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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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<head>
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<!-- 2020-08-03 lun. 15:33 -->
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<!-- 2020-08-03 lun. 15:42 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Finite Element Model with Simscape</title>
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<meta name="generator" content="Org mode" />
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@ -34,60 +34,60 @@
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgabca705">1. Amplified Piezoelectric Actuator - 3D elements</a>
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<li><a href="#org71cd323">1. Amplified Piezoelectric Actuator - 3D elements</a>
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<ul>
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<li><a href="#orgc2a67b0">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#orgf3dcf66">1.2. Output parameters</a></li>
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<li><a href="#orgf1c1c31">1.3. Piezoelectric parameters</a></li>
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<li><a href="#org3ad0597">1.4. Identification of the Dynamics</a></li>
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<li><a href="#org2a76cb4">1.5. Comparison with Ansys</a></li>
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<li><a href="#orgde64055">1.6. Force Sensor</a></li>
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<li><a href="#org2619ee6">1.7. Distributed Actuator</a></li>
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<li><a href="#org0a2021d">1.8. Distributed Actuator and Force Sensor</a></li>
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<li><a href="#org12f63ae">1.9. Dynamics from input voltage to displacement</a></li>
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<li><a href="#orgc1a02b7">1.10. Dynamics from input voltage to output voltage</a></li>
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<li><a href="#orgab9c056">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org42c8d07">1.2. Output parameters</a></li>
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<li><a href="#org6561967">1.3. Piezoelectric parameters</a></li>
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<li><a href="#orgddd3cad">1.4. Identification of the Dynamics</a></li>
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<li><a href="#org8daed84">1.5. Comparison with Ansys</a></li>
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<li><a href="#orgc22a98a">1.6. Force Sensor</a></li>
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<li><a href="#org251d0e8">1.7. Distributed Actuator</a></li>
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<li><a href="#orgacd6070">1.8. Distributed Actuator and Force Sensor</a></li>
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<li><a href="#org63ac6c4">1.9. Dynamics from input voltage to displacement</a></li>
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<li><a href="#org07a18c3">1.10. Dynamics from input voltage to output voltage</a></li>
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</ul>
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</li>
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<li><a href="#org697500c">2. APA300ML</a>
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<li><a href="#org12ed48f">2. APA300ML</a>
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<ul>
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<li><a href="#orgd625483">2.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org85c9cb3">2.2. Output parameters</a></li>
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<li><a href="#orgd69806c">2.3. Piezoelectric parameters</a></li>
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<li><a href="#orgd09ae18">2.4. Identification of the APA Characteristics</a>
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<li><a href="#orgda6e732">2.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org4cf9c6e">2.2. Output parameters</a></li>
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<li><a href="#org2b612f9">2.3. Piezoelectric parameters</a></li>
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<li><a href="#orgedd29dc">2.4. Identification of the APA Characteristics</a>
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<ul>
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<li><a href="#org3f1eed2">2.4.1. Stiffness</a></li>
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<li><a href="#orgc9c707a">2.4.2. Resonance Frequency</a></li>
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<li><a href="#orgbb3e97b">2.4.3. Amplification factor</a></li>
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<li><a href="#org739f84a">2.4.4. Stroke</a></li>
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<li><a href="#org9c27963">2.4.1. Stiffness</a></li>
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<li><a href="#orgc01b2f9">2.4.2. Resonance Frequency</a></li>
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<li><a href="#org934e234">2.4.3. Amplification factor</a></li>
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<li><a href="#org2874b23">2.4.4. Stroke</a></li>
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</ul>
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</li>
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<li><a href="#org99acb40">2.5. Identification of the Dynamics</a></li>
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<li><a href="#org783d12d">2.6. IFF</a></li>
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<li><a href="#orgb1f98aa">2.7. DVF</a></li>
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<li><a href="#org5f49459">2.5. Identification of the Dynamics</a></li>
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<li><a href="#org051104c">2.6. IFF</a></li>
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<li><a href="#org1e28770">2.7. DVF</a></li>
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</ul>
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</li>
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<li><a href="#orge14c536">3. Flexible Joint</a>
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<li><a href="#orge4cfde0">3. Flexible Joint</a>
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<ul>
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<li><a href="#org47e2edd">3.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#orgf861171">3.2. Output parameters</a></li>
