Finalize flexible joint study and add index link
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<head>
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<!-- 2020-05-05 mar. 10:34 -->
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<!-- 2020-05-05 mar. 10:44 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Study of the Flexible Joints</title>
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<title>Study of the Flexible Joints</title>
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<meta name="generator" content="Org mode" />
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<meta name="generator" content="Org mode" />
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@ -36,21 +35,21 @@
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<h2>Table of Contents</h2>
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<div id="text-table-of-contents">
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<ul>
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<ul>
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<li><a href="#org83db6d9">1. Rotational Stiffness</a>
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<li><a href="#orge032d30">1. Bending and Torsional Stiffness</a>
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<ul>
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<ul>
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<li><a href="#orgd487aa8">1.1. Initialization</a></li>
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<li><a href="#org4af6fbb">1.1. Initialization</a></li>
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<li><a href="#orgbc5ab48">1.2. Realistic Rotational Stiffness Values</a>
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<li><a href="#orgde60939">1.2. Realistic Bending Stiffness Values</a>
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<ul>
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<ul>
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<li><a href="#orgfa496e1">1.2.1. Direct Velocity Feedback</a></li>
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<li><a href="#org1f64e69">1.2.1. Direct Velocity Feedback</a></li>
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<li><a href="#org2cf681e">1.2.2. Primary Plant</a></li>
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<li><a href="#org7eb4054">1.2.2. Primary Plant</a></li>
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<li><a href="#org17b7568">1.2.3. Conclusion</a></li>
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<li><a href="#org81a1a77">1.2.3. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#org8ad3f34">1.3. Parametric Study</a>
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<li><a href="#org8ad3f34">1.3. Parametric Study</a>
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<ul>
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<ul>
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<li><a href="#org067911e">1.3.1. Direct Velocity Feedback</a></li>
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<li><a href="#org1575b3d">1.3.1. Direct Velocity Feedback</a></li>
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<li><a href="#org3d67d1c">1.3.2. Primary Control</a></li>
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<li><a href="#orgb35fa00">1.3.2. Primary Control</a></li>
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<li><a href="#org700e2da">1.3.3. Conclusion</a></li>
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<li><a href="#org4a1264f">1.3.3. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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</ul>
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</ul>
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@ -59,20 +58,22 @@
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<ul>
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<ul>
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<li><a href="#org969d9e7">2.1. Realistic Translation Stiffness Values</a>
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<li><a href="#org969d9e7">2.1. Realistic Translation Stiffness Values</a>
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<ul>
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<ul>
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<li><a href="#org4af6fbb">2.1.1. Initialization</a></li>
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<li><a href="#org14d57c4">2.1.1. Initialization</a></li>
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<li><a href="#org5135788">2.1.2. Direct Velocity Feedback</a></li>
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<li><a href="#org790d5e4">2.1.2. Direct Velocity Feedback</a></li>
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<li><a href="#org7eb4054">2.1.3. Primary Plant</a></li>
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<li><a href="#orgddae25e">2.1.3. Primary Plant</a></li>
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<li><a href="#org7ebf071">2.1.4. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#org0275632">2.2. Parametric study</a>
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<li><a href="#org0275632">2.2. Parametric study</a>
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<ul>
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<ul>
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<li><a href="#org1f64e69">2.2.1. Direct Velocity Feedback</a></li>
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<li><a href="#org5ed48b8">2.2.1. Direct Velocity Feedback</a></li>
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<li><a href="#orgb35fa00">2.2.2. Primary Control</a></li>
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<li><a href="#org5d9965b">2.2.2. Primary Control</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#org81a1a77">2.3. Conclusion</a></li>
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<li><a href="#org8ee81cd">2.3. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#orgb8a9692">3. Conclusion</a></li>
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</ul>
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</ul>
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</div>
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</div>
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</div>
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</div>
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@ -86,16 +87,16 @@ Ideally, we want the x and y rotations to be free and all the translations to be
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However, this is never the case and be have to consider:
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However, this is never the case and be have to consider:
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</p>
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</p>
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<ul class="org-ul">
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<ul class="org-ul">
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<li>Finite x and y rotational stiffnesses (Section <a href="#org3eb4121">1</a>)</li>
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<li>Finite bending stiffnesses (Section <a href="#org3eb4121">1</a>)</li>
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<li>Translation stiffness in the direction of the legs (Section <a href="#org8f4d83b">2</a>)</li>
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<li>Axial stiffness in the direction of the legs (Section <a href="#org8f4d83b">2</a>)</li>
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</ul>
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</ul>
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<p>
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<p>
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This may impose some limitations, also, the goal is to specify the required joints stiffnesses.
