Change link to image
This commit is contained in:
parent
5b56f3566c
commit
ee9b56a06e
301
index.html
301
index.html
@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2020-11-13 ven. 08:56 -->
|
||||
<!-- 2021-01-04 lun. 13:57 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>NASS - Finite Element Models with Simscape</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@ -30,46 +30,47 @@
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgb231366">1. APA300ML</a>
|
||||
<li><a href="#org47bc5a9">1. APA300ML</a>
|
||||
<ul>
|
||||
<li><a href="#orga4e3f9c">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org4f3db59">1.2. Piezoelectric parameters</a></li>
|
||||
<li><a href="#org364e184">1.3. Simscape Model</a></li>
|
||||
<li><a href="#org8bf66af">1.4. Identification of the APA Characteristics</a>
|
||||
<li><a href="#org0dad7b4">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#orge18130e">1.2. Piezoelectric parameters</a></li>
|
||||
<li><a href="#org8a2e574">1.3. Simscape Model</a></li>
|
||||
<li><a href="#org26ea26b">1.4. Identification of the APA Characteristics</a>
|
||||
<ul>
|
||||
<li><a href="#orgc2b9be5">1.4.1. Stiffness</a></li>
|
||||
<li><a href="#orgd55eeff">1.4.2. Resonance Frequency</a></li>
|
||||
<li><a href="#org59f7b55">1.4.3. Amplification factor</a></li>
|
||||
<li><a href="#orga970d47">1.4.4. Stroke</a></li>
|
||||
<li><a href="#org0fa017e">1.4.1. Stiffness</a></li>
|
||||
<li><a href="#org574c989">1.4.2. Resonance Frequency</a></li>
|
||||
<li><a href="#org612b77e">1.4.3. Amplification factor</a></li>
|
||||
<li><a href="#orgdf73676">1.4.4. Stroke</a></li>
|
||||
<li><a href="#orgd96b688">1.4.5. Stroke BIS</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org875f674">1.5. Identification of the Dynamics from actuator to replace displacement</a></li>
|
||||
<li><a href="#org926378e">1.6. Identification of the Dynamics from actuator to force sensor</a></li>
|
||||
<li><a href="#org0b533cc">1.7. Identification for a simpler model</a></li>
|
||||
<li><a href="#orgd7e3154">1.8. Integral Force Feedback</a></li>
|
||||
<li><a href="#orga767e88">1.5. Identification of the Dynamics from actuator to replace displacement</a></li>
|
||||
<li><a href="#org9f54be7">1.6. Identification of the Dynamics from actuator to force sensor</a></li>
|
||||
<li><a href="#org7d96497">1.7. Identification for a simpler model</a></li>
|
||||
<li><a href="#orgf0dad41">1.8. Integral Force Feedback</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orge12e432">2. First Flexible Joint Geometry</a>
|
||||
<li><a href="#org538ff3f">2. First Flexible Joint Geometry</a>
|
||||
<ul>
|
||||
<li><a href="#org91559c3">2.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org0c0ae39">2.2. Identification of the parameters using Simscape and looking at the Stiffness Matrix</a></li>
|
||||
<li><a href="#orgb1eeb49">2.3. Simpler Model</a></li>
|
||||
<li><a href="#org01a224b">2.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org4b0797c">2.2. Identification of the parameters using Simscape and looking at the Stiffness Matrix</a></li>
|
||||
<li><a href="#org764d26e">2.3. Simpler Model</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org6fa0f81">3. Optimized Flexible Joint</a>
|
||||
<li><a href="#org6f963d0">3. Optimized Flexible Joint</a>
|
||||
<ul>
|
||||
<li><a href="#orgadfaeb7">3.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org1a74e71">3.2. Identification of the parameters using Simscape</a></li>
|
||||
<li><a href="#org3ba1fee">3.3. Simpler Model</a></li>
|
||||
<li><a href="#orgec51432">3.4. Comparison with a stiffer Flexible Joint</a></li>
|
||||
<li><a href="#orgc5406d6">3.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org4c2abff">3.2. Identification of the parameters using Simscape</a></li>
|
||||
<li><a href="#org40e908d">3.3. Simpler Model</a></li>
|
||||
<li><a href="#org14a611d">3.4. Comparison with a stiffer Flexible Joint</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org91975b5">4. Complete Strut with Encoder</a>
|
||||
<li><a href="#orgeb13ea0">4. Complete Strut with Encoder</a>
|
||||
<ul>
|
||||
<li><a href="#orgd829824">4.1. Introduction</a></li>
|
||||
<li><a href="#orgd7f754c">4.2. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org5019141">4.3. Piezoelectric parameters</a></li>
|
||||
<li><a href="#org72bb8f1">4.4. Identification of the Dynamics</a></li>
|
||||
<li><a href="#org7c76927">4.1. Introduction</a></li>
|
||||
<li><a href="#org20586d2">4.2. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
||||
<li><a href="#org04b2ce1">4.3. Piezoelectric parameters</a></li>
|
||||
<li><a href="#org0e8a535">4.4. Identification of the Dynamics</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
@ -84,22 +85,22 @@ In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are d
|
||||
It is divided in the following sections:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Section <a href="#org31bfe65">1</a>:
|
||||
<li>Section <a href="#orgacf2789">1</a>:
|
||||
A super-element of the Amplified Piezoelectric Actuator APA300ML used for the NASS is exported using Ansys and imported in Simscape.
