1607 lines
67 KiB
HTML
1607 lines
67 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="#org21b7020">1. Undamped System</a>
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<ul>
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<li><a href="#org5851b7a">1.1. Identification of the dynamics for Active Damping</a>
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<ul>
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<li><a href="#org74aed57">1.1.1. Initialize the Simulation</a></li>
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<li><a href="#org32dc6b8">1.1.2. Identification</a></li>
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<li><a href="#org467a586">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="#orgcd8379a">1.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org3284883">1.2.1. Simulation</a></li>
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<li><a href="#org700a2b4">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="#org4f2a70b">2. Integral Force Feedback</a>
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<ul>
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<li><a href="#orgf33234d">2.1. Control Design</a>
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<ul>
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<li><a href="#orgd9afa23">2.1.1. Plant</a></li>
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<li><a href="#org43379d2">2.1.2. Control Design</a></li>
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<li><a href="#orgbc20ed4">2.1.3. Diagonal Controller</a></li>
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<li><a href="#org90db654">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="#orgaaa96ff">2.2. Tomography Experiment</a>
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<ul>
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<li><a href="#orgf74a390">2.2.1. Simulation with IFF Controller</a></li>
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<li><a href="#org95de904">2.2.2. Simulation with IFF Controller with added High Pass Filter</a></li>
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<li><a href="#org2b12e17">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="#org0fd785e">2.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org9c38d50">3. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#org03f9812">3.1. Control Design</a>
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<ul>
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<li><a href="#org0426ac1">3.1.1. Plant</a></li>
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<li><a href="#orgbb062d7">3.1.2. Control Design</a></li>
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<li><a href="#org1bdfb4e">3.1.3. Diagonal Controller</a></li>
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</ul>
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</li>
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<li><a href="#org1787430">3.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org8c867a4">3.2.1. Initialize the Simulation</a></li>
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<li><a href="#org8ca9d2f">3.2.2. Simulation</a></li>
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<li><a href="#org85c9eb6">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="#org7ea48ad">3.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgddee501">4. Inertial Control</a>
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<ul>
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<li><a href="#org183d718">4.1. Control Design</a>
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<ul>
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<li><a href="#org3b0c93b">4.1.1. Plant</a></li>
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<li><a href="#org0613819">4.1.2. Control Design</a></li>
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<li><a href="#org7eb6d4a">4.1.3. Diagonal Controller</a></li>
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</ul>
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</li>
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<li><a href="#orgb837286">4.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org088d0cf">4.2.1. Initialize the Simulation</a></li>
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<li><a href="#orge0acdea">4.2.2. Simulation</a></li>
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<li><a href="#orgb9346a9">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="#org971b7df">4.3. Conclusion</a></li>
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</ul>
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</li>
|
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<li><a href="#orgb30a5ab">5. Comparison</a>
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<ul>
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<li><a href="#org056c3e4">5.1. Load the plants</a></li>
|
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<li><a href="#org75158e7">5.2. Sensitivity to Disturbance</a></li>
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<li><a href="#orgca4880d">5.3. Damped Plant</a></li>
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<li><a href="#org4b14fbd">5.4. Tomography Experiment</a>
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<ul>
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<li><a href="#org2213b1c">5.4.1. Frequency Domain</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="#orge02060f">6. Useful Functions</a>
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<ul>
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<li><a href="#org0b9e75d">6.1. prepareTomographyExperiment</a>
|
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<ul>
|
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<li><a href="#org637f0d7">Function Description</a></li>
|
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<li><a href="#orgac8374d">Optional Parameters</a></li>
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<li><a href="#orgb19cd54">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="#orgcb992ae">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="#org0e807ab">2</a>: the integral force feedback is used</li>
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<li>In section <a href="#orgef7f6c4">3</a>: the direct velocity feedback is used</li>
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<li>In section <a href="#org1930728">4</a>: inertial control is used</li>
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</ul>
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<p>