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This may impose some limitations, also, the goal is to specify the required joints stiffnesses (summarized in Section <a href="#org6614f42">3</a>).
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</p>
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</p>
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<div id="outline-container-org83db6d9" class="outline-2">
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<div id="outline-container-orge032d30" class="outline-2">
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<h2 id="org83db6d9"><span class="section-number-2">1</span> Rotational Stiffness</h2>
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<h2 id="orge032d30"><span class="section-number-2">1</span> Bending and Torsional Stiffness</h2>
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<div class="outline-text-2" id="text-1">
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<div class="outline-text-2" id="text-1">
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<p>
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<p>
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<a id="org3eb4121"></a>
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<a id="org3eb4121"></a>
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@ -105,8 +106,8 @@ In this section, we wish to study the effect of the rotation flexibility of the
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</p>
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</p>
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</div>
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</div>
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<div id="outline-container-orgd487aa8" class="outline-3">
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<div id="outline-container-org4af6fbb" class="outline-3">
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<h3 id="orgd487aa8"><span class="section-number-3">1.1</span> Initialization</h3>
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<h3 id="org4af6fbb"><span class="section-number-3">1.1</span> Initialization</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="outline-text-3" id="text-1-1">
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<p>
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<p>
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Let’s initialize all the stages with default parameters.
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Let’s initialize all the stages with default parameters.
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@ -134,8 +135,8 @@ initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-orgbc5ab48" class="outline-3">
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<div id="outline-container-orgde60939" class="outline-3">
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<h3 id="orgbc5ab48"><span class="section-number-3">1.2</span> Realistic Rotational Stiffness Values</h3>
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<h3 id="orgde60939"><span class="section-number-3">1.2</span> Realistic Bending Stiffness Values</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="outline-text-3" id="text-1-2">
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<p>
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<p>
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Let’s compare the ideal case (zero stiffness in rotation and infinite stiffness in translation) with a more realistic case:
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Let’s compare the ideal case (zero stiffness in rotation and infinite stiffness in translation) with a more realistic case:
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@ -167,8 +168,8 @@ This corresponds to the optimal identified stiffness.
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</p>
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</p>
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</div>
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</div>
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<div id="outline-container-orgfa496e1" class="outline-4">
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<div id="outline-container-org1f64e69" class="outline-4">
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<h4 id="orgfa496e1"><span class="section-number-4">1.2.1</span> Direct Velocity Feedback</h4>
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<h4 id="org1f64e69"><span class="section-number-4">1.2.1</span> Direct Velocity Feedback</h4>
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<div class="outline-text-4" id="text-1-2-1">
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<div class="outline-text-4" id="text-1-2-1">
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<p>
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<p>
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We identify the dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness.
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We identify the dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness.
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@ -188,8 +189,8 @@ It is shown that the adding of stiffness for the flexible joints does increase a
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org2cf681e" class="outline-4">
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<div id="outline-container-org7eb4054" class="outline-4">
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<h4 id="org2cf681e"><span class="section-number-4">1.2.2</span> Primary Plant</h4>
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<h4 id="org7eb4054"><span class="section-number-4">1.2.2</span> Primary Plant</h4>
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<div class="outline-text-4" id="text-1-2-2">
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<div class="outline-text-4" id="text-1-2-2">
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<p>
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<p>
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Let’s now identify the dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs).
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Let’s now identify the dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs).
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@ -209,12 +210,12 @@ The plant dynamics is not found to be changing significantly.
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org17b7568" class="outline-4">
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<div id="outline-container-org81a1a77" class="outline-4">
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<h4 id="org17b7568"><span class="section-number-4">1.2.3</span> Conclusion</h4>
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<h4 id="org81a1a77"><span class="section-number-4">1.2.3</span> Conclusion</h4>
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<div class="outline-text-4" id="text-1-2-3">
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<div class="outline-text-4" id="text-1-2-3">
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<div class="important">
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<div class="important">
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<p>
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<p>
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Considering realistic flexible joint rotational stiffness for the nano-hexapod does not seems to impose any limitation on the DVF control nor on the primary control.
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Considering realistic flexible joint bending stiffness for the nano-hexapod does not seems to impose any limitation on the DVF control nor on the primary control.
