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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-11-10 mar. 13:41 --> <!-- 2020-11-10 mar. 13:46 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Piezoelectric Force Sensor - Test Bench</title> <title>Piezoelectric Force Sensor - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -34,29 +34,29 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orga887666">1. Change of Stiffness due to Sensors stack being open/closed circuit</a> <li><a href="#orgc978fd7">1. Change of Stiffness due to Sensors stack being open/closed circuit</a>
<ul> <ul>
<li><a href="#org632bb0b">1.1. Load Data</a></li> <li><a href="#org806a9c3">1.1. Load Data</a></li>
<li><a href="#org06862e1">1.2. Transfer Functions</a></li> <li><a href="#orgd3a8e11">1.2. Transfer Functions</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd3fb351">2. Effect of a Resistor in Parallel with the Stack Sensor</a> <li><a href="#org12cffb3">2. Effect of a Resistor in Parallel with the Stack Sensor</a>
<ul> <ul>
<li><a href="#orgf3e29cf">2.1. Excitation steps and measured generated voltage</a></li> <li><a href="#org3d3c9c5">2.1. Excitation steps and measured generated voltage</a></li>
<li><a href="#org93b0595">2.2. Estimation of the voltage offset and discharge time constant</a></li> <li><a href="#orge91c0f3">2.2. Estimation of the voltage offset and discharge time constant</a></li>
<li><a href="#orgc749ef4">2.3. Estimation of the ADC input impedance</a></li> <li><a href="#org45317a1">2.3. Estimation of the ADC input impedance</a></li>
<li><a href="#org66bf743">2.4. Explanation of the Voltage offset</a></li> <li><a href="#orgbdebc17">2.4. Explanation of the Voltage offset</a></li>
<li><a href="#org3c86684">2.5. Effect of an additional Parallel Resistor</a></li> <li><a href="#orgaf9774b">2.5. Effect of an additional Parallel Resistor</a></li>
<li><a href="#org4ae0b53">2.6. Obtained voltage offset and time constant with the added resistor</a></li> <li><a href="#org0931a42">2.6. Obtained voltage offset and time constant with the added resistor</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org81c5db6">3. Generated Number of Charge / Voltage</a> <li><a href="#orgf8de1e8">3. Generated Number of Charge / Voltage</a>
<ul> <ul>
<li><a href="#org55eecf7">3.1. Data Loading</a></li> <li><a href="#org1378faa">3.1. Data Loading</a></li>
<li><a href="#org46592d5">3.2. Excitation signal and corresponding displacement</a></li> <li><a href="#org18bda16">3.2. Excitation signal and corresponding displacement</a></li>
<li><a href="#org6e6b1f7">3.3. Generated Voltage</a></li> <li><a href="#org2647e0c">3.3. Generated Voltage</a></li>
<li><a href="#org4ed9610">3.4. Generated Charge</a></li> <li><a href="#org74ab9f0">3.4. Generated Charge</a></li>
<li><a href="#org69bd84e">3.5. Generated Voltage/Charge as a function of the displacement</a></li> <li><a href="#org4241ea4">3.5. Generated Voltage/Charge as a function of the displacement</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -71,19 +71,19 @@ In this document is studied how a piezoelectric stack can be used to measured th
It is divided in the following sections: It is divided in the following sections:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Section <a href="#orgcbe0c6f">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> <li>Section <a href="#orgede3aab">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>
<li>Section <a href="#org72d0a53">2</a>: the effect of a resistor in parallel with the sensor stack is studied</li> <li>Section <a href="#orgb1a09bb">2</a>: the effect of a resistor in parallel with the sensor stack is studied</li>
<li>Section <a href="#org22b743e">3</a>: the voltage / number of charge generated by the sensor as a function of the displacement is measured</li> <li>Section <a href="#org49d4bd9">3</a>: the voltage / number of charge generated by the sensor as a function of the displacement is measured</li>
</ul> </ul>
<div id="outline-container-orga887666" class="outline-2"> <div id="outline-container-orgc978fd7" class="outline-2">
<h2 id="orga887666"><span class="section-number-2">1</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2> <h2 id="orgc978fd7"><span class="section-number-2">1</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="orgcbe0c6f"></a> <a id="orgede3aab"></a>
</p> </p>
<p> <p>
The experimental Setup is schematically represented in Figure <a href="#org27d7f75">1</a>. The experimental Setup is schematically represented in Figure <a href="#org874417a">1</a>.
