1762 lines
71 KiB
HTML
1762 lines
71 KiB
HTML
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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="#org6fe0183">1. Undamped System</a>
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<ul>
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<li><a href="#orgc80160b">1.1. Identification of the dynamics for Active Damping</a>
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<ul>
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<li><a href="#org636461d">1.1.1. Initialize the Simulation</a></li>
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<li><a href="#orgea36ee5">1.1.2. Identification</a></li>
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<li><a href="#org2dfc68c">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="#org954f141">1.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org791d4b3">1.2.1. Simulation</a></li>
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<li><a href="#orge0ff76e">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="#org00773fe">2. Integral Force Feedback</a>
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<ul>
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<li><a href="#orgb873e29">2.1. Control Design</a>
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<ul>
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<li><a href="#orgf590470">2.1.1. Plant</a></li>
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<li><a href="#org10ed84e">2.1.2. Control Design</a></li>
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<li><a href="#orgd129b36">2.1.3. Diagonal Controller</a></li>
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<li><a href="#org9b5fe8e">2.1.4. IFF with High Pass Filter</a></li>
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</ul>
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</li>
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<li><a href="#org90345f6">2.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org33daed9">2.2.1. Simulation with IFF Controller</a></li>
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<li><a href="#org94161a4">2.2.2. Simulation with IFF Controller with added High Pass Filter</a></li>
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<li><a href="#org9767f66">2.2.3. Compare with Undamped system</a></li>
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</ul>
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</li>
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<li><a href="#orgd16ca11">2.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgfad54f0">3. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#orgcf2e837">3.1. Control Design</a>
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<ul>
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<li><a href="#org76b1cfe">3.1.1. Plant</a></li>
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<li><a href="#orgd83abae">3.1.2. Control Design</a></li>
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<li><a href="#orge21c84c">3.1.3. Diagonal Controller</a></li>
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</ul>
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</li>
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<li><a href="#orgbe85f18">3.2. Tomography Experiment</a>
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<ul>
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<li><a href="#orgee67221">3.2.1. Initialize the Simulation</a></li>
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<li><a href="#org76ee3e3">3.2.2. Simulation</a></li>
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<li><a href="#org3c3feec">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="#org5035edc">3.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org7454716">4. Inertial Control</a>
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<ul>
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<li><a href="#org8e08998">4.1. Control Design</a>
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<ul>
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<li><a href="#orgf2db463">4.1.1. Plant</a></li>
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<li><a href="#org93cb5d8">4.1.2. Control Design</a></li>
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<li><a href="#orgd002ae1">4.1.3. Diagonal Controller</a></li>
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</ul>
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</li>
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<li><a href="#orgca448ac">4.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org632ee5a">4.2.1. Initialize the Simulation</a></li>
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<li><a href="#org10654aa">4.2.2. Simulation</a></li>
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<li><a href="#org1239f7c">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="#org9674a40">4.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org251a441">5. Variability of the system dynamics for Active Damping</a>
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<ul>
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<li><a href="#orgd178f46">5.1. Variation of the Sample Mass</a></li>
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<li><a href="#org38b8d50">5.2. Variation of the Spindle Angle</a></li>
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<li><a href="#org666ca9f">5.3. Variation of the Spindle Rotation Speed</a></li>
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<li><a href="#org15eb4a9">5.4. Variation of the Tilt Angle</a></li>
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<li><a href="#org8d56329">5.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org4e51ab2">6. Comparison</a>
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<ul>
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<li><a href="#org22beca8">6.1. Load the plants</a></li>
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<li><a href="#orgcaacc66">6.2. Sensitivity to Disturbance</a></li>
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<li><a href="#org1b7fd80">6.3. Damped Plant</a></li>
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<li><a href="#org0f12cf8">6.4. Tomography Experiment</a>
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<ul>
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<li><a href="#orgdb48e43">6.4.1. Load the Simulation Data</a></li>
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<li><a href="#orgfbe1bad">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="#orgb197610">7. Useful Functions</a>
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<ul>
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<li><a href="#org6783ec6">7.1. prepareTomographyExperiment</a>
