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</div><div id="content">
<h1 class="title">Active Damping applied on the Simscape Model</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org43bc922">1. Undamped System</a>
<ul>
<li><a href="#org9a8111b">1.1. Identification of the dynamics for Active Damping</a>
<ul>
<li><a href="#org813e9d0">1.1.1. Initialize the Simulation</a></li>
<li><a href="#org85a96c0">1.1.2. Identification</a></li>
<li><a href="#orgc478ad1">1.1.3. Obtained Plants for Active Damping</a></li>
</ul>
</li>
<li><a href="#org22150e6">1.2. Tomography Experiment</a>
<ul>
<li><a href="#org931bbc3">1.2.1. Simulation</a></li>
<li><a href="#org97e15e5">1.2.2. Results</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgeca85c7">2. Integral Force Feedback</a>
<ul>
<li><a href="#org8e730eb">2.1. Control Design</a>
<ul>
<li><a href="#org4aae4a5">2.1.1. Plant</a></li>
<li><a href="#org9230021">2.1.2. Control Design</a></li>
<li><a href="#orgc48be49">2.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#org521b83c">2.2. Tomography Experiment</a>
<ul>
<li><a href="#org80693d0">2.2.1. Initialize the Simulation</a></li>
<li><a href="#org828fe0c">2.2.2. Simulation</a></li>
<li><a href="#orgba367cd">2.2.3. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#org64c89c0">2.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org1bec1c8">3. Direct Velocity Feedback</a>
<ul>
<li><a href="#org34fcfd6">3.1. Control Design</a>
<ul>
<li><a href="#org2e5695f">3.1.1. Plant</a></li>
<li><a href="#org8feed7c">3.1.2. Control Design</a></li>
<li><a href="#org5d88841">3.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#orgd0cf173">3.2. Tomography Experiment</a>
<ul>
<li><a href="#org41f51f2">3.2.1. Initialize the Simulation</a></li>
<li><a href="#org0da77b8">3.2.2. Simulation</a></li>
<li><a href="#org8956847">3.2.3. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#org4a46d6a">3.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgf8012d0">4. Inertial Control</a>
<ul>
<li><a href="#org47e2207">4.1. Control Design</a>
<ul>
<li><a href="#orga1c06d5">4.1.1. Plant</a></li>
<li><a href="#orgee9c27b">4.1.2. Control Design</a></li>
<li><a href="#org6241541">4.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#org9625401">4.2. Tomography Experiment</a>
<ul>
<li><a href="#orgf3c8835">4.2.1. Initialize the Simulation</a></li>
<li><a href="#org457a68a">4.2.2. Simulation</a></li>
<li><a href="#org5c8213d">4.2.3. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#org4e39ecb">4.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgb97eda0">5. Comparison</a>
<ul>
<li><a href="#org7e7c35d">5.1. Load the plants</a></li>
<li><a href="#org7c0e10c">5.2. Sensitivity to Disturbance</a></li>
<li><a href="#org34d3217">5.3. Damped Plant</a></li>
<li><a href="#orgc2cfa6b">5.4. Tomography Experiment</a>
<ul>
<li><a href="#orgb357d35">5.4.1. Frequency Domain</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgb95a1fb">6. Useful Functions</a>
<ul>
<li><a href="#org624fc0d">6.1. prepareTomographyExperiment</a>
<ul>
<li><a href="#org4917bc7">6.1.1. Function Description</a></li>
<li><a href="#org3c7b365">6.1.2. Optional Parameters</a></li>
<li><a href="#org758e52a">6.1.3. Initialize the Simulation</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<p>
First, in section <a href="#orgcd6de97">1</a>, we will looked at the undamped system.
