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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2019-11-05 mar. 11:27 --> <!-- 2019-11-11 lun. 14:50 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Simscape Uniaxial Model</title> <title>Simscape Uniaxial Model</title>
@ -280,72 +280,72 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org5379e01">1. Simscape Model</a></li> <li><a href="#orgb71e7ae">1. Simscape Model</a></li>
<li><a href="#org985bb58">2. Undamped System</a> <li><a href="#orga5d5945">2. Undamped System</a>
<ul> <ul>
<li><a href="#org282af69">2.1. Init</a></li> <li><a href="#org2fbbd0e">2.1. Init</a></li>
<li><a href="#orgc86b374">2.2. Identification</a></li> <li><a href="#org33d8ecc">2.2. Identification</a></li>
<li><a href="#org3f8d2fb">2.3. Sensitivity to Disturbances</a></li> <li><a href="#org8c5d7f8">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#org364e9bb">2.4. Noise Budget</a></li> <li><a href="#org97a5979">2.4. Noise Budget</a></li>
<li><a href="#orgb4daaef">2.5. Plant</a></li> <li><a href="#org7525f32">2.5. Plant</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orga653f73">3. Integral Force Feedback</a> <li><a href="#orgc6b843b">3. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#org0151f36">3.1. Control Design</a></li> <li><a href="#org78be696">3.1. Control Design</a></li>
<li><a href="#org98318db">3.2. Identification</a></li> <li><a href="#orgef1c965">3.2. Identification</a></li>
<li><a href="#orgff50004">3.3. Sensitivity to Disturbance</a></li> <li><a href="#orgca3bd8a">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#org466c9e5">3.4. Damped Plant</a></li> <li><a href="#orgb7e6096">3.4. Damped Plant</a></li>
<li><a href="#org2c6af48">3.5. Conclusion</a></li> <li><a href="#org4f0a2b9">3.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd931aba">4. Relative Motion Control</a> <li><a href="#orgcc4cdcc">4. Relative Motion Control</a>
<ul> <ul>
<li><a href="#org4c925ca">4.1. Control Design</a></li> <li><a href="#orgd198cd8">4.1. Control Design</a></li>
<li><a href="#org64a2751">4.2. Identification</a></li> <li><a href="#orgcf5bb38">4.2. Identification</a></li>
<li><a href="#org03b5726">4.3. Sensitivity to Disturbance</a></li> <li><a href="#orgb8479f2">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#orgcf70df5">4.4. Damped Plant</a></li> <li><a href="#org9e3dd36">4.4. Damped Plant</a></li>
<li><a href="#orga259511">4.5. Conclusion</a></li> <li><a href="#org3cd3d80">4.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgb0f2fac">5. Direct Velocity Feedback</a> <li><a href="#org9fd5335">5. Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#org83437ab">5.1. Control Design</a></li> <li><a href="#org80df2a6">5.1. Control Design</a></li>
<li><a href="#orgd6906f3">5.2. Identification</a></li> <li><a href="#orgf585eca">5.2. Identification</a></li>
<li><a href="#org2f6bd60">5.3. Sensitivity to Disturbance</a></li> <li><a href="#org8b0401b">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#org0c90e43">5.4. Damped Plant</a></li> <li><a href="#org5f335db">5.4. Damped Plant</a></li>
<li><a href="#orgb63901b">5.5. Conclusion</a></li> <li><a href="#orged3cacf">5.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org7970e47">6. With Cedrat Piezo-electric Actuators</a> <li><a href="#org54f600e">6. With Cedrat Piezo-electric Actuators</a>
<ul> <ul>
<li><a href="#org575c09c">6.1. Identification</a></li> <li><a href="#org9619137">6.1. Identification</a></li>
<li><a href="#org2d4d30c">6.2. Control Design</a></li> <li><a href="#org0702041">6.2. Control Design</a></li>
<li><a href="#org1101905">6.3. Identification</a></li> <li><a href="#org432c3b9">6.3. Identification</a></li>
<li><a href="#orgafc6298">6.4. Sensitivity to Disturbance</a></li> <li><a href="#org92524a2">6.4. Sensitivity to Disturbance</a></li>
<li><a href="#orgebe455d">6.5. Damped Plant</a></li> <li><a href="#org36995c4">6.5. Damped Plant</a></li>
<li><a href="#org33843ee">6.6. Conclusion</a></li> <li><a href="#org293c60a">6.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org43dd103">7. Comparison of Active Damping Techniques</a> <li><a href="#org3679584">7. Comparison of Active Damping Techniques</a>
<ul> <ul>
<li><a href="#orgbd3fe7b">7.1. Load the plants</a></li> <li><a href="#org7ead2f2">7.1. Load the plants</a></li>
<li><a href="#org82a27fa">7.2. Sensitivity to Disturbance</a></li> <li><a href="#org7b3030d">7.2. Sensitivity to Disturbance</a></li>
<li><a href="#org0dc21b7">7.3. Noise Budget</a></li> <li><a href="#org4f38837">7.3. Noise Budget</a></li>
<li><a href="#orgf592486">7.4. Damped Plant</a></li> <li><a href="#org1cab4a1">7.4. Damped Plant</a></li>
<li><a href="#orgfc2e28b">7.5. Conclusion</a></li> <li><a href="#org89243de">7.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgded5bc7">8. Voice Coil</a> <li><a href="#orgf7fa09b">8. Voice Coil</a>
<ul> <ul>
<li><a href="#orgbba145f">8.1. Init</a></li> <li><a href="#org5bfd692">8.1. Init</a></li>
<li><a href="#org465be28">8.2. Identification</a></li> <li><a href="#org145a9df">8.2. Identification</a></li>
<li><a href="#orgda14068">8.3. Sensitivity to Disturbances</a></li> <li><a href="#org3b53ae6">8.3. Sensitivity to Disturbances</a></li>
<li><a href="#org49bb7e7">8.4. Noise Budget</a></li> <li><a href="#org33c2392">8.4. Noise Budget</a></li>
<li><a href="#org04357b8">8.5. Integral Force Feedback</a></li> <li><a href="#org332ecb6">8.5. Integral Force Feedback</a></li>
<li><a href="#org83d9caa">8.6. Identification of the Damped Plant</a></li> <li><a href="#orgd420efb">8.6. Identification of the Damped Plant</a></li>
<li><a href="#orge278186">8.7. Noise Budget</a></li> <li><a href="#org99ecd1f">8.7. Noise Budget</a></li>
<li><a href="#org152df36">8.8. Conclusion</a></li> <li><a href="#orgffe5e36">8.8. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -360,15 +360,15 @@ 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. This is done in order to more easily study the system and evaluate control techniques.
