Add updated plant with correct hexapod
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
|
||||
<h1 class="title">HAC-LAC 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="#orgbda92b6">1. Undamped System</a>
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||||
<ul>
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||||
<li><a href="#org919aa7c">1.1. Identification of the plant</a>
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||||
<ul>
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||||
<li><a href="#org953f3ee">1.1.1. Initialize the Simulation</a></li>
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||||
<li><a href="#org4b160cb">1.1.2. Identification</a></li>
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||||
<li><a href="#orgdb4e9c8">1.1.3. Display TF</a></li>
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||||
<li><a href="#org7844ee6">1.1.4. Obtained Plants for Active Damping</a></li>
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</ul>
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||||
</li>
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||||
<li><a href="#org3009033">1.2. Tomography Experiment</a>
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<ul>
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||||
<li><a href="#org2c866cf">1.2.1. Simulation</a></li>
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<li><a href="#orga5a7537">1.2.2. Results</a></li>
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</ul>
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||||
</li>
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<li><a href="#org69a746f">1.3. Verification of the transfer function from nano hexapod to metrology</a>
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||||
<ul>
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||||
<li><a href="#orgc2ab9cc">1.3.1. Initialize the Simulation</a></li>
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||||
<li><a href="#org1541bdb">1.3.2. Identification</a></li>
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||||
<li><a href="#orgd924cdb">1.3.3. Display TF</a></li>
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||||
<li><a href="#org608ec72">1.3.4. Obtained Plants for Active Damping</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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<div id="outline-container-orgbda92b6" class="outline-2">
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<h2 id="orgbda92b6"><span class="section-number-2">1</span> Undamped System</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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||||
<a id="org0dabcfd"></a>
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||||
</p>
|
||||
</div>
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||||
|
||||
<div id="outline-container-org919aa7c" class="outline-3">
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<h3 id="org919aa7c"><span class="section-number-3">1.1</span> Identification of the plant</h3>
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<div class="outline-text-3" id="text-1-1">
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</div>
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||||
<div id="outline-container-org953f3ee" class="outline-4">
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||||
<h4 id="org953f3ee"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4>
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||||
<div class="outline-text-4" id="text-1-1-1">
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<p>
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||||
We initialize all the stages with the default parameters.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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||||
initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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||||
</pre>
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</div>
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<p>
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||||
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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||||
</p>
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
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initializeSample(<span class="org-string">'mass'</span>, 50);
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</pre>
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</div>
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<p>
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No disturbances.
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</p>
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||||
<div class="org-src-container">
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<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
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</pre>
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||||
</div>
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||||
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||||
<p>
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||||
We set the references to zero.
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||||
</p>
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<div class="org-src-container">
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||||
<pre class="src src-matlab">initializeReferences();
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||||
</pre>
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||||
</div>
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||||
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||||
<p>
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||||
And all the controllers are set to 0.
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||||
</p>
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab">K = tf(zeros(6));
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save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
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K_ine = tf(zeros(6));
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save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_ine'</span>, <span class="org-string">'-append'</span>);
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||||
K_iff = tf(zeros(6));
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save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
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||||
K_dvf = tf(zeros(6));
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save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
||||
</pre>
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||||
</div>
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||||
</div>
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||||
</div>
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||||
|
||||
<div id="outline-container-org4b160cb" class="outline-4">
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||||
<h4 id="org4b160cb"><span class="section-number-4">1.1.2</span> Identification</h4>
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||||
<div class="outline-text-4" id="text-1-1-2">
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||||
<p>
|
||||
First, we identify the dynamics of the system using the <code>linearize</code> function.
