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<title>Evaluating the Plant Uncertainty in various experimental conditions</title>
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</div><div id="content">
<h1 class="title">Evaluating the Plant Uncertainty in various experimental conditions</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgea4f0d4">1. Variation of the Sample Mass</a></li>
<li><a href="#orga0077c1">2. Variation of the Sample Resonance Frequency</a></li>
<li><a href="#orgb49a967">3. Variation of the Spindle Angle</a>
<li><a href="#org7f3fda7">1. Variation of the Sample Mass</a></li>
<li><a href="#org97d416c">2. Variation of the Sample Resonance Frequency</a></li>
<li><a href="#org9ccc313">3. Variation of the Spindle Angle</a>
<ul>
<li><a href="#org027e6cb">3.1. Identification</a></li>
<li><a href="#org5ba7e6b">3.1. Identification</a></li>
</ul>
</li>
<li><a href="#org9081b0f">4. Variation of the Spindle Rotation Speed</a>
<li><a href="#org6dbbac7">4. Variation of the Spindle Rotation Speed</a>
<ul>
<li><a href="#orgd625617">4.1. Initialization of gravity compensation forces</a></li>
<li><a href="#orgd69bd8a">4.2. Identification</a></li>
<li><a href="#org70dd336">4.3. Plots</a></li>
<li><a href="#org41be335">4.1. Initialization of gravity compensation forces</a></li>
<li><a href="#org26868c4">4.2. Identification</a></li>
<li><a href="#org21d01d9">4.3. Plots</a></li>
</ul>
</li>
<li><a href="#orgc4bba39">5. Variation of the Tilt Angle</a></li>
<li><a href="#orgd6b6bfd">6. Variation of the micro-hexapod pose</a></li>
<li><a href="#org9b1c640">7. Conclusion</a></li>
<li><a href="#org9ef371a">5. Variation of the Tilt Angle</a></li>
<li><a href="#orgf2e2276">6. Variation of the micro-hexapod pose</a></li>
<li><a href="#orgb9c798c">7. Conclusion</a></li>
</ul>
</div>
</div>
@@ -64,12 +68,12 @@ The goal of this document is to study how the dynamics of the system is changing
These experimental conditions are:
</p>
<ul class="org-ul">
<li>Section <a href="#org73362ad">1</a>: Sample mass (from 1Kg to 50Kg)</li>
<li>Section <a href="#org5d9a396">2</a>: Sample dynamics (mostly main resonance frequency)</li>
<li>Section <a href="#org58b9cae">3</a>: The spindle angle</li>
<li>Section <a href="#org5b594de">4</a>: The spindle rotation speed (from 1rpm to 60rpm)</li>
<li>Section <a href="#org4fe1245">5</a>: The tilt angle (from -3 to 3 degrees)</li>
<li>Section <a href="#orgec1048c">6</a>: Pose of the micro-hexapod</li>
<li>Section <a href="#org47bac11">1</a>: Sample mass (from 1Kg to 50Kg)</li>
<li>Section <a href="#orgbedba6e">2</a>: Sample dynamics (mostly main resonance frequency)</li>
<li>Section <a href="#org385fb52">3</a>: The spindle angle</li>
<li>Section <a href="#orgc000f2f">4</a>: The spindle rotation speed (from 1rpm to 60rpm)</li>
<li>Section <a href="#orgaa8ad1d">5</a>: The tilt angle (from -3 to 3 degrees)</li>
<li>Section <a href="#orgd12218c">6</a>: Pose of the micro-hexapod</li>
</ul>
<p>
@@ -89,14 +93,14 @@ The variability of the dynamics is studied for two nano-hexapod concepts:
</ul>
<p>
The conclusions are drawn in Section <a href="#org16cf0c6">7</a>
The conclusions are drawn in Section <a href="#org1e30cfe">7</a>
</p>
<div id="outline-container-orgea4f0d4" class="outline-2">
<h2 id="orgea4f0d4"><span class="section-number-2">1</span> Variation of the Sample Mass</h2>
<div id="outline-container-org7f3fda7" class="outline-2">
<h2 id="org7f3fda7"><span class="section-number-2">1</span> Variation of the Sample Mass</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org73362ad"></a>
<a id="org47bac11"></a>
</p>
<p>
We here study the change of dynamics due to the sample mass.