</p> </p>
<p> <p>
@ -91,7 +91,7 @@ The dynamics from the voltage \(u\) used to drive the actuator stacks to the enc
</p> </p>
<div id="org27d7f75" class="figure"> <div id="org874417a" class="figure">
<p><img src="figs/exp_setup_schematic.png" alt="exp_setup_schematic.png" /> <p><img src="figs/exp_setup_schematic.png" alt="exp_setup_schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Schematic of the Experiment</p> <p><span class="figure-number">Figure 1: </span>Schematic of the Experiment</p>
@ -106,7 +106,7 @@ When the switch is closed, this correspond of having a measurement electronics w
We wish here to see how the system dynamics is changing in the two extreme cases. We wish here to see how the system dynamics is changing in the two extreme cases.
</p> </p>
<div class="note" id="org4171ed0"> <div class="note" id="orgdfeaa4d">
<p> <p>
The equipment used in the test bench are: The equipment used in the test bench are:
</p> </p>
@ -120,8 +120,8 @@ The equipment used in the test bench are:
</div> </div>
</div> </div>
<div id="outline-container-org632bb0b" class="outline-3"> <div id="outline-container-org806a9c3" class="outline-3">
<h3 id="org632bb0b"><span class="section-number-3">1.1</span> Load Data</h3> <h3 id="org806a9c3"><span class="section-number-3">1.1</span> Load Data</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<div class="org-src-container"> <div class="org-src-container">
<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>); <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>);
@ -131,8 +131,8 @@ sc = load(<span class="org-string">'identification_short_circuit.mat'</span>, <s
</div> </div>
</div> </div>
<div id="outline-container-org06862e1" class="outline-3"> <div id="outline-container-orgd3a8e11" class="outline-3">
<h3 id="org06862e1"><span class="section-number-3">1.2</span> Transfer Functions</h3> <h3 id="orgd3a8e11"><span class="section-number-3">1.2</span> Transfer Functions</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% Sampling Time [s]</span> <pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% Sampling Time [s]</span>
@ -150,26 +150,25 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div> </div>
<div id="orgaafdea3" class="figure"> <div id="orga9fdab5" class="figure">
<p><img src="figs/stiffness_force_sensor_coherence.png" alt="stiffness_force_sensor_coherence.png" /> <p><img src="figs/stiffness_force_sensor_coherence.png" alt="stiffness_force_sensor_coherence.png" />
</p> </p>
</div> </div>
<div id="org1ce5c9d" class="figure">
<div id="orgc2be608" class="figure">
<p><img src="figs/stiffness_force_sensor_bode.png" alt="stiffness_force_sensor_bode.png" /> <p><img src="figs/stiffness_force_sensor_bode.png" alt="stiffness_force_sensor_bode.png" />
</p> </p>
</div> </div>
<div id="org59bf971" class="figure"> <div id="org2d932e9" class="figure">
<p><img src="figs/stiffness_force_sensor_bode_zoom.png" alt="stiffness_force_sensor_bode_zoom.png" /> <p><img src="figs/stiffness_force_sensor_bode_zoom.png" alt="stiffness_force_sensor_bode_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Zoom on the change of resonance</p> <p><span class="figure-number">Figure 4: </span>Zoom on the change of resonance</p>
</div> </div>
<div class="important" id="org2d5ecc1"> <div class="important" id="org284d89a">
<p> <p>
The change of resonance frequency / stiffness is very small and is not important here. The change of resonance frequency / stiffness is very small and is not important here.