</p> </p>
<div id="outline-container-org5379e01" class="outline-2"> <div id="outline-container-orgb71e7ae" class="outline-2">
<h2 id="org5379e01"><span class="section-number-2">1</span> Simscape Model</h2> <h2 id="orgb71e7ae"><span class="section-number-2">1</span> Simscape Model</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="org233f30c"></a> <a id="org4affa13"></a>
</p> </p>
<p> <p>
A schematic of the uniaxial model used for simulations is represented in figure <a href="#orgb72b23c">1</a>. A schematic of the uniaxial model used for simulations is represented in figure <a href="#orge3c5fac">1</a>.
</p> </p>
<p> <p>
@ -412,7 +412,7 @@ The control signal \(u\) is:
</ul> </ul>
<div id="orgb72b23c" class="figure"> <div id="orge3c5fac" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" /> <p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p> <p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p>
@ -421,11 +421,11 @@ The control signal \(u\) is:
<p> <p>
Few active damping techniques will be compared in order to decide which sensor is to be included in the system. 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="#orgf6769a3">2</a>. Schematics of the active damping techniques are displayed in figure <a href="#org4593626">2</a>.
</p> </p>
<div id="orgf6769a3" class="figure"> <div id="org4593626" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" /> <p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p> <p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p>
@ -433,18 +433,18 @@ Schematics of the active damping techniques are displayed in figure <a href="#or
</div> </div>
</div> </div>
<div id="outline-container-org985bb58" class="outline-2"> <div id="outline-container-orga5d5945" class="outline-2">
<h2 id="org985bb58"><span class="section-number-2">2</span> Undamped System</h2> <h2 id="orga5d5945"><span class="section-number-2">2</span> Undamped System</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org99f2016"></a> <a id="orge23ab54"></a>
</p> </p>
<p> <p>
Let's start by study the undamped system. Let's start by study the undamped system.
</p> </p>
</div> </div>
<div id="outline-container-org282af69" class="outline-3"> <div id="outline-container-org2fbbd0e" class="outline-3">
<h3 id="org282af69"><span class="section-number-3">2.1</span> Init</h3> <h3 id="org2fbbd0e"><span class="section-number-3">2.1</span> Init</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -456,8 +456,8 @@ All the controllers are set to 0 (Open Loop).
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-orgc86b374" class="outline-3"> <div id="outline-container-org33d8ecc" class="outline-3">
<h3 id="orgc86b374"><span class="section-number-3">2.2</span> Identification</h3> <h3 id="org33d8ecc"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We identify the dynamics of the system. We identify the dynamics of the system.
@ -520,19 +520,19 @@ Finally, we save the identified system dynamics for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org3f8d2fb" class="outline-3"> <div id="outline-container-org8c5d7f8" class="outline-3">
<h3 id="org3f8d2fb"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3> <h3 id="org8c5d7f8"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We show several plots representing the sensitivity to disturbances: We show several plots representing the sensitivity to disturbances:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>in figure <a href="#org65e5bc4">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="#org811b66a">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="#org01c7629">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="#org5df06c0">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> </ul>
<div id="org65e5bc4" class="figure"> <div id="org811b66a" class="figure">
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" /> <p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
</p> </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> <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>
@ -540,7 +540,7 @@ We show several plots representing the sensitivity to disturbances:
<div id="org01c7629" class="figure"> <div id="org5df06c0" class="figure">
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" /> <p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
</p> </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> <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>
@ -548,8 +548,8 @@ We show several plots representing the sensitivity to disturbances:
</div> </div>
</div> </div>
<div id="outline-container-org364e9bb" class="outline-3"> <div id="outline-container-org97a5979" class="outline-3">
<h3 id="org364e9bb"><span class="section-number-3">2.4</span> Noise Budget</h3> <h3 id="org97a5979"><span class="section-number-3">2.4</span> Noise Budget</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We first load the measured PSD of the disturbance. We first load the measured PSD of the disturbance.
@ -561,12 +561,12 @@ We first load the measured PSD of the disturbance.
<p> <p>
The effect of these disturbances on the distance \(D\) is computed below. The effect of these disturbances on the distance \(D\) is computed below.
The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#org062cf88">5</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#orgf07d38b">6</a>. The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#org415c8fd">5</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org52ed86e">6</a>.
</p> </p>
<p> <p>
The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#orgf07d38b">6</a>. The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org52ed86e">6</a>.
</p> </p>
<pre class="example"> <pre class="example">
3.3793e-06 3.3793e-06
@ -574,32 +574,32 @@ The Root Mean Square value of the obtained displacement \(D\) is computed below
<div id="org062cf88" class="figure"> <div id="org415c8fd" class="figure">
<p><img src="figs/uniaxial-psd-dist.png" alt="uniaxial-psd-dist.png" /> <p><img src="figs/uniaxial-psd-dist.png" alt="uniaxial-psd-dist.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>caption (<a href="./figs/uniaxial-psd-dist.png">png</a>, <a href="./figs/uniaxial-psd-dist.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 5: </span>PSD of the effect of disturbances on \(D\) (<a href="./figs/uniaxial-psd-dist.png">png</a>, <a href="./figs/uniaxial-psd-dist.pdf">pdf</a>)</p>
</div> </div>
<div id="orgf07d38b" class="figure"> <div id="org52ed86e" class="figure">
<p><img src="figs/uniaxial-cas-dist.png" alt="uniaxial-cas-dist.png" /> <p><img src="figs/uniaxial-cas-dist.png" alt="uniaxial-cas-dist.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>caption (<a href="./figs/uniaxial-cas-dist.png">png</a>, <a href="./figs/uniaxial-cas-dist.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 6: </span>CAS of the effect of disturbances on \(D\) (<a href="./figs/uniaxial-cas-dist.png">png</a>, <a href="./figs/uniaxial-cas-dist.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgb4daaef" class="outline-3"> <div id="outline-container-org7525f32" class="outline-3">
<h3 id="orgb4daaef"><span class="section-number-3">2.5</span> Plant</h3> <h3 id="org7525f32"><span class="section-number-3">2.5</span> Plant</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <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="#orgcb273be">7</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="#org209e53c">7</a>.