@@ -107,34 +111,34 @@ We initialize all the stages with the default parameters.
We identify the dynamics for the following sample masses, both with a soft and stiff nano-hexapod.
</p>
<div class="org-src-container">
<pre class="src src-matlab">masses = [1, 10, 50]; % [kg]
<pre class="src src-matlab"> masses = [1, 10, 50]; <span class="org-comment">% [kg]</span>
</pre>
</div>
<p>
The following transfer functions are shown:
</p>
<ul class="org-ul">
<li>Figure <a href="#orgfcb2492">1</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orga2c8402">2</a>: From actuator forces to relative displacement of each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org389df4f">3</a> (resp. <a href="#orgb5aaedd">4</a>): From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction (resp. in the Z direction)</li>
<li>Figure <a href="#org556def6">1</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orga92f0d2">2</a>: From actuator forces to relative displacement of each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org67c5df8">3</a> (resp. <a href="#org3ed9a76">4</a>): From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction (resp. in the Z direction)</li>
</ul>
<div id="orgfcb2492" class="figure">
<div id="org556def6" class="figure">
<p><img src="figs/dynamics_variability_iff_sample_mass.png" alt="dynamics_variability_iff_sample_mass.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Variability of the dynamics from actuator force to force sensor with the Sample Mass (<a href="./figs/dynamics_variability_iff_sample_mass.png">png</a>, <a href="./figs/dynamics_variability_iff_sample_mass.pdf">pdf</a>)</p>
</div>
<div id="orga2c8402" class="figure">
<div id="orga92f0d2" class="figure">
<p><img src="figs/dynamics_variability_dvf_sample_mass.png" alt="dynamics_variability_dvf_sample_mass.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Variability of the dynamics from actuator force to relative motion sensor with the Sample Mass (<a href="./figs/dynamics_variability_dvf_sample_mass.png">png</a>, <a href="./figs/dynamics_variability_dvf_sample_mass.pdf">pdf</a>)</p>
</div>
<div id="org389df4f" class="figure">
<div id="org67c5df8" class="figure">
<p><img src="figs/dynamics_variability_err_x_sample_mass.png" alt="dynamics_variability_err_x_sample_mass.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Variability of the dynamics from Forces applied in task space (X direction) to the displacement of the sample in the X direction (<a href="./figs/dynamics_variability_err_x_sample_mass.png">png</a>, <a href="./figs/dynamics_variability_err_x_sample_mass.pdf">pdf</a>)</p>
@@ -142,12 +146,12 @@ The following transfer functions are shown:
<div id="orgb5aaedd" class="figure">
<div id="org3ed9a76" class="figure">
<p><img src="figs/dynamics_variability_err_z_sample_mass.png" alt="dynamics_variability_err_z_sample_mass.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Variability of the dynamics from vertical forces applied in the task space to the displacement of the sample in the vertical direction (<a href="./figs/dynamics_variability_err_z_sample_mass.png">png</a>, <a href="./figs/dynamics_variability_err_z_sample_mass.pdf">pdf</a>)</p>
</div>
<div class="important">
<div class="important" id="org753fd54">
<p>
Let&rsquo;s note \(\omega_0\) the first resonance which corresponds to the resonance of the payload+nano-hexapod top platform resonating on top of the nano-hexapod base.
</p>
@@ -203,51 +207,51 @@ This is more easily seem with the soft nano-hexapod as the resonance \(\omega_0\
</div>
</div>
<div id="outline-container-orga0077c1" class="outline-2">
<h2 id="orga0077c1"><span class="section-number-2">2</span> Variation of the Sample Resonance Frequency</h2>
<div id="outline-container-org97d416c" class="outline-2">
<h2 id="org97d416c"><span class="section-number-2">2</span> Variation of the Sample Resonance Frequency</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org5d9a396"></a>
<a id="orgbedba6e"></a>
</p>
<p>
We initialize all the stages with the default parameters.
We identify the dynamics for the following sample resonance frequency.
