Swap two figures
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@ -3,7 +3,7 @@
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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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<!-- 2020-11-10 mar. 12:55 -->
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<!-- 2020-11-10 mar. 13:00 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Piezoelectric Force Sensor - Test Bench</title>
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<meta name="generator" content="Org mode" />
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@ -34,17 +34,17 @@
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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="#orga1465ad">1. Change of Stiffness due to Sensors stack being open/closed circuit</a>
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<li><a href="#orgfa4ffe0">1. Change of Stiffness due to Sensors stack being open/closed circuit</a>
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<ul>
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<li><a href="#orgd924c73">1.1. Load Data</a></li>
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<li><a href="#org59cc20a">1.2. Transfer Functions</a></li>
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<li><a href="#org664356d">1.1. Load Data</a></li>
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<li><a href="#orgb329298">1.2. Transfer Functions</a></li>
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</ul>
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</li>
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<li><a href="#org76a1832">2. Generated Number of Charge / Voltage</a>
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<li><a href="#orgcc12929">2. Generated Number of Charge / Voltage</a>
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<ul>
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<li><a href="#org1fa991d">2.1. Steps</a></li>
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<li><a href="#org5e9eb44">2.2. Add Parallel Resistor</a></li>
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<li><a href="#org15676e1">2.3. Sinus</a></li>
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<li><a href="#org7a46587">2.1. Steps</a></li>
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<li><a href="#org9938615">2.2. Add Parallel Resistor</a></li>
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<li><a href="#org3e71d2e">2.3. Sinus</a></li>
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</ul>
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</li>
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</ul>
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@ -56,20 +56,20 @@ In this document is studied how a piezoelectric stack can be used to measured th
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org887b61a">1</a>: the effect of the input impedance of the electronics connected to the force sensor stack on the stiffness of the stack is studied</li>
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<li>Section <a href="#org2b5f630">2</a>:</li>
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<li>Section <a href="#org574ce5b">1</a>: the effect of the input impedance of the electronics connected to the force sensor stack on the stiffness of the stack is studied</li>
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<li>Section <a href="#org3d96d6c">2</a>:</li>
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</ul>
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<div id="outline-container-orga1465ad" class="outline-2">
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<h2 id="orga1465ad"><span class="section-number-2">1</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2>
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<div id="outline-container-orgfa4ffe0" class="outline-2">
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<h2 id="orgfa4ffe0"><span class="section-number-2">1</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org887b61a"></a>
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<a id="org574ce5b"></a>
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</p>
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</div>
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<div id="outline-container-orgd924c73" class="outline-3">
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<h3 id="orgd924c73"><span class="section-number-3">1.1</span> Load Data</h3>
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<div id="outline-container-org664356d" class="outline-3">
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<h3 id="org664356d"><span class="section-number-3">1.1</span> Load Data</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">oc = load(<span class="org-string">'identification_open_circuit.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>);
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@ -79,8 +79,8 @@ sc = load(<span class="org-string">'identification_short_circuit.mat'</span>, <s
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</div>
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</div>
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<div id="outline-container-org59cc20a" class="outline-3">
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<h3 id="org59cc20a"><span class="section-number-3">1.2</span> Transfer Functions</h3>
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<div id="outline-container-orgb329298" class="outline-3">
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<h3 id="orgb329298"><span class="section-number-3">1.2</span> Transfer Functions</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">Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% Sampling Time [s]</span>
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@ -98,26 +98,26 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
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</div>
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<div id="org3c75143" class="figure">
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<div id="org07156da" class="figure">
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<p><img src="figs/stiffness_force_sensor_coherence.png" alt="stiffness_force_sensor_coherence.png" />
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</p>
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</div>
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<div id="org4424b1c" class="figure">
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<div id="org4e249d7" class="figure">
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<p><img src="figs/stiffness_force_sensor_bode.png" alt="stiffness_force_sensor_bode.png" />
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</p>
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</div>
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<div id="org216fcc3" class="figure">
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<div id="org503058b" class="figure">
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<p><img src="figs/stiffness_force_sensor_bode_zoom.png" alt="stiffness_force_sensor_bode_zoom.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Zoom on the change of resonance</p>
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</div>
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<div class="important" id="org9ea3712">
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<div class="important" id="org93bdd08">
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<p>
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The change of resonance frequency / stiffness is very small and is not important here.
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</p>
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@ -127,11 +127,11 @@ The change of resonance frequency / stiffness is very small and is not important
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</div>
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</div>
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<div id="outline-container-org76a1832" class="outline-2">
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<h2 id="org76a1832"><span class="section-number-2">2</span> Generated Number of Charge / Voltage</h2>
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<div id="outline-container-orgcc12929" class="outline-2">
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<h2 id="orgcc12929"><span class="section-number-2">2</span> Generated Number of Charge / Voltage</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org2b5f630"></a>
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<a id="org3d96d6c"></a>
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</p>
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<p>
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Two stacks are used as actuator (in parallel) and one stack is used as sensor.