|
||||
The static and dynamical properties of the APA300ML are then estimated using the Simscape model.</li>
|
||||
<li>Section <a href="#orga0ece29">2</a>:
|
||||
<li>Section <a href="#org5898d43">2</a>:
|
||||
A first geometry of a Flexible joint is modelled and its characteristics are identified from the Stiffness matrix as well as from the Simscape model.</li>
|
||||
<li>Section <a href="#org513c349">3</a>:
|
||||
<li>Section <a href="#orga75acbf">3</a>:
|
||||
An optimized flexible joint is developed for the Nano-Hexapod and is then imported in a Simscape model.</li>
|
||||
<li>Section <a href="#orgcff61d6">4</a>:
|
||||
<li>Section <a href="#orgbd31e29">4</a>:
|
||||
A super element of a complete strut is studied.</li>
|
||||
</ul>
|
||||
|
||||
<div id="outline-container-orgb231366" class="outline-2">
|
||||
<h2 id="orgb231366"><span class="section-number-2">1</span> APA300ML</h2>
|
||||
<div id="outline-container-org47bc5a9" class="outline-2">
|
||||
<h2 id="org47bc5a9"><span class="section-number-2">1</span> APA300ML</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
<a id="org31bfe65"></a>
|
||||
<a id="orgacf2789"></a>
|
||||
</p>
|
||||
<p>
|
||||
In this section, the Amplified Piezoelectric Actuator APA300ML (<a href="doc/APA300ML.pdf">doc</a>) is modeled using a Finite Element Software.
|
||||
@ -107,19 +108,19 @@ Then a <i>super element</i> is exported and imported in Simscape where its dynam
|
||||
</p>
|
||||
|
||||
<p>
|
||||
A 3D view of the Amplified Piezoelectric Actuator (APA300ML) is shown in Figure <a href="#orgfaefa60">1</a>.
|
||||
A 3D view of the Amplified Piezoelectric Actuator (APA300ML) is shown in Figure <a href="#orgbeb87aa">1</a>.
|
||||
The remote point used are also shown in this figure.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgfaefa60" class="figure">
|
||||
<div id="orgbeb87aa" class="figure">
|
||||
<p><img src="figs/apa300ml_ansys.jpg" alt="apa300ml_ansys.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Ansys FEM of the APA300ML</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orga4e3f9c" class="outline-3">
|
||||
<h3 id="orga4e3f9c"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-org0dad7b4" class="outline-3">
|
||||
<h3 id="org0dad7b4"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -573,14 +574,14 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can now use th
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4f3db59" class="outline-3">
|
||||
<h3 id="org4f3db59"><span class="section-number-3">1.2</span> Piezoelectric parameters</h3>
|
||||
<div id="outline-container-orge18130e" class="outline-3">
|
||||
<h3 id="orge18130e"><span class="section-number-3">1.2</span> Piezoelectric parameters</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<p>
|
||||
In order to make the conversion from applied voltage to generated force or from the strain to the generated voltage, we need to defined some parameters corresponding to the piezoelectric material:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">d33 = 300e<span class="org-type">-</span>12; <span class="org-comment">% Strain constant [m/V]</span>
|
||||
<pre class="src src-matlab">d33 = 600e<span class="org-type">-</span>12; <span class="org-comment">% Strain constant [m/V]</span>
|
||||
n = 80; <span class="org-comment">% Number of layers per stack</span>
|
||||
eT = 1.6e<span class="org-type">-</span>8; <span class="org-comment">% Permittivity under constant stress [F/m]</span>
|
||||
sD = 1e<span class="org-type">-</span>11; <span class="org-comment">% Compliance under constant electric displacement [m2/N]</span>
|
||||
@ -589,11 +590,24 @@ C = 5e<span class="org-type">-</span>6; <span class="org-comment">% Stack c
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
PZT-4
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">d33 = 300e<span class="org-type">-</span>12; <span class="org-comment">% Strain constant [m/V]</span>
|
||||
n = 80; <span class="org-comment">% Number of layers per stack</span>
|
||||
eT = 5.3e<span class="org-type">-</span>9; <span class="org-comment">% Permittivity under constant stress [F/m]</span>
|
||||
sD = 1e<span class="org-type">-</span>11; <span class="org-comment">% Compliance under constant electric displacement [m2/N]</span>
|
||||