</p>
<p>
Then, we will compare three active damping techniques:
</p>
<ul class="org-ul">
<li>In section <a href="#org45880cb">2</a>: the integral force feedback is used</li>
<li>In section <a href="#org88df20b">3</a>: the direct velocity feedback is used</li>
<li>In section <a href="#orgcb7853a">4</a>: inertial control is used</li>
</ul>
<p>
For each of the active damping technique, we will:
</p>
<ul class="org-ul">
<li>Look at the damped plant</li>
<li>Simulate tomography experiments</li>
<li>Compare the sensitivity from disturbances</li>
</ul>
<p>
The disturbances are:
</p>
<ul class="org-ul">
<li>Ground motion</li>
<li>Motion errors of all the stages</li>
</ul>
<div id="outline-container-org43bc922" class="outline-2">
<h2 id="org43bc922"><span class="section-number-2">1</span> Undamped System</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orgcd6de97"></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-org9a8111b" class="outline-3">
<h3 id="org9a8111b"><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-org813e9d0" class="outline-4">
<h4 id="org813e9d0"><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-org85a96c0" class="outline-4">
<h4 id="org85a96c0"><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-orgc478ad1" class="outline-4">
<h4 id="orgc478ad1"><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="org26a36fc" 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="orgb866959" 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="orgbeb0fe2" 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-org22150e6" class="outline-3">
<h3 id="org22150e6"><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-org931bbc3" class="outline-4">
<h4 id="org931bbc3"><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-org97e15e5" class="outline-4">
<h4 id="org97e15e5"><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="orge980ab1" 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="org669dfe3" 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-orgeca85c7" class="outline-2">
<h2 id="orgeca85c7"><span class="section-number-2">2</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org45880cb"></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-org8e730eb" class="outline-3">
<h3 id="org8e730eb"><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-org4aae4a5" class="outline-4">
<h4 id="org4aae4a5"><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="#orgc1d7801">6</a>).
</p>
<div id="orgc1d7801" 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-org9230021" class="outline-4">
<h4 id="org9230021"><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="#orgb6d4182">7</a>.
</p>
<div id="orgb6d4182" 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-orgc48be49" class="outline-4">
<h4 id="orgc48be49"><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>
<div id="outline-container-org521b83c" class="outline-3">
<h3 id="org521b83c"><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-org80693d0" class="outline-4">
<h4 id="org80693d0"><span class="section-number-4">2.2.1</span> Initialize the Simulation</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>
</div>
</div>
<div id="outline-container-org828fe0c" class="outline-4">
<h4 id="org828fe0c"><span class="section-number-4">2.2.2</span> Simulation</h4>
<div class="outline-text-4" id="text-2-2-2">
<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_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-orgba367cd" class="outline-4">
<h4 id="orgba367cd"><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>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</pre>
</div>
<div id="org8a913a4" 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 8: </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="org5a68859" 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 9: </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-org64c89c0" class="outline-3">
<h3 id="org64c89c0"><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-org1bec1c8" class="outline-2">
<h2 id="org1bec1c8"><span class="section-number-2">3</span> Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org88df20b"></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-org34fcfd6" class="outline-3">
<h3 id="org34fcfd6"><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-org2e5695f" class="outline-4">
<h4 id="org2e5695f"><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="#org7fbb7c6">10</a>).
</p>
<div id="org7fbb7c6" class="figure">
<p><img src="figs/dvf_plant.png" alt="dvf_plant.png" />
</p>
<p><span class="figure-number">Figure 10: </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-org8feed7c" class="outline-4">
<h4 id="org8feed7c"><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="#orgdcfd988">11</a>.
</p>
<div id="orgdcfd988" class="figure">
<p><img src="figs/dvf_open_loop.png" alt="dvf_open_loop.png" />
</p>
<p><span class="figure-number">Figure 11: </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-org5d88841" class="outline-4">
<h4 id="org5d88841"><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-orgd0cf173" class="outline-3">
<h3 id="orgd0cf173"><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-org41f51f2" class="outline-4">
<h4 id="org41f51f2"><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-org0da77b8" class="outline-4">
<h4 id="org0da77b8"><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-org8956847" class="outline-4">
<h4 id="org8956847"><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="orgd62f9ce" 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 12: </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="org8213265" 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 13: </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-org4a46d6a" class="outline-3">
<h3 id="org4a46d6a"><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-orgf8012d0" class="outline-2">
<h2 id="orgf8012d0"><span class="section-number-2">4</span> Inertial Control</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="orgcb7853a"></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> velocity of the platform to the actuator force input.
</p>
</div>
<div id="outline-container-org47e2207" class="outline-3">
<h3 id="org47e2207"><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-orga1c06d5" class="outline-4">
<h4 id="orga1c06d5"><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="#org8ebf5ec">14</a>).