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<ul>
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<li><a href="#org8c75d0b">Function Description</a></li>
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<li><a href="#org356aa82">Optional Parameters</a></li>
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<li><a href="#org93e527a">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="#org4b60bdf">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>
|
|
<ul class="org-ul">
|
|
<li>In section <a href="#org0dadbd2">2</a>: the integral force feedback is used</li>
|
|
<li>In section <a href="#org47344de">3</a>: the direct velocity feedback is used</li>
|
|
<li>In section <a href="#org6b70b5e">4</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-org6fe0183" class="outline-2">
|
|
<h2 id="org6fe0183"><span class="section-number-2">1</span> Undamped System</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
<a id="org4b60bdf"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/undamped_system.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
<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-orgc80160b" class="outline-3">
|
|
<h3 id="orgc80160b"><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-org636461d" class="outline-4">
|
|
<h4 id="org636461d"><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(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Ry_period'</span>, 1);
|
|
</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-orgea36ee5" class="outline-4">
|
|
<h4 id="orgea36ee5"><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, 1, 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-org2dfc68c" class="outline-4">
|
|
<h4 id="org2dfc68c"><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="org9596ae8" 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="orgf1a57c2" 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="org8b0a38f" 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-org954f141" class="outline-3">
|
|
<h3 id="org954f141"><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-org791d4b3" class="outline-4">
|
|
<h4 id="org791d4b3"><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-orge0ff76e" class="outline-4">
|
|
<h4 id="orge0ff76e"><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="org81f06c2" 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="orgca816f1" 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-org00773fe" class="outline-2">
|
|
<h2 id="org00773fe"><span class="section-number-2">2</span> Integral Force Feedback</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="org0dadbd2"></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-orgb873e29" class="outline-3">
|
|
<h3 id="orgb873e29"><span class="section-number-3">2.1</span> Control Design</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
</div>
|
|
<div id="outline-container-orgf590470" class="outline-4">
|
|
<h4 id="orgf590470"><span class="section-number-4">2.1.1</span> Plant</h4>
|
|
<div class="outline-text-4" id="text-2-1-1">
|
|
<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="#orgdbd61f0">6</a>).
|
|
</p>
|
|
|
|
|
|
<div id="orgdbd61f0" class="figure">
|
|
<p><img src="figs/iff_plant.png" alt="iff_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </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-org10ed84e" class="outline-4">
|
|
<h4 id="org10ed84e"><span class="section-number-4">2.1.2</span> Control Design</h4>
|
|
<div class="outline-text-4" id="text-2-1-2">
|
|
<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="#org438bb64">7</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org438bb64" class="figure">
|
|
<p><img src="figs/iff_open_loop.png" alt="iff_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </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-orgd129b36" class="outline-4">
|
|
<h4 id="orgd129b36"><span class="section-number-4">2.1.3</span> Diagonal Controller</h4>
|
|
<div class="outline-text-4" id="text-2-1-3">
|
|
<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-org9b5fe8e" class="outline-4">
|
|
<h4 id="org9b5fe8e"><span class="section-number-4">2.1.4</span> IFF with High Pass Filter</h4>
|
|
<div class="outline-text-4" id="text-2-1-4">
|
|
<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="#orgf886eba">8</a>.
|
|
</p>
|
|
|
|
<div id="orgf886eba" class="figure">
|
|
<p><img src="figs/iff_hpf_open_loop.png" alt="iff_hpf_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </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-org90345f6" class="outline-3">
|
|
<h3 id="org90345f6"><span class="section-number-3">2.2</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
</div>
|
|
<div id="outline-container-org33daed9" class="outline-4">
|
|
<h4 id="org33daed9"><span class="section-number-4">2.2.1</span> Simulation with IFF Controller</h4>
|
|
<div class="outline-text-4" id="text-2-2-1">
|
|
<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-org94161a4" class="outline-4">
|
|
<h4 id="org94161a4"><span class="section-number-4">2.2.2</span> Simulation with IFF Controller with added High Pass Filter</h4>
|
|
<div class="outline-text-4" id="text-2-2-2">
|
|
<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-org9767f66" class="outline-4">
|
|
<h4 id="org9767f66"><span class="section-number-4">2.2.3</span> Compare with Undamped system</h4>
|
|
<div class="outline-text-4" id="text-2-2-3">
|
|
<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="org1451aab" 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 9: </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="org89b268b" 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 10: </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="org5d3f340" 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 11: </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-orgd16ca11" class="outline-3">
|
|
<h3 id="orgd16ca11"><span class="section-number-3">2.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<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-orgfad54f0" class="outline-2">
|
|
<h2 id="orgfad54f0"><span class="section-number-2">3</span> Direct Velocity Feedback</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="org47344de"></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-orgcf2e837" class="outline-3">
|
|
<h3 id="orgcf2e837"><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-org76b1cfe" class="outline-4">
|
|
<h4 id="org76b1cfe"><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 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="#org1a782ba">12</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org1a782ba" class="figure">
|
|