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<li><a href="#orgb1e271b">3.3. Flexible Joint Characteristics</a></li>
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<li><a href="#org9df3f37">3.4. Identification</a></li>
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<li><a href="#orgca3d7e7">3.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#orgb6376e0">3.2. Output parameters</a></li>
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<li><a href="#org92f65bd">3.3. Flexible Joint Characteristics</a></li>
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<li><a href="#orgd334b90">3.4. Identification</a></li>
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</ul>
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</li>
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<li><a href="#org9474f65">4. Integral Force Feedback with Amplified Piezo</a>
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<li><a href="#org1351f3f">4. Integral Force Feedback with Amplified Piezo</a>
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<ul>
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<li><a href="#org822dc95">4.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#orge6c3b1d">4.2. IFF Plant</a></li>
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<li><a href="#orgcaa5e98">4.3. IFF controller</a></li>
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<li><a href="#org5851778">4.4. Closed Loop System</a></li>
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<li><a href="#orga590a65">4.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org5ddfecc">4.2. IFF Plant</a></li>
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<li><a href="#org76400d1">4.3. IFF controller</a></li>
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<li><a href="#org8c42386">4.4. Closed Loop System</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgabca705" class="outline-2">
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<h2 id="orgabca705"><span class="section-number-2">1</span> Amplified Piezoelectric Actuator - 3D elements</h2>
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<div id="outline-container-org71cd323" class="outline-2">
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<h2 id="org71cd323"><span class="section-number-2">1</span> Amplified Piezoelectric Actuator - 3D elements</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The idea here is to:
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@ -101,8 +101,8 @@ The idea here is to:
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</ul>
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</div>
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<div id="outline-container-orgc2a67b0" class="outline-3">
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<h3 id="orgc2a67b0"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
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<div id="outline-container-orgab9c056" class="outline-3">
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<h3 id="orgab9c056"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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We first extract the stiffness and mass matrices.
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@ -128,8 +128,8 @@ Then, we extract the coordinates of the interface nodes.
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</div>
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</div>
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<div id="outline-container-orgf3dcf66" class="outline-3">
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<h3 id="orgf3dcf66"><span class="section-number-3">1.2</span> Output parameters</h3>
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<div id="outline-container-org42c8d07" class="outline-3">
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<h3 id="org42c8d07"><span class="section-number-3">1.2</span> Output parameters</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab">load('./mat/piezo_amplified_3d.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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@ -168,7 +168,7 @@ Then, we extract the coordinates of the interface nodes.
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</table>
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<div id="orgf4319ab" class="figure">
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<div id="org8f635f5" class="figure">
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<p><img src="figs/amplified_piezo_interface_nodes.png" alt="amplified_piezo_interface_nodes.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Interface Nodes for the Amplified Piezo Actuator</p>
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@ -626,8 +626,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
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</div>
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<div id="outline-container-orgf1c1c31" class="outline-3">
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<h3 id="orgf1c1c31"><span class="section-number-3">1.3</span> Piezoelectric parameters</h3>
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<div id="outline-container-org6561967" class="outline-3">
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<h3 id="org6561967"><span class="section-number-3">1.3</span> Piezoelectric parameters</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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Parameters for the APA95ML:
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@ -688,8 +688,8 @@ where:
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</div>
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</div>
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<div id="outline-container-org3ad0597" class="outline-3">
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<h3 id="org3ad0597"><span class="section-number-3">1.4</span> Identification of the Dynamics</h3>
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<div id="outline-container-orgddd3cad" class="outline-3">
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<h3 id="orgddd3cad"><span class="section-number-3">1.4</span> Identification of the Dynamics</h3>
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<div class="outline-text-3" id="text-1-4">
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<p>
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The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
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@ -741,7 +741,7 @@ And the dynamics is identified.