It corresponds to the plant to control. It corresponds to the plant to control.
</p> </p>
<div id="orgcb273be" class="figure"> <div id="org209e53c" class="figure">
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" /> <p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 7: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
@ -608,21 +608,21 @@ It corresponds to the plant to control.
</div> </div>
</div> </div>
<div id="outline-container-orga653f73" class="outline-2"> <div id="outline-container-orgc6b843b" class="outline-2">
<h2 id="orga653f73"><span class="section-number-2">3</span> Integral Force Feedback</h2> <h2 id="orgc6b843b"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org0f88f24"></a> <a id="org5d395a2"></a>
</p> </p>
<div id="orga00e5a6" class="figure"> <div id="orgea17388" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" /> <p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p> <p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p>
</div> </div>
</div> </div>
<div id="outline-container-org0151f36" class="outline-3"> <div id="outline-container-org78be696" class="outline-3">
<h3 id="org0151f36"><span class="section-number-3">3.1</span> Control Design</h3> <h3 id="org78be696"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<div class="org-src-container"> <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 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>;
@ -634,7 +634,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
</p> </p>
<div id="orgf741d44" class="figure"> <div id="org952556f" class="figure">
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" /> <p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </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> <p><span class="figure-number">Figure 9: </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>
@ -649,7 +649,7 @@ The controller for each pair of actuator/sensor is:
</div> </div>
<div id="org331d87b" class="figure"> <div id="orgf9d4fb1" class="figure">
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" /> <p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </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> <p><span class="figure-number">Figure 10: </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>
@ -657,8 +657,8 @@ The controller for each pair of actuator/sensor is:
</div> </div>
</div> </div>
<div id="outline-container-org98318db" class="outline-3"> <div id="outline-container-orgef1c965" class="outline-3">
<h3 id="org98318db"><span class="section-number-3">3.2</span> Identification</h3> <h3 id="orgef1c965"><span class="section-number-3">3.2</span> Identification</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
@ -741,18 +741,18 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-orgff50004" class="outline-3"> <div id="outline-container-orgca3bd8a" class="outline-3">
<h3 id="orgff50004"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3> <h3 id="orgca3bd8a"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<div id="orgbc9fdaa" class="figure"> <div id="org0740db4" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" /> <p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </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> <p><span class="figure-number">Figure 11: </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>
<div id="org0f6056d" class="figure"> <div id="org02782a2" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" /> <p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </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> <p><span class="figure-number">Figure 12: </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>
@ -760,11 +760,11 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-org466c9e5" class="outline-3"> <div id="outline-container-orgb7e6096" class="outline-3">
<h3 id="org466c9e5"><span class="section-number-3">3.4</span> Damped Plant</h3> <h3 id="orgb7e6096"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<div id="orge4f80dd" class="figure"> <div id="orge1b1f09" class="figure">
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" /> <p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </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> <p><span class="figure-number">Figure 13: </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>
@ -772,8 +772,8 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-org2c6af48" class="outline-3"> <div id="outline-container-org4f0a2b9" class="outline-3">
<h3 id="org2c6af48"><span class="section-number-3">3.5</span> Conclusion</h3> <h3 id="org4f0a2b9"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<div class="important"> <div class="important">
<p> <p>
@ -785,25 +785,25 @@ Integral Force Feedback:
</div> </div>
</div> </div>
<div id="outline-container-orgd931aba" class="outline-2"> <div id="outline-container-orgcc4cdcc" class="outline-2">
<h2 id="orgd931aba"><span class="section-number-2">4</span> Relative Motion Control</h2> <h2 id="orgcc4cdcc"><span class="section-number-2">4</span> Relative Motion Control</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<p> <p>
<a id="orgd4bc59d"></a> <a id="org30fd654"></a>
</p> </p>
<p> <p>
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input. In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
</p> </p>
<div id="org38e55a9" class="figure"> <div id="orge8dc6c5" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" /> <p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p> <p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p>
</div> </div>
</div> </div>
<div id="outline-container-org4c925ca" class="outline-3"> <div id="outline-container-orgd198cd8" class="outline-3">
<h3 id="org4c925ca"><span class="section-number-3">4.1</span> Control Design</h3> <h3 id="orgd198cd8"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<div class="org-src-container"> <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 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>;
@ -815,7 +815,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
</p> </p>
<div id="org8d77310" class="figure"> <div id="org34aa38e" class="figure">
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" /> <p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </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> <p><span class="figure-number">Figure 15: </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>
@ -831,7 +831,7 @@ A Low pass Filter is added to make the controller transfer function proper.
</div> </div>
<div id="org5ac4f8e" class="figure"> <div id="orgaf673bf" class="figure">
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" /> <p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 16: </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> <p><span class="figure-number">Figure 16: </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>
@ -839,8 +839,8 @@ A Low pass Filter is added to make the controller transfer function proper.