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</p>
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</p>
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<p>
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<p>
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@ -235,7 +236,7 @@ This will help to determine the requirements on the joint’s stiffness.
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</p>
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</p>
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<p>
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<p>
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Let’s consider the following rotational stiffness of the flexible joints:
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Let’s consider the following bending stiffness of the flexible joints:
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</p>
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</p>
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<div class="org-src-container">
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<div class="org-src-container">
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<pre class="src src-matlab">Ks = [1, 5, 10, 50, 100]; % [Nm/rad]
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<pre class="src src-matlab">Ks = [1, 5, 10, 50, 100]; % [Nm/rad]
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@ -247,8 +248,8 @@ We also consider here a nano-hexapod with the identified optimal actuator stiffn
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</p>
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</p>
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</div>
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</div>
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<div id="outline-container-org067911e" class="outline-4">
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<div id="outline-container-org1575b3d" class="outline-4">
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<h4 id="org067911e"><span class="section-number-4">1.3.1</span> Direct Velocity Feedback</h4>
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<h4 id="org1575b3d"><span class="section-number-4">1.3.1</span> Direct Velocity Feedback</h4>
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<div class="outline-text-4" id="text-1-3-1">
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<div class="outline-text-4" id="text-1-3-1">
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<p>
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<p>
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The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#org8fbbf9d">3</a>.
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The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#org8fbbf9d">3</a>.
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@ -259,7 +260,7 @@ The corresponding Root Locus plot is shown in Figure <a href="#orgb9f3389">4</a>
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</p>
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</p>
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<p>
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<p>
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It is shown that the rotational stiffness of the flexible joints does indeed change a little the dynamics, but critical damping is stiff achievable with Direct Velocity Feedback.
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It is shown that the bending stiffness of the flexible joints does indeed change a little the dynamics, but critical damping is stiff achievable with Direct Velocity Feedback.
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</p>
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</p>
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@ -278,32 +279,32 @@ It is shown that the rotational stiffness of the flexible joints does indeed cha
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org3d67d1c" class="outline-4">
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<div id="outline-container-orgb35fa00" class="outline-4">
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<h4 id="org3d67d1c"><span class="section-number-4">1.3.2</span> Primary Control</h4>
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<h4 id="orgb35fa00"><span class="section-number-4">1.3.2</span> Primary Control</h4>
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<div class="outline-text-4" id="text-1-3-2">
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<div class="outline-text-4" id="text-1-3-2">
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<p>
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<p>
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The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#orgb739560">5</a>.
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The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#orgb739560">5</a>.
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</p>
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</p>
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<p>
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<p>
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It is shown that the rotational stiffness of the flexible joints have very little impact on the dynamics.
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It is shown that the bending stiffness of the flexible joints have very little impact on the dynamics.
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</p>
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</p>
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<div id="orgb739560" class="figure">
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<div id="orgb739560" class="figure">
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<p><img src="figs/flex_joints_rot_study_primary_plant.png" alt="flex_joints_rot_study_primary_plant.png" />
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<p><img src="figs/flex_joints_rot_study_primary_plant.png" alt="flex_joints_rot_study_primary_plant.png" />
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</p>
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</p>
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<p><span class="figure-number">Figure 5: </span>Diagonal elements of the transfer function matrix from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) for the considered rotational stiffnesses</p>
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<p><span class="figure-number">Figure 5: </span>Diagonal elements of the transfer function matrix from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) for the considered bending stiffnesses</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org700e2da" class="outline-4">
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<div id="outline-container-org4a1264f" class="outline-4">
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<h4 id="org700e2da"><span class="section-number-4">1.3.3</span> Conclusion</h4>
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<h4 id="org4a1264f"><span class="section-number-4">1.3.3</span> Conclusion</h4>
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<div class="outline-text-4" id="text-1-3-3">
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<div class="outline-text-4" id="text-1-3-3">
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<div class="important">
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<div class="important">
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<p>
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<p>
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The rotational stiffness of the flexible joint does not significantly change the dynamics.
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The bending stiffness of the flexible joint does not significantly change the dynamics.