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||||
</p>
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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||||
options = linearizeOptions;
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||||
options.SampleTime = 0;
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||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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||||
mdl = <span class="org-string">'sim_nass_hac_lac'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/HAC'</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">'/Compute Error in NASS base'</span>], 2, <span class="org-string">'openoutput'</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">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
|
||||
G_cart = minreal(G<span class="org-type">*</span>inv(nano_hexapod.J<span class="org-type">'</span>));
|
||||
G_cart.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">G_legs = minreal(inv(nano_hexapod.J)<span class="org-type">*</span>G);
|
||||
G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-string">'e2'</span>, <span class="org-string">'e3'</span>, <span class="org-string">'e4'</span>, <span class="org-string">'e5'</span>, <span class="org-string">'e6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdb4e9c8" class="outline-4">
|
||||
<h4 id="orgdb4e9c8"><span class="section-number-4">1.1.3</span> Display TF</h4>
|
||||
<div class="outline-text-4" id="text-1-1-3">
|
||||
|
||||
<div id="org37b9be3" class="figure">
|
||||
<p><img src="figs/plant_G_cart.png" alt="plant_G_cart.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Transfer Function from forces applied by the nano-hexapod to position error (<a href="./figs/plant_G_cart.png">png</a>, <a href="./figs/plant_G_cart.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7844ee6" class="outline-4">
|
||||
<h4 id="org7844ee6"><span class="section-number-4">1.1.4</span> Obtained Plants for Active Damping</h4>
|
||||
<div class="outline-text-4" id="text-1-1-4">
|
||||
|
||||
<div id="org505566d" 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 2: </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="org46c7102" 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 3: </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="org6c61332" 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 4: </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-org3009033" class="outline-3">
|
||||
<h3 id="org3009033"><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-org2c866cf" class="outline-4">
|
||||
<h4 id="org2c866cf"><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-orga5a7537" class="outline-4">
|
||||
<h4 id="orga5a7537"><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="org43abdf9" 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 5: </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="orgb984994" 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 6: </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 id="outline-container-org69a746f" class="outline-3">
|
||||
<h3 id="org69a746f"><span class="section-number-3">1.3</span> Verification of the transfer function from nano hexapod to metrology</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
</div>
|
||||
<div id="outline-container-orgc2ab9cc" class="outline-4">
|
||||
<h4 id="orgc2ab9cc"><span class="section-number-4">1.3.1</span> Initialize the Simulation</h4>
|
||||
<div class="outline-text-4" id="text-1-3-1">
|
||||
<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>
|
||||
No disturbances.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
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-org1541bdb" class="outline-4">
|
||||
<h4 id="org1541bdb"><span class="section-number-4">1.3.2</span> Identification</h4>
|
||||
<div class="outline-text-4" id="text-1-3-2">
|
||||
<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_hac_lac'</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">'/HAC'</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">'/Compute Error in NASS base'</span>], 2, <span class="org-string">'openoutput'</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">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
|
||||
G_cart = minreal(G<span class="org-type">*</span>inv(nano_hexapod.J<span class="org-type">'</span>));
|
||||
G_cart.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">G_legs = minreal(inv(nano_hexapod.J)<span class="org-type">*</span>G);
|
||||
G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-string">'e2'</span>, <span class="org-string">'e3'</span>, <span class="org-string">'e4'</span>, <span class="org-string">'e5'</span>, <span class="org-string">'e6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd924cdb" class="outline-4">
|
||||
<h4 id="orgd924cdb"><span class="section-number-4">1.3.3</span> Display TF</h4>
|
||||
<div class="outline-text-4" id="text-1-3-3">
|
||||
|
||||
<div id="orgc842d08" class="figure">
|
||||
<p><img src="figs/plant_G_cart.png" alt="plant_G_cart.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Transfer Function from forces applied by the nano-hexapod to position error (<a href="./figs/plant_G_cart.png">png</a>, <a href="./figs/plant_G_cart.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org608ec72" class="outline-4">
|
||||
<h4 id="org608ec72"><span class="section-number-4">1.3.4</span> Obtained Plants for Active Damping</h4>
|
||||
<div class="outline-text-4" id="text-1-3-4">
|
||||
|
||||
<div id="org253e2e8" 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 8: </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="orgf988b83" 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 9: </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="org54d695a" 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 10: </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>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-01-29 mer. 20:35</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@ -167,7 +167,7 @@ First, we identify the dynamics of the system using the =linearize= function.
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend();
|
||||
legend('location', 'southwest');
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
Loading…
Reference in New Issue
Block a user