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</p>
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<p>
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The two identified dynamics are compared in Figure <a href="#org1459802">2</a>.
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The two identified dynamics are compared in Figure <a href="#org0d0b642">2</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">%% Name of the Simulink File
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@ -757,7 +757,7 @@ Ghm = -linearize(mdl, io);
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</div>
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<div id="org1459802" class="figure">
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<div id="org0d0b642" class="figure">
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<p><img src="figs/dynamics_act_disp_comp_mass.png" alt="dynamics_act_disp_comp_mass.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Dynamics from \(F\) to \(d\) without a payload and with a 10kg payload</p>
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@ -765,8 +765,8 @@ Ghm = -linearize(mdl, io);
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</div>
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</div>
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<div id="outline-container-org2a76cb4" class="outline-3">
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<h3 id="org2a76cb4"><span class="section-number-3">1.5</span> Comparison with Ansys</h3>
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||||
<div id="outline-container-org8daed84" class="outline-3">
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<h3 id="org8daed84"><span class="section-number-3">1.5</span> Comparison with Ansys</h3>
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<div class="outline-text-3" id="text-1-5">
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<p>
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Let’s import the results from an Harmonic response analysis in Ansys.
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@ -778,11 +778,11 @@ Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
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</div>
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<p>
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The obtained dynamics from the Simscape model and from the Ansys analysis are compare in Figure <a href="#org7e4a176">3</a>.
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The obtained dynamics from the Simscape model and from the Ansys analysis are compare in Figure <a href="#org3c4c607">3</a>.
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</p>
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<div id="org7e4a176" class="figure">
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<div id="org3c4c607" class="figure">
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<p><img src="figs/dynamics_force_disp_comp_anasys.png" alt="dynamics_force_disp_comp_anasys.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Comparison of the obtained dynamics using Simscape with the harmonic response analysis using Ansys</p>
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@ -790,15 +790,15 @@ The obtained dynamics from the Simscape model and from the Ansys analysis are co
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</div>
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</div>
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<div id="outline-container-orgde64055" class="outline-3">
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<h3 id="orgde64055"><span class="section-number-3">1.6</span> Force Sensor</h3>
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<div id="outline-container-orgc22a98a" class="outline-3">
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<h3 id="orgc22a98a"><span class="section-number-3">1.6</span> Force Sensor</h3>
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<div class="outline-text-3" id="text-1-6">
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<p>
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The dynamics is identified from internal forces applied between nodes 3 and 11 to the relative displacement of nodes 11 and 13.
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</p>
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<p>
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||||
The obtained dynamics is shown in Figure <a href="#org4a892bf">4</a>.
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The obtained dynamics is shown in Figure <a href="#orgf53147f">4</a>.
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</p>
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<div class="org-src-container">
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@ -838,7 +838,7 @@ Gfm = linearize(mdl, io);
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</div>
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<div id="org4a892bf" class="figure">
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<div id="orgf53147f" class="figure">
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<p><img src="figs/dynamics_force_force_sensor_comp_mass.png" alt="dynamics_force_force_sensor_comp_mass.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Dynamics from \(F\) to \(F_m\) for \(m=0\) and \(m = 10kg\)</p>
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@ -846,8 +846,8 @@ Gfm = linearize(mdl, io);
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</div>
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</div>
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<div id="outline-container-org2619ee6" class="outline-3">
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<h3 id="org2619ee6"><span class="section-number-3">1.7</span> Distributed Actuator</h3>
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||||
<div id="outline-container-org251d0e8" class="outline-3">
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||||
<h3 id="org251d0e8"><span class="section-number-3">1.7</span> Distributed Actuator</h3>
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<div class="outline-text-3" id="text-1-7">
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<div class="org-src-container">
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<pre class="src src-matlab">m = 0;
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@ -896,8 +896,8 @@ Gdm = linearize(mdl, io);
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</div>
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</div>
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||||
<div id="outline-container-org0a2021d" class="outline-3">
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<h3 id="org0a2021d"><span class="section-number-3">1.8</span> Distributed Actuator and Force Sensor</h3>
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||||
<div id="outline-container-orgacd6070" class="outline-3">
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||||
<h3 id="orgacd6070"><span class="section-number-3">1.8</span> Distributed Actuator and Force Sensor</h3>
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||||
<div class="outline-text-3" id="text-1-8">
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||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">m = 0;
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@ -937,8 +937,8 @@ Gfdm = linearize(mdl, io);
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||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-org12f63ae" class="outline-3">
|
||||
<h3 id="org12f63ae"><span class="section-number-3">1.9</span> Dynamics from input voltage to displacement</h3>
|
||||
<div id="outline-container-org63ac6c4" class="outline-3">
|
||||
<h3 id="org63ac6c4"><span class="section-number-3">1.9</span> Dynamics from input voltage to displacement</h3>
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||||
<div class="outline-text-3" id="text-1-9">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">m = 5;
|
||||
@ -950,7 +950,7 @@ And the dynamics is identified.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The two identified dynamics are compared in Figure <a href="#org1459802">2</a>.