ka = 235e6; <span class="org-comment">% Stack stiffness [N/m]</span>
|
||||
C = 5e<span class="org-type">-</span>6; <span class="org-comment">% Stack capactiance [F]</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The ratio of the developed force to applied voltage is:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\label{org26cf049}
|
||||
\label{orgbc04a1b}
|
||||
F_a = g_a V_a, \quad g_a = d_{33} n k_a
|
||||
\end{equation}
|
||||
<p>
|
||||
@ -624,7 +638,7 @@ If we take the numerical values, we obtain:
|
||||
From (<a href="#citeproc_bib_item_1">Fleming and Leang 2014</a>) (page 123), the relation between relative displacement of the sensor stack and generated voltage is:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\label{orgd71c6e4}
|
||||
\label{orgb1b83fa}
|
||||
V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h
|
||||
\end{equation}
|
||||
<p>
|
||||
@ -653,8 +667,8 @@ If we take the numerical values, we obtain:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org364e184" class="outline-3">
|
||||
<h3 id="org364e184"><span class="section-number-3">1.3</span> Simscape Model</h3>
|
||||
<div id="outline-container-org8a2e574" class="outline-3">
|
||||
<h3 id="org8a2e574"><span class="section-number-3">1.3</span> Simscape Model</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
|
||||
@ -669,7 +683,7 @@ Let’s say we use two stacks as a force sensor and one stack as an actuator
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
The interface nodes are shown in Figure <a href="#orgfaefa60">1</a>.
|
||||
The interface nodes are shown in Figure <a href="#orgbeb87aa">1</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -678,12 +692,12 @@ One mass is fixed at one end of the piezo-electric stack actuator (remove point
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8bf66af" class="outline-3">
|
||||
<h3 id="org8bf66af"><span class="section-number-3">1.4</span> Identification of the APA Characteristics</h3>
|
||||
<div id="outline-container-org26ea26b" class="outline-3">
|
||||
<h3 id="org26ea26b"><span class="section-number-3">1.4</span> Identification of the APA Characteristics</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
</div>
|
||||
<div id="outline-container-orgc2b9be5" class="outline-4">
|
||||
<h4 id="orgc2b9be5"><span class="section-number-4">1.4.1</span> Stiffness</h4>
|
||||
<div id="outline-container-org0fa017e" class="outline-4">
|
||||
<h4 id="org0fa017e"><span class="section-number-4">1.4.1</span> Stiffness</h4>
|
||||
<div class="outline-text-4" id="text-1-4-1">
|
||||
<p>
|
||||
The transfer function from vertical external force to the relative vertical displacement is identified.
|
||||
@ -708,16 +722,16 @@ The specified stiffness in the datasheet is \(k = 1.8\, [N/\mu m]\).
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd55eeff" class="outline-4">
|
||||
<h4 id="orgd55eeff"><span class="section-number-4">1.4.2</span> Resonance Frequency</h4>
|
||||
<div id="outline-container-org574c989" class="outline-4">
|
||||
<h4 id="org574c989"><span class="section-number-4">1.4.2</span> Resonance Frequency</h4>
|
||||
<div class="outline-text-4" id="text-1-4-2">
|
||||
<p>
|
||||
The resonance frequency is specified to be between 650Hz and 840Hz.
|
||||
This is also the case for the FEM model (Figure <a href="#org5a0e1d6">2</a>).
|
||||
This is also the case for the FEM model (Figure <a href="#org0692940">2</a>).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org5a0e1d6" class="figure">
|
||||
<div id="org0692940" class="figure">
|
||||
<p><img src="figs/apa300ml_resonance.png" alt="apa300ml_resonance.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>First resonance is around 800Hz</p>
|
||||
@ -725,8 +739,8 @@ This is also the case for the FEM model (Figure <a href="#org5a0e1d6">2</a>).
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org59f7b55" class="outline-4">
|
||||
<h4 id="org59f7b55"><span class="section-number-4">1.4.3</span> Amplification factor</h4>
|
||||
<div id="outline-container-org612b77e" class="outline-4">
|
||||
<h4 id="org612b77e"><span class="section-number-4">1.4.3</span> Amplification factor</h4>
|
||||
<div class="outline-text-4" id="text-1-4-3">
|
||||
<p>
|
||||
The amplification factor is the ratio of the vertical displacement to the stack displacement.