<p><img src="figs/dvf_plant.png" alt="dvf_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </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-orgd83abae" class="outline-4">
|
|
<h4 id="orgd83abae"><span class="section-number-4">3.1.2</span> Control Design</h4>
|
|
<div class="outline-text-4" id="text-3-1-2">
|
|
<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="#org6d24b9e">13</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org6d24b9e" class="figure">
|
|
<p><img src="figs/dvf_open_loop.png" alt="dvf_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </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-orge21c84c" class="outline-4">
|
|
<h4 id="orge21c84c"><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_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-orgbe85f18" class="outline-3">
|
|
<h3 id="orgbe85f18"><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-orgee67221" class="outline-4">
|
|
<h4 id="orgee67221"><span class="section-number-4">3.2.1</span> Initialize the Simulation</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 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-org76ee3e3" class="outline-4">
|
|
<h4 id="org76ee3e3"><span class="section-number-4">3.2.2</span> Simulation</h4>
|
|
<div class="outline-text-4" id="text-3-2-2">
|
|
<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-org3c3feec" class="outline-4">
|
|
<h4 id="org3c3feec"><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_dvf'</span>);
|
|
t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgc5a4b37" 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 14: </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="orgceb56ef" 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 15: </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="org4f83701" 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 16: </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-org5035edc" class="outline-3">
|
|
<h3 id="org5035edc"><span class="section-number-3">3.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="important">
|
|
<p>
|
|
Direct Velocity Feedback:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li></li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7454716" class="outline-2">
|
|
<h2 id="org7454716"><span class="section-number-2">4</span> Inertial Control</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org6b70b5e"></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-org8e08998" class="outline-3">
|
|
<h3 id="org8e08998"><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-orgf2db463" class="outline-4">
|
|
<h4 id="orgf2db463"><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_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="#org7ac479f">17</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org7ac479f" class="figure">
|
|
<p><img src="figs/ine_plant.png" alt="ine_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </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-org93cb5d8" class="outline-4">
|
|
<h4 id="org93cb5d8"><span class="section-number-4">4.1.2</span> Control Design</h4>
|
|
<div class="outline-text-4" id="text-4-1-2">
|
|
<p>
|
|
The controller is defined below and the obtained loop gain is shown in figure <a href="#orgbc888e6">18</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="orgbc888e6" class="figure">
|
|
<p><img src="figs/ine_open_loop_gain.png" alt="ine_open_loop_gain.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </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-orgd002ae1" class="outline-4">
|
|
<h4 id="orgd002ae1"><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_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-orgca448ac" class="outline-3">
|
|
<h3 id="orgca448ac"><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-org632ee5a" class="outline-4">
|
|
<h4 id="org632ee5a"><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 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-org10654aa" class="outline-4">
|
|
<h4 id="org10654aa"><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_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-org1239f7c" class="outline-4">
|
|
<h4 id="org1239f7c"><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_ine'</span>);
|
|
t = linspace(0, 3, length(En_ine(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orga2e86ca" 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 19: </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="orgc2f3c81" 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 20: </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="org063e44f" 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 21: </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-org9674a40" class="outline-3">
|
|
<h3 id="org9674a40"><span class="section-number-3">4.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<div class="important">
|
|
<p>
|
|
Inertial Control:
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org251a441" class="outline-2">
|
|
<h2 id="org251a441"><span class="section-number-2">5</span> Variability of the system dynamics for Active Damping</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org6b7fd8b"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/act_damp_variability_plant.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd178f46" class="outline-3">
|
|
<h3 id="orgd178f46"><span class="section-number-3">5.1</span> Variation of the Sample Mass</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<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="orga652177" 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 22: </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="org13cc9a9" 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 23: </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="orgeb9d959" 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 24: </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-org38b8d50" class="outline-3">
|
|
<h3 id="org38b8d50"><span class="section-number-3">5.2</span> Variation of the Spindle Angle</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<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="orgff4ce66" 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 25: </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="org42b1d97" 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 26: </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="org62e8794" 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 27: </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-org666ca9f" class="outline-3">
|
|