|
||||
The two identified dynamics are compared in Figure <a href="#org0d0b642">2</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">%% Name of the Simulink File
|
||||
@ -972,8 +972,8 @@ G = -linearize(mdl, io);
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc1a02b7" class="outline-3">
|
||||
<h3 id="orgc1a02b7"><span class="section-number-3">1.10</span> Dynamics from input voltage to output voltage</h3>
|
||||
<div id="outline-container-org07a18c3" class="outline-3">
|
||||
<h3 id="org07a18c3"><span class="section-number-3">1.10</span> Dynamics from input voltage to output voltage</h3>
|
||||
<div class="outline-text-3" id="text-1-10">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">m = 5;
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@ -996,19 +996,19 @@ G = -linearize(mdl, io);
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</div>
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</div>
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||||
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||||
<div id="outline-container-org697500c" class="outline-2">
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||||
<h2 id="org697500c"><span class="section-number-2">2</span> APA300ML</h2>
|
||||
<div id="outline-container-org12ed48f" class="outline-2">
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<h2 id="org12ed48f"><span class="section-number-2">2</span> APA300ML</h2>
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||||
<div class="outline-text-2" id="text-2">
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||||
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||||
<div id="orga28293a" class="figure">
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||||
<div id="orgc4c274c" class="figure">
|
||||
<p><img src="figs/apa300ml_ansys.jpg" alt="apa300ml_ansys.jpg" />
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</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Ansys FEM of the APA300ML</p>
|
||||
</div>
|
||||
</div>
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||||
|
||||
<div id="outline-container-orgd625483" class="outline-3">
|
||||
<h3 id="orgd625483"><span class="section-number-3">2.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-orgda6e732" class="outline-3">
|
||||
<h3 id="orgda6e732"><span class="section-number-3">2.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -1040,8 +1040,8 @@ Then, we extract the coordinates of the interface nodes.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org85c9cb3" class="outline-3">
|
||||
<h3 id="org85c9cb3"><span class="section-number-3">2.2</span> Output parameters</h3>
|
||||
<div id="outline-container-org4cf9c6e" class="outline-3">
|
||||
<h3 id="org4cf9c6e"><span class="section-number-3">2.2</span> Output parameters</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load('./mat/APA300ML.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
|
||||
@ -1482,8 +1482,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd69806c" class="outline-3">
|
||||
<h3 id="orgd69806c"><span class="section-number-3">2.3</span> Piezoelectric parameters</h3>
|
||||
<div id="outline-container-org2b612f9" class="outline-3">
|
||||
<h3 id="org2b612f9"><span class="section-number-3">2.3</span> Piezoelectric parameters</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
Parameters for the APA95ML:
|
||||
@ -1544,12 +1544,12 @@ where:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd09ae18" class="outline-3">
|
||||
<h3 id="orgd09ae18"><span class="section-number-3">2.4</span> Identification of the APA Characteristics</h3>
|
||||
<div id="outline-container-orgedd29dc" class="outline-3">
|
||||
<h3 id="orgedd29dc"><span class="section-number-3">2.4</span> Identification of the APA Characteristics</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
</div>
|
||||
<div id="outline-container-org3f1eed2" class="outline-4">
|
||||
<h4 id="org3f1eed2"><span class="section-number-4">2.4.1</span> Stiffness</h4>
|
||||
<div id="outline-container-org9c27963" class="outline-4">
|
||||
<h4 id="org9c27963"><span class="section-number-4">2.4.1</span> Stiffness</h4>
|
||||
<div class="outline-text-4" id="text-2-4-1">
|
||||
<p>
|
||||
The transfer function from vertical external force to the relative vertical displacement is identified.