|
||||
@ -759,8 +773,8 @@ This is actually correct and approximately corresponds to the ratio of the piezo
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga970d47" class="outline-4">
|
||||
<h4 id="orga970d47"><span class="section-number-4">1.4.4</span> Stroke</h4>
|
||||
<div id="outline-container-orgdf73676" class="outline-4">
|
||||
<h4 id="orgdf73676"><span class="section-number-4">1.4.4</span> Stroke</h4>
|
||||
<div class="outline-text-4" id="text-1-4-4">
|
||||
<p>
|
||||
Estimation of the actuator stroke:
|
||||
@ -789,10 +803,19 @@ This is exactly the specified stroke in the data-sheet.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd96b688" class="outline-4">
|
||||
<h4 id="orgd96b688"><span class="section-number-4">1.4.5</span> Stroke BIS</h4>
|
||||
<div class="outline-text-4" id="text-1-4-5">
|
||||
<ul class="org-ul">
|
||||
<li class="off"><code>[ ]</code> Identified the stroke form the transfer function from V to z</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org875f674" class="outline-3">
|
||||
<h3 id="org875f674"><span class="section-number-3">1.5</span> Identification of the Dynamics from actuator to replace displacement</h3>
|
||||
<div id="outline-container-orga767e88" class="outline-3">
|
||||
<h3 id="orga767e88"><span class="section-number-3">1.5</span> Identification of the Dynamics from actuator to replace displacement</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<p>
|
||||
We first set the mass to be approximately zero.
|
||||
@ -805,17 +828,17 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0bf96a7" class="figure">
|
||||
<div id="org5d7489b" class="figure">
|
||||
<p><img src="figs/apa300ml_plant_dynamics.png" alt="apa300ml_plant_dynamics.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Transfer function from forces applied by the stack to the axial displacement of the APA</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is shown in Figure <a href="#orgf443cba">4</a>.
|
||||
The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is shown in Figure <a href="#org7a8f7be">4</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgf443cba" class="figure">
|
||||
<div id="org7a8f7be" class="figure">
|
||||
<p><img src="figs/apa300ml_dvf_root_locus.png" alt="apa300ml_dvf_root_locus.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Root Locus for Direct Velocity Feedback</p>
|
||||
@ -823,28 +846,28 @@ The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org926378e" class="outline-3">
|
||||
<h3 id="org926378e"><span class="section-number-3">1.6</span> Identification of the Dynamics from actuator to force sensor</h3>
|
||||
<div id="outline-container-org9f54be7" class="outline-3">
|
||||
<h3 id="org9f54be7"><span class="section-number-3">1.6</span> Identification of the Dynamics from actuator to force sensor</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
<p>
|
||||
Let’s use 2 stacks as a force sensor and 1 stack as force actuator.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The transfer function from actuator voltage to sensor voltage is identified and shown in Figure <a href="#org0571899">5</a>.
|
||||
The transfer function from actuator voltage to sensor voltage is identified and shown in Figure <a href="#org01c41a7">5</a>.
|
||||
</p>
|
||||
|
||||
<div id="org0571899" class="figure">
|
||||
<div id="org01c41a7" class="figure">
|
||||
<p><img src="figs/apa300ml_iff_plant.png" alt="apa300ml_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Transfer function from actuator to force sensor</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
For root locus corresponding to IFF is shown in Figure <a href="#org4c7369c">6</a>.
|
||||
For root locus corresponding to IFF is shown in Figure <a href="#orge4c647a">6</a>.
|
||||
</p>
|
||||
|
||||
<div id="org4c7369c" class="figure">
|
||||
<div id="orge4c647a" class="figure">
|
||||
<p><img src="figs/apa300ml_iff_root_locus.png" alt="apa300ml_iff_root_locus.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Root Locus for IFF</p>
|
||||
@ -852,8 +875,8 @@ For root locus corresponding to IFF is shown in Figure <a href="#org4c7369c">6</
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0b533cc" class="outline-3">
|
||||
<h3 id="org0b533cc"><span class="section-number-3">1.7</span> Identification for a simpler model</h3>
|
||||
<div id="outline-container-org7d96497" class="outline-3">
|
||||
<h3 id="org7d96497"><span class="section-number-3">1.7</span> Identification for a simpler model</h3>
|
||||
<div class="outline-text-3" id="text-1-7">
|
||||
<p>
|
||||
The goal in this section is to identify the parameters of a simple APA model from the FEM.
|
||||
@ -865,12 +888,12 @@ The presented model is based on (<a href="#citeproc_bib_item_2">Souleille et al.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The model represents the Amplified Piezo Actuator (APA) from Cedrat-Technologies (Figure <a href="#orgdda4959">7</a>).
|
||||
The model represents the Amplified Piezo Actuator (APA) from Cedrat-Technologies (Figure <a href="#org53587dc">7</a>).
|
||||
The parameters are shown in the table below.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgdda4959" class="figure">
|
||||
<div id="org53587dc" class="figure">
|
||||
<p><img src="./figs/souleille18_model_piezo.png" alt="souleille18_model_piezo.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator</p>
|
||||
@ -1019,11 +1042,11 @@ And the DC gain is adjusted for the force sensor:
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The dynamics of the FEM model and the simpler model are compared in Figure <a href="#org25d35cd">8</a>.