</p> </p>
@ -179,25 +178,25 @@ The change of resonance frequency / stiffness is very small and is not important
</div> </div>
</div> </div>
<div id="outline-container-orgd3fb351" class="outline-2"> <div id="outline-container-org12cffb3" class="outline-2">
<h2 id="orgd3fb351"><span class="section-number-2">2</span> Effect of a Resistor in Parallel with the Stack Sensor</h2> <h2 id="org12cffb3"><span class="section-number-2">2</span> Effect of a Resistor in Parallel with the Stack Sensor</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org72d0a53"></a> <a id="orgb1a09bb"></a>
</p> </p>
<p> <p>
The setup is shown in Figure <a href="#org21d0104">5</a> where two stacks are used as actuator (in parallel) and one stack is used as sensor. The setup is shown in Figure <a href="#orgfcaafb7">5</a> where two stacks are used as actuator (in parallel) and one stack is used as sensor.
The voltage amplifier used has a gain of 20 [V/V] (Cedrat LA75B). The voltage amplifier used has a gain of 20 [V/V] (Cedrat LA75B).
</p> </p>
<div id="org21d0104" class="figure"> <div id="orgfcaafb7" class="figure">
<p><img src="figs/force_sensor_setup.png" alt="force_sensor_setup.png" /> <p><img src="figs/force_sensor_setup.png" alt="force_sensor_setup.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Schematic of the setup</p> <p><span class="figure-number">Figure 5: </span>Schematic of the setup</p>
</div> </div>
<div class="note" id="orgdd0ed7a"> <div class="note" id="org3904317">
<p> <p>
The equipment used in the test bench are: The equipment used in the test bench are:
</p> </p>
@ -211,8 +210,8 @@ The equipment used in the test bench are:
</div> </div>
</div> </div>
<div id="outline-container-orgf3e29cf" class="outline-3"> <div id="outline-container-org3d3c9c5" class="outline-3">
<h3 id="orgf3e29cf"><span class="section-number-3">2.1</span> Excitation steps and measured generated voltage</h3> <h3 id="org3d3c9c5"><span class="section-number-3">2.1</span> Excitation steps and measured generated voltage</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
The measured data is loaded. The measured data is loaded.
@ -223,10 +222,10 @@ The measured data is loaded.
</div> </div>
<p> <p>
The excitation signal (steps) and measured voltage across the sensor stack are shown in Figure <a href="#org8a7c66b">6</a>. The excitation signal (steps) and measured voltage across the sensor stack are shown in Figure <a href="#orgbed6888">6</a>.
</p> </p>
<div id="org8a7c66b" class="figure"> <div id="orgbed6888" class="figure">
<p><img src="figs/force_sen_steps_time_domain.png" alt="force_sen_steps_time_domain.png" /> <p><img src="figs/force_sen_steps_time_domain.png" alt="force_sen_steps_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Time domain signal during the 3 actuator voltage steps</p> <p><span class="figure-number">Figure 6: </span>Time domain signal during the 3 actuator voltage steps</p>
@ -234,8 +233,8 @@ The excitation signal (steps) and measured voltage across the sensor stack are s
</div> </div>
</div> </div>
<div id="outline-container-org93b0595" class="outline-3"> <div id="outline-container-orge91c0f3" class="outline-3">
<h3 id="org93b0595"><span class="section-number-3">2.2</span> Estimation of the voltage offset and discharge time constant</h3> <h3 id="orge91c0f3"><span class="section-number-3">2.2</span> Estimation of the voltage offset and discharge time constant</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
The measured voltage shows an exponential decay which indicates that the charge across the capacitor formed by the stack is discharging into a resistor. The measured voltage shows an exponential decay which indicates that the charge across the capacitor formed by the stack is discharging into a resistor.