</div> </div>
</div> </div>
<div id="outline-container-org64a2751" class="outline-3"> <div id="outline-container-orgcf5bb38" class="outline-3">
<h3 id="org64a2751"><span class="section-number-3">4.2</span> Identification</h3> <h3 id="orgcf5bb38"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
@ -924,18 +924,18 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
<div id="outline-container-org03b5726" class="outline-3"> <div id="outline-container-orgb8479f2" class="outline-3">
<h3 id="org03b5726"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3> <h3 id="orgb8479f2"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div id="org9d3c40d" class="figure"> <div id="orga612d6b" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" /> <p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
</p> </p>
<p><span class="figure-number">Figure 17: </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> <p><span class="figure-number">Figure 17: </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>
<div id="org97c0227" class="figure"> <div id="org525bbf8" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" /> <p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
</p> </p>
<p><span class="figure-number">Figure 18: </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> <p><span class="figure-number">Figure 18: </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>
@ -943,11 +943,11 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-orgcf70df5" class="outline-3"> <div id="outline-container-org9e3dd36" class="outline-3">
<h3 id="orgcf70df5"><span class="section-number-3">4.4</span> Damped Plant</h3> <h3 id="org9e3dd36"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<div id="org73b1d75" class="figure"> <div id="org1f3d1fb" class="figure">
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" /> <p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
</p> </p>
<p><span class="figure-number">Figure 19: </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> <p><span class="figure-number">Figure 19: </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>
@ -955,8 +955,8 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-orga259511" class="outline-3"> <div id="outline-container-org3cd3d80" class="outline-3">
<h3 id="orga259511"><span class="section-number-3">4.5</span> Conclusion</h3> <h3 id="org3cd3d80"><span class="section-number-3">4.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-5"> <div class="outline-text-3" id="text-4-5">
<div class="important"> <div class="important">
<p> <p>
@ -968,25 +968,25 @@ Relative Motion Control:
</div> </div>
</div> </div>
<div id="outline-container-orgb0f2fac" class="outline-2"> <div id="outline-container-org9fd5335" class="outline-2">
<h2 id="orgb0f2fac"><span class="section-number-2">5</span> Direct Velocity Feedback</h2> <h2 id="org9fd5335"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
<p> <p>
<a id="org1655ed1"></a> <a id="org6af5294"></a>
</p> </p>
<p> <p>
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input. In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
</p> </p>
<div id="org9c6dfe4" class="figure"> <div id="orgb69aba0" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" /> <p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
</p> </p>
<p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p> <p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p>
</div> </div>
</div> </div>
<div id="outline-container-org83437ab" class="outline-3"> <div id="outline-container-org80df2a6" class="outline-3">
<h3 id="org83437ab"><span class="section-number-3">5.1</span> Control Design</h3> <h3 id="org80df2a6"><span class="section-number-3">5.1</span> Control Design</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<div class="org-src-container"> <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 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>;
@ -994,7 +994,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div> </div>
<div id="org28bd4a3" class="figure"> <div id="org8ef9378" class="figure">
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" /> <p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 21: </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> <p><span class="figure-number">Figure 21: </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>
@ -1006,7 +1006,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div> </div>
<div id="org3b9273f" class="figure"> <div id="orgd6cd975" class="figure">
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" /> <p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
</p> </p>
<p><span class="figure-number">Figure 22: </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> <p><span class="figure-number">Figure 22: </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>
@ -1014,8 +1014,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div> </div>
</div> </div>
<div id="outline-container-orgd6906f3" class="outline-3"> <div id="outline-container-orgf585eca" class="outline-3">
<h3 id="orgd6906f3"><span class="section-number-3">5.2</span> Identification</h3> <h3 id="orgf585eca"><span class="section-number-3">5.2</span> Identification</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
@ -1098,18 +1098,18 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-org2f6bd60" class="outline-3"> <div id="outline-container-org8b0401b" class="outline-3">
<h3 id="org2f6bd60"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3> <h3 id="org8b0401b"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div id="orged28a54" class="figure"> <div id="orgf96e285" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" /> <p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
</p> </p>
<p><span class="figure-number">Figure 23: </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> <p><span class="figure-number">Figure 23: </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>
<div id="org76a4395" class="figure"> <div id="org10e4399" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" /> <p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
</p> </p>
<p><span class="figure-number">Figure 24: </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> <p><span class="figure-number">Figure 24: </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>
@ -1117,11 +1117,11 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-org0c90e43" class="outline-3"> <div id="outline-container-org5f335db" class="outline-3">
<h3 id="org0c90e43"><span class="section-number-3">5.4</span> Damped Plant</h3> <h3 id="org5f335db"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-4"> <div class="outline-text-3" id="text-5-4">
<div id="orgfbee72a" class="figure"> <div id="org5432972" class="figure">
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" /> <p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
</p> </p>
<p><span class="figure-number">Figure 25: </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> <p><span class="figure-number">Figure 25: </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>
@ -1129,8 +1129,8 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-orgb63901b" class="outline-3"> <div id="outline-container-orged3cacf" class="outline-3">
<h3 id="orgb63901b"><span class="section-number-3">5.5</span> Conclusion</h3> <h3 id="orged3cacf"><span class="section-number-3">5.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-5"> <div class="outline-text-3" id="text-5-5">
<div class="important"> <div class="important">
<p> <p>
@ -1141,25 +1141,25 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org7970e47" class="outline-2"> <div id="outline-container-org54f600e" class="outline-2">
<h2 id="org7970e47"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2> <h2 id="org54f600e"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-6">
<p> <p>
<a id="org86ab0ae"></a> <a id="org64ee63d"></a>
</p> </p>
<p> <p>
The model used for the Cedrat actuator is shown in figure <a href="#orgd05de0b">26</a>. The model used for the Cedrat actuator is shown in figure <a href="#orgc9104bb">26</a>.
