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'sim_nass_active_damping'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we save the simulation results for further analysis
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">En_ine = En;
|
|
Eg_ine = Eg;
|
|
save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En_ine'</span>, <span class="org-string">'Eg_ine'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfd09099" class="outline-4">
|
|
<h4 id="orgfd09099"><span class="section-number-4">5.2.3</span> Compare with Undamped system</h4>
|
|
<div class="outline-text-4" id="text-5-2-3">
|
|
<p>
|
|
We load the results of tomography experiments.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'En_ine'</span>);
|
|
t = linspace(0, 3, length(En_ine(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org1f18df3" class="figure">
|
|
<p><img src="figs/nass_act_damp_ine_sim_tomo_xy.png" alt="nass_act_damp_ine_sim_tomo_xy.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 40: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_ine_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_xy.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org16410dd" class="figure">
|
|
<p><img src="figs/nass_act_damp_ine_sim_tomo_trans.png" alt="nass_act_damp_ine_sim_tomo_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 41: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_ine_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgb8ccc00" class="figure">
|
|
<p><img src="figs/nass_act_damp_ine_sim_tomo_rot.png" alt="nass_act_damp_ine_sim_tomo_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 42: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_ine_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5a63825" class="outline-3">
|
|
<h3 id="org5a63825"><span class="section-number-3">5.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<div class="important">
|
|
<p>
|
|
Inertial Control:
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org230c9f4" class="outline-2">
|
|
<h2 id="org230c9f4"><span class="section-number-2">6</span> Comparison</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="org36034dc"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org4baffd6" class="outline-3">
|
|
<h3 id="org4baffd6"><span class="section-number-3">6.1</span> Load the plants</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_ine'</span>, <span class="org-string">'G_dvf'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga058c69" class="outline-3">
|
|
<h3 id="orga058c69"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-6-2">
|
|
|
|
<div id="org287ecb6" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ground_motion_z.png" alt="sensitivity_comp_ground_motion_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 43: </span>Sensitivity to ground motion in the Z direction on the Z motion error (<a href="./figs/sensitivity_comp_ground_motion_z.png">png</a>, <a href="./figs/sensitivity_comp_ground_motion_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="org43ef4d9" class="figure">
|
|
<p><img src="figs/sensitivity_comp_direct_forces_z.png" alt="sensitivity_comp_direct_forces_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 44: </span>Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (<a href="./figs/sensitivity_comp_direct_forces_z.png">png</a>, <a href="./figs/sensitivity_comp_direct_forces_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org694aa4d" class="figure">
|
|
<p><img src="figs/sensitivity_comp_spindle_z.png" alt="sensitivity_comp_spindle_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 45: </span>Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (<a href="./figs/sensitivity_comp_spindle_z.png">png</a>, <a href="./figs/sensitivity_comp_spindle_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgefc9b61" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ty_z.png" alt="sensitivity_comp_ty_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 46: </span>Sensitivity to forces applied in the Z direction by the Y translation stage on the Z motion error (<a href="./figs/sensitivity_comp_ty_z.png">png</a>, <a href="./figs/sensitivity_comp_ty_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="org09a62ce" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ty_x.png" alt="sensitivity_comp_ty_x.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 47: </span>Sensitivity to forces applied in the X direction by the Y translation stage on the X motion error (<a href="./figs/sensitivity_comp_ty_x.png">png</a>, <a href="./figs/sensitivity_comp_ty_x.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7d53c0f" class="outline-3">
|
|
<h3 id="org7d53c0f"><span class="section-number-3">6.3</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-6-3">
|
|
|
|
<div id="orgea4578a" class="figure">
|
|
<p><img src="figs/plant_comp_damping_z.png" alt="plant_comp_damping_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 48: </span>Plant for the \(z\) direction for different active damping technique used (<a href="./figs/plant_comp_damping_z.png">png</a>, <a href="./figs/plant_comp_damping_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgcf7fd3d" class="figure">
|
|
<p><img src="figs/plant_comp_damping_x.png" alt="plant_comp_damping_x.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 49: </span>Plant for the \(x\) direction for different active damping technique used (<a href="./figs/plant_comp_damping_x.png">png</a>, <a href="./figs/plant_comp_damping_x.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org0ee741c" class="figure">
|
|
<p><img src="figs/plant_comp_damping_coupling.png" alt="plant_comp_damping_coupling.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 50: </span>Comparison of one off-diagonal plant for different damping technique applied (<a href="./figs/plant_comp_damping_coupling.png">png</a>, <a href="./figs/plant_comp_damping_coupling.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org70d41b8" class="outline-3">
|
|
<h3 id="org70d41b8"><span class="section-number-3">6.4</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-6-4">
|
|
</div>
|
|
<div id="outline-container-org604ad48" class="outline-4">
|
|
<h4 id="org604ad48"><span class="section-number-4">6.4.1</span> Load the Simulation Data</h4>
|
|
<div class="outline-text-4" id="text-6-4-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'En_iff_hpf'</span>, <span class="org-string">'En_dvf'</span>, <span class="org-string">'En_ine'</span>);
|
|
En_iff = En_iff_hpf;
|
|
