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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<h1 class="title">Simscape Uniaxial Model</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org119d8dc">1. Simscape Model</a></li>
<li><a href="#org95b633d">2. Undamped System</a>
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<ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#orga87af67">2.1. Init</a></li>
<li><a href="#org2d53583">2.2. Identification</a></li>
<li><a href="#orgc443c0b">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#orgdb21910">2.4. Plant</a></li>
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</ul>
</li>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org497a34a">3. Integral Force Feedback</a>
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<ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org90d6383">3.1. Control Design</a></li>
<li><a href="#orge5c43d3">3.2. Identification</a></li>
<li><a href="#orgdc6e62f">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#orgf2883d8">3.4. Damped Plant</a></li>
<li><a href="#orgb766da3">3.5. Conclusion</a></li>
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</ul>
</li>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org0216063">4. Relative Motion Control</a>
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<ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#orgda1c98e">4.1. Control Design</a></li>
<li><a href="#orge3806a0">4.2. Identification</a></li>
<li><a href="#orge58c47d">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org70ec2cf">4.4. Damped Plant</a></li>
<li><a href="#orga845b21">4.5. Conclusion</a></li>
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</ul>
</li>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org7666422">5. Direct Velocity Feedback</a>
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<ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org58e4d64">5.1. Control Design</a></li>
<li><a href="#org7e8b911">5.2. Identification</a></li>
<li><a href="#org2adcafe">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#orge8b5bd9">5.4. Damped Plant</a></li>
<li><a href="#org22d6515">5.5. Conclusion</a></li>
Add uniaxial folder with analysis of active damping techniques
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</ul>
</li>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org55010b4">6. Comparison of Active Damping Techniques</a>
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<ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<li><a href="#org5cb1e25">6.1. Load the plants</a></li>
<li><a href="#orgc746216">6.2. Sensitivity to Disturbance</a></li>
<li><a href="#orgcd1790f">6.3. Damped Plant</a></li>
<li><a href="#org9a602cb">6.4. Conclusion</a></li>
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</ul>
</li>
</ul>
</div>
</div>
<p>
The idea is to use the same model as the full Simscape Model but to restrict the motion only in the vertical direction.
</p>
<p>
This is done in order to more easily study the system and evaluate control techniques.
</p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org119d8dc" class="outline-2">
<h2 id="org119d8dc"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
<p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#org20bfb11">1</a>.
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</p>
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<p>
The perturbations \(w\) are:
</p>
<ul class="org-ul">
<li>\(F_s\): direct forces applied to the sample such as inertia forces and cable forces</li>
<li>\(F_{rz}\): parasitic forces due to the rotation of the spindle</li>
<li>\(F_{ty}\): parasitic forces due to scans with the translation stage</li>
<li>\(D_w\): ground motion</li>
</ul>
<p>
The quantity to \(z\) to control is:
</p>
<ul class="org-ul">
<li>\(D\): the position of the sample with respect to the granite</li>
</ul>
<p>
The measured quantities \(v\) are:
</p>
<ul class="org-ul">
<li>\(D\): the position of the sample with respect to the granite</li>
</ul>
<p>
We study the use of an additional sensor:
</p>
<ul class="org-ul">
<li>\(F_n\): a force sensor located in the nano-hexapod</li>
<li>\(v_n\): an absolute velocity sensor located on the top platform of the nano-hexapod</li>
<li>\(d_r\): a relative motion sensor located in the nano-hexapod</li>
</ul>
<p>
The control signal \(u\) is:
</p>
<ul class="org-ul">
<li>\(F\) the force applied by the nano-hexapod actuator</li>
</ul>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org20bfb11" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p>
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</div>
Update Analysis
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<p>
Update Analysis
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Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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Schematics of the active damping techniques are displayed in figure <a href="#org2eb3599">2</a>.
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</p>
Update Analysis
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org2eb3599" class="figure">
Update Analysis
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<p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org95b633d" class="outline-2">
<h2 id="org95b633d"><span class="section-number-2">2</span> Undamped System</h2>
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<div class="outline-text-2" id="text-2">
<p>
Let's start by study the undamped system.
</p>
</div>
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<div id="outline-container-orga87af67" class="outline-3">
<h3 id="orga87af67"><span class="section-number-3">2.1</span> Init</h3>
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<div class="outline-text-3" id="text-2-1">
<p>
We initialize all the stages with the default parameters.
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
</p>
<p>
All the controllers are set to 0 (Open Loop).
