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Analysis of active damping techniques with simscape model

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Some flexibility is added to the sample
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Thomas Dehaeze
2019-10-25 16:02:23 +02:00
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-10-25 ven. 12:32 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Simscape Uniaxial Model</title>
@@ -280,48 +280,48 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgd9a890c">1. Simscape Model</a></li>
<li><a href="#orgeafc497">2. Undamped System</a>
<li><a href="#org119d8dc">1. Simscape Model</a></li>
<li><a href="#org95b633d">2. Undamped System</a>
<ul>
<li><a href="#org631c716">2.1. Init</a></li>
<li><a href="#orgbbef650">2.2. Identification</a></li>
<li><a href="#orgb5102fd">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#orgafe8970">2.4. Plant</a></li>
<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>
</ul>
</li>
<li><a href="#orgeab4870">3. Integral Force Feedback</a>
<li><a href="#org497a34a">3. Integral Force Feedback</a>
<ul>
<li><a href="#org6cf62a2">3.1. Control Design</a></li>
<li><a href="#orgf9a5f33">3.2. Identification</a></li>
<li><a href="#org7a80859">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#org7bab9e9">3.4. Damped Plant</a></li>
<li><a href="#orgaac01c0">3.5. Conclusion</a></li>
<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>
</ul>
</li>
<li><a href="#org8d9b463">4. Relative Motion Control</a>
<li><a href="#org0216063">4. Relative Motion Control</a>
<ul>
<li><a href="#orgbf2540a">4.1. Control Design</a></li>
<li><a href="#org1d106d7">4.2. Identification</a></li>
<li><a href="#orgeb7d680">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org573eda0">4.4. Damped Plant</a></li>
<li><a href="#org02ca488">4.5. Conclusion</a></li>
<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>
</ul>
</li>
<li><a href="#org57948ea">5. Direct Velocity Feedback</a>
<li><a href="#org7666422">5. Direct Velocity Feedback</a>
<ul>
<li><a href="#org4b4d061">5.1. Control Design</a></li>
<li><a href="#orgd4f4973">5.2. Identification</a></li>
<li><a href="#org6cfeae5">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#org89e0408">5.4. Damped Plant</a></li>
<li><a href="#orgc27bce5">5.5. Conclusion</a></li>
<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>
</ul>
</li>
<li><a href="#org6dd07d9">6. Comparison of Active Damping Techniques</a>
<li><a href="#org55010b4">6. Comparison of Active Damping Techniques</a>
<ul>
<li><a href="#orgd62929a">6.1. Load the plants</a></li>
<li><a href="#orgbd35b93">6.2. Sensitivity to Disturbance</a></li>
<li><a href="#org72ab5fd">6.3. Damped Plant</a></li>
<li><a href="#org2c43078">6.4. Conclusion</a></li>
<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>
</ul>
</li>
</ul>
@@ -336,11 +336,11 @@ The idea is to use the same model as the full Simscape Model but to restrict the
This is done in order to more easily study the system and evaluate control techniques.
</p>
<div id="outline-container-orgd9a890c" class="outline-2">
<h2 id="orgd9a890c"><span class="section-number-2">1</span> Simscape Model</h2>
<div id="outline-container-org119d8dc" class="outline-2">
<h2 id="org119d8dc"><span class="section-number-2">1</span> Simscape Model</h2>
<div class="outline-text-2" id="text-1">
<p>
A schematic of the uniaxial model used for simulations is represented in figure <a href="#org9234e2b">1</a>.
A schematic of the uniaxial model used for simulations is represented in figure <a href="#org20bfb11">1</a>.
</p>
<p>
@@ -384,7 +384,7 @@ The control signal \(u\) is:
</ul>
<div id="org9234e2b" class="figure">
<div id="org20bfb11" class="figure">
<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>
@@ -393,11 +393,11 @@ The control signal \(u\) is:
<p>
Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
Schematics of the active damping techniques are displayed in figure <a href="#org49f5486">2</a>.
Schematics of the active damping techniques are displayed in figure <a href="#org2eb3599">2</a>.
</p>
<div id="org49f5486" class="figure">
<div id="org2eb3599" class="figure">
<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>
@@ -405,16 +405,16 @@ Schematics of the active damping techniques are displayed in figure <a href="#or
</div>
</div>
<div id="outline-container-orgeafc497" class="outline-2">
<h2 id="orgeafc497"><span class="section-number-2">2</span> Undamped System</h2>
<div id="outline-container-org95b633d" class="outline-2">
<h2 id="org95b633d"><span class="section-number-2">2</span> Undamped System</h2>
<div class="outline-text-2" id="text-2">
<p>
Let's start by study the undamped system.