</p> </p>
<div id="orgd05de0b" class="figure"> <div id="orgc9104bb" class="figure">
<p><img src="figs/cedrat-uniaxial-actuator.png" alt="cedrat-uniaxial-actuator.png" /> <p><img src="figs/cedrat-uniaxial-actuator.png" alt="cedrat-uniaxial-actuator.png" />
</p> </p>
<p><span class="figure-number">Figure 26: </span>Schematic of the model used for the Cedrat Actuator</p> <p><span class="figure-number">Figure 26: </span>Schematic of the model used for the Cedrat Actuator</p>
</div> </div>
</div> </div>
<div id="outline-container-org575c09c" class="outline-3"> <div id="outline-container-org9619137" class="outline-3">
<h3 id="org575c09c"><span class="section-number-3">6.1</span> Identification</h3> <h3 id="org9619137"><span class="section-number-3">6.1</span> Identification</h3>
<div class="outline-text-3" id="text-6-1"> <div class="outline-text-3" id="text-6-1">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
@ -1247,15 +1247,15 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
</div> </div>
</div> </div>
<div id="outline-container-org2d4d30c" class="outline-3"> <div id="outline-container-org0702041" class="outline-3">
<h3 id="org2d4d30c"><span class="section-number-3">6.2</span> Control Design</h3> <h3 id="org0702041"><span class="section-number-3">6.2</span> Control Design</h3>
<div class="outline-text-3" id="text-6-2"> <div class="outline-text-3" id="text-6-2">
<p> <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. 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> </p>
<div id="org3651b4e" class="figure"> <div id="org2f4f9cc" class="figure">
<p><img src="figs/uniaxial_cedrat_plant.png" alt="uniaxial_cedrat_plant.png" /> <p><img src="figs/uniaxial_cedrat_plant.png" alt="uniaxial_cedrat_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 27: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_cedrat_plant.png">png</a>, <a href="./figs/uniaxial_cedrat_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 27: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_cedrat_plant.png">png</a>, <a href="./figs/uniaxial_cedrat_plant.pdf">pdf</a>)</p>
@ -1270,7 +1270,7 @@ The controller for each pair of actuator/sensor is:
</div> </div>
<div id="org6ed3ff4" class="figure"> <div id="orgb4dfba9" class="figure">
<p><img src="figs/uniaxial_cedrat_open_loop.png" alt="uniaxial_cedrat_open_loop.png" /> <p><img src="figs/uniaxial_cedrat_open_loop.png" alt="uniaxial_cedrat_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 28: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_cedrat_open_loop.png">png</a>, <a href="./figs/uniaxial_cedrat_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 28: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_cedrat_open_loop.png">png</a>, <a href="./figs/uniaxial_cedrat_open_loop.pdf">pdf</a>)</p>
@ -1278,8 +1278,8 @@ The controller for each pair of actuator/sensor is:
</div> </div>
</div> </div>
<div id="outline-container-org1101905" class="outline-3"> <div id="outline-container-org432c3b9" class="outline-3">
<h3 id="org1101905"><span class="section-number-3">6.3</span> Identification</h3> <h3 id="org432c3b9"><span class="section-number-3">6.3</span> Identification</h3>
<div class="outline-text-3" id="text-6-3"> <div class="outline-text-3" id="text-6-3">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
@ -1363,18 +1363,18 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
</div> </div>
</div> </div>
<div id="outline-container-orgafc6298" class="outline-3"> <div id="outline-container-org92524a2" class="outline-3">
<h3 id="orgafc6298"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3> <h3 id="org92524a2"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-6-4"> <div class="outline-text-3" id="text-6-4">
<div id="org57267c2" class="figure"> <div id="orga3eef15" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_cedrat.png" alt="uniaxial_sensitivity_dist_cedrat.png" /> <p><img src="figs/uniaxial_sensitivity_dist_cedrat.png" alt="uniaxial_sensitivity_dist_cedrat.png" />
</p> </p>
<p><span class="figure-number">Figure 29: </span>Sensitivity to disturbance once the CEDRAT controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_cedrat.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 29: </span>Sensitivity to disturbance once the CEDRAT controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_cedrat.pdf">pdf</a>)</p>
</div> </div>
<div id="org89fd25b" class="figure"> <div id="org1c759e8" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_cedrat.png" alt="uniaxial_sensitivity_dist_stages_cedrat.png" /> <p><img src="figs/uniaxial_sensitivity_dist_stages_cedrat.png" alt="uniaxial_sensitivity_dist_stages_cedrat.png" />
</p> </p>
<p><span class="figure-number">Figure 30: </span>Sensitivity to force disturbances in various stages when CEDRAT is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 30: </span>Sensitivity to force disturbances in various stages when CEDRAT is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.pdf">pdf</a>)</p>
@ -1382,11 +1382,11 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
</div> </div>
</div> </div>
<div id="outline-container-orgebe455d" class="outline-3"> <div id="outline-container-org36995c4" class="outline-3">
<h3 id="orgebe455d"><span class="section-number-3">6.5</span> Damped Plant</h3> <h3 id="org36995c4"><span class="section-number-3">6.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-6-5"> <div class="outline-text-3" id="text-6-5">
<div id="org0979790" class="figure"> <div id="org0a5327e" class="figure">
<p><img src="figs/uniaxial_plant_cedrat_damped.png" alt="uniaxial_plant_cedrat_damped.png" /> <p><img src="figs/uniaxial_plant_cedrat_damped.png" alt="uniaxial_plant_cedrat_damped.png" />
</p> </p>
<p><span class="figure-number">Figure 31: </span>Damped Plant after CEDRAT is applied (<a href="./figs/uniaxial_plant_cedrat_damped.png">png</a>, <a href="./figs/uniaxial_plant_cedrat_damped.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 31: </span>Damped Plant after CEDRAT is applied (<a href="./figs/uniaxial_plant_cedrat_damped.png">png</a>, <a href="./figs/uniaxial_plant_cedrat_damped.pdf">pdf</a>)</p>
@ -1394,8 +1394,8 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
</div> </div>
</div> </div>
<div id="outline-container-org33843ee" class="outline-3"> <div id="outline-container-org293c60a" class="outline-3">
<h3 id="org33843ee"><span class="section-number-3">6.6</span> Conclusion</h3> <h3 id="org293c60a"><span class="section-number-3">6.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-6-6"> <div class="outline-text-3" id="text-6-6">
<div class="important"> <div class="important">
<p> <p>
@ -1407,15 +1407,15 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-org43dd103" class="outline-2"> <div id="outline-container-org3679584" class="outline-2">
<h2 id="org43dd103"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2> <h2 id="org3679584"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
<div class="outline-text-2" id="text-7"> <div class="outline-text-2" id="text-7">
<p> <p>
<a id="org59d45b8"></a> <a id="org43accf4"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgbd3fe7b" class="outline-3"> <div id="outline-container-org7ead2f2" class="outline-3">
<h3 id="orgbd3fe7b"><span class="section-number-3">7.1</span> Load the plants</h3> <h3 id="org7ead2f2"><span class="section-number-3">7.1</span> Load the plants</h3>
<div class="outline-text-3" id="text-7-1"> <div class="outline-text-3" id="text-7-1">
<div class="org-src-container"> <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 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>;
@ -1424,11 +1424,11 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-org82a27fa" class="outline-3"> <div id="outline-container-org7b3030d" class="outline-3">
<h3 id="org82a27fa"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3> <h3 id="org7b3030d"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-7-2"> <div class="outline-text-3" id="text-7-2">
<div id="org53c3b19" class="figure"> <div id="org6a0735b" class="figure">
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" /> <p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
</p> </p>
<p><span class="figure-number">Figure 32: </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> <p><span class="figure-number">Figure 32: </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>
@ -1436,21 +1436,21 @@ This gives similar results than with a classical force sensor.