</p>
</div>
</div>
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<div id="outline-container-org2d53583" class="outline-3">
<h3 id="org2d53583"><span class="section-number-3">2.2</span> Identification</h3>
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<div class="outline-text-3" id="text-2-2">
<p>
We identify the dynamics of the system.
</p>
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<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 = <span class="org-highlight-numbers-number">0</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
</pre>
</div>
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<p>
The inputs and outputs are defined below and corresponds to the name of simulink blocks.
</p>
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<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied on the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied by the NASS</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdrz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">9</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute displacement of the granite</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
</pre>
</div>
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<p>
Finally, we use the <code>linearize</code> Matlab function to extract a state space model from the simscape model.
</p>
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<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
G.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
<span class="org-string">'Frz'</span><span class="org-rainbow-delimiters-depth-1">}</span>; <span class="org-comment">% Parasitic Force Rz [N]</span>
G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre>
</div>
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<p>
Finally, we save the identified system dynamics for further analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
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</div>
</div>
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<div id="outline-container-orgc443c0b" class="outline-3">
<h3 id="orgc443c0b"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
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<div class="outline-text-3" id="text-2-3">
<p>
We show several plots representing the sensitivity to disturbances:
</p>
<ul class="org-ul">
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<li>in figure <a href="#org4d3097e">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
<li>in figure <a href="#orgfd7633d">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
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</ul>
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org4d3097e" class="figure">
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<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
</p>
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<p><span class="figure-number">Figure 3: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
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</div>
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<div id="orgfd7633d" class="figure">
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<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
</p>
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<p><span class="figure-number">Figure 4: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-force-dist.pdf">pdf</a>)</p>
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</div>
</div>
</div>
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<div id="outline-container-orgdb21910" class="outline-3">
<h3 id="orgdb21910"><span class="section-number-3">2.4</span> Plant</h3>
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<div class="outline-text-3" id="text-2-4">
<p>
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The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#orgee21d6a">5</a>.
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It corresponds to the plant to control.
</p>
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<div id="orgee21d6a" class="figure">
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<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
</p>
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<p><span class="figure-number">Figure 5: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
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</div>
</div>
</div>
</div>
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<div id="outline-container-org497a34a" class="outline-2">
<h2 id="org497a34a"><span class="section-number-2">3</span> Integral Force Feedback</h2>
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<div class="outline-text-2" id="text-3">
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<p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<a id="org61a9736"></a>
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</p>
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orgf30b3b3" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Uniaxial IFF Control Schematic</p>
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</div>
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</div>
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<div id="outline-container-org90d6383" class="outline-3">
<h3 id="org90d6383"><span class="section-number-3">3.1</span> Control Design</h3>
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<div class="outline-text-3" id="text-3-1">
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<div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</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.
</p>
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<div id="org13e2d05" class="figure">
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<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
</p>
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<p><span class="figure-number">Figure 7: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
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</div>
<p>
The controller for each pair of actuator/sensor is:
</p>
<div class="org-src-container">
<pre class="src src-matlab">K_iff = <span class="org-type">-</span><span class="org-highlight-numbers-number">1000</span><span class="org-type">/</span>s;
</pre>
</div>
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<div id="org928425f" class="figure">
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<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
</p>
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<p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
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</div>
</div>
</div>
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<div id="outline-container-orge5c43d3" class="outline-3">
<h3 id="orge5c43d3"><span class="section-number-3">3.2</span> Identification</h3>
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<div class="outline-text-3" id="text-3-2">
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<p>
Let's initialize the system prior to identification.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
All the controllers are set to 0.
</p>
<div class="org-src-container">
<pre class="src src-matlab">K = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_iff = <span class="org-type">-</span>K_iff;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_rmc = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_dvf = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<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 = <span class="org-highlight-numbers-number">0</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied on the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied by the NASS</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdrz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">9</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute displacement of the granite</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G_iff = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
G_iff.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
<span class="org-string">'Frz'</span><span class="org-rainbow-delimiters-depth-1">}</span>; <span class="org-comment">% Parasitic Force Rz [N]</span>
G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre>
</div>
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<div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
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</div>
</div>
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<div id="outline-container-orgdc6e62f" class="outline-3">
<h3 id="orgdc6e62f"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
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<div class="outline-text-3" id="text-3-3">
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<div id="org8df8488" class="figure">
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<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
</p>
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<p><span class="figure-number">Figure 9: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
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</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org6003ced" class="figure">
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<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
</p>
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<p><span class="figure-number">Figure 10: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-orgf2883d8" class="outline-3">
<h3 id="orgf2883d8"><span class="section-number-3">3.4</span> Damped Plant</h3>
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<div class="outline-text-3" id="text-3-4">
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org2071f90" class="figure">
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<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
</p>
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<p><span class="figure-number">Figure 11: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-orgb766da3" class="outline-3">
<h3 id="orgb766da3"><span class="section-number-3">3.5</span> Conclusion</h3>
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<div class="outline-text-3" id="text-3-5">
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<div class="important">
<p>
Integral Force Feedback:
</p>
</div>
</div>
</div>
</div>
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<div id="outline-container-org0216063" class="outline-2">
<h2 id="org0216063"><span class="section-number-2">4</span> Relative Motion Control</h2>
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<div class="outline-text-2" id="text-4">
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<p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<a id="orgcf7a709"></a>
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</p>
<p>
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
</p>
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org8ed07c5" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Uniaxial RMC Control Schematic</p>
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</div>
Update Analysis
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</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-orgda1c98e" class="outline-3">
<h3 id="orgda1c98e"><span class="section-number-3">4.1</span> Control Design</h3>
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<div class="outline-text-3" id="text-4-1">
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<div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</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.