</p>
<div class="org-src-container">
<pre class="src src-matlab">mass_w = [50, 100, 500]; % [Hz]
mass = 10; % [Kg]
<pre class="src src-matlab"> mass_w = [50, 100, 500]; <span class="org-comment">% [Hz]</span>
mass = 10; <span class="org-comment">% [Kg]</span>
</pre>
</div>
<p>
The following transfer functions are shown:
</p>
<ul class="org-ul">
<li>Figure <a href="#org9b4645f">5</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orga4f9971">6</a>: From actuator forces to relative displacement of each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orgfdf548b">7</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
<li>Figure <a href="#orgfae24b1">5</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orgd64155a">6</a>: From actuator forces to relative displacement of each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org09a9db4">7</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
</ul>
<div id="org9b4645f" class="figure">
<div id="orgfae24b1" class="figure">
<p><img src="figs/dynamics_variability_iff_sample_w.png" alt="dynamics_variability_iff_sample_w.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Variability of the dynamics from actuator force to force sensor with the Sample Mass (<a href="./figs/dynamics_variability_iff_sample_w.png">png</a>, <a href="./figs/dynamics_variability_iff_sample_w.pdf">pdf</a>)</p>
</div>
<div id="orga4f9971" class="figure">
<div id="orgd64155a" class="figure">
<p><img src="figs/dynamics_variability_dvf_sample_w.png" alt="dynamics_variability_dvf_sample_w.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Variability of the dynamics from actuator force to relative motion sensor with the Sample Mass (<a href="./figs/dynamics_variability_dvf_sample_w.png">png</a>, <a href="./figs/dynamics_variability_dvf_sample_w.pdf">pdf</a>)</p>
</div>
<div id="orgfdf548b" class="figure">
<div id="org09a9db4" class="figure">
<p><img src="figs/dynamics_variability_err_sample_w.png" alt="dynamics_variability_err_sample_w.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Variability of the dynamics from a torque applied on the sample by the nano-hexapod in the X direction to the rotation of the sample around the X axis (<a href="./figs/dynamics_variability_err_sample_w.png">png</a>, <a href="./figs/dynamics_variability_err_sample_w.pdf">pdf</a>)</p>
</div>
<div class="important">
<div class="important" id="org11cbcec">
<p>
Let&rsquo;s note \(\omega_m\) the frequency of the resonance of the Payload.
</p>
@@ -293,22 +297,22 @@ Let&rsquo;s note \(\omega_m\) the frequency of the resonance of the Payload.
</div>
</div>
<div id="outline-container-orgb49a967" class="outline-2">
<h2 id="orgb49a967"><span class="section-number-2">3</span> Variation of the Spindle Angle</h2>
<div id="outline-container-org9ccc313" class="outline-2">
<h2 id="org9ccc313"><span class="section-number-2">3</span> Variation of the Spindle Angle</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org58b9cae"></a>
<a id="org385fb52"></a>
</p>
</div>
<div id="outline-container-org027e6cb" class="outline-3">
<h3 id="org027e6cb"><span class="section-number-3">3.1</span> Identification</h3>
<div id="outline-container-org5ba7e6b" class="outline-3">
<h3 id="org5ba7e6b"><span class="section-number-3">3.1</span> Identification</h3>
<div class="outline-text-3" id="text-3-1">
<p>
We identify the dynamics for the following Tilt stage angles.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSample('mass', 50);
Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad]
<pre class="src src-matlab"> initializeSample(<span class="org-string">'mass'</span>, 50);
Rz_amplitudes = [0, <span class="org-constant">pi</span><span class="org-type">/</span>4, <span class="org-constant">pi</span><span class="org-type">/</span>2, <span class="org-constant">pi</span>]; <span class="org-comment">% [rad]</span>
</pre>
</div>
</div>
@@ -319,19 +323,19 @@ Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad]
The following transfer functions are shown:
</p>
<ul class="org-ul">
<li>Figure <a href="#orgcfb9db7">8</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orgd07dc03">9</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
<li>Figure <a href="#org6e010ad">8</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org3fbceeb">9</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
</ul>
<div id="orgcfb9db7" class="figure">
<div id="org6e010ad" class="figure">
<p><img src="figs/dynamics_variability_iff_spindle_angle.png" alt="dynamics_variability_iff_spindle_angle.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Variability of the dynamics from the actuator force to the force sensor with the Spindle Angle (<a href="./figs/dynamics_variability_iff_spindle_angle.png">png</a>, <a href="./figs/dynamics_variability_iff_spindle_angle.pdf">pdf</a>)</p>
</div>
<div id="orgd07dc03" class="figure">
<div id="org3fbceeb" class="figure">
<p><img src="figs/dynamics_variability_err_spindle_angle.png" alt="dynamics_variability_err_spindle_angle.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Variability of the dynamics from actuator force to absolute velocity with the Spindle Angle (<a href="./figs/dynamics_variability_err_spindle_angle.png">png</a>, <a href="./figs/dynamics_variability_err_spindle_angle.pdf">pdf</a>)</p>
@@ -339,7 +343,7 @@ The following transfer functions are shown:
</div>
<div class="outline-text-2" id="text-3">
<div class="important">
<div class="important" id="orgf2503f0">
<p>
The Spindle angle has no visible effect for the soft nano-hexapod.