|
||||
@ -1574,16 +1574,16 @@ The specified stiffness in the datasheet is \(k = 1.8\, [N/\mu m]\).
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc9c707a" class="outline-4">
|
||||
<h4 id="orgc9c707a"><span class="section-number-4">2.4.2</span> Resonance Frequency</h4>
|
||||
<div id="outline-container-orgc01b2f9" class="outline-4">
|
||||
<h4 id="orgc01b2f9"><span class="section-number-4">2.4.2</span> Resonance Frequency</h4>
|
||||
<div class="outline-text-4" id="text-2-4-2">
|
||||
<p>
|
||||
The resonance frequency is specified to be between 650Hz and 840Hz.
|
||||
This is also the case for the FEM model (Figure <a href="#org358524e">6</a>).
|
||||
This is also the case for the FEM model (Figure <a href="#org78bd63c">6</a>).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org358524e" class="figure">
|
||||
<div id="org78bd63c" class="figure">
|
||||
<p><img src="figs/apa300ml_resonance.png" alt="apa300ml_resonance.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>First resonance is around 800Hz</p>
|
||||
@ -1591,8 +1591,8 @@ This is also the case for the FEM model (Figure <a href="#org358524e">6</a>).
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbb3e97b" class="outline-4">
|
||||
<h4 id="orgbb3e97b"><span class="section-number-4">2.4.3</span> Amplification factor</h4>
|
||||
<div id="outline-container-org934e234" class="outline-4">
|
||||
<h4 id="org934e234"><span class="section-number-4">2.4.3</span> Amplification factor</h4>
|
||||
<div class="outline-text-4" id="text-2-4-3">
|
||||
<p>
|
||||
The amplification factor is the ratio of the axial displacement to the stack displacement.
|
||||
@ -1625,8 +1625,8 @@ If we take the ratio of the piezo height and length (approximation of the amplif
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org739f84a" class="outline-4">
|
||||
<h4 id="org739f84a"><span class="section-number-4">2.4.4</span> Stroke</h4>
|
||||
<div id="outline-container-org2874b23" class="outline-4">
|
||||
<h4 id="org2874b23"><span class="section-number-4">2.4.4</span> Stroke</h4>
|
||||
<div class="outline-text-4" id="text-2-4-4">
|
||||
<p>
|
||||
Estimation of the actuator stroke:
|
||||
@ -1657,8 +1657,8 @@ This is exactly the specified stroke in the data-sheet.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org99acb40" class="outline-3">
|
||||
<h3 id="org99acb40"><span class="section-number-3">2.5</span> Identification of the Dynamics</h3>
|
||||
<div id="outline-container-org5f49459" class="outline-3">
|
||||
<h3 id="org5f49459"><span class="section-number-3">2.5</span> Identification of the Dynamics</h3>
|
||||
<div class="outline-text-3" id="text-2-5">
|
||||
<p>
|
||||
The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
|
||||
@ -1684,7 +1684,7 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6e16b45" class="figure">
|
||||
<div id="orgd6baf63" class="figure">
|
||||
<p><img src="figs/apa300ml_plant_dynamics.png" alt="apa300ml_plant_dynamics.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Transfer function from forces applied by the stack to the axial displacement of the APA</p>
|
||||
@ -1692,29 +1692,29 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org783d12d" class="outline-3">
|
||||
<h3 id="org783d12d"><span class="section-number-3">2.6</span> IFF</h3>
|
||||
<div id="outline-container-org051104c" class="outline-3">
|
||||
<h3 id="org051104c"><span class="section-number-3">2.6</span> IFF</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<p>
|
||||
Let’s use 2 stacks as actuators and 1 stack as force sensor.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The transfer function from actuator to sensors is identified and shown in Figure <a href="#orga7f2199">8</a>.