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</p>
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</p>
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</div>
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</div>
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@ -340,8 +341,8 @@ Cz_M = 1*ones(6,1); % [N/(m/s)]
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org4af6fbb" class="outline-4">
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<div id="outline-container-org14d57c4" class="outline-4">
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<h4 id="org4af6fbb"><span class="section-number-4">2.1.1</span> Initialization</h4>
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<h4 id="org14d57c4"><span class="section-number-4">2.1.1</span> Initialization</h4>
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<div class="outline-text-4" id="text-2-1-1">
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<div class="outline-text-4" id="text-2-1-1">
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<p>
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<p>
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Let’s initialize all the stages with default parameters.
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Let’s initialize all the stages with default parameters.
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@ -369,8 +370,8 @@ initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org5135788" class="outline-4">
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<div id="outline-container-org790d5e4" class="outline-4">
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<h4 id="org5135788"><span class="section-number-4">2.1.2</span> Direct Velocity Feedback</h4>
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<h4 id="org790d5e4"><span class="section-number-4">2.1.2</span> Direct Velocity Feedback</h4>
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<div class="outline-text-4" id="text-2-1-2">
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<div class="outline-text-4" id="text-2-1-2">
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<p>
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<p>
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The dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness are identified.
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The dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness are identified.
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@ -389,8 +390,8 @@ The obtained dynamics are shown in Figure <a href="#org78dd87a">6</a>.
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org7eb4054" class="outline-4">
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<div id="outline-container-orgddae25e" class="outline-4">
|
||||||
<h4 id="org7eb4054"><span class="section-number-4">2.1.3</span> Primary Plant</h4>
|
<h4 id="orgddae25e"><span class="section-number-4">2.1.3</span> Primary Plant</h4>
|
||||||
<div class="outline-text-4" id="text-2-1-3">
|
<div class="outline-text-4" id="text-2-1-3">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
|
<pre class="src src-matlab">Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
|
||||||
@ -410,6 +411,18 @@ The dynamics is compare with and without the joint flexibility in Figure <a href
|
|||||||
<p><img src="figs/flex_joints_trans_primary_plant_L.png" alt="flex_joints_trans_primary_plant_L.png" />
|
<p><img src="figs/flex_joints_trans_primary_plant_L.png" alt="flex_joints_trans_primary_plant_L.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 7: </span>Dynamics from \(\bm{\tau}^\prime_i\) to \(\bm{\epsilon}_{\mathcal{X}_n,i}\) with infinite axis stiffnes (solid) and with realistic axial stiffness (dashed)</p>
|
<p><span class="figure-number">Figure 7: </span>Dynamics from \(\bm{\tau}^\prime_i\) to \(\bm{\epsilon}_{\mathcal{X}_n,i}\) with infinite axis stiffnes (solid) and with realistic axial stiffness (dashed)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org7ebf071" class="outline-4">
|
||||||
|
<h4 id="org7ebf071"><span class="section-number-4">2.1.4</span> Conclusion</h4>
|
||||||
|
<div class="outline-text-4" id="text-2-1-4">
|
||||||
|
<div class="important">
|
||||||
|
<p>
|
||||||
|
For the realistic value of the flexible joint axial stiffness, the dynamics is not much impact, and this should not be a problem for control.
|
||||||
|
</p>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -435,8 +448,8 @@ We also consider here a nano-hexapod with the identified optimal actuator stiffn
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org1f64e69" class="outline-4">
|
<div id="outline-container-org5ed48b8" class="outline-4">
|
||||||
<h4 id="org1f64e69"><span class="section-number-4">2.2.1</span> Direct Velocity Feedback</h4>
|
<h4 id="org5ed48b8"><span class="section-number-4">2.2.1</span> Direct Velocity Feedback</h4>
|
||||||
<div class="outline-text-4" id="text-2-2-1">
|
<div class="outline-text-4" id="text-2-2-1">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#orgab9ab86">8</a>.
|
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#orgab9ab86">8</a>.
|
||||||
@ -452,7 +465,7 @@ If the axial stiffness of the flexible joints is \(K_a > 10^7\,[N/m]\) (here \(1
|
|||||||
|
|
||||||
<p>
|
<p>
|
||||||
This is more clear by looking at the root locus (Figures <a href="#org9d43966">9</a> and <a href="#org987d98e">10</a>).
|
This is more clear by looking at the root locus (Figures <a href="#org9d43966">9</a> and <a href="#org987d98e">10</a>).
|
||||||
It can be seen that very little active damping can be achieve for rotational joint axial stiffnesses below \(10^7\,[N/m]\).