</p>
@@ -354,23 +358,23 @@ This is probably due to the fact that the micro-station compliance is not unifor
</div>
</div>
<div id="outline-container-org9081b0f" class="outline-2">
<h2 id="org9081b0f"><span class="section-number-2">4</span> Variation of the Spindle Rotation Speed</h2>
<div id="outline-container-org6dbbac7" class="outline-2">
<h2 id="org6dbbac7"><span class="section-number-2">4</span> Variation of the Spindle Rotation Speed</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="org5b594de"></a>
<a id="orgc000f2f"></a>
</p>
</div>
<div id="outline-container-orgd625617" class="outline-3">
<h3 id="orgd625617"><span class="section-number-3">4.1</span> Initialization of gravity compensation forces</h3>
<div id="outline-container-org41be335" class="outline-3">
<h3 id="org41be335"><span class="section-number-3">4.1</span> Initialization of gravity compensation forces</h3>
<div class="outline-text-3" id="text-4-1">
<p>
We initialize all the stages such that their joints are blocked and we record the total forces/torques applied in each of these joints.
We set a payload mass of 10Kg.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSample('type', 'init', 'mass', 10);
nano_hexapod = initializeNanoHexapod( 'type', 'init');
<pre class="src src-matlab"> initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>, <span class="org-string">'mass'</span>, 10);
nano_hexapod = initializeNanoHexapod( <span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
</pre>
</div>
@@ -379,56 +383,56 @@ Finally, we simulate the system and same the forces/torques applied in each join
</p>
</div>
</div>
<div id="outline-container-orgd69bd8a" class="outline-3">
<h3 id="orgd69bd8a"><span class="section-number-3">4.2</span> Identification</h3>
<div id="outline-container-org26868c4" class="outline-3">
<h3 id="org26868c4"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2">
<p>
We initialize the stages with forces/torques compensating the gravity forces.