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@ -142,8 +142,8 @@ The amplifier gain is 20V/V (Cedrat LA75B).
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</p>
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</div>
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<div id="outline-container-org1fa991d" class="outline-3">
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<h3 id="org1fa991d"><span class="section-number-3">2.1</span> Steps</h3>
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<div id="outline-container-org7a46587" class="outline-3">
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<h3 id="org7a46587"><span class="section-number-3">2.1</span> Steps</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'force_sensor_steps.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'v'</span>);
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@ -163,7 +163,7 @@ xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-stri
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</div>
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<div id="orgf889803" class="figure">
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<div id="orgda3ef57" class="figure">
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<p><img src="figs/force_sen_steps_time_domain.png" alt="force_sen_steps_time_domain.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Time domain signal during the 3 actuator voltage steps</p>
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@ -262,7 +262,7 @@ Rin = abs(mean(tau))<span class="org-type">/</span>Cp;
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The input impedance of the Speedgoat’s ADC should then be close to \(1.5\,M\Omega\) (specified at \(1\,M\Omega\)).
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</p>
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<div class="important" id="org572654b">
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<div class="important" id="org7c6e263">
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<p>
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How can we explain the voltage offset?
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</p>
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@ -270,12 +270,12 @@ How can we explain the voltage offset?
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</div>
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<p>
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As shown in Figure <a href="#org7c2c57f">5</a> (taken from (<a href="#citeproc_bib_item_1">Reza and Andrew 2006</a>)), an input voltage offset is due to the input bias current \(i_n\).
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As shown in Figure <a href="#org1036a3b">5</a> (taken from (<a href="#citeproc_bib_item_1">Reza and Andrew 2006</a>)), an input voltage offset is due to the input bias current \(i_n\).
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</p>
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<div id="org7c2c57f" class="figure">
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<p><img src="figs/force_sensor_model_electronics.png" alt="force_sensor_model_electronics.png" />
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<div id="org1036a3b" class="figure">
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<p><img src="figs/force_sensor_model_electronics_without_R.png" alt="force_sensor_model_electronics_without_R.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right)</p>
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</div>
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@ -338,18 +338,18 @@ Which is much more acceptable.
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</div>
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</div>
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<div id="outline-container-org5e9eb44" class="outline-3">
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<h3 id="org5e9eb44"><span class="section-number-3">2.2</span> Add Parallel Resistor</h3>
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<div id="outline-container-org9938615" class="outline-3">
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<h3 id="org9938615"><span class="section-number-3">2.2</span> Add Parallel Resistor</h3>
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<div class="outline-text-3" id="text-2-2">
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<p>
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A resistor \(R_p \approx 100\,k\Omega\) is added in parallel with the force sensor as shown in Figure <a href="#org1fac5a7">6</a>.
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A resistor \(R_p \approx 100\,k\Omega\) is added in parallel with the force sensor as shown in Figure <a href="#orgbf8a90f">6</a>.
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</p>
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<div id="org1fac5a7" class="figure">
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<p><img src="figs/force_sensor_model_electronics_without_R.png" alt="force_sensor_model_electronics_without_R.png" />
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<div id="orgbf8a90f" class="figure">
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<p><img src="figs/force_sensor_model_electronics.png" alt="force_sensor_model_electronics.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with added resistor \(R_p\)</p>
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<p><span class="figure-number">Figure 6: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor \(R_p\)</p>
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</div>
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<div class="org-src-container">
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@ -370,7 +370,7 @@ xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-stri
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</div>
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<div id="org29964b5" class="figure">
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<div id="orgf9378d8" class="figure">
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<p><img src="figs/force_sen_steps_time_domain_par_R.png" alt="force_sen_steps_time_domain_par_R.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Time domain signal during the actuator voltage steps</p>
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@ -514,8 +514,8 @@ This validates the model of the ADC and the effectiveness of the added resistor.
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</div>
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</div>
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<div id="outline-container-org15676e1" class="outline-3">
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<h3 id="org15676e1"><span class="section-number-3">2.3</span> Sinus</h3>
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<div id="outline-container-org3e71d2e" class="outline-3">
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<h3 id="org3e71d2e"><span class="section-number-3">2.3</span> Sinus</h3>
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<div class="outline-text-3" id="text-2-3">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'force_sensor_sin.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'v'</span>);
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@ -528,11 +528,11 @@ t = t(t<span class="org-type">></span>25);
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</div>
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<p>
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The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#org1fbf89d">8</a>).
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The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#org2ae5f53">8</a>).