|
||||
The transfer function from actuator to sensors is identified and shown in Figure <a href="#org521d0e8">8</a>.
|
||||
</p>
|
||||
|
||||
<div id="orga7f2199" class="figure">
|
||||
<div id="org521d0e8" class="figure">
|
||||
<p><img src="figs/apa300ml_iff_plant.png" alt="apa300ml_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Transfer function from actuator to force sensor</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
For root locus corresponding to IFF is shown in Figure <a href="#org30c4ec4">9</a>.
|
||||
For root locus corresponding to IFF is shown in Figure <a href="#org7ea3704">9</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org30c4ec4" class="figure">
|
||||
<div id="org7ea3704" class="figure">
|
||||
<p><img src="figs/apa300ml_iff_root_locus.png" alt="apa300ml_iff_root_locus.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Root Locus for IFF</p>
|
||||
@ -1722,25 +1722,25 @@ For root locus corresponding to IFF is shown in Figure <a href="#org30c4ec4">9</
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb1f98aa" class="outline-3">
|
||||
<h3 id="orgb1f98aa"><span class="section-number-3">2.7</span> DVF</h3>
|
||||
<div id="outline-container-org1e28770" class="outline-3">
|
||||
<h3 id="org1e28770"><span class="section-number-3">2.7</span> DVF</h3>
|
||||
<div class="outline-text-3" id="text-2-7">
|
||||
<p>
|
||||
Now the dynamics from the stack actuator to the relative motion sensor is identified and shown in Figure <a href="#orgdde20bb">10</a>.
|
||||
Now the dynamics from the stack actuator to the relative motion sensor is identified and shown in Figure <a href="#org84b27a1">10</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgdde20bb" class="figure">
|
||||
<div id="org84b27a1" class="figure">
|
||||
<p><img src="figs/apa300ml_dvf_plant.png" alt="apa300ml_dvf_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Transfer function from stack actuator to relative motion sensor</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The root locus for DVF is shown in Figure <a href="#orga5b36de">11</a>.
|
||||
The root locus for DVF is shown in Figure <a href="#org9f595b0">11</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga5b36de" class="figure">
|
||||
<div id="org9f595b0" class="figure">
|
||||
<p><img src="figs/apa300ml_dvf_root_locus.png" alt="apa300ml_dvf_root_locus.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Root Locus for Direct Velocity Feedback</p>
|
||||
@ -1749,12 +1749,19 @@ The root locus for DVF is shown in Figure <a href="#orga5b36de">11</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge14c536" class="outline-2">
|
||||
<h2 id="orge14c536"><span class="section-number-2">3</span> Flexible Joint</h2>
|
||||
<div id="outline-container-orge4cfde0" class="outline-2">
|
||||
<h2 id="orge4cfde0"><span class="section-number-2">3</span> Flexible Joint</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
|
||||
<div id="org329f4b9" class="figure">
|
||||
<p><img src="figs/flexor_id16_screenshot.png" alt="flexor_id16_screenshot.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Flexor studied</p>
|
||||
</div>
|
||||
<div id="outline-container-org47e2edd" class="outline-3">
|
||||
<h3 id="org47e2edd"><span class="section-number-3">3.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgca3d7e7" class="outline-3">
|
||||
<h3 id="orgca3d7e7"><span class="section-number-3">3.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -1780,8 +1787,8 @@ Then, we extract the coordinates of the interface nodes.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf861171" class="outline-3">
|
||||
