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<title>Compensating the gravity forces to start at steady state</title>
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</div><div id="content">
<h1 class="title">Compensating the gravity forces to start at steady state</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org356e04b">1. Initialization of the Experimental Conditions</a></li>
<li><a href="#org263e5db">2. Without compensation</a></li>
<li><a href="#orgfd6d9e9">3. Simulation to compute the required force in each joint</a></li>
<li><a href="#org44bde7a">4. New simulation with compensation of gravity forces</a></li>
<li><a href="#orgb714922">5. Conclusion</a></li>
<li><a href="#orgb5e305a">1. Initialization of the Experimental Conditions</a></li>
<li><a href="#org96a269f">2. Without compensation</a></li>
<li><a href="#orged240b5">3. Simulation to compute the required force in each joint</a></li>
<li><a href="#org25738bf">4. New simulation with compensation of gravity forces</a></li>
<li><a href="#orgb003af1">5. Conclusion</a></li>
</ul>
</div>
</div>
@@ -41,19 +36,19 @@ In this file is shown a technique used to compensate the gravity forces at t=0.
</p>
<p>
The problem is that in presence of gravity, the system does not start at steady state and experience a transient phase (section <a href="#org4bc70b2">2</a>).
The problem is that in presence of gravity, the system does not start at steady state and experience a transient phase (section <a href="#orgf3b9673">2</a>).
</p>
<p>
In order to start the simulation at steady state in presence of gravity:
</p>
<ul class="org-ul">
<li>section <a href="#org2de8ac1">3</a>: first the stages are initialize in such a way that they are rigid, and the forces/torques applied at the location of their joints is measured</li>
<li>section <a href="#org5364ea3">4</a>: Then, the equilibrium position of each joint is modified in such a way that at t=0, the forces in each joints exactly compensate the forces due to gravity forces</li>
<li>section <a href="#orgaf044de">3</a>: first the stages are initialize in such a way that they are rigid, and the forces/torques applied at the location of their joints is measured</li>
<li>section <a href="#orga475c79">4</a>: Then, the equilibrium position of each joint is modified in such a way that at t=0, the forces in each joints exactly compensate the forces due to gravity forces</li>
</ul>
<div id="outline-container-org356e04b" class="outline-2">
<h2 id="org356e04b"><span class="section-number-2">1</span> Initialization of the Experimental Conditions</h2>
<div id="outline-container-orgb5e305a" class="outline-2">
<h2 id="orgb5e305a"><span class="section-number-2">1</span> Initialization of the Experimental Conditions</h2>
<div class="outline-text-2" id="text-1">
<p>
We don&rsquo;t inject any perturbations and no reference tracking.
@@ -76,11 +71,11 @@ initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span clas
</div>
</div>
<div id="outline-container-org263e5db" class="outline-2">
<h2 id="org263e5db"><span class="section-number-2">2</span> Without compensation</h2>
<div id="outline-container-org96a269f" class="outline-2">
<h2 id="org96a269f"><span class="section-number-2">2</span> Without compensation</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org4bc70b2"></a>
<a id="orgf3b9673"></a>
Let&rsquo;s simulate the system without any compensation of gravity forces.
</p>
@@ -111,10 +106,10 @@ sim_no_compensation = simout;
</div>
<p>
And we can observe on Figure <a href="#org0568928">1</a> that there are some motion in the system.
And we can observe on Figure <a href="#org3568468">1</a> that there are some motion in the system.
</p>
<div id="org0568928" class="figure">
<div id="org3568468" class="figure">
<p><img src="figs/transient_phase_gravity_no_compensation.png" alt="transient_phase_gravity_no_compensation.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Motion of the sample at the start of the simulation in presence of gravity (<a href="./figs/transient_phase_gravity_no_compensation.png">png</a>, <a href="./figs/transient_phase_gravity_no_compensation.pdf">pdf</a>)</p>
@@ -122,11 +117,11 @@ And we can observe on Figure <a href="#org0568928">1</a> that there are some mot
</div>
</div>
<div id="outline-container-orgfd6d9e9" class="outline-2">
<h2 id="orgfd6d9e9"><span class="section-number-2">3</span> Simulation to compute the required force in each joint</h2>
<div id="outline-container-orged240b5" class="outline-2">
<h2 id="orged240b5"><span class="section-number-2">3</span> Simulation to compute the required force in each joint</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org2de8ac1"></a>
<a id="orgaf044de"></a>
We here wish to simulate the system in order to compute the required force in each joint to compensate the gravity forces.
</p>
@@ -318,11 +313,11 @@ We save these forces in <code>Foffset.mat</code>.
</div>
</div>
<div id="outline-container-org44bde7a" class="outline-2">
<h2 id="org44bde7a"><span class="section-number-2">4</span> New simulation with compensation of gravity forces</h2>
<div id="outline-container-org25738bf" class="outline-2">
<h2 id="org25738bf"><span class="section-number-2">4</span> New simulation with compensation of gravity forces</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="org5364ea3"></a>
<a id="orga475c79"></a>
We now initialize the stages with the option <code>Foffset</code>.
</p>
<div class="org-src-container">
@@ -358,17 +353,17 @@ sim_compensation = simout;
Verification that nothing is moving
</p>
<div id="orgc677acf" class="figure">
<div id="org2b3d436" class="figure">
<p><img src="figs/transient_phase_gravity_compensation.png" alt="transient_phase_gravity_compensation.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Motion of the sample at the start of the simulation in presence of gravity when compensating the gravity forces (<a href="./figs/transient_phase_gravity_compensation.png">png</a>, <a href="./figs/transient_phase_gravity_compensation.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orgb714922" class="outline-2">
<h2 id="orgb714922"><span class="section-number-2">5</span> Conclusion</h2>
<div id="outline-container-orgb003af1" class="outline-2">
<h2 id="orgb003af1"><span class="section-number-2">5</span> Conclusion</h2>
<div class="outline-text-2" id="text-5">
<div class="important">
<div class="important" id="org3329ee9">
<p>
This initialization technique permits to compute the required forces/torques to be applied in each joint in order to compensate for gravity forces.
This initialization should be redone for each configuration (change of sample mass, change of tilt angle), but not when changing the stiffness of joints, for instant when changing from lorentz based nano-hexapod or piezo based.
@@ -380,7 +375,7 @@ This initialization should be redone for each configuration (change of sample ma
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-17 ven. 09:34</p>
<p class="date">Created: 2021-02-20 sam. 23:07</p>
</div>
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