t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc2877fd" class="outline-4">
|
|
<h4 id="orgc2877fd"><span class="section-number-4">6.4.2</span> Frequency Domain Analysis</h4>
|
|
<div class="outline-text-4" id="text-6-4-2">
|
|
<p>
|
|
Window used for <code>pwelch</code> function.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">n_av = 8;
|
|
han_win = hanning(ceil(length(En(<span class="org-type">:</span>, 1))<span class="org-type">/</span>n_av));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org50bc9af" class="figure">
|
|
<p><img src="figs/act_damp_tomo_exp_comp_psd_trans.png" alt="act_damp_tomo_exp_comp_psd_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 51: </span>PSD of the translation errors in the X direction for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_psd_trans.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_psd_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org333cdfb" class="figure">
|
|
<p><img src="figs/act_damp_tomo_exp_comp_psd_rot.png" alt="act_damp_tomo_exp_comp_psd_rot.png" />
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</p>
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<p><span class="figure-number">Figure 52: </span>PSD of the rotation errors in the X direction for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_psd_rot.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_psd_rot.pdf">pdf</a>)</p>
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</div>
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<div id="org29382b7" class="figure">
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<p><img src="figs/act_damp_tomo_exp_comp_cps_trans.png" alt="act_damp_tomo_exp_comp_cps_trans.png" />
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</p>
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<p><span class="figure-number">Figure 53: </span>CPS of the translation errors in the X direction for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_cps_trans.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_cps_trans.pdf">pdf</a>)</p>
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</div>
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<div id="orgcc5d27e" class="figure">
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<p><img src="figs/act_damp_tomo_exp_comp_cps_rot.png" alt="act_damp_tomo_exp_comp_cps_rot.png" />
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</p>
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<p><span class="figure-number">Figure 54: </span>CPS of the rotation errors in the X direction for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_cps_rot.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_cps_rot.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-orgbe23ba6" class="outline-2">
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<h2 id="orgbe23ba6"><span class="section-number-2">7</span> Useful Functions</h2>
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<div class="outline-text-2" id="text-7">
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</div>
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<div id="outline-container-orge26884f" class="outline-3">
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<h3 id="orge26884f"><span class="section-number-3">7.1</span> prepareTomographyExperiment</h3>
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<div class="outline-text-3" id="text-7-1">
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<p>
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<a id="org2453c47"></a>
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</p>
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<p>
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This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">here</a>.
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</p>
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</div>
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<div id="outline-container-orgbd71c69" class="outline-4">
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<h4 id="orgbd71c69">Function Description</h4>
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<div class="outline-text-4" id="text-orgbd71c69">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>)
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</pre>
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</div>
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</div>
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</div>
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|
|
<div id="outline-container-org79eafae" class="outline-4">
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<h4 id="org79eafae">Optional Parameters</h4>
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<div class="outline-text-4" id="text-org79eafae">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">arguments
|
|
args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
|
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args.sample_mass (1,1) double {mustBeNumeric, mustBePositive} = 50
|
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args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
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<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
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|
</div>
|
|
</div>
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|
|
<div id="outline-container-orge7b78fc" class="outline-4">
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<h4 id="orge7b78fc">Initialize the Simulation</h4>
|
|
<div class="outline-text-4" id="text-orge7b78fc">
|
|
<p>
|
|
We initialize all the stages with the default parameters.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, args.nass_actuator);
|
|
initializeSample(<span class="org-string">'mass'</span>, args.sample_mass);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the references to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, args.Ry_period);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And all the controllers are set to 0.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_ine = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_ine'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(zeros(6));
|
|
save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-02-04 mar. 16:13</p>
|
|
</div>
|
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</body>
|
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</html>
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