</p>
<div id="org8ebf5ec" class="figure">
<p><img src="figs/ine_plant.png" alt="ine_plant.png" />
</p>
<p><span class="figure-number">Figure 14: </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-orgee9c27b" class="outline-4">
<h4 id="orgee9c27b"><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="#orgf0d92b7">15</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">K_ine = 1e3<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="orgf0d92b7" class="figure">
<p><img src="figs/ine_open_loop_gain.png" alt="ine_open_loop_gain.png" />
</p>
<p><span class="figure-number">Figure 15: </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-org6241541" class="outline-4">
<h4 id="org6241541"><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-org9625401" class="outline-3">
<h3 id="org9625401"><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-orgf3c8835" class="outline-4">
<h4 id="orgf3c8835"><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-org457a68a" class="outline-4">
<h4 id="org457a68a"><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-org5c8213d" class="outline-4">
<h4 id="org5c8213d"><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="orga568df8" 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 16: </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="org90aff48" 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 17: </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-org4e39ecb" class="outline-3">
<h3 id="org4e39ecb"><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-orgb97eda0" class="outline-2">
<h2 id="orgb97eda0"><span class="section-number-2">5</span> Comparison</h2>
<div class="outline-text-2" id="text-5">
<p>
<a id="org00d859c"></a>
</p>
</div>
<div id="outline-container-org7e7c35d" class="outline-3">
<h3 id="org7e7c35d"><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-org7c0e10c" class="outline-3">
<h3 id="org7c0e10c"><span class="section-number-3">5.2</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-5-2">
<div id="org1f40d6f" 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 18: </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="org489ca09" 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 19: </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="orgdc0124f" class="figure">
<p><img src="figs/sensitivity_comp_spindle_z.png" alt="sensitivity_comp_spindle_z.png" />
</p>
<p><span class="figure-number">Figure 20: </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="orgddca189" class="figure">
<p><img src="figs/sensitivity_comp_ty_z.png" alt="sensitivity_comp_ty_z.png" />
</p>
<p><span class="figure-number">Figure 21: </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="orgba56d42" class="figure">
<p><img src="figs/sensitivity_comp_ty_x.png" alt="sensitivity_comp_ty_x.png" />
</p>
<p><span class="figure-number">Figure 22: </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-org34d3217" class="outline-3">
<h3 id="org34d3217"><span class="section-number-3">5.3</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-3">
<div id="org14da053" class="figure">
<p><img src="figs/plant_comp_damping_z.png" alt="plant_comp_damping_z.png" />
</p>
<p><span class="figure-number">Figure 23: </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="org1eac68b" class="figure">
<p><img src="figs/plant_comp_damping_x.png" alt="plant_comp_damping_x.png" />
</p>
<p><span class="figure-number">Figure 24: </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="orge00f3b6" class="figure">
<p><img src="figs/plant_comp_damping_coupling.png" alt="plant_comp_damping_coupling.png" />
</p>
<p><span class="figure-number">Figure 25: </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-orgc2cfa6b" class="outline-3">
<h3 id="orgc2cfa6b"><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-orgb357d35" class="outline-4">
<h4 id="orgb357d35"><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(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));
[pdx, f] = pwelch(Ern(<span class="org-type">:</span>, 1), han_win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="outline-container-orgb95a1fb" class="outline-2">
<h2 id="orgb95a1fb"><span class="section-number-2">6</span> Useful Functions</h2>
<div class="outline-text-2" id="text-6">
</div>
<div id="outline-container-org624fc0d" class="outline-3">
<h3 id="org624fc0d"><span class="section-number-3">6.1</span> prepareTomographyExperiment</h3>
<div class="outline-text-3" id="text-6-1">
<p>
<a id="org2f22626"></a>
</p>
<p>
This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">here</a>.
</p>
</div>
<div id="outline-container-org4917bc7" class="outline-4">
<h4 id="org4917bc7"><span class="section-number-4">6.1.1</span> Function Description</h4>
<div class="outline-text-4" id="text-6-1-1">
<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-org3c7b365" class="outline-4">
<h4 id="org3c7b365"><span class="section-number-4">6.1.2</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-6-1-2">
<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-org758e52a" class="outline-4">
<h4 id="org758e52a"><span class="section-number-4">6.1.3</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-6-1-3">
<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: 2020-01-15 mer. 16:22</p>
</div>
</body>
</html>