|
||||
The dynamics of the FEM model and the simpler model are compared in Figure <a href="#org7cfb675">8</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org25d35cd" class="figure">
|
||||
<div id="org7cfb675" class="figure">
|
||||
<p><img src="figs/apa300ml_comp_simpler_model.png" alt="apa300ml_comp_simpler_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Comparison of the Dynamics between the FEM model and the simplified one</p>
|
||||
@ -1034,10 +1057,10 @@ The simplified model has also been implemented in Simscape.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The dynamics of the Simscape simplified model is identified and compared with the FEM one in Figure <a href="#org3ca18e2">9</a>.
|
||||
The dynamics of the Simscape simplified model is identified and compared with the FEM one in Figure <a href="#orgc636980">9</a>.
|
||||
</p>
|
||||
|
||||
<div id="org3ca18e2" class="figure">
|
||||
<div id="orgc636980" class="figure">
|
||||
<p><img src="figs/apa300ml_comp_simpler_simscape.png" alt="apa300ml_comp_simpler_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Comparison of the Dynamics between the FEM model and the simplified simscape model</p>
|
||||
@ -1045,8 +1068,8 @@ The dynamics of the Simscape simplified model is identified and compared with th
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd7e3154" class="outline-3">
|
||||
<h3 id="orgd7e3154"><span class="section-number-3">1.8</span> Integral Force Feedback</h3>
|
||||
<div id="outline-container-orgf0dad41" class="outline-3">
|
||||
<h3 id="orgf0dad41"><span class="section-number-3">1.8</span> Integral Force Feedback</h3>
|
||||
<div class="outline-text-3" id="text-1-8">
|
||||
<p>
|
||||
In this section, Integral Force Feedback control architecture is applied on the APA300ML.
|
||||
@ -1062,18 +1085,18 @@ The payload mass is set to 10kg.
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained dynamics is shown in Figure <a href="#org41e4933">10</a>.
|
||||
The obtained dynamics is shown in Figure <a href="#org358bae7">10</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org41e4933" class="figure">
|
||||
<div id="org358bae7" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_plant.png" alt="piezo_amplified_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>IFF Plant</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The controller is defined below and the loop gain is shown in Figure <a href="#org8791595">11</a>.
|
||||
The controller is defined below and the loop gain is shown in Figure <a href="#org629e523">11</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Kiff = <span class="org-type">-</span>1e3<span class="org-type">/</span>s;
|
||||
@ -1081,29 +1104,29 @@ The controller is defined below and the loop gain is shown in Figure <a href="#o
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org8791595" class="figure">
|
||||
<div id="org629e523" 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 11: </span>IFF Loop Gain</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Now the closed-loop system is identified again and compare with the open loop system in Figure <a href="#org9002d80">12</a>.
|
||||
Now the closed-loop system is identified again and compare with the open loop system in Figure <a href="#orgd74147f">12</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It is the expected behavior as shown in the Figure <a href="#orgf085b71">13</a> (from (<a href="#citeproc_bib_item_2">Souleille et al. 2018</a>)).
|
||||
It is the expected behavior as shown in the Figure <a href="#org63ec752">13</a> (from (<a href="#citeproc_bib_item_2">Souleille et al. 2018</a>)).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org9002d80" class="figure">
|
||||
<div id="orgd74147f" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_comp.png" alt="piezo_amplified_iff_comp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>OL and CL transfer functions</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgf085b71" class="figure">
|
||||
<div id="org63ec752" class="figure">
|
||||
<p><img src="figs/souleille18_results.png" alt="souleille18_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Results obtained in <a class='org-ref-reference' href="#souleille18_concep_activ_mount_space_applic">souleille18_concep_activ_mount_space_applic</a></p>
|
||||
@ -1113,14 +1136,14 @@ It is the expected behavior as shown in the Figure <a href="#orgf085b71">13</a>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-orge12e432" class="outline-2">
|
||||
<h2 id="orge12e432"><span class="section-number-2">2</span> First Flexible Joint Geometry</h2>
|
||||
<div id="outline-container-org538ff3f" class="outline-2">
|
||||
<h2 id="org538ff3f"><span class="section-number-2">2</span> First Flexible Joint Geometry</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="orga0ece29"></a>
|
||||
<a id="org5898d43"></a>
|
||||
</p>
|
||||
<p>
|
||||
The studied flexor is shown in Figure <a href="#orgcd75ab8">14</a>.
|
||||
The studied flexor is shown in Figure <a href="#org5ab2fb3">14</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -1133,14 +1156,14 @@ A simplified model of the flexor is then developped.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgcd75ab8" class="figure">
|
||||
<div id="org5ab2fb3" class="figure">
|
||||
<p><img src="figs/flexor_id16_screenshot.png" alt="flexor_id16_screenshot.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Flexor studied</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org91559c3" class="outline-3">
|
||||
<h3 id="org91559c3"><span class="section-number-3">2.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-org01a224b" class="outline-3">
|
||||
<h3 id="org01a224b"><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.