<h3 id="orgf861171"><span class="section-number-3">3.2</span> Output parameters</h3>
|
||||
<div id="outline-container-orgb6376e0" class="outline-3">
|
||||
<h3 id="orgb6376e0"><span class="section-number-3">3.2</span> Output parameters</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
|
||||
@ -2182,8 +2189,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb1e271b" class="outline-3">
|
||||
<h3 id="orgb1e271b"><span class="section-number-3">3.3</span> Flexible Joint Characteristics</h3>
|
||||
<div id="outline-container-org92f65bd" class="outline-3">
|
||||
<h3 id="org92f65bd"><span class="section-number-3">3.3</span> Flexible Joint Characteristics</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
@ -2231,8 +2238,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9df3f37" class="outline-3">
|
||||
<h3 id="org9df3f37"><span class="section-number-3">3.4</span> Identification</h3>
|
||||
<div id="outline-container-orgd334b90" class="outline-3">
|
||||
<h3 id="orgd334b90"><span class="section-number-3">3.4</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">m = 10;
|
||||
@ -2302,12 +2309,16 @@ G = linearize(mdl, io);
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9474f65" class="outline-2">
|
||||
<h2 id="org9474f65"><span class="section-number-2">4</span> Integral Force Feedback with Amplified Piezo</h2>
|
||||
<div id="outline-container-org1351f3f" class="outline-2">
|
||||
<h2 id="org1351f3f"><span class="section-number-2">4</span> Integral Force Feedback with Amplified Piezo</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
In this section, we try to replicate the results obtained in (<a href="#citeproc_bib_item_2">Souleille et al. 2018</a>).
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org822dc95" class="outline-3">
|
||||
<h3 id="org822dc95"><span class="section-number-3">4.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
|
||||
<div id="outline-container-orga590a65" class="outline-3">
|
||||
<h3 id="orga590a65"><span class="section-number-3">4.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -2328,11 +2339,11 @@ Then, we extract the coordinates of the interface nodes.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge6c3b1d" class="outline-3">
|
||||
<h3 id="orge6c3b1d"><span class="section-number-3">4.2</span> IFF Plant</h3>
|
||||
<div id="outline-container-org5ddfecc" class="outline-3">
|
||||
<h3 id="org5ddfecc"><span class="section-number-3">4.2</span> IFF Plant</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
The transfer function from the force actuator to the force sensor is identified and shown in Figure <a href="#org59a7b86">12</a>.
|
||||
The transfer function from the force actuator to the force sensor is identified and shown in Figure <a href="#orgb98e9a1">13</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -2369,19 +2380,19 @@ Gf = linearize(mdl, io);
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org59a7b86" class="figure">
|
||||
<div id="orgb98e9a1" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_plant.png" alt="piezo_amplified_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>IFF Plant</p>
|
||||
<p><span class="figure-number">Figure 13: </span>IFF Plant</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcaa5e98" class="outline-3">
|
||||
<h3 id="orgcaa5e98"><span class="section-number-3">4.3</span> IFF controller</h3>
|
||||
<div id="outline-container-org76400d1" class="outline-3">
|
||||
<h3 id="org76400d1"><span class="section-number-3">4.3</span> IFF controller</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<p>
|
||||
The controller is defined and the loop gain is shown in Figure <a href="#orgfc2083c">13</a>.