<div id="org9fcda32" class="figure"> <div id="orgecd4e90" class="figure">
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" /> <p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
</p> </p>
<p><span class="figure-number">Figure 33: </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> <p><span class="figure-number">Figure 33: </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>
<div id="orgb63ab99" class="figure"> <div id="orgdaf4675" class="figure">
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" /> <p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
</p> </p>
<p><span class="figure-number">Figure 34: </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> <p><span class="figure-number">Figure 34: </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>
<div id="orgd60bc47" class="figure"> <div id="org08001e9" class="figure">
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" /> <p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
</p> </p>
<p><span class="figure-number">Figure 35: </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> <p><span class="figure-number">Figure 35: </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>
@ -1458,8 +1458,8 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-org0dc21b7" class="outline-3"> <div id="outline-container-org4f38837" class="outline-3">
<h3 id="org0dc21b7"><span class="section-number-3">7.3</span> Noise Budget</h3> <h3 id="org4f38837"><span class="section-number-3">7.3</span> Noise Budget</h3>
<div class="outline-text-3" id="text-7-3"> <div class="outline-text-3" id="text-7-3">
<p> <p>
We first load the measured PSD of the disturbance. We first load the measured PSD of the disturbance.
@ -1471,10 +1471,10 @@ We first load the measured PSD of the disturbance.
<p> <p>
The effect of these disturbances on the distance \(D\) is computed for all active damping techniques. The effect of these disturbances on the distance \(D\) is computed for all active damping techniques.
We then compute the Cumulative Amplitude Spectrum (figure <a href="#org7065c50">36</a>). We then compute the Cumulative Amplitude Spectrum (figure <a href="#orgea4a3e5">36</a>).
</p> </p>
<div id="org7065c50" class="figure"> <div id="orgea4a3e5" class="figure">
<p><img src="figs/uniaxial-comp-cas-dist.png" alt="uniaxial-comp-cas-dist.png" /> <p><img src="figs/uniaxial-comp-cas-dist.png" alt="uniaxial-comp-cas-dist.png" />
</p> </p>
<p><span class="figure-number">Figure 36: </span>Comparison of the Cumulative Amplitude Spectrum of \(D\) for different active damping techniques (<a href="./figs/uniaxial-comp-cas-dist.png">png</a>, <a href="./figs/uniaxial-comp-cas-dist.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 36: </span>Comparison of the Cumulative Amplitude Spectrum of \(D\) for different active damping techniques (<a href="./figs/uniaxial-comp-cas-dist.png">png</a>, <a href="./figs/uniaxial-comp-cas-dist.pdf">pdf</a>)</p>
@ -1483,7 +1483,7 @@ We then compute the Cumulative Amplitude Spectrum (figure <a href="#org7065c50">
<p> <p>
The obtained Root Mean Square Value for each active damping technique is shown below. The obtained Root Mean Square Value for each active damping technique is shown below.
</p> </p>
<table id="orgb85f411" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org4d742c7" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Obtain Root Mean Square value of \(D\) for each Active Damping Technique applied</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Obtain Root Mean Square value of \(D\) for each Active Damping Technique applied</caption>
<colgroup> <colgroup>
@ -1526,11 +1526,11 @@ It is important to note that the effect of direct forces applied to the sample a
</div> </div>
</div> </div>
<div id="outline-container-orgf592486" class="outline-3"> <div id="outline-container-org1cab4a1" class="outline-3">
<h3 id="orgf592486"><span class="section-number-3">7.4</span> Damped Plant</h3> <h3 id="org1cab4a1"><span class="section-number-3">7.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-7-4"> <div class="outline-text-3" id="text-7-4">
<div id="org8d5fcfc" class="figure"> <div id="orgd715679" class="figure">
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" /> <p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 37: </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> <p><span class="figure-number">Figure 37: </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>
@ -1538,10 +1538,10 @@ It is important to note that the effect of direct forces applied to the sample a
</div> </div>
</div> </div>
<div id="outline-container-orgfc2e28b" class="outline-3"> <div id="outline-container-org89243de" class="outline-3">
<h3 id="orgfc2e28b"><span class="section-number-3">7.5</span> Conclusion</h3> <h3 id="org89243de"><span class="section-number-3">7.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-7-5"> <div class="outline-text-3" id="text-7-5">
<table id="org56bbb29" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org25a4511" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Comparison of proposed active damping techniques</caption> <caption class="t-above"><span class="table-number">Table 2:</span> Comparison of proposed active damping techniques</caption>
<colgroup> <colgroup>
@ -1608,15 +1608,15 @@ It is important to note that the effect of direct forces applied to the sample a
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgded5bc7" class="outline-2"> <div id="outline-container-orgf7fa09b" class="outline-2">
<h2 id="orgded5bc7"><span class="section-number-2">8</span> Voice Coil</h2> <h2 id="orgf7fa09b"><span class="section-number-2">8</span> Voice Coil</h2>
<div class="outline-text-2" id="text-8"> <div class="outline-text-2" id="text-8">
<p> <p>
<a id="orga8a45b8"></a> <a id="org42314a9"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgbba145f" class="outline-3"> <div id="outline-container-org5bfd692" class="outline-3">
<h3 id="orgbba145f"><span class="section-number-3">8.1</span> Init</h3> <h3 id="org5bfd692"><span class="section-number-3">8.1</span> Init</h3>
<div class="outline-text-3" id="text-8-1"> <div class="outline-text-3" id="text-8-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -1628,8 +1628,8 @@ All the controllers are set to 0 (Open Loop).