|
||||
@ -1552,8 +1575,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0c0ae39" class="outline-3">
|
||||
<h3 id="org0c0ae39"><span class="section-number-3">2.2</span> Identification of the parameters using Simscape and looking at the Stiffness Matrix</h3>
|
||||
<div id="outline-container-org4b0797c" class="outline-3">
|
||||
<h3 id="org4b0797c"><span class="section-number-3">2.2</span> Identification of the parameters using Simscape and looking at the Stiffness Matrix</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
@ -1610,15 +1633,15 @@ And we find the same parameters as the one estimated from the Stiffness matrix.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb1eeb49" class="outline-3">
|
||||
<h3 id="orgb1eeb49"><span class="section-number-3">2.3</span> Simpler Model</h3>
|
||||
<div id="outline-container-org764d26e" class="outline-3">
|
||||
<h3 id="org764d26e"><span class="section-number-3">2.3</span> Simpler Model</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#orgc8a4dd1">15</a>.
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#orge7ffb5f">15</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgc8a4dd1" class="figure">
|
||||
<div id="orge7ffb5f" class="figure">
|
||||
<p><img src="figs/flexible_joint_simscape.png" alt="flexible_joint_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Bushing Joint used to model the flexible joint</p>
|
||||
@ -1643,7 +1666,7 @@ The two obtained dynamics are compared in Figure
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org168dbda" class="figure">
|
||||
<div id="orgb81ed17" class="figure">
|
||||
<p><img src="figs/flexor_ID16_compare_bushing_joint.png" alt="flexor_ID16_compare_bushing_joint.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Comparison of the Joint compliance between the FEM model and the simpler model</p>
|
||||
@ -1652,29 +1675,29 @@ The two obtained dynamics are compared in Figure
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6fa0f81" class="outline-2">
|
||||
<h2 id="org6fa0f81"><span class="section-number-2">3</span> Optimized Flexible Joint</h2>
|
||||
<div id="outline-container-org6f963d0" class="outline-2">
|
||||
<h2 id="org6f963d0"><span class="section-number-2">3</span> Optimized Flexible Joint</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org513c349"></a>
|
||||
<a id="orga75acbf"></a>
|
||||
</p>
|
||||
<p>
|
||||
The joint geometry has been optimized using Ansys to have lower bending stiffness while keeping a large axial stiffness.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The obtained geometry is shown in Figure <a href="#orge1d8231">17</a>.
|
||||
The obtained geometry is shown in Figure <a href="#orgbba929b">17</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orge1d8231" class="figure">
|
||||
<div id="orgbba929b" class="figure">
|
||||
<p><img src="figs/flexor_025_MDoF.jpg" alt="flexor_025_MDoF.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Flexor studied</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgadfaeb7" class="outline-3">
|
||||
<h3 id="orgadfaeb7"><span class="section-number-3">3.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-orgc5406d6" class="outline-3">
|
||||
<h3 id="orgc5406d6"><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.
|
||||
@ -2088,8 +2111,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1a74e71" class="outline-3">
|
||||
<h3 id="org1a74e71"><span class="section-number-3">3.2</span> Identification of the parameters using Simscape</h3>
|
||||
<div id="outline-container-org4c2abff" class="outline-3">
|
||||
<h3 id="org4c2abff"><span class="section-number-3">3.2</span> Identification of the parameters using Simscape</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
@ -2146,15 +2169,15 @@ And we find the same parameters as the one estimated from the Stiffness matrix.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3ba1fee" class="outline-3">
|
||||
<h3 id="org3ba1fee"><span class="section-number-3">3.3</span> Simpler Model</h3>
|
||||
<div id="outline-container-org40e908d" class="outline-3">
|
||||
<h3 id="org40e908d"><span class="section-number-3">3.3</span> Simpler Model</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#orgc8a4dd1">15</a>.
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#orge7ffb5f">15</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org1f2487e" class="figure">
|
||||
<div id="org2043324" class="figure">
|
||||
<p><img src="figs/flexible_joint_simscape.png" alt="flexible_joint_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Bushing Joint used to model the flexible joint</p>
|
||||
@ -2179,7 +2202,7 @@ The two obtained dynamics are compared in Figure
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org520525f" class="figure">
|
||||
<div id="org8f50015" class="figure">
|
||||
<p><img src="figs/flexor_ID16_compare_bushing_joint.png" alt="flexor_ID16_compare_bushing_joint.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Comparison of the Joint compliance between the FEM model and the simpler model</p>
|
||||
@ -2187,8 +2210,8 @@ The two obtained dynamics are compared in Figure
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgec51432" class="outline-3">
|
||||
<h3 id="orgec51432"><span class="section-number-3">3.4</span> Comparison with a stiffer Flexible Joint</h3>
|
||||
<div id="outline-container-org14a611d" class="outline-3">
|
||||
<h3 id="org14a611d"><span class="section-number-3">3.4</span> Comparison with a stiffer Flexible Joint</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
The stiffness matrix with the flexible joint with a “hinge” size of 0.50mm is loaded.