|
||||
The controller is defined and the loop gain is shown in Figure <a href="#org50ab4b8">14</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Kiff = -1e12/s;
|
||||
@ -2389,16 +2400,16 @@ The controller is defined and the loop gain is shown in Figure <a href="#orgfc20
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgfc2083c" class="figure">
|
||||
<div id="org50ab4b8" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_loop_gain.png" alt="piezo_amplified_iff_loop_gain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>IFF Loop Gain</p>
|
||||
<p><span class="figure-number">Figure 14: </span>IFF Loop Gain</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5851778" class="outline-3">
|
||||
<h3 id="org5851778"><span class="section-number-3">4.4</span> Closed Loop System</h3>
|
||||
<div id="outline-container-org8c42386" class="outline-3">
|
||||
<h3 id="org8c42386"><span class="section-number-3">4.4</span> Closed Loop System</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">m = 10;
|
||||
@ -2441,31 +2452,36 @@ G.OutputName = {'x1', 'Fs'};
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orga087bcd" class="figure">
|
||||
<div id="orgc068c38" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_comp.png" alt="piezo_amplified_iff_comp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>OL and CL transfer functions</p>
|
||||
<p><span class="figure-number">Figure 15: </span>OL and CL transfer functions</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="orgb3333f6" class="figure">
|
||||
<div id="orgb4c1cac" class="figure">
|
||||
<p><img src="figs/souleille18_results.png" alt="souleille18_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Results obtained in <a class='org-ref-reference' href="#souleille18_concep_activ_mount_space_applic">souleille18_concep_activ_mount_space_applic</a></p>
|
||||
<p><span class="figure-number">Figure 16: </span>Results obtained in <a class='org-ref-reference' href="#souleille18_concep_activ_mount_space_applic">souleille18_concep_activ_mount_space_applic</a></p>
|
||||
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
|
||||
<div class="csl-bib-body">
|
||||
<div class="csl-entry"><a name="citeproc_bib_item_1"></a>Fleming, Andrew J., and Kam K. Leang. 2014. <i>Design, Modeling and Control of Nanopositioning Systems</i>. Advances in Industrial Control. Springer International Publishing. <a href="https://doi.org/10.1007/978-3-319-06617-2">https://doi.org/10.1007/978-3-319-06617-2</a>.</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="csl-entry"><a name="citeproc_bib_item_2"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” <i>CEAS Space Journal</i> 10 (2). Springer:157–65.</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-08-03 lun. 15:33</p>
|
||||
<p class="date">Created: 2020-08-03 lun. 15:42</p>
|
||||
</div>
|
||||
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|
||||
</html>
|
||||
|
||||
@ -1561,6 +1561,9 @@ The dynamics is identified from the applied force to the measured relative displ
|
||||
#+end_src
|
||||
|
||||
* Integral Force Feedback with Amplified Piezo
|
||||
** Introduction :ignore:
|
||||
In this section, we try to replicate the results obtained in cite:souleille18_concep_activ_mount_space_applic.
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
@ -1817,3 +1820,7 @@ The controller is defined and the loop gain is shown in Figure [[fig:piezo_ampli
|
||||
#+name: fig:souleille18_results
|
||||
#+caption: Results obtained in cite:souleille18_concep_activ_mount_space_applic
|
||||
[[file:figs/souleille18_results.png]]
|
||||
|
||||
* Bibliography :ignore:
|
||||
bibliographystyle:unsrt
|
||||
bibliography:ref.bib
|
||||
|
||||
21
ref.bib
Normal file
21
ref.bib
Normal file
@ -0,0 +1,21 @@
|
||||
@article{souleille18_concep_activ_mount_space_applic,
|
||||
author = {Souleille, Adrien and Lampert, Thibault and Lafarga, V and Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues, Gon{\c{c}}alo and Collette, Christophe},
|
||||
title = {A Concept of Active Mount for Space Applications},
|
||||
journal = {CEAS Space Journal},
|
||||
volume = {10},
|
||||
number = {2},
|
||||
pages = {157--165},
|
||||
year = {2018},
|
||||
publisher = {Springer},
|
||||
}
|
||||
|
||||
@book{fleming14_desig_model_contr_nanop_system,
|
||||
author = {Andrew J. Fleming and Kam K. Leang},
|
||||
title = {Design, Modeling and Control of Nanopositioning Systems},
|
||||
year = {2014},
|
||||
publisher = {Springer International Publishing},
|
||||
url = {https://doi.org/10.1007/978-3-319-06617-2},
|
||||
doi = {10.1007/978-3-319-06617-2},
|
||||
pages = {nil},
|
||||
series = {Advances in Industrial Control},
|
||||
}
|
||||
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Reference in New Issue
Block a user