</p>
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<div id="org75fbb9f" class="figure">
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<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
</p>
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<p><span class="figure-number">Figure 13: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
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</div>
<p>
The Relative Motion Controller 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_rmc = s<span class="org-type">*</span><span class="org-highlight-numbers-number">50000</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">10000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orgc5d2eb6" class="figure">
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<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
</p>
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<p><span class="figure-number">Figure 14: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
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</div>
</div>
</div>
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<div id="outline-container-orge3806a0" class="outline-3">
<h3 id="orge3806a0"><span class="section-number-3">4.2</span> Identification</h3>
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<div class="outline-text-3" id="text-4-2">
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<p>
Let's initialize the system prior to identification.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And initialize the controllers.
</p>
<div class="org-src-container">
<pre class="src src-matlab">K = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_iff = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_rmc = <span class="org-type">-</span>K_rmc;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_dvf = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<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 = <span class="org-highlight-numbers-number">0</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied on the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied by the NASS</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdrz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">9</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute displacement of the granite</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G_rmc = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
G_rmc.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
<span class="org-string">'Frz'</span><span class="org-rainbow-delimiters-depth-1">}</span>; <span class="org-comment">% Parasitic Force Rz [N]</span>
G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre>
</div>
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<div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
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</div>
</div>
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<div id="outline-container-orge58c47d" class="outline-3">
<h3 id="orge58c47d"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
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<div class="outline-text-3" id="text-4-3">
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<div id="orgd910119" class="figure">
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<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
</p>
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<p><span class="figure-number">Figure 15: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
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</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org6610f06" class="figure">
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<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
</p>
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<p><span class="figure-number">Figure 16: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org70ec2cf" class="outline-3">
<h3 id="org70ec2cf"><span class="section-number-3">4.4</span> Damped Plant</h3>
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<div class="outline-text-3" id="text-4-4">
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org7508a42" class="figure">
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<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
</p>
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<p><span class="figure-number">Figure 17: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
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</div>
</div>
</div>
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<div id="outline-container-orga845b21" class="outline-3">
<h3 id="orga845b21"><span class="section-number-3">4.5</span> Conclusion</h3>
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<div class="outline-text-3" id="text-4-5">
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<div class="important">
<p>
Relative Motion Control:
</p>
</div>
</div>
</div>
</div>
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<div id="outline-container-org7666422" class="outline-2">
<h2 id="org7666422"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
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<div class="outline-text-2" id="text-5">
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<p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<a id="org6b8afcf"></a>
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</p>
<p>
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
</p>
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orga86445d" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Uniaxial DVF Control Schematic</p>
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</div>
Update Analysis
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</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org58e4d64" class="outline-3">
<h3 id="org58e4d64"><span class="section-number-3">5.1</span> Control Design</h3>
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<div class="outline-text-3" id="text-5-1">
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<div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orgf4888fb" class="figure">
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<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
</p>
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<p><span class="figure-number">Figure 19: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
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</div>
<div class="org-src-container">
<pre class="src src-matlab">K_dvf = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5e4</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org1a62235" class="figure">
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<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
</p>
Update Analysis
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<p><span class="figure-number">Figure 20: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
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</div>
</div>
</div>
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<div id="outline-container-org7e8b911" class="outline-3">
<h3 id="org7e8b911"><span class="section-number-3">5.2</span> Identification</h3>
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<div class="outline-text-3" id="text-5-2">
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<p>
Let's initialize the system prior to identification.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And initialize the controllers.