|
||||
@ -2255,38 +2278,38 @@ Its parameters are compared with the Flexible Joint with a size of 0.25mm in the
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org91975b5" class="outline-2">
|
||||
<h2 id="org91975b5"><span class="section-number-2">4</span> Complete Strut with Encoder</h2>
|
||||
<div id="outline-container-orgeb13ea0" class="outline-2">
|
||||
<h2 id="orgeb13ea0"><span class="section-number-2">4</span> Complete Strut with Encoder</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orgcff61d6"></a>
|
||||
<a id="orgbd31e29"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgd829824" class="outline-3">
|
||||
<h3 id="orgd829824"><span class="section-number-3">4.1</span> Introduction</h3>
|
||||
<div id="outline-container-org7c76927" class="outline-3">
|
||||
<h3 id="org7c76927"><span class="section-number-3">4.1</span> Introduction</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
Now, the full nano-hexapod strut is modelled using Ansys.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The 3D as well as the interface nodes are shown in Figure <a href="#org9f2a66d">20</a>.
|
||||
The 3D as well as the interface nodes are shown in Figure <a href="#org3c30082">20</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org9f2a66d" class="figure">
|
||||
<p><img src="figs/strut_encoder_nodes.jpg" alt="strut_encoder_nodes.jpg" />
|
||||
<div id="org3c30082" class="figure">
|
||||
<p><img src="figs/strut_fem_nodes.jpg" alt="strut_fem_nodes.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Interface points</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
A side view is shown in Figure <a href="#org3437ed1">21</a>.
|
||||
A side view is shown in Figure <a href="#org3938962">21</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org3437ed1" class="figure">
|
||||
<p><img src="figs/strut_encoder_nodes_side.jpg" alt="strut_encoder_nodes_side.jpg" />
|
||||
<div id="org3938962" class="figure">
|
||||
<p><img src="figs/strut_fem_nodes_side.jpg" alt="strut_fem_nodes_side.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Interface points - Side view</p>
|
||||
</div>
|
||||
@ -2297,8 +2320,8 @@ The flexible joints used have a 0.25mm width size.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd7f754c" class="outline-3">
|
||||
<h3 id="orgd7f754c"><span class="section-number-3">4.2</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-org20586d2" class="outline-3">
|
||||
<h3 id="org20586d2"><span class="section-number-3">4.2</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -2760,18 +2783,18 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5019141" class="outline-3">
|
||||
<h3 id="org5019141"><span class="section-number-3">4.3</span> Piezoelectric parameters</h3>
|
||||
<div id="outline-container-org04b2ce1" class="outline-3">
|
||||
<h3 id="org04b2ce1"><span class="section-number-3">4.3</span> Piezoelectric parameters</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<p>
|
||||
Parameters for the APA300ML:
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">d33 = 3e<span class="org-type">-</span>10; <span class="org-comment">% Strain constant [m/V]</span>
|
||||
<pre class="src src-matlab">d33 = 300e<span class="org-type">-</span>12; <span class="org-comment">% Strain constant [m/V]</span>
|
||||
n = 80; <span class="org-comment">% Number of layers per stack</span>
|
||||
eT = 1.6e<span class="org-type">-</span>8; <span class="org-comment">% Permittivity under constant stress [F/m]</span>
|
||||
sD = 2e<span class="org-type">-</span>11; <span class="org-comment">% Elastic compliance under constant electric displacement [m2/N]</span>
|
||||
sD = 1e<span class="org-type">-</span>11; <span class="org-comment">% Compliance under constant electric displacement [m2/N]</span>
|
||||
ka = 235e6; <span class="org-comment">% Stack stiffness [N/m]</span>
|
||||
C = 5e<span class="org-type">-</span>6; <span class="org-comment">% Stack capactiance [F]</span>
|
||||
</pre>
|
||||
@ -2785,8 +2808,8 @@ ns = 1; <span class="org-comment">% Number of stacks used as force sensor</span>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org72bb8f1" class="outline-3">
|
||||
<h3 id="org72bb8f1"><span class="section-number-3">4.4</span> Identification of the Dynamics</h3>
|
||||
<div id="outline-container-org0e8a535" class="outline-3">
|
||||
<h3 id="org0e8a535"><span class="section-number-3">4.4</span> Identification of the Dynamics</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
<p>
|
||||
The dynamics is identified from the applied force to the measured relative displacement.