</p>
</div>
<div id="outline-container-org631c716" class="outline-3">
<h3 id="org631c716"><span class="section-number-3">2.1</span> Init</h3>
<div id="outline-container-orga87af67" class="outline-3">
<h3 id="orga87af67"><span class="section-number-3">2.1</span> Init</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We initialize all the stages with the default parameters.
@@ -426,8 +426,8 @@ All the controllers are set to 0 (Open Loop).
</p>
</div>
</div>
<div id="outline-container-orgbbef650" class="outline-3">
<h3 id="orgbbef650"><span class="section-number-3">2.2</span> Identification</h3>
<div id="outline-container-org2d53583" class="outline-3">
<h3 id="org2d53583"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We identify the dynamics of the system.
@@ -490,19 +490,19 @@ Finally, we save the identified system dynamics for further analysis.
</div>
</div>
<div id="outline-container-orgb5102fd" class="outline-3">
<h3 id="orgb5102fd"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
<div id="outline-container-orgc443c0b" class="outline-3">
<h3 id="orgc443c0b"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We show several plots representing the sensitivity to disturbances:
</p>
<ul class="org-ul">
<li>in figure <a href="#orge3abf0f">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="#org25d95cb">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>
<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>
</ul>
<div id="orge3abf0f" class="figure">
<div id="org4d3097e" class="figure">
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
</p>
<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>
@@ -510,7 +510,7 @@ We show several plots representing the sensitivity to disturbances:
<div id="org25d95cb" class="figure">
<div id="orgfd7633d" class="figure">
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
</p>
<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>
@@ -518,16 +518,16 @@ We show several plots representing the sensitivity to disturbances:
</div>
</div>
<div id="outline-container-orgafe8970" class="outline-3">
<h3 id="orgafe8970"><span class="section-number-3">2.4</span> Plant</h3>
<div id="outline-container-orgdb21910" class="outline-3">
<h3 id="orgdb21910"><span class="section-number-3">2.4</span> Plant</h3>
<div class="outline-text-3" id="text-2-4">
<p>
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="#org62d1d12">5</a>.
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>.
It corresponds to the plant to control.
</p>
<div id="org62d1d12" class="figure">
<div id="orgee21d6a" class="figure">
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
</p>
<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>
@@ -536,21 +536,21 @@ It corresponds to the plant to control.
</div>
</div>
<div id="outline-container-orgeab4870" class="outline-2">
<h2 id="orgeab4870"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div id="outline-container-org497a34a" class="outline-2">
<h2 id="org497a34a"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org04c8f6e"></a>
<a id="org61a9736"></a>
</p>
<div id="orge50f87e" class="figure">
<div id="orgf30b3b3" class="figure">
<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>
</div>
</div>
<div id="outline-container-org6cf62a2" class="outline-3">
<h3 id="org6cf62a2"><span class="section-number-3">3.1</span> Control Design</h3>
<div id="outline-container-org90d6383" class="outline-3">
<h3 id="org90d6383"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1">
<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>;
@@ -562,7 +562,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
</p>
<div id="org26ea3c1" class="figure">
<div id="org13e2d05" class="figure">
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
</p>
<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>
@@ -577,7 +577,7 @@ The controller for each pair of actuator/sensor is:
</div>
<div id="org27d1bb0" class="figure">
<div id="org928425f" class="figure">
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
</p>
<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>
@@ -585,8 +585,8 @@ The controller for each pair of actuator/sensor is:
</div>
</div>
<div id="outline-container-orgf9a5f33" class="outline-3">
<h3 id="orgf9a5f33"><span class="section-number-3">3.2</span> Identification</h3>
<div id="outline-container-orge5c43d3" class="outline-3">
<h3 id="orge5c43d3"><span class="section-number-3">3.2</span> Identification</h3>
<div class="outline-text-3" id="text-3-2">
<p>
Let's initialize the system prior to identification.