|
It can be seen that very little active damping can be achieve for axial stiffnesses below \(10^7\,[N/m]\).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
@ -469,12 +482,6 @@ It can be seen that very little active damping can be achieve for rotational joi
|
|||||||
<p><span class="figure-number">Figure 9: </span>Root Locus for all the considered axial Stiffnesses</p>
|
<p><span class="figure-number">Figure 9: </span>Root Locus for all the considered axial Stiffnesses</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">xlim([-1e3, 0]);
|
|
||||||
ylim([0, 1e3]);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
<div id="org987d98e" class="figure">
|
<div id="org987d98e" class="figure">
|
||||||
<p><img src="figs/flex_joints_trans_study_root_locus_unzoom.png" alt="flex_joints_trans_study_root_locus_unzoom.png" />
|
<p><img src="figs/flex_joints_trans_study_root_locus_unzoom.png" alt="flex_joints_trans_study_root_locus_unzoom.png" />
|
||||||
@ -484,8 +491,8 @@ ylim([0, 1e3]);
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgb35fa00" class="outline-4">
|
<div id="outline-container-org5d9965b" class="outline-4">
|
||||||
<h4 id="orgb35fa00"><span class="section-number-4">2.2.2</span> Primary Control</h4>
|
<h4 id="org5d9965b"><span class="section-number-4">2.2.2</span> Primary Control</h4>
|
||||||
<div class="outline-text-4" id="text-2-2-2">
|
<div class="outline-text-4" id="text-2-2-2">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#org6070692">11</a>.
|
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#org6070692">11</a>.
|
||||||
@ -501,8 +508,8 @@ The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org81a1a77" class="outline-3">
|
<div id="outline-container-org8ee81cd" class="outline-3">
|
||||||
<h3 id="org81a1a77"><span class="section-number-3">2.3</span> Conclusion</h3>
|
<h3 id="org8ee81cd"><span class="section-number-3">2.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-2-3">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@ -510,7 +517,7 @@ The axial stiffness of the flexible joints should be maximized.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
For the considered actuator stiffness \(k = 10^5\,[N/m]\), the axial stiffness of the rotational joints should ideally be above \(10^7\,[N/m]\).
|
For the considered actuator stiffness \(k = 10^5\,[N/m]\), the axial stiffness of the flexible joints should ideally be above \(10^7\,[N/m]\).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -522,13 +529,34 @@ We may interpolate the results and say that the axial joint stiffness should be
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb8a9692" class="outline-2">
|
||||||
|
<h2 id="orgb8a9692"><span class="section-number-2">3</span> Conclusion</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<p>
|
||||||
|
<a id="org6614f42"></a>
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="important">
|
||||||
|
<p>
|
||||||
|
For the identified optimal actuator stiffness \(k = 10^5\,[N/m]\), the flexible joint should have the following stiffness properties:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>Bending Stiffness: \(K_b < 50\,[Nm/rad]\)</li>
|
||||||
|
<li>Torsion Stiffness: \(K_t < 50\,[Nm/rad]\)</li>
|
||||||
|
<li>Axial Stiffness: \(K_a > 10^7\,[N/m]\)</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</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: 2020-05-05 mar. 10:34</p>
|
<p class="date">Created: 2020-05-05 mar. 10:44</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
@ -4,7 +4,7 @@
|
|||||||
"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>
|
||||||
<!-- 2020-04-17 ven. 09:35 -->
|
<!-- 2020-05-05 mar. 10:44 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Simscape Model of the Nano-Active-Stabilization-System</title>
|
<title>Simscape Model of the Nano-Active-Stabilization-System</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -40,9 +40,10 @@
|
|||||||
<li><a href="#orge777d0f">11. Effect of the payload’s “impedance” on the plant dynamics (link)</a></li>
|
<li><a href="#orge777d0f">11. Effect of the payload’s “impedance” on the plant dynamics (link)</a></li>
|
||||||
<li><a href="#orga323881">12. Effect of Experimental conditions on the plant dynamics (link)</a></li>
|
<li><a href="#orga323881">12. Effect of Experimental conditions on the plant dynamics (link)</a></li>
|
||||||
<li><a href="#orge7b9b41">13. Optimal Stiffness of the nano-hexapod to reduce plant uncertainty (link)</a></li>
|
<li><a href="#orge7b9b41">13. Optimal Stiffness of the nano-hexapod to reduce plant uncertainty (link)</a></li>