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For each of the active damping technique, we will:
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</p>
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<ul class="org-ul">
|
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<li>Look at the damped plant</li>
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<li>Simulate tomography experiments</li>
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<li>Compare the sensitivity from disturbances</li>
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</ul>
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<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-org21b7020" class="outline-2">
|
|
<h2 id="org21b7020"><span class="section-number-2">1</span> Undamped System</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
<a id="orgcb992ae"></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-org5851b7a" class="outline-3">
|
|
<h3 id="org5851b7a"><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-org74aed57" class="outline-4">
|
|
<h4 id="org74aed57"><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>
|
|
|
|
<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-org32dc6b8" class="outline-4">
|
|
<h4 id="org32dc6b8"><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, 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-org467a586" class="outline-4">
|
|
<h4 id="org467a586"><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 id="org9992a9d" 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="org5adefaa" 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="org071d839" 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>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-orgcd8379a" class="outline-3">
|
|
<h3 id="orgcd8379a"><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-org3284883" class="outline-4">
|
|
<h4 id="org3284883"><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-org700a2b4" class="outline-4">
|
|
<h4 id="org700a2b4"><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="org9eef789" 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="org5e9adc2" 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-org4f2a70b" class="outline-2">
|
|
<h2 id="org4f2a70b"><span class="section-number-2">2</span> Integral Force Feedback</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="org0e807ab"></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-orgf33234d" class="outline-3">
|
|
<h3 id="orgf33234d"><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-orgd9afa23" class="outline-4">
|
|
<h4 id="orgd9afa23"><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="#org2c9189d">6</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org2c9189d" 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-org43379d2" class="outline-4">
|
|
<h4 id="org43379d2"><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="#org85fcfd6">7</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org85fcfd6" 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-orgbc20ed4" class="outline-4">
|
|
<h4 id="orgbc20ed4"><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-org90db654" class="outline-4">
|
|
<h4 id="org90db654"><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>
|
|
w_lpf = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>200; <span class="org-comment">% Cut-off frequency for the low 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) <span class="org-type">*</span> 1<span class="org-type">/</span>(s<span class="org-type">/</span>w_lpf <span class="org-type">+</span> 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The corresponding loop gains are shown in figure <a href="#org7f0bc2b">8</a>.
|
|
</p>
|
|
|
|
<div id="org7f0bc2b" 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-orgaaa96ff" class="outline-3">
|
|
<h3 id="orgaaa96ff"><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-orgf74a390" class="outline-4">
|
|
<h4 id="orgf74a390"><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-org95de904" class="outline-4">
|
|
<h4 id="org95de904"><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-org2b12e17" class="outline-4">
|
|
<h4 id="org2b12e17"><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="orgb5b8a36" 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="org013fbdc" 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="org9a53f55" 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-org0fd785e" class="outline-3">
|
|
<h3 id="org0fd785e"><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-org9c38d50" class="outline-2">
|
|
<h2 id="org9c38d50"><span class="section-number-2">3</span> Direct Velocity Feedback</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="orgef7f6c4"></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-org03f9812" class="outline-3">
|
|
<h3 id="org03f9812"><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-org0426ac1" class="outline-4">
|
|
<h4 id="org0426ac1"><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="#orgce4a669">12</a>).
|
|
</p>
|
|
|
|
|
|
<div id="orgce4a669" 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-orgbb062d7" class="outline-4">
|
|
<h4 id="orgbb062d7"><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="#org5e3387d">13</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org5e3387d" 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-org1bdfb4e" class="outline-4">
|
|
<h4 id="org1bdfb4e"><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-org1787430" class="outline-3">
|
|
<h3 id="org1787430"><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-org8c867a4" class="outline-4">
|
|
<h4 id="org8c867a4"><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-org8ca9d2f" class="outline-4">
|
|
<h4 id="org8ca9d2f"><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-org85c9eb6" class="outline-4">
|
|
<h4 id="org85c9eb6"><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="org8d6a1b3" 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="org1faad36" 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="org1d30432" 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-org7ea48ad" class="outline-3">
|
|
<h3 id="org7ea48ad"><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-orgddee501" class="outline-2">
|
|
<h2 id="orgddee501"><span class="section-number-2">4</span> Inertial Control</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org1930728"></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-org183d718" class="outline-3">
|
|
<h3 id="org183d718"><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-org3b0c93b" class="outline-4">
|
|
<h4 id="org3b0c93b"><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="#orgd2495ce">17</a>).