@ -324,8 +323,8 @@ The obtained values are shown below.
</div> </div>
</div> </div>
<div id="outline-container-orgc749ef4" class="outline-3"> <div id="outline-container-org45317a1" class="outline-3">
<h3 id="orgc749ef4"><span class="section-number-3">2.3</span> Estimation of the ADC input impedance</h3> <h3 id="org45317a1"><span class="section-number-3">2.3</span> Estimation of the ADC input impedance</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
With the capacitance being \(C = 4.4 \mu F\), the internal impedance of the Speedgoat ADC can be computed as follows: With the capacitance being \(C = 4.4 \mu F\), the internal impedance of the Speedgoat ADC can be computed as follows:
@ -347,15 +346,15 @@ The input impedance of the Speedgoat&rsquo;s ADC should then be close to \(1.5\,
</div> </div>
</div> </div>
<div id="outline-container-org66bf743" class="outline-3"> <div id="outline-container-orgbdebc17" class="outline-3">
<h3 id="org66bf743"><span class="section-number-3">2.4</span> Explanation of the Voltage offset</h3> <h3 id="orgbdebc17"><span class="section-number-3">2.4</span> Explanation of the Voltage offset</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
As shown in Figure <a href="#org8a7c66b">6</a>, the voltage across the Piezoelectric sensor stack shows a constant voltage offset. As shown in Figure <a href="#orgbed6888">6</a>, the voltage across the Piezoelectric sensor stack shows a constant voltage offset.
</p> </p>
<p> <p>
We can explain this offset by looking at the electrical model shown in Figure <a href="#orgc43b1a9">7</a> (taken from (<a href="#citeproc_bib_item_1">Reza and Andrew 2006</a>)). We can explain this offset by looking at the electrical model shown in Figure <a href="#orgb1098d2">7</a> (taken from (<a href="#citeproc_bib_item_1">Reza and Andrew 2006</a>)).
</p> </p>
<p> <p>
@ -364,7 +363,7 @@ Note that the impedance of the piezoelectric stack is much larger that that at D
</p> </p>
<div id="orgc43b1a9" class="figure"> <div id="orgb1098d2" class="figure">
<p><img src="figs/force_sensor_model_electronics_without_R.png" alt="force_sensor_model_electronics_without_R.png" /> <p><img src="figs/force_sensor_model_electronics_without_R.png" alt="force_sensor_model_electronics_without_R.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right)</p> <p><span class="figure-number">Figure 7: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right)</p>
@ -384,11 +383,11 @@ The estimated input bias current is then:
</div> </div>
</div> </div>
<div id="outline-container-org3c86684" class="outline-3"> <div id="outline-container-orgaf9774b" class="outline-3">
<h3 id="org3c86684"><span class="section-number-3">2.5</span> Effect of an additional Parallel Resistor</h3> <h3 id="orgaf9774b"><span class="section-number-3">2.5</span> Effect of an additional Parallel Resistor</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
Be looking at Figure <a href="#orgc43b1a9">7</a>, we can see that an additional resistor in parallel with \(R_{in}\) would have two effects: Be looking at Figure <a href="#orgb1098d2">7</a>, we can see that an additional resistor in parallel with \(R_{in}\) would have two effects:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>reduce the input voltage offset <li>reduce the input voltage offset
@ -431,11 +430,11 @@ Which is much more acceptable.
<p> <p>
A resistor \(R_p \approx 100\,k\Omega\) is then added in parallel with the force sensor as shown in Figure <a href="#org98410d2">8</a>. A resistor \(R_p \approx 100\,k\Omega\) is then added in parallel with the force sensor as shown in Figure <a href="#orga7065ec">8</a>.