|
||||||
<li><a href="#org14a10e8">14. Active Damping Techniques on the full Simscape Model (link)</a></li>
|
<li><a href="#org5f73af9">14. Effect of flexible joints on the plant dynamics (link)</a></li>
|
||||||
<li><a href="#orgd818a00">15. Control of the Nano-Active-Stabilization-System (link)</a></li>
|
<li><a href="#org14a10e8">15. Active Damping Techniques on the full Simscape Model (link)</a></li>
|
||||||
<li><a href="#org361f405">16. Useful Matlab Functions (link)</a></li>
|
<li><a href="#orgd818a00">16. Control of the Nano-Active-Stabilization-System (link)</a></li>
|
||||||
|
<li><a href="#org361f405">17. Useful Matlab Functions (link)</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -200,18 +201,28 @@ Conclusion are drawn about what experimental conditions are critical on the vari
|
|||||||
<h2 id="orge7b9b41"><span class="section-number-2">13</span> Optimal Stiffness of the nano-hexapod to reduce plant uncertainty (<a href="uncertainty_optimal_stiffness.html">link</a>)</h2>
|
<h2 id="orge7b9b41"><span class="section-number-2">13</span> Optimal Stiffness of the nano-hexapod to reduce plant uncertainty (<a href="uncertainty_optimal_stiffness.html">link</a>)</h2>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org14a10e8" class="outline-2">
|
<div id="outline-container-org5f73af9" class="outline-2">
|
||||||
<h2 id="org14a10e8"><span class="section-number-2">14</span> Active Damping Techniques on the full Simscape Model (<a href="control_active_damping.html">link</a>)</h2>
|
<h2 id="org5f73af9"><span class="section-number-2">14</span> Effect of flexible joints on the plant dynamics (<a href="flexible_joints_study.html">link</a>)</h2>
|
||||||
<div class="outline-text-2" id="text-14">
|
<div class="outline-text-2" id="text-14">
|
||||||
<p>
|
<p>
|
||||||
|
In this document is studied how the flexible joint stiffnesses (in flexion, torsion and compression) is affecting the plant dynamics.
|
||||||
|
Conclusion are drawn on the required stiffness properties of the flexible joints.
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org14a10e8" class="outline-2">
|
||||||
|
<h2 id="org14a10e8"><span class="section-number-2">15</span> Active Damping Techniques on the full Simscape Model (<a href="control_active_damping.html">link</a>)</h2>
|
||||||
|
<div class="outline-text-2" id="text-15">
|
||||||
|
<p>
|
||||||
Active damping techniques are applied to the full Simscape model.
|
Active damping techniques are applied to the full Simscape model.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgd818a00" class="outline-2">
|
<div id="outline-container-orgd818a00" class="outline-2">
|
||||||
<h2 id="orgd818a00"><span class="section-number-2">15</span> Control of the Nano-Active-Stabilization-System (<a href="control.html">link</a>)</h2>
|
<h2 id="orgd818a00"><span class="section-number-2">16</span> Control of the Nano-Active-Stabilization-System (<a href="control.html">link</a>)</h2>
|
||||||
<div class="outline-text-2" id="text-15">
|
<div class="outline-text-2" id="text-16">
|
||||||
<p>
|
<p>
|
||||||
In this file are gathered all studies about the control the Nano-Active-Stabilization-System.
|
In this file are gathered all studies about the control the Nano-Active-Stabilization-System.
|
||||||
</p>
|
</p>
|
||||||
@ -219,8 +230,8 @@ In this file are gathered all studies about the control the Nano-Active-Stabiliz
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org361f405" class="outline-2">
|
<div id="outline-container-org361f405" class="outline-2">
|
||||||
<h2 id="org361f405"><span class="section-number-2">16</span> Useful Matlab Functions (<a href="./functions.html">link</a>)</h2>
|
<h2 id="org361f405"><span class="section-number-2">17</span> Useful Matlab Functions (<a href="./functions.html">link</a>)</h2>
|
||||||
<div class="outline-text-2" id="text-16">
|
<div class="outline-text-2" id="text-17">
|
||||||
<p>
|
<p>
|
||||||
Many matlab functions are shared among all the files of the projects.
|
Many matlab functions are shared among all the files of the projects.
|
||||||
</p>
|
</p>
|
||||||
@ -233,7 +244,7 @@ These functions are all defined <a href="./functions.html">here</a>.
|
|||||||
</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: 2020-04-17 ven. 09:35</p>
|
<p class="date">Created: 2020-05-05 mar. 10:44</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
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Loading…
Reference in New Issue
Block a user