|
||||
@ -2798,7 +2821,7 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgda90142" class="figure">
|
||||
<div id="org63dfee9" class="figure">
|
||||
<p><img src="figs/dynamics_encoder_full_strut.png" alt="dynamics_encoder_full_strut.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Dynamics from the force actuator to the measured motion by the encoder</p>
|
||||
@ -2819,7 +2842,7 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-11-13 ven. 08:56</p>
|
||||
<p class="date">Created: 2021-01-04 lun. 13:57</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
39
index.org
39
index.org
@ -168,7 +168,7 @@ Using =K=, =M= and =int_xyz=, we can now use the =Reduced Order Flexible Solid=
|
||||
** Piezoelectric parameters
|
||||
In order to make the conversion from applied voltage to generated force or from the strain to the generated voltage, we need to defined some parameters corresponding to the piezoelectric material:
|
||||
#+begin_src matlab
|
||||
d33 = 300e-12; % Strain constant [m/V]
|
||||
d33 = 600e-12; % Strain constant [m/V]
|
||||
n = 80; % Number of layers per stack
|
||||
eT = 1.6e-8; % Permittivity under constant stress [F/m]
|
||||
sD = 1e-11; % Compliance under constant electric displacement [m2/N]
|
||||
@ -176,6 +176,16 @@ In order to make the conversion from applied voltage to generated force or from
|
||||
C = 5e-6; % Stack capactiance [F]
|
||||
#+end_src
|
||||
|
||||
PZT-4
|
||||
#+begin_src matlab
|
||||
d33 = 300e-12; % Strain constant [m/V]
|
||||
n = 80; % Number of layers per stack
|
||||
eT = 5.3e-9; % Permittivity under constant stress [F/m]
|
||||
sD = 1e-11; % Compliance under constant electric displacement [m2/N]
|
||||
ka = 235e6; % Stack stiffness [N/m]
|
||||
C = 5e-6; % Stack capactiance [F]
|
||||
#+end_src
|
||||
|
||||
The ratio of the developed force to applied voltage is:
|
||||
#+name: eq:piezo_voltage_to_force
|
||||
\begin{equation}
|
||||
@ -231,7 +241,7 @@ One mass is fixed at one end of the piezo-electric stack actuator (remove point
|
||||
** Identification of the APA Characteristics
|
||||
*** Stiffness
|
||||
#+begin_src matlab :exports none
|
||||
m = 0.001;
|
||||
m = 0.0001;
|
||||
#+end_src
|
||||
|
||||
The transfer function from vertical external force to the relative vertical displacement is identified.
|
||||
@ -334,6 +344,23 @@ with:
|
||||
|
||||
This is exactly the specified stroke in the data-sheet.
|
||||
|
||||
*** TODO Stroke BIS
|
||||
- [ ] Identified the stroke form the transfer function from V to z
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%% Name of the Simulink File
|
||||
mdl = 'APA300ML';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/V'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/d'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
1e6*170*abs(dcgain(G))
|
||||
#+end_src
|
||||
|
||||
** Identification of the Dynamics from actuator to replace displacement
|
||||
We first set the mass to be approximately zero.
|
||||
#+begin_src matlab :exports none
|
||||
@ -1495,13 +1522,13 @@ The 3D as well as the interface nodes are shown in Figure [[fig:strut_encoder_po
|
||||
|
||||
#+name: fig:strut_encoder_points3
|
||||
#+caption: Interface points
|
||||
[[file:figs/strut_encoder_nodes.jpg]]
|
||||
[[file:figs/strut_fem_nodes.jpg]]
|
||||
|
||||
A side view is shown in Figure [[fig:strut_encoder_nodes_side]].
|
||||
|
||||
#+name: fig:strut_encoder_nodes_side
|
||||
#+caption: Interface points - Side view
|
||||
[[file:figs/strut_encoder_nodes_side.jpg]]
|
||||
[[file:figs/strut_fem_nodes_side.jpg]]
|
||||
|
||||
The flexible joints used have a 0.25mm width size.
|
||||
|
||||
@ -1608,10 +1635,10 @@ Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= sims
|
||||
Parameters for the APA300ML:
|
||||
|
||||
#+begin_src matlab
|
||||
d33 = 3e-10; % Strain constant [m/V]
|
||||
d33 = 300e-12; % Strain constant [m/V]
|
||||
n = 80; % Number of layers per stack
|
||||
eT = 1.6e-8; % Permittivity under constant stress [F/m]
|
||||
sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N]
|
||||
sD = 1e-11; % Compliance under constant electric displacement [m2/N]
|
||||
ka = 235e6; % Stack stiffness [N/m]
|
||||
C = 5e-6; % Stack capactiance [F]
|
||||
#+end_src
|
||||
|
||||
Loading…
Reference in New Issue
Block a user