</p> </p>
<div id="org98410d2" class="figure"> <div id="orga7065ec" class="figure">
<p><img src="figs/force_sensor_model_electronics.png" alt="force_sensor_model_electronics.png" /> <p><img src="figs/force_sensor_model_electronics.png" alt="force_sensor_model_electronics.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor \(R_p\)</p> <p><span class="figure-number">Figure 8: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor \(R_p\)</p>
@ -443,8 +442,8 @@ A resistor \(R_p \approx 100\,k\Omega\) is then added in parallel with the force
</div> </div>
</div> </div>
<div id="outline-container-org4ae0b53" class="outline-3"> <div id="outline-container-org0931a42" class="outline-3">
<h3 id="org4ae0b53"><span class="section-number-3">2.6</span> Obtained voltage offset and time constant with the added resistor</h3> <h3 id="org0931a42"><span class="section-number-3">2.6</span> Obtained voltage offset and time constant with the added resistor</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<p> <p>
After the resistor is added, the same steps response is performed. After the resistor is added, the same steps response is performed.
@ -456,11 +455,11 @@ After the resistor is added, the same steps response is performed.
</div> </div>
<p> <p>
The results are shown in Figure <a href="#org3c913c7">9</a>. The results are shown in Figure <a href="#org162f5d0">9</a>.
</p> </p>
<div id="org3c913c7" class="figure"> <div id="org162f5d0" class="figure">
<p><img src="figs/force_sen_steps_time_domain_par_R.png" alt="force_sen_steps_time_domain_par_R.png" /> <p><img src="figs/force_sen_steps_time_domain_par_R.png" alt="force_sen_steps_time_domain_par_R.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Time domain signal during the actuator voltage steps</p> <p><span class="figure-number">Figure 9: </span>Time domain signal during the actuator voltage steps</p>
@ -572,19 +571,19 @@ This validates the model of the ADC and the effectiveness of the added resistor.
</div> </div>
</div> </div>
<div id="outline-container-org81c5db6" class="outline-2"> <div id="outline-container-orgf8de1e8" class="outline-2">
<h2 id="org81c5db6"><span class="section-number-2">3</span> Generated Number of Charge / Voltage</h2> <h2 id="orgf8de1e8"><span class="section-number-2">3</span> Generated Number of Charge / Voltage</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org22b743e"></a> <a id="org49d4bd9"></a>
</p> </p>
<p> <p>
In this section, we wish to estimate the relation between the displacement performed by the stack actuator and the generated voltage/charge on the sensor stack. In this section, we wish to estimate the relation between the displacement performed by the stack actuator and the generated voltage/charge on the sensor stack.
</p> </p>
</div> </div>
<div id="outline-container-org55eecf7" class="outline-3"> <div id="outline-container-org1378faa" class="outline-3">
<h3 id="org55eecf7"><span class="section-number-3">3.1</span> Data Loading</h3> <h3 id="org1378faa"><span class="section-number-3">3.1</span> Data Loading</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
The measured data is loaded and the first 25 seconds of data corresponding to transient data are removed. The measured data is loaded and the first 25 seconds of data corresponding to transient data are removed.
@ -602,22 +601,22 @@ t = t(t<span class="org-type">&gt;</span>25);
</div> </div>
</div> </div>
<div id="outline-container-org46592d5" class="outline-3"> <div id="outline-container-org18bda16" class="outline-3">
<h3 id="org46592d5"><span class="section-number-3">3.2</span> Excitation signal and corresponding displacement</h3> <h3 id="org18bda16"><span class="section-number-3">3.2</span> Excitation signal and corresponding displacement</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#org4706469">10</a>). The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#org2ddf80f">10</a>).
</p> </p>
<div id="org4706469" class="figure"> <div id="org2ddf80f" class="figure">
<p><img src="figs/force_sensor_sin_u.png" alt="force_sensor_sin_u.png" /> <p><img src="figs/force_sensor_sin_u.png" alt="force_sensor_sin_u.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Driving Voltage</p> <p><span class="figure-number">Figure 10: </span>Driving Voltage</p>
</div> </div>
<p> <p>
The corresponding displacement as measured by the encoder is shown in Figure <a href="#org1d38208">11</a>. The corresponding displacement as measured by the encoder is shown in Figure <a href="#org7dd9b3b">11</a>.