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org465be28" class="outline-3"> <div id="outline-container-org145a9df" class="outline-3">
<h3 id="org465be28"><span class="section-number-3">8.2</span> Identification</h3> <h3 id="org145a9df"><span class="section-number-3">8.2</span> Identification</h3>
<div class="outline-text-3" id="text-8-2"> <div class="outline-text-3" id="text-8-2">
<p> <p>
We identify the dynamics of the system. We identify the dynamics of the system.
@ -1692,8 +1692,8 @@ Finally, we save the identified system dynamics for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgda14068" class="outline-3"> <div id="outline-container-org3b53ae6" class="outline-3">
<h3 id="orgda14068"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3> <h3 id="org3b53ae6"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-8-3"> <div class="outline-text-3" id="text-8-3">
<p> <p>
We load the dynamics when using a piezo-electric nano hexapod to compare the results. We load the dynamics when using a piezo-electric nano hexapod to compare the results.
@ -1707,19 +1707,19 @@ We load the dynamics when using a piezo-electric nano hexapod to compare the res
We show several plots representing the sensitivity to disturbances: We show several plots representing the sensitivity to disturbances:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>in figure <a href="#org164997f">38</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="#org34141f6">38</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="#org6542b94">39</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="#orgbbc6e41">39</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> </ul>
<div id="org164997f" class="figure"> <div id="org34141f6" class="figure">
<p><img src="figs/uniaxial-sensitivity-vc-disturbances.png" alt="uniaxial-sensitivity-vc-disturbances.png" /> <p><img src="figs/uniaxial-sensitivity-vc-disturbances.png" alt="uniaxial-sensitivity-vc-disturbances.png" />
</p> </p>
<p><span class="figure-number">Figure 38: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-disturbances.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 38: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-disturbances.pdf">pdf</a>)</p>
</div> </div>
<div id="org6542b94" class="figure"> <div id="orgbbc6e41" class="figure">
<p><img src="figs/uniaxial-sensitivity-vc-force-dist.png" alt="uniaxial-sensitivity-vc-force-dist.png" /> <p><img src="figs/uniaxial-sensitivity-vc-force-dist.png" alt="uniaxial-sensitivity-vc-force-dist.png" />
</p> </p>
<p><span class="figure-number">Figure 39: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-force-dist.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 39: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-force-dist.pdf">pdf</a>)</p>
@ -1727,8 +1727,8 @@ We show several plots representing the sensitivity to disturbances:
</div> </div>
</div> </div>
<div id="outline-container-org49bb7e7" class="outline-3"> <div id="outline-container-org33c2392" class="outline-3">
<h3 id="org49bb7e7"><span class="section-number-3">8.4</span> Noise Budget</h3> <h3 id="org33c2392"><span class="section-number-3">8.4</span> Noise Budget</h3>
<div class="outline-text-3" id="text-8-4"> <div class="outline-text-3" id="text-8-4">
<p> <p>
We first load the measured PSD of the disturbance. We first load the measured PSD of the disturbance.
@ -1740,11 +1740,11 @@ We first load the measured PSD of the disturbance.
<p> <p>
The effect of these disturbances on the distance \(D\) is computed below. The effect of these disturbances on the distance \(D\) is computed below.
The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#orgecf9cc7">40</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org91093e7">41</a>. The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#orgf38f860">40</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org661a0fa">41</a>.
</p> </p>
<p> <p>
The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org91093e7">41</a>. The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org661a0fa">41</a>.
</p> </p>
<pre class="example"> <pre class="example">
4.8793e-06 4.8793e-06
@ -1752,14 +1752,14 @@ The Root Mean Square value of the obtained displacement \(D\) is computed below
<div id="orgecf9cc7" class="figure"> <div id="orgf38f860" class="figure">
<p><img src="figs/uniaxial-vc-psd-dist.png" alt="uniaxial-vc-psd-dist.png" /> <p><img src="figs/uniaxial-vc-psd-dist.png" alt="uniaxial-vc-psd-dist.png" />
</p> </p>
<p><span class="figure-number">Figure 40: </span>PSD of the displacement \(D\) due to disturbances (<a href="./figs/uniaxial-vc-psd-dist.png">png</a>, <a href="./figs/uniaxial-vc-psd-dist.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 40: </span>PSD of the displacement \(D\) due to disturbances (<a href="./figs/uniaxial-vc-psd-dist.png">png</a>, <a href="./figs/uniaxial-vc-psd-dist.pdf">pdf</a>)</p>
</div> </div>
<div id="org91093e7" class="figure"> <div id="org661a0fa" class="figure">
<p><img src="figs/uniaxial-vc-cas-dist.png" alt="uniaxial-vc-cas-dist.png" /> <p><img src="figs/uniaxial-vc-cas-dist.png" alt="uniaxial-vc-cas-dist.png" />
</p> </p>
<p><span class="figure-number">Figure 41: </span>CAS of the displacement \(D\) due the disturbances (<a href="./figs/uniaxial-vc-cas-dist.png">png</a>, <a href="./figs/uniaxial-vc-cas-dist.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 41: </span>CAS of the displacement \(D\) due the disturbances (<a href="./figs/uniaxial-vc-cas-dist.png">png</a>, <a href="./figs/uniaxial-vc-cas-dist.pdf">pdf</a>)</p>
@ -1777,8 +1777,8 @@ Thus, it may be desirable to use voice coil actuators.
