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Analysis of IFF with amplified actuators

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Thomas Dehaeze
2020-05-20 16:55:50 +02:00
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11 changed files with 244 additions and 26 deletions
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docs/amplified_piezoelectric_stack.html
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<!-- 2020-05-20 mer. 16:41 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Amplified Piezoelectric Stack Actuator</title>
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<ul>
<li><a href="#org996fd7c">1. Simplified Model</a>
<ul>
<li><a href="#org0dc544d">1.1. Parameters</a></li>
<li><a href="#org08e3567">1.2. Identification</a></li>
<li><a href="#orgbba342e">1.3. Root Locus</a></li>
<li><a href="#org1e2b26f">1.1. Parameters</a></li>
<li><a href="#orgac18acf">1.2. Identification</a></li>
<li><a href="#orgd6c324c">1.3. Root Locus</a></li>
</ul>
</li>
<li><a href="#orgf1a765f">2. Rotating X-Y platform</a>
<ul>
<li><a href="#org1e2b26f">2.1. Parameters</a></li>
<li><a href="#orgb0841c5">2.2. Identification</a></li>
<li><a href="#orgd6c324c">2.3. Root Locus</a></li>
<li><a href="#orgd4866c5">2.1. Parameters</a></li>
<li><a href="#orgcfc57a7">2.2. Identification</a></li>
<li><a href="#org8d3f9bd">2.3. Root Locus</a></li>
<li><a href="#org069f401">2.4. Analysis</a></li>
</ul>
</li>
<li><a href="#org3c74f7f">3. Stewart Platform with Amplified Actuators</a>
<ul>
<li><a href="#org5a7c6dc">3.1. Initialization</a></li>
<li><a href="#orgac18acf">3.2. Identification</a></li>
<li><a href="#orgf0cb0e7">3.2. Identification</a></li>
<li><a href="#org14c7063">3.3. Controller Design</a></li>
<li><a href="#org043ce40">3.4. Effect of the Low Authority Control on the Primary Plant</a></li>
<li><a href="#orgbc2f246">3.5. Effect of the Low Authority Control on the Sensibility to Disturbances</a></li>
</ul>
</li>
</ul>
@@ -131,8 +132,8 @@ The parameters are shown in the table below.
<h2 id="org996fd7c"><span class="section-number-2">1</span> Simplified Model</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org0dc544d" class="outline-3">
<h3 id="org0dc544d"><span class="section-number-3">1.1</span> Parameters</h3>
<div id="outline-container-org1e2b26f" class="outline-3">
<h3 id="org1e2b26f"><span class="section-number-3">1.1</span> Parameters</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-matlab">m = 1; % [kg]
@@ -162,8 +163,8 @@ IFF Controller:
</div>
</div>
<div id="outline-container-org08e3567" class="outline-3">
<h3 id="org08e3567"><span class="section-number-3">1.2</span> Identification</h3>
<div id="outline-container-orgac18acf" class="outline-3">
<h3 id="orgac18acf"><span class="section-number-3">1.2</span> Identification</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Identification in open-loop.
@@ -218,8 +219,8 @@ Giff.OutputName = {'Fs', 'x1'};
</div>
</div>
<div id="outline-container-orgbba342e" class="outline-3">
<h3 id="orgbba342e"><span class="section-number-3">1.3</span> Root Locus</h3>
<div id="outline-container-orgd6c324c" class="outline-3">
<h3 id="orgd6c324c"><span class="section-number-3">1.3</span> Root Locus</h3>
<div class="outline-text-3" id="text-1-3">
<div id="org85cd6e5" class="figure">
@@ -235,8 +236,8 @@ Giff.OutputName = {'Fs', 'x1'};
<h2 id="orgf1a765f"><span class="section-number-2">2</span> Rotating X-Y platform</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org1e2b26f" class="outline-3">
<h3 id="org1e2b26f"><span class="section-number-3">2.1</span> Parameters</h3>
<div id="outline-container-orgd4866c5" class="outline-3">
<h3 id="orgd4866c5"><span class="section-number-3">2.1</span> Parameters</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">m = 1; % [kg]
@@ -263,8 +264,8 @@ h = 0.2; % [m]
</div>
</div>
<div id="outline-container-orgb0841c5" class="outline-3">
<h3 id="orgb0841c5"><span class="section-number-3">2.2</span> Identification</h3>
<div id="outline-container-orgcfc57a7" class="outline-3">
<h3 id="orgcfc57a7"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Rotating speed in rad/s:
@@ -313,8 +314,8 @@ end
</div>
</div>
<div id="outline-container-orgd6c324c" class="outline-3">
<h3 id="orgd6c324c"><span class="section-number-3">2.3</span> Root Locus</h3>
<div id="outline-container-org8d3f9bd" class="outline-3">
<h3 id="org8d3f9bd"><span class="section-number-3">2.3</span> Root Locus</h3>
<div class="outline-text-3" id="text-2-3">
<div id="orgccd3396" class="figure">
@@ -412,8 +413,8 @@ We set the stiffness of the payload fixation:
</div>
</div>
<div id="outline-container-orgac18acf" class="outline-3">
<h3 id="orgac18acf"><span class="section-number-3">3.2</span> Identification</h3>
<div id="outline-container-orgf0cb0e7" class="outline-3">
<h3 id="orgf0cb0e7"><span class="section-number-3">3.2</span> Identification</h3>
<div class="outline-text-3" id="text-3-2">
<div class="org-src-container">
<pre class="src src-matlab">K = tf(zeros(6));
@@ -479,12 +480,57 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
<div id="outline-container-org043ce40" class="outline-3">
<h3 id="org043ce40"><span class="section-number-3">3.4</span> Effect of the Low Authority Control on the Primary Plant</h3>
<div class="outline-text-3" id="text-3-4">
<div id="org904efc3" class="figure">
<p><img src="figs/amplified_piezo_iff_plant_damped_X.png" alt="amplified_piezo_iff_plant_damped_X.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Primary plant in the task space with (dashed) and without (solid) IFF</p>
</div>
<div id="orgddf3013" class="figure">
<p><img src="figs/amplified_piezo_iff_damped_plant_L.png" alt="amplified_piezo_iff_damped_plant_L.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Primary plant in the space of the legs with (dashed) and without (solid) IFF</p>
</div>
<div id="orgd940ce9" class="figure">
<p><img src="figs/amplified_piezo_iff_damped_coupling_X.png" alt="amplified_piezo_iff_damped_coupling_X.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Coupling in the primary plant in the task with (dashed) and without (solid) IFF</p>
</div>
<div id="org4278690" class="figure">
<p><img src="figs/amplified_piezo_iff_damped_coupling_L.png" alt="amplified_piezo_iff_damped_coupling_L.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Coupling in the primary plant in the space of the legs with (dashed) and without (solid) IFF</p>
</div>
</div>
</div>
<div id="outline-container-orgbc2f246" class="outline-3">
<h3 id="orgbc2f246"><span class="section-number-3">3.5</span> Effect of the Low Authority Control on the Sensibility to Disturbances</h3>
<div class="outline-text-3" id="text-3-5">
<div id="org56179cd" class="figure">
<p><img src="figs/amplified_piezo_iff_disturbances.png" alt="amplified_piezo_iff_disturbances.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Norm of the transfer function from vertical disturbances to vertical position error with (dashed) and without (solid) Integral Force Feedback applied</p>
</div>
<div class="important">
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-05-20 mer. 16:41</p>
<p class="date">Created: 2020-05-20 mer. 16:56</p>
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