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</p>
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<div id="org1fbf89d" class="figure">
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<div id="org2ae5f53" class="figure">
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<p><img src="figs/force_sensor_sin_u.png" alt="force_sensor_sin_u.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>Driving Voltage</p>
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@ -552,11 +552,11 @@ The full stroke as measured by the encoder is:
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<p>
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Its signal is shown in Figure <a href="#org1d74efa">9</a>.
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Its signal is shown in Figure <a href="#org3458f57">9</a>.
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</p>
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<div id="org1d74efa" class="figure">
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<div id="org3458f57" class="figure">
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<p><img src="figs/force_sensor_sin_encoder.png" alt="force_sensor_sin_encoder.png" />
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</p>
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<p><span class="figure-number">Figure 9: </span>Encoder measurement</p>
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@ -567,7 +567,7 @@ The generated voltage by the stack is shown in Figure
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</p>
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<div id="org077a6d7" class="figure">
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<div id="orga69980e" class="figure">
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<p><img src="figs/force_sensor_sin_stack.png" alt="force_sensor_sin_stack.png" />
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</p>
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<p><span class="figure-number">Figure 10: </span>Voltage measured on the stack used as a sensor</p>
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@ -582,10 +582,10 @@ The capacitance of the stack is
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</div>
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<p>
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The corresponding generated charge is then shown in Figure <a href="#org4baf062">11</a>.
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The corresponding generated charge is then shown in Figure <a href="#orgeafdaf5">11</a>.
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</p>
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<div id="org4baf062" class="figure">
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<div id="orgeafdaf5" class="figure">
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<p><img src="figs/force_sensor_sin_charge.png" alt="force_sensor_sin_charge.png" />
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</p>
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<p><span class="figure-number">Figure 11: </span>Generated Charge</p>
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@ -593,7 +593,7 @@ The corresponding generated charge is then shown in Figure <a href="#org4baf062"
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<p>
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The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#org8b9df34">12</a>.
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The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#org83e4a49">12</a>.
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</p>
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<div class="org-src-container">
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@ -602,7 +602,7 @@ The relation between the generated voltage and the measured displacement is almo
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</div>
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<div id="org8b9df34" class="figure">
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<div id="org83e4a49" class="figure">
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<p><img src="figs/force_sensor_linear_relation.png" alt="force_sensor_linear_relation.png" />
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</p>
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<p><span class="figure-number">Figure 12: </span>Almost linear relation between the relative displacement and the generated voltage</p>
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@ -631,7 +631,7 @@ With a 16bits ADC, the resolution will then be equals to (in [nm]):
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-11-10 mar. 12:55</p>
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<p class="date">Created: 2020-11-10 mar. 13:00</p>
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</div>
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</body>
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</html>
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16
index.org
16
index.org
@ -165,8 +165,6 @@ In this document is studied how a piezoelectric stack can be used to measured th
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<<sec:charge_voltage_estimation>>
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** Introduction :ignore:
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Two stacks are used as actuator (in parallel) and one stack is used as sensor.
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The amplifier gain is 20V/V (Cedrat LA75B).
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@ -276,11 +274,11 @@ The input impedance of the Speedgoat's ADC should then be close to $1.5\,M\Omega
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How can we explain the voltage offset?
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#+end_important
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As shown in Figure [[fig:force_sensor_model_electronics]] (taken from cite:reza06_piezoel_trans_vibrat_contr_dampin), an input voltage offset is due to the input bias current $i_n$.
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As shown in Figure [[fig:force_sensor_model_electronics_without_R]] (taken from cite:reza06_piezoel_trans_vibrat_contr_dampin), an input voltage offset is due to the input bias current $i_n$.
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#+name: fig:force_sensor_model_electronics
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#+name: fig:force_sensor_model_electronics_without_R
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#+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right)
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[[file:figs/force_sensor_model_electronics.png]]
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[[file:figs/force_sensor_model_electronics_without_R.png]]
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The estimated input bias current is then:
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#+begin_src matlab
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@ -330,11 +328,11 @@ With this parallel resistance value, the voltage offset would be:
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Which is much more acceptable.
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** Add Parallel Resistor
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A resistor $R_p \approx 100\,k\Omega$ is added in parallel with the force sensor as shown in Figure [[fig:force_sensor_model_electronics_without_R]].
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A resistor $R_p \approx 100\,k\Omega$ is added in parallel with the force sensor as shown in Figure [[fig:force_sensor_model_electronics]].
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#+name: fig:force_sensor_model_electronics_without_R
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#+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with added resistor $R_p$
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[[file:figs/force_sensor_model_electronics_without_R.png]]
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#+name: fig:force_sensor_model_electronics
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#+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor $R_p$
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[[file:figs/force_sensor_model_electronics.png]]
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#+begin_src matlab
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load('force_sensor_steps_R_82k7.mat', 't', 'encoder', 'u', 'v');
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