We identify the dynamics for the following Spindle rotation periods.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Rz_periods = [60, 6, 2, 1]; % [s]
<pre class="src src-matlab"> Rz_periods = [60, 6, 2, 1]; <span class="org-comment">% [s]</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org70dd336" class="outline-3">
<h3 id="org70dd336"><span class="section-number-3">4.3</span> Plots</h3>
<div id="outline-container-org21d01d9" class="outline-3">
<h3 id="org21d01d9"><span class="section-number-3">4.3</span> Plots</h3>
<div class="outline-text-3" id="text-4-3">
<p>
The following transfer functions are shown:
</p>
<ul class="org-ul">
<li>Figure <a href="#org82ab7aa">10</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org3f98487">11</a>: From actuator forces to relative displacement of each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org0d347dd">12</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
<li>Figure <a href="#org61e9acd">13</a>: From forces applied in the task space in the X direction by the nano-hexapod to displacement of the sample in the Y direction (coupling)</li>
<li>Figure <a href="#org47f402f">10</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org4b3b7f6">11</a>: From actuator forces to relative displacement of each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org53196fc">12</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
<li>Figure <a href="#org38e5c6e">13</a>: From forces applied in the task space in the X direction by the nano-hexapod to displacement of the sample in the Y direction (coupling)</li>
</ul>
<div id="org82ab7aa" class="figure">
<div id="org47f402f" class="figure">
<p><img src="figs/dynamics_variability_iff_spindle_speed.png" alt="dynamics_variability_iff_spindle_speed.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Variability of the dynamics from the actuator force to the force sensor with the Spindle rotation speed (<a href="./figs/dynamics_variability_iff_spindle_speed.png">png</a>, <a href="./figs/dynamics_variability_iff_spindle_speed.pdf">pdf</a>)</p>
</div>
<div id="org3f98487" class="figure">
<div id="org4b3b7f6" class="figure">
<p><img src="figs/dynamics_variability_dvf_spindle_speed.png" alt="dynamics_variability_dvf_spindle_speed.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Variability of the dynamics from the actuator force to the relative motion sensor with the Spindle rotation speed (<a href="./figs/dynamics_variability_dvf_spindle_speed.png">png</a>, <a href="./figs/dynamics_variability_dvf_spindle_speed.pdf">pdf</a>)</p>
</div>
<div id="org0d347dd" class="figure">
<div id="org53196fc" class="figure">
<p><img src="figs/dynamics_variability_err_spindle_speed.png" alt="dynamics_variability_err_spindle_speed.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Variability of the dynamics from the actuator force in the task force to the position error of the sample (<a href="./figs/dynamics_variability_err_spindle_speed.png">png</a>, <a href="./figs/dynamics_variability_err_spindle_speed.pdf">pdf</a>)</p>
</div>
<div id="org61e9acd" class="figure">
<div id="org38e5c6e" class="figure">
<p><img src="figs/dynamics_variability_err_spindle_speed_coupling.png" alt="dynamics_variability_err_spindle_speed_coupling.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Variability of the coupling from the actuator force in the task force to the position error of the sample (<a href="./figs/dynamics_variability_err_spindle_speed_coupling.png">png</a>, <a href="./figs/dynamics_variability_err_spindle_speed_coupling.pdf">pdf</a>)</p>
@@ -437,7 +441,7 @@ The following transfer functions are shown:
</div>
<div class="outline-text-2" id="text-4">
<div class="important">
<div class="important" id="org8004dbd">
<p>
For the stiff nano-hexapod, the rotation speed of the Spindle does not affect the (main) dynamics.
It only affects the coupling due to Coriolis forces.
@@ -461,43 +465,43 @@ Also, the coupling from forces applied in the X direction to induced displacemen
</div>
</div>
<div id="outline-container-orgc4bba39" class="outline-2">
<h2 id="orgc4bba39"><span class="section-number-2">5</span> Variation of the Tilt Angle</h2>
<div id="outline-container-org9ef371a" class="outline-2">
<h2 id="org9ef371a"><span class="section-number-2">5</span> Variation of the Tilt Angle</h2>
<div class="outline-text-2" id="text-5">
<p>
<a id="org4fe1245"></a>
<a id="orgaa8ad1d"></a>
</p>
<p>
We initialize all the stages with the default parameters.
We identify the dynamics for the following Tilt stage angles.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSample('mass', 50);
Ry_amplitudes = [-3*pi/180 0 3*pi/180]; % [rad]
<pre class="src src-matlab"> initializeSample(<span class="org-string">'mass'</span>, 50);
Ry_amplitudes = [<span class="org-type">-</span>3<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>180 0 3<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>180]; <span class="org-comment">% [rad]</span>
</pre>
</div>
<p>
The following transfer functions are shown:
</p>
<ul class="org-ul">
<li>Figure <a href="#org8eda147">14</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#orgfacbfbb">15</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
<li>Figure <a href="#orgfdee6dd">14</a>: From actuator forces to force sensors in each nano-hexapod&rsquo;s leg</li>
<li>Figure <a href="#org59428f5">15</a>: From forces applied in the task space by the nano-hexapod to displacement of the sample in the X direction</li>
</ul>
<div id="org8eda147" class="figure">
<div id="orgfdee6dd" class="figure">
<p><img src="figs/dynamics_variability_iff_tilt_angle.png" alt="dynamics_variability_iff_tilt_angle.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Variability of the dynamics from the actuator force to the force sensor with the Tilt stage Angle (<a href="./figs/dynamics_variability_iff_tilt_angle.png">png</a>, <a href="./figs/dynamics_variability_iff_tilt_angle.pdf">pdf</a>)</p>
</div>
<div id="orgfacbfbb" class="figure">
<div id="org59428f5" class="figure">
<p><img src="figs/dynamics_variability_err_tilt_angle.png" alt="dynamics_variability_err_tilt_angle.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Variability of the dynamics from the actuator force in the task space to the displacement of the sample (<a href="./figs/dynamics_variability_err_tilt_angle.png">png</a>, <a href="./figs/dynamics_variability_err_tilt_angle.pdf">pdf</a>)</p>
</div>
<div class="important">
<div class="important" id="org0740801">
<p>
The tilt angle has no visible effect on the dynamics.