|
|
</p>
|
|
|
|
|
|
<div id="orgd2495ce" 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-org0613819" class="outline-4">
|
|
<h4 id="org0613819"><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="#org766b991">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="org766b991" 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-org7eb6d4a" class="outline-4">
|
|
<h4 id="org7eb6d4a"><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-orgb837286" class="outline-3">
|
|
<h3 id="orgb837286"><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-org088d0cf" class="outline-4">
|
|
<h4 id="org088d0cf"><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-orge0acdea" class="outline-4">
|
|
<h4 id="orge0acdea"><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-orgb9346a9" class="outline-4">
|
|
<h4 id="orgb9346a9"><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="orga44ff4c" 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="orgaf24027" 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="org3935c70" 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-org971b7df" class="outline-3">
|
|
<h3 id="org971b7df"><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-orgb30a5ab" class="outline-2">
|
|
<h2 id="orgb30a5ab"><span class="section-number-2">5</span> Comparison</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org145a075"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org056c3e4" class="outline-3">
|
|
<h3 id="org056c3e4"><span class="section-number-3">5.1</span> Load the plants</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<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-org75158e7" class="outline-3">
|
|
<h3 id="org75158e7"><span class="section-number-3">5.2</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
|
|
<div id="org1fd62ca" 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 22: </span>caption (<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="orgf88bf41" 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 23: </span>caption (<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="org38bd3f1" class="figure">
|
|
<p><img src="figs/sensitivity_comp_spindle_z.png" alt="sensitivity_comp_spindle_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 24: </span>caption (<a href="./figs/sensitivity_comp_spindle_z.png">png</a>, <a href="./figs/sensitivity_comp_spindle_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org028eb1e" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ty_z.png" alt="sensitivity_comp_ty_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 25: </span>caption (<a href="./figs/sensitivity_comp_ty_z.png">png</a>, <a href="./figs/sensitivity_comp_ty_z.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="org35bcb61" class="figure">
|
|
<p><img src="figs/sensitivity_comp_ty_x.png" alt="sensitivity_comp_ty_x.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 26: </span>caption (<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-orgca4880d" class="outline-3">
|
|
<h3 id="orgca4880d"><span class="section-number-3">5.3</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
|
|
<div id="org8b00ca9" class="figure">
|
|
<p><img src="figs/plant_comp_damping_z.png" alt="plant_comp_damping_z.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 27: </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="org9b6dd84" class="figure">
|
|
<p><img src="figs/plant_comp_damping_x.png" alt="plant_comp_damping_x.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 28: </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="orga1e06be" class="figure">
|
|
<p><img src="figs/plant_comp_damping_coupling.png" alt="plant_comp_damping_coupling.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 29: </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-org4b14fbd" class="outline-3">
|
|
<h3 id="org4b14fbd"><span class="section-number-3">5.4</span> Tomography Experiment</h3>
|
|
<div class="outline-text-3" id="text-5-4">
|
|
<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_dvf'</span>, <span class="org-string">'En_ine'</span>);
|
|
t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">rms(sqrt(En(<span class="org-type">:</span>, 1)<span class="org-type">.^</span>2 <span class="org-type">+</span> En(<span class="org-type">:</span>, 2)<span class="org-type">.^</span>2 <span class="org-type">+</span> En(<span class="org-type">:</span>, 3)<span class="org-type">.^</span>2))
|
|
rms(sqrt(En_ine(<span class="org-type">:</span>, 1)<span class="org-type">.^</span>2 <span class="org-type">+</span> En_ine(<span class="org-type">:</span>, 2)<span class="org-type">.^</span>2 <span class="org-type">+</span> En_ine(<span class="org-type">:</span>, 3)<span class="org-type">.^</span>2))
|
|
rms(sqrt(En_dvf(<span class="org-type">:</span>, 1)<span class="org-type">.^</span>2 <span class="org-type">+</span> En_dvf(<span class="org-type">:</span>, 2)<span class="org-type">.^</span>2 <span class="org-type">+</span> En_dvf(<span class="org-type">:</span>, 3)<span class="org-type">.^</span>2))
|
|
rms(sqrt(En_iff(<span class="org-type">:</span>, 1)<span class="org-type">.^</span>2 <span class="org-type">+</span> En_iff(<span class="org-type">:</span>, 2)<span class="org-type">.^</span>2 <span class="org-type">+</span> En_iff(<span class="org-type">:</span>, 3)<span class="org-type">.^</span>2))
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2213b1c" class="outline-4">
|
|
<h4 id="org2213b1c"><span class="section-number-4">5.4.1</span> Frequency Domain</h4>
|
|
<div class="outline-text-4" id="text-5-4-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Ts = t(2)<span class="org-type">-</span>t(1); <span class="org-comment">% Sample Time for the Data [s]</span>
|
|
|
|
n_av = 8;
|
|
han_win = hanning(ceil(length(En(<span class="org-type">:</span>, 1))<span class="org-type">/</span>n_av));
|
|
|
|