@@ -669,18 +669,18 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-org7a80859" class="outline-3">
<h3 id="org7a80859"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div id="outline-container-orgdc6e62f" class="outline-3">
<h3 id="orgdc6e62f"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-3-3">
<div id="orgca12220" class="figure">
<div id="org8df8488" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
</p>
<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>
</div>
<div id="org19c25c8" class="figure">
<div id="org6003ced" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
</p>
<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>
@@ -688,11 +688,11 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-org7bab9e9" class="outline-3">
<h3 id="org7bab9e9"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div id="outline-container-orgf2883d8" class="outline-3">
<h3 id="orgf2883d8"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-4">
<div id="org60ea1f1" class="figure">
<div id="org2071f90" class="figure">
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
</p>
<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>
@@ -700,8 +700,8 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-orgaac01c0" class="outline-3">
<h3 id="orgaac01c0"><span class="section-number-3">3.5</span> Conclusion</h3>
<div id="outline-container-orgb766da3" class="outline-3">
<h3 id="orgb766da3"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
<div class="important">
<p>
@@ -713,25 +713,25 @@ Integral Force Feedback:
</div>
</div>
<div id="outline-container-org8d9b463" class="outline-2">
<h2 id="org8d9b463"><span class="section-number-2">4</span> Relative Motion Control</h2>
<div id="outline-container-org0216063" class="outline-2">
<h2 id="org0216063"><span class="section-number-2">4</span> Relative Motion Control</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="orgdc4ae31"></a>
<a id="orgcf7a709"></a>
</p>
<p>
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
</p>
<div id="org46f85ef" class="figure">
<div id="org8ed07c5" class="figure">
<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>
</div>
</div>
<div id="outline-container-orgbf2540a" class="outline-3">
<h3 id="orgbf2540a"><span class="section-number-3">4.1</span> Control Design</h3>
<div id="outline-container-orgda1c98e" class="outline-3">
<h3 id="orgda1c98e"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1">
<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>;
@@ -743,7 +743,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
</p>
<div id="orgc47e343" class="figure">
<div id="org75fbb9f" class="figure">
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
</p>
<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>
@@ -759,7 +759,7 @@ A Low pass Filter is added to make the controller transfer function proper.
</div>
<div id="org9c157b6" class="figure">
<div id="orgc5d2eb6" class="figure">
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
</p>
<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>
@@ -767,8 +767,8 @@ A Low pass Filter is added to make the controller transfer function proper.
</div>
</div>
<div id="outline-container-org1d106d7" class="outline-3">
<h3 id="org1d106d7"><span class="section-number-3">4.2</span> Identification</h3>
<div id="outline-container-orge3806a0" class="outline-3">
<h3 id="orge3806a0"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2">
<p>
Let's initialize the system prior to identification.
@@ -852,18 +852,18 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
<div id="outline-container-orgeb7d680" class="outline-3">
<h3 id="orgeb7d680"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div id="outline-container-orge58c47d" class="outline-3">
<h3 id="orge58c47d"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-4-3">
<div id="org7a8bd68" class="figure">
<div id="orgd910119" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
</p>
<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>
</div>
<div id="orgb8fed93" class="figure">
<div id="org6610f06" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
</p>
<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>
@@ -871,11 +871,11 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-org573eda0" class="outline-3">
<h3 id="org573eda0"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div id="outline-container-org70ec2cf" class="outline-3">
<h3 id="org70ec2cf"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-4">
<div id="org1f8e935" class="figure">
<div id="org7508a42" class="figure">
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
</p>
<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>
@@ -883,8 +883,8 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-org02ca488" class="outline-3">
<h3 id="org02ca488"><span class="section-number-3">4.5</span> Conclusion</h3>
<div id="outline-container-orga845b21" class="outline-3">
<h3 id="orga845b21"><span class="section-number-3">4.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-5">
<div class="important">
<p>
@@ -896,25 +896,25 @@ Relative Motion Control:
</div>
</div>
<div id="outline-container-org57948ea" class="outline-2">
<h2 id="org57948ea"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
<div id="outline-container-org7666422" class="outline-2">
<h2 id="org7666422"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-5">
<p>
<a id="orgdd11541"></a>
<a id="org6b8afcf"></a>
</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>
<div id="org0fcd7e7" class="figure">
<div id="orga86445d" class="figure">
<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>
</div>
</div>
<div id="outline-container-org4b4d061" class="outline-3">
<h3 id="org4b4d061"><span class="section-number-3">5.1</span> Control Design</h3>
<div id="outline-container-org58e4d64" class="outline-3">
<h3 id="org58e4d64"><span class="section-number-3">5.1</span> Control Design</h3>
<div class="outline-text-3" id="text-5-1">
<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>;
@@ -922,7 +922,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div>
<div id="orgbf7145f" class="figure">
<div id="orgf4888fb" class="figure">
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
</p>
<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>
@@ -934,7 +934,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div>
<div id="org1b6adf4" class="figure">
<div id="org1a62235" class="figure">
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
</p>
<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>
@@ -942,8 +942,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div>
</div>
<div id="outline-container-orgd4f4973" class="outline-3">
<h3 id="orgd4f4973"><span class="section-number-3">5.2</span> Identification</h3>
<div id="outline-container-org7e8b911" class="outline-3">
<h3 id="org7e8b911"><span class="section-number-3">5.2</span> Identification</h3>
<div class="outline-text-3" id="text-5-2">
<p>
Let's initialize the system prior to identification.