<h3 id="org666ca9f"><span class="section-number-3">5.3</span> Variation of the Spindle Rotation Speed</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<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, 10, 1]; <span class="org-comment">% [s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div id="orga1f7e51" 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 28: </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="orga7cdd5a" 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 29: </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="org71d0bf3" 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 30: </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="orgb10a098" 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 31: </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="org5e0bd6d" 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 32: </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="org563d245" 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 33: </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-org15eb4a9" class="outline-3">
|
|
<h3 id="org15eb4a9"><span class="section-number-3">5.4</span> Variation of the Tilt Angle</h3>
|
|
<div class="outline-text-3" id="text-5-4">
|
|
<p>
|
|
We identify the dynamics for the following Tilt stage angles.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Ry_amplitudes = [0, 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="orge5256c0" 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 34: </span>Variability of the IFF plant with the Spindle 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="orgba17469" 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 35: </span>Variability of the DVF plant with the Spindle 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="org0980537" 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 36: </span>Variability of the Inertial plant with the Spindle 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-org8d56329" class="outline-3">
|
|
<h3 id="org8d56329"><span class="section-number-3">5.5</span> Conclusion</h3>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4e51ab2" class="outline-2">
|
|
<h2 id="org4e51ab2"><span class="section-number-2">6</span> Comparison</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="orgf33360e"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org22beca8" class="outline-3">
|
|
<h3 id="org22beca8"><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-orgcaacc66" class="outline-3">
|
|
<h3 id="orgcaacc66"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-6-2">
|
|
|
|
<div id="org0c239f2" 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 37: </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="org4f32465" 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 38: </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="orga66cdb4" class="figure">
|
|
<p><img src="figs/sensitivity_comp_spindle_z.png" alt="sensitivity_comp_spindle_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 39: </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="org3b81956" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ty_z.png" alt="sensitivity_comp_ty_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 40: </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="org3efedb8" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ty_x.png" alt="sensitivity_comp_ty_x.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 41: </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-org1b7fd80" class="outline-3">
|
|
<h3 id="org1b7fd80"><span class="section-number-3">6.3</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-6-3">
|
|
|
|
<div id="org60a4299" class="figure">
|
|
<p><img src="figs/plant_comp_damping_z.png" alt="plant_comp_damping_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 42: </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="org98e5aba" class="figure">
|
|
<p><img src="figs/plant_comp_damping_x.png" alt="plant_comp_damping_x.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 43: </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="orgaf2a08d" class="figure">
|
|
<p><img src="figs/plant_comp_damping_coupling.png" alt="plant_comp_damping_coupling.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 44: </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-org0f12cf8" class="outline-3">
|
|
<h3 id="org0f12cf8"><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-orgdb48e43" class="outline-4">
|
|
<h4 id="orgdb48e43"><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-orgfbe1bad" class="outline-4">
|
|
<h4 id="orgfbe1bad"><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="org43af128" 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 45: </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="orgb7ab850" class="figure">
|
|
<p><img src="figs/act_damp_tomo_exp_comp_psd_rot.png" alt="act_damp_tomo_exp_comp_psd_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 46: </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>
|
|
</div>
|
|
|
|
|
|
<div id="org33665ff" class="figure">
|
|
<p><img src="figs/act_damp_tomo_exp_comp_cps_trans.png" alt="act_damp_tomo_exp_comp_cps_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 47: </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>
|
|
</div>
|
|
|
|
|
|
<div id="org69f3425" class="figure">
|
|
<p><img src="figs/act_damp_tomo_exp_comp_cps_rot.png" alt="act_damp_tomo_exp_comp_cps_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 48: </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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb197610" class="outline-2">
|
|
<h2 id="orgb197610"><span class="section-number-2">7</span> Useful Functions</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
</div>
|
|
<div id="outline-container-org6783ec6" class="outline-3">
|
|
<h3 id="org6783ec6"><span class="section-number-3">7.1</span> prepareTomographyExperiment</h3>
|
|
<div class="outline-text-3" id="text-7-1">
|
|
<p>
|
|
<a id="org6e9cabc"></a>
|
|
</p>
|
|
|
|
<p>
|
|
This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">here</a>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org8c75d0b" class="outline-4">
|
|
<h4 id="org8c75d0b">Function Description</h4>
|
|
<div class="outline-text-4" id="text-org8c75d0b">
|
|
<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">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org356aa82" class="outline-4">
|
|
<h4 id="org356aa82">Optional Parameters</h4>
|
|
<div class="outline-text-4" id="text-org356aa82">
|
|
<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>
|
|
args.sample_mass (1,1) double {mustBeNumeric, mustBePositive} = 50
|
|
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org93e527a" class="outline-4">
|
|
<h4 id="org93e527a">Initialize the Simulation</h4>
|
|
<div class="outline-text-4" id="text-org93e527a">
|
|
<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: 2020-01-21 mar. 17:28</p>
|
|
</div>
|
|
</body>
|
|
</html>
|