</p>
<div class="org-src-container">
<pre class="src src-matlab">K = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_iff = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_rmc = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_dvf = <span class="org-type">-</span>K_dvf;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<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 = <span class="org-highlight-numbers-number">0</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied on the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied by the NASS</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdrz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">9</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute displacement of the granite</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G_dvf = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
G_dvf.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
<span class="org-string">'Frz'</span><span class="org-rainbow-delimiters-depth-1">}</span>; <span class="org-comment">% Parasitic Force Rz [N]</span>
G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre>
</div>
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<div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
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</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org2adcafe" class="outline-3">
<h3 id="org2adcafe"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
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<div class="outline-text-3" id="text-5-3">
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<div id="org9ca6224" class="figure">
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<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
</p>
Update Analysis
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<p><span class="figure-number">Figure 21: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
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</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orgd0ada58" class="figure">
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<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
</p>
Update Analysis
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<p><span class="figure-number">Figure 22: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-orge8b5bd9" class="outline-3">
<h3 id="orge8b5bd9"><span class="section-number-3">5.4</span> Damped Plant</h3>
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<div class="outline-text-3" id="text-5-4">
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org55c6262" class="figure">
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<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
</p>
Update Analysis
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<p><span class="figure-number">Figure 23: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org22d6515" class="outline-3">
<h3 id="org22d6515"><span class="section-number-3">5.5</span> Conclusion</h3>
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<div class="outline-text-3" id="text-5-5">
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<div class="important">
<p>
Direct Velocity Feedback:
</p>
</div>
</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org55010b4" class="outline-2">
<h2 id="org55010b4"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
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<div class="outline-text-2" id="text-6">
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<p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<a id="org9b9c235"></a>
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</p>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-org5cb1e25" class="outline-3">
<h3 id="org5cb1e25"><span class="section-number-3">6.1</span> Load the plants</h3>
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<div class="outline-text-3" id="text-6-1">
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<div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-orgc746216" class="outline-3">
<h3 id="orgc746216"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
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<div class="outline-text-3" id="text-6-2">
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orga056e76" class="figure">
Update Analysis
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<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
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</p>
Update Analysis
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<p><span class="figure-number">Figure 24: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
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</div>
Update Analysis
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org5bfe138" class="figure">
Update Analysis
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<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
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</p>
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<p><span class="figure-number">Figure 25: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org4e0c629" class="figure">
Update Analysis
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<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
</p>
<p><span class="figure-number">Figure 26: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="orgae22af6" class="figure">
Update Analysis
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<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
</p>
<p><span class="figure-number">Figure 27: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
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</div>
</div>
</div>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="outline-container-orgcd1790f" class="outline-3">
<h3 id="orgcd1790f"><span class="section-number-3">6.3</span> Damped Plant</h3>
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<div class="outline-text-3" id="text-6-3">
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Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<div id="org38fbe3d" class="figure">
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<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
</p>
Update Analysis
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<p><span class="figure-number">Figure 28: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
</div>
</div>
</div>
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<div id="outline-container-org9a602cb" class="outline-3">
<h3 id="org9a602cb"><span class="section-number-3">6.4</span> Conclusion</h3>
Update Analysis
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<div class="outline-text-3" id="text-6-4">
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
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<table id="orgf039db4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-left">IFF</th>
<th scope="col" class="org-left">RMC</th>
<th scope="col" class="org-left">DVF</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Sensor Type</td>
<td class="org-left">Force sensor</td>
<td class="org-left">Relative Motion</td>
<td class="org-left">Inertial</td>
</tr>
<tr>
<td class="org-left">Guaranteed Stability</td>
<td class="org-left">+</td>
<td class="org-left">+</td>
<td class="org-left">-</td>
</tr>
<tr>
<td class="org-left">Sensitivity (\(D_w\))</td>
<td class="org-left">-</td>
<td class="org-left">+</td>
<td class="org-left">-</td>
</tr>
<tr>
<td class="org-left">Sensitivity (\(F_s\))</td>
<td class="org-left">- (at low freq)</td>
<td class="org-left">+</td>
<td class="org-left">+</td>
</tr>
<tr>
<td class="org-left">Sensitivity (\(F_{ty,rz}\))</td>
<td class="org-left">+</td>
<td class="org-left">-</td>
<td class="org-left">+</td>
</tr>
</tbody>
</table>
<div class="important">
<p>
The next step is to take into account the power spectral density of each disturbance.
</p>
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</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
Analysis of active damping techniques with simscape model Some flexibility is added to the sample
2019-10-25 16:02:23 +02:00
<p class="date">Created: 2019-10-25 ven. 16:02</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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