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org04357b8" class="outline-3"> <div id="outline-container-org332ecb6" class="outline-3">
<h3 id="org04357b8"><span class="section-number-3">8.5</span> Integral Force Feedback</h3> <h3 id="org332ecb6"><span class="section-number-3">8.5</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-8-5"> <div class="outline-text-3" id="text-8-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">K_iff = <span class="org-type">-</span><span class="org-highlight-numbers-number">20</span><span class="org-type">/</span>s; <pre class="src src-matlab">K_iff = <span class="org-type">-</span><span class="org-highlight-numbers-number">20</span><span class="org-type">/</span>s;
@ -1786,7 +1786,7 @@ Thus, it may be desirable to use voice coil actuators.
</div> </div>
<div id="orgb31c44e" class="figure"> <div id="orgd31f0b8" class="figure">
<p><img src="figs/uniaxial_iff_vc_open_loop.png" alt="uniaxial_iff_vc_open_loop.png" /> <p><img src="figs/uniaxial_iff_vc_open_loop.png" alt="uniaxial_iff_vc_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 42: </span>Open Loop Transfer Function for IFF control when using a voice coil actuator (<a href="./figs/uniaxial_iff_vc_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_vc_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 42: </span>Open Loop Transfer Function for IFF control when using a voice coil actuator (<a href="./figs/uniaxial_iff_vc_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_vc_open_loop.pdf">pdf</a>)</p>
@ -1794,8 +1794,8 @@ Thus, it may be desirable to use voice coil actuators.
</div> </div>
</div> </div>
<div id="outline-container-org83d9caa" class="outline-3"> <div id="outline-container-orgd420efb" class="outline-3">
<h3 id="org83d9caa"><span class="section-number-3">8.6</span> Identification of the Damped Plant</h3> <h3 id="orgd420efb"><span class="section-number-3">8.6</span> Identification of the Damped Plant</h3>
<div class="outline-text-3" id="text-8-6"> <div class="outline-text-3" id="text-8-6">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
@ -1873,14 +1873,14 @@ G_vc_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
</div> </div>
</div> </div>
<div id="outline-container-orge278186" class="outline-3"> <div id="outline-container-org99ecd1f" class="outline-3">
<h3 id="orge278186"><span class="section-number-3">8.7</span> Noise Budget</h3> <h3 id="org99ecd1f"><span class="section-number-3">8.7</span> Noise Budget</h3>
<div class="outline-text-3" id="text-8-7"> <div class="outline-text-3" id="text-8-7">
<p> <p>
We compute the obtain PSD of the displacement \(D\) when using IFF. We compute the obtain PSD of the displacement \(D\) when using IFF.
</p> </p>
<div id="orgd1d775f" class="figure"> <div id="orgda5106f" class="figure">
<p><img src="figs/uniaxial-cas-iff-vc.png" alt="uniaxial-cas-iff-vc.png" /> <p><img src="figs/uniaxial-cas-iff-vc.png" alt="uniaxial-cas-iff-vc.png" />
</p> </p>
<p><span class="figure-number">Figure 43: </span>CAS of the displacement \(D\) (<a href="./figs/uniaxial-cas-iff-vc.png">png</a>, <a href="./figs/uniaxial-cas-iff-vc.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 43: </span>CAS of the displacement \(D\) (<a href="./figs/uniaxial-cas-iff-vc.png">png</a>, <a href="./figs/uniaxial-cas-iff-vc.pdf">pdf</a>)</p>
@ -1888,8 +1888,8 @@ We compute the obtain PSD of the displacement \(D\) when using IFF.
</div> </div>
</div> </div>
<div id="outline-container-org152df36" class="outline-3"> <div id="outline-container-orgffe5e36" class="outline-3">
<h3 id="org152df36"><span class="section-number-3">8.8</span> Conclusion</h3> <h3 id="orgffe5e36"><span class="section-number-3">8.8</span> Conclusion</h3>
<div class="outline-text-3" id="text-8-8"> <div class="outline-text-3" id="text-8-8">
<div class="important"> <div class="important">
<p> <p>
@ -1907,7 +1907,7 @@ Similarly, it would require much lower bandwidth to attain the same level of dis
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-11-05 mar. 11:27</p> <p class="date">Created: 2019-11-11 lun. 14:50</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

6
uniaxial/index.org
View File

@ -825,7 +825,7 @@ The Root Mean Square value of the obtained displacement $D$ is computed below an
plot(dist_f.f, psd_rz_d, 'DisplayName', '$R_z$'); plot(dist_f.f, psd_rz_d, 'DisplayName', '$R_z$');
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('CAS of the effect of disturbances on $D$ $\left[\frac{m^2}{Hz}\right]$'); xlabel('Frequency [Hz]'); ylabel('PSD of the effect of disturbances on $D$ $\left[\frac{m^2}{Hz}\right]$'); xlabel('Frequency [Hz]');
legend('location', 'northeast') legend('location', 'northeast')
xlim([0.5, 500]); xlim([0.5, 500]);
#+end_src #+end_src
@ -836,7 +836,7 @@ The Root Mean Square value of the obtained displacement $D$ is computed below an
#+end_src #+end_src
#+NAME: fig:uniaxial-psd-dist #+NAME: fig:uniaxial-psd-dist
#+CAPTION: caption ([[./figs/uniaxial-psd-dist.png][png]], [[./figs/uniaxial-psd-dist.pdf][pdf]]) #+CAPTION: PSD of the effect of disturbances on $D$ ([[./figs/uniaxial-psd-dist.png][png]], [[./figs/uniaxial-psd-dist.pdf][pdf]])
[[file:figs/uniaxial-psd-dist.png]] [[file:figs/uniaxial-psd-dist.png]]
@ -862,7 +862,7 @@ The Root Mean Square value of the obtained displacement $D$ is computed below an
#+end_src #+end_src
#+NAME: fig:uniaxial-cas-dist #+NAME: fig:uniaxial-cas-dist
#+CAPTION: caption ([[./figs/uniaxial-cas-dist.png][png]], [[./figs/uniaxial-cas-dist.pdf][pdf]]) #+CAPTION: CAS of the effect of disturbances on $D$ ([[./figs/uniaxial-cas-dist.png][png]], [[./figs/uniaxial-cas-dist.pdf][pdf]])
[[file:figs/uniaxial-cas-dist.png]] [[file:figs/uniaxial-cas-dist.png]]
** Plant ** Plant