[pxx, f] = pwelch(En(<span class="org-type">:</span>, 1), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pxx_ine, <span class="org-type">~</span>] = pwelch(En_ine(<span class="org-type">:</span>, 1), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pxx_dvf, <span class="org-type">~</span>] = pwelch(En_dvf(<span class="org-type">:</span>, 1), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pxx_iff, <span class="org-type">~</span>] = pwelch(En_iff(<span class="org-type">:</span>, 1), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
|
|
[pyy, <span class="org-type">~</span>] = pwelch(En(<span class="org-type">:</span>, 2), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pyy_ine, <span class="org-type">~</span>] = pwelch(En_ine(<span class="org-type">:</span>, 2), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pyy_dvf, <span class="org-type">~</span>] = pwelch(En_dvf(<span class="org-type">:</span>, 2), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pyy_iff, <span class="org-type">~</span>] = pwelch(En_iff(<span class="org-type">:</span>, 2), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
|
|
[pzz, <span class="org-type">~</span>] = pwelch(En(<span class="org-type">:</span>, 3), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pzz_ine, <span class="org-type">~</span>] = pwelch(En_ine(<span class="org-type">:</span>, 3), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pzz_dvf, <span class="org-type">~</span>] = pwelch(En_dvf(<span class="org-type">:</span>, 3), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pzz_iff, <span class="org-type">~</span>] = pwelch(En_iff(<span class="org-type">:</span>, 3), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
|
|
[prx, <span class="org-type">~</span>] = pwelch(En(<span class="org-type">:</span>, 4), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[prx_ine, <span class="org-type">~</span>] = pwelch(En_ine(<span class="org-type">:</span>, 4), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[prx_dvf, <span class="org-type">~</span>] = pwelch(En_dvf(<span class="org-type">:</span>, 4), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[prx_iff, <span class="org-type">~</span>] = pwelch(En_iff(<span class="org-type">:</span>, 4), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
|
|
[pry, <span class="org-type">~</span>] = pwelch(En(<span class="org-type">:</span>, 5), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pry_ine, <span class="org-type">~</span>] = pwelch(En_ine(<span class="org-type">:</span>, 5), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pry_dvf, <span class="org-type">~</span>] = pwelch(En_dvf(<span class="org-type">:</span>, 5), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[pry_iff, <span class="org-type">~</span>] = pwelch(En_iff(<span class="org-type">:</span>, 5), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
|
|
[prz, <span class="org-type">~</span>] = pwelch(En(<span class="org-type">:</span>, 6), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[prz_ine, <span class="org-type">~</span>] = pwelch(En_ine(<span class="org-type">:</span>, 6), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[prz_dvf, <span class="org-type">~</span>] = pwelch(En_dvf(<span class="org-type">:</span>, 6), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[prz_iff, <span class="org-type">~</span>] = pwelch(En_iff(<span class="org-type">:</span>, 6), han_win, [], [], 1<span class="org-type">/</span>Ts);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(f, prx_ine, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Inertial'</span>)
|
|
plot(f, prx_dvf, <span class="org-string">'DisplayName'</span>, <span class="org-string">'DVF'</span>)
|
|
plot(f, prx_iff, <span class="org-string">'DisplayName'</span>, <span class="org-string">'IFF'</span>)
|
|
plot(f, prx, <span class="org-string">'k--'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Undamped'</span>)
|
|
hold off;
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
|
ylabel(<span class="org-string">'Power Spectral Density [$m^2/Hz$]'</span>);
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
|
|
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
|
|
xlim([1, 500]);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(f, pxx_ine, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Inertial'</span>)
|
|
plot(f, pxx_dvf, <span class="org-string">'DisplayName'</span>, <span class="org-string">'DVF'</span>)
|
|
plot(f, pxx_iff, <span class="org-string">'DisplayName'</span>, <span class="org-string">'IFF'</span>)
|
|
plot(f, pxx, <span class="org-string">'k--'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Undamped'</span>)
|
|
hold off;
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>);
|
|
ylabel(<span class="org-string">'Power Spectral Density [$m^2/Hz$]'</span>);
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
|
|
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
|
|
xlim([1, 500]);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge02060f" class="outline-2">
|
|
<h2 id="orge02060f"><span class="section-number-2">6</span> Useful Functions</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
</div>
|
|
<div id="outline-container-org0b9e75d" class="outline-3">
|
|
<h3 id="org0b9e75d"><span class="section-number-3">6.1</span> prepareTomographyExperiment</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<p>
|
|
<a id="orgbc5dfba"></a>
|
|
</p>
|
|
|
|
<p>
|
|
This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">here</a>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org637f0d7" class="outline-4">
|
|
<h4 id="org637f0d7">Function Description</h4>
|
|
<div class="outline-text-4" id="text-org637f0d7">
|
|
<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-orgac8374d" class="outline-4">
|
|
<h4 id="orgac8374d">Optional Parameters</h4>
|
|
<div class="outline-text-4" id="text-orgac8374d">
|
|
<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-orgb19cd54" class="outline-4">
|
|
<h4 id="orgb19cd54">Initialize the Simulation</h4>
|
|
<div class="outline-text-4" id="text-orgb19cd54">
|
|
<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: 2020-01-20 lun. 17:18</p>
|
|
</div>
|
|
</body>
|
|
</html>
|