</p>
@@ -506,34 +510,34 @@ The tilt angle has no visible effect on the dynamics.
</div>
</div>
<div id="outline-container-orgd6b6bfd" class="outline-2">
<h2 id="orgd6b6bfd"><span class="section-number-2">6</span> Variation of the micro-hexapod pose</h2>
<div id="outline-container-orgf2e2276" class="outline-2">
<h2 id="orgf2e2276"><span class="section-number-2">6</span> Variation of the micro-hexapod pose</h2>
<div class="outline-text-2" id="text-6">
<p>
<a id="orgec1048c"></a>
<a id="orgd12218c"></a>
</p>
<p>
We initialize all the stages with the default parameters.
We identify the dynamics for the following translations of the micro-hexapod in the X direction.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Tx_amplitudes = [0, 5e-3, 10e-3]; % [m]
<pre class="src src-matlab"> Tx_amplitudes = [0, 5e<span class="org-type">-</span>3, 10e<span class="org-type">-</span>3]; <span class="org-comment">% [m]</span>
</pre>
</div>
<div id="org110386d" class="figure">
<div id="org54a59e1" class="figure">
<p><img src="figs/dynamics_variability_iff_micro_hexapod_x.png" alt="dynamics_variability_iff_micro_hexapod_x.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Variability of the dynamics from the actuator force to the force sensor with the Tilt stage Angle (<a href="./figs/dynamics_variability_iff_micro_hexapod_x.png">png</a>, <a href="./figs/dynamics_variability_iff_micro_hexapod_x.pdf">pdf</a>)</p>
</div>
<div id="org62de399" class="figure">
<div id="org78a9a9d" class="figure">
<p><img src="figs/dynamics_variability_err_micro_hexapod_x.png" alt="dynamics_variability_err_micro_hexapod_x.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Variability of the dynamics from the actuator force in the task space to the displacement of the sample (<a href="./figs/dynamics_variability_err_micro_hexapod_x.png">png</a>, <a href="./figs/dynamics_variability_err_micro_hexapod_x.pdf">pdf</a>)</p>
</div>
<div class="important">
<div class="important" id="org2e2f159">
<p>
The pose of the micro-hexapod has negligible effect on the dynamics.
</p>
@@ -542,14 +546,14 @@ The pose of the micro-hexapod has negligible effect on the dynamics.
</div>
</div>
<div id="outline-container-org9b1c640" class="outline-2">
<h2 id="org9b1c640"><span class="section-number-2">7</span> Conclusion</h2>
<div id="outline-container-orgb9c798c" class="outline-2">
<h2 id="orgb9c798c"><span class="section-number-2">7</span> Conclusion</h2>
<div class="outline-text-2" id="text-7">
<p>
<a id="org16cf0c6"></a>
<a id="org1e30cfe"></a>
</p>
<div class="important">
<div class="important" id="orgdd4393b">
<p>
From all the experimental condition studied, the only ones that have significant effect on the dynamics are:
</p>
@@ -603,7 +607,7 @@ From all the experimental condition studied, the only ones that have significant
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-05-05 mar. 10:34</p>
<p class="date">Created: 2021-02-20 sam. 23:08</p>
</div>
</body>
</html>