653 lines
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653 lines
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<title>HAC-LAC applied on the Simscape Model</title>
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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">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="#org68eabc2">1. Undamped System</a>
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<ul>
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<li><a href="#org05b902d">1.1. Identification of the plant</a>
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<ul>
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<li><a href="#orgfd2208d">1.1.1. Initialize the Simulation</a></li>
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<li><a href="#orgd132773">1.1.2. Identification</a></li>
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<li><a href="#org9d87e76">1.1.3. Display TF</a></li>
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<li><a href="#org5c51ae8">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="#orgaf40de5">1.2. Tomography Experiment</a>
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<ul>
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<li><a href="#org5a1507e">1.2.1. Simulation</a></li>
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<li><a href="#org9498b7b">1.2.2. Results</a></li>
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</ul>
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</li>
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<li><a href="#orgdcbab01">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="#orga716982">1.3.1. Initialize the Simulation</a></li>
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<li><a href="#org2a3d76d">1.3.2. Identification</a></li>
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<li><a href="#org86a6b3a">1.3.3. Display TF</a></li>
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<li><a href="#org51e23f6">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-org68eabc2" class="outline-2">
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<h2 id="org68eabc2"><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="org632e852"></a>
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</p>
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</div>
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<div id="outline-container-org05b902d" class="outline-3">
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<h3 id="org05b902d"><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-orgfd2208d" class="outline-4">
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<h4 id="orgfd2208d"><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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<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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<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">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-orgd132773" class="outline-4">
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<h4 id="orgd132773"><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>
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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">'nass_model'</span>;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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clear io; io_i = 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'En'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Metrology Outputs</span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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G = linearize(mdl, io, options);
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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>};
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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>};
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
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G_cart = minreal(G<span class="org-type">*</span>inv(nano_hexapod.J<span class="org-type">'</span>));
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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>};
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</pre>
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</div>
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<div class="org-src-container">
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<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-org9d87e76" class="outline-4">
|
|
<h4 id="org9d87e76"><span class="section-number-4">1.1.3</span> Display TF</h4>
|
|
<div class="outline-text-4" id="text-1-1-3">
|
|
|
|
<div id="org0cc732b" 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-org5c51ae8" class="outline-4">
|
|
<h4 id="org5c51ae8"><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="org76f625d" 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="org8206b3b" 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="org145c602" 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-orgaf40de5" class="outline-3">
|
|
<h3 id="orgaf40de5"><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-org5a1507e" class="outline-4">
|
|
<h4 id="org5a1507e"><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_simulink.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</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">'nass_model'</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-org9498b7b" class="outline-4">
|
|
<h4 id="org9498b7b"><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="org5746ec3" 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="orgb29225c" 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-orgdcbab01" class="outline-3">
|
|
<h3 id="orgdcbab01"><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-orga716982" class="outline-4">
|
|
<h4 id="orga716982"><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">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2a3d76d" class="outline-4">
|
|
<h4 id="org2a3d76d"><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">'nass_model'</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">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'En'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Metrology Outputs</span>
|
|
|
|
<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-org86a6b3a" class="outline-4">
|
|
<h4 id="org86a6b3a"><span class="section-number-4">1.3.3</span> Display TF</h4>
|
|
<div class="outline-text-4" id="text-1-3-3">
|
|
|
|
<div id="org37e58f3" 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-org51e23f6" class="outline-4">
|
|
<h4 id="org51e23f6"><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="orga98bcf7" 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="orgf5e6d6e" 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="orgfe31dcc" 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: 2020-02-25 mar. 18:08</p>
|
|
</div>
|
|
</body>
|
|
</html>
|