@@ -1026,18 +1026,18 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-org6cfeae5" class="outline-3">
<h3 id="org6cfeae5"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
<div id="outline-container-org2adcafe" class="outline-3">
<h3 id="org2adcafe"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-5-3">
<div id="org6fb6e94" class="figure">
<div id="org9ca6224" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
</p>
<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>
</div>
<div id="org6f13385" class="figure">
<div id="orgd0ada58" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
</p>
<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>
@@ -1045,11 +1045,11 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-org89e0408" class="outline-3">
<h3 id="org89e0408"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div id="outline-container-orge8b5bd9" class="outline-3">
<h3 id="orge8b5bd9"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-4">
<div id="org7051238" class="figure">
<div id="org55c6262" class="figure">
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
</p>
<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>
@@ -1057,8 +1057,8 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div>
</div>
<div id="outline-container-orgc27bce5" class="outline-3">
<h3 id="orgc27bce5"><span class="section-number-3">5.5</span> Conclusion</h3>
<div id="outline-container-org22d6515" class="outline-3">
<h3 id="org22d6515"><span class="section-number-3">5.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-5">
<div class="important">
<p>
@@ -1069,15 +1069,15 @@ Direct Velocity Feedback:
</div>
</div>
</div>
<div id="outline-container-org6dd07d9" class="outline-2">
<h2 id="org6dd07d9"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
<div id="outline-container-org55010b4" class="outline-2">
<h2 id="org55010b4"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
<div class="outline-text-2" id="text-6">
<p>
<a id="org5272a4c"></a>
<a id="org9b9c235"></a>
</p>
</div>
<div id="outline-container-orgd62929a" class="outline-3">
<h3 id="orgd62929a"><span class="section-number-3">6.1</span> Load the plants</h3>
<div id="outline-container-org5cb1e25" class="outline-3">
<h3 id="org5cb1e25"><span class="section-number-3">6.1</span> Load the plants</h3>
<div class="outline-text-3" id="text-6-1">
<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>;
@@ -1086,11 +1086,11 @@ Direct Velocity Feedback:
</div>
</div>
<div id="outline-container-orgbd35b93" class="outline-3">
<h3 id="orgbd35b93"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
<div id="outline-container-orgc746216" class="outline-3">
<h3 id="orgc746216"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-6-2">
<div id="org5eda09f" class="figure">
<div id="orga056e76" class="figure">
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
</p>
<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>
@@ -1098,21 +1098,21 @@ Direct Velocity Feedback:
<div id="org1fae0e7" class="figure">
<div id="org5bfe138" class="figure">
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
</p>
<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>
<div id="orgb2bd39c" class="figure">
<div id="org4e0c629" class="figure">
<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>
<div id="org1f00826" class="figure">
<div id="orgae22af6" class="figure">
<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>
@@ -1120,11 +1120,11 @@ Direct Velocity Feedback:
</div>
</div>
<div id="outline-container-org72ab5fd" class="outline-3">
<h3 id="org72ab5fd"><span class="section-number-3">6.3</span> Damped Plant</h3>
<div id="outline-container-orgcd1790f" class="outline-3">
<h3 id="orgcd1790f"><span class="section-number-3">6.3</span> Damped Plant</h3>
<div class="outline-text-3" id="text-6-3">
<div id="org0296cfa" class="figure">
<div id="org38fbe3d" class="figure">
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
</p>
<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>
@@ -1132,10 +1132,10 @@ Direct Velocity Feedback:
</div>
</div>
<div id="outline-container-org2c43078" class="outline-3">
<h3 id="org2c43078"><span class="section-number-3">6.4</span> Conclusion</h3>
<div id="outline-container-org9a602cb" class="outline-3">
<h3 id="org9a602cb"><span class="section-number-3">6.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-6-4">
<table id="orga82a170" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgf039db4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
<colgroup>
@@ -1205,7 +1205,7 @@ The next step is to take into account the power spectral density of each disturb
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-25 ven. 12:32</p>
<p class="date">Created: 2019-10-25 ven. 16:02</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

2
uniaxial/index.org
View File

@@ -2217,7 +2217,7 @@ Direct Velocity Feedback:
title('$F_{rz}$ to $D$');
hold on;
plot(freqs, abs(squeeze(freqresp(G ('D', 'Frz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'OL');
plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Frz'), freqs, 'Hz'))), 'k' , 'DisplayName', 'IFF');
plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Frz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Frz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Frz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
hold off;