</p> </p>
<p> <p>
@ -634,7 +633,7 @@ The full stroke is:
<div id="org1d38208" class="figure"> <div id="org7dd9b3b" class="figure">
<p><img src="figs/force_sensor_sin_encoder.png" alt="force_sensor_sin_encoder.png" /> <p><img src="figs/force_sensor_sin_encoder.png" alt="force_sensor_sin_encoder.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Encoder measurement</p> <p><span class="figure-number">Figure 11: </span>Encoder measurement</p>
@ -642,15 +641,15 @@ The full stroke is:
</div> </div>
</div> </div>
<div id="outline-container-org6e6b1f7" class="outline-3"> <div id="outline-container-org2647e0c" class="outline-3">
<h3 id="org6e6b1f7"><span class="section-number-3">3.3</span> Generated Voltage</h3> <h3 id="org2647e0c"><span class="section-number-3">3.3</span> Generated Voltage</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
The generated voltage by the stack is shown in Figure <a href="#org267434e">12</a>. The generated voltage by the stack is shown in Figure <a href="#orga623ff4">12</a>.
</p> </p>
<div id="org267434e" class="figure"> <div id="orga623ff4" class="figure">
<p><img src="figs/force_sensor_sin_stack.png" alt="force_sensor_sin_stack.png" /> <p><img src="figs/force_sensor_sin_stack.png" alt="force_sensor_sin_stack.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Voltage measured on the stack used as a sensor</p> <p><span class="figure-number">Figure 12: </span>Voltage measured on the stack used as a sensor</p>
@ -658,8 +657,8 @@ The generated voltage by the stack is shown in Figure <a href="#org267434e">12</
</div> </div>
</div> </div>
<div id="outline-container-org4ed9610" class="outline-3"> <div id="outline-container-org74ab9f0" class="outline-3">
<h3 id="org4ed9610"><span class="section-number-3">3.4</span> Generated Charge</h3> <h3 id="org74ab9f0"><span class="section-number-3">3.4</span> Generated Charge</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<p> <p>
The capacitance of the stack is The capacitance of the stack is
@ -681,11 +680,11 @@ where \(U_C\) is the voltage in Volts, \(Q\) the charge in Coulombs and \(C\) th
<p> <p>
The corresponding generated charge is then shown in Figure <a href="#org0331333">13</a>. The corresponding generated charge is then shown in Figure <a href="#orgcf66ed5">13</a>.
</p> </p>
<div id="org0331333" class="figure"> <div id="orgcf66ed5" class="figure">
<p><img src="figs/force_sensor_sin_charge.png" alt="force_sensor_sin_charge.png" /> <p><img src="figs/force_sensor_sin_charge.png" alt="force_sensor_sin_charge.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Generated Charge</p> <p><span class="figure-number">Figure 13: </span>Generated Charge</p>
@ -693,11 +692,11 @@ The corresponding generated charge is then shown in Figure <a href="#org0331333"
</div> </div>
</div> </div>
<div id="outline-container-org69bd84e" class="outline-3"> <div id="outline-container-org4241ea4" class="outline-3">
<h3 id="org69bd84e"><span class="section-number-3">3.5</span> Generated Voltage/Charge as a function of the displacement</h3> <h3 id="org4241ea4"><span class="section-number-3">3.5</span> Generated Voltage/Charge as a function of the displacement</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<p> <p>
The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#org6b7aee0">14</a>. The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#org2f61fcf">14</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -706,7 +705,7 @@ The relation between the generated voltage and the measured displacement is almo
</div> </div>
<div id="org6b7aee0" class="figure"> <div id="org2f61fcf" class="figure">
<p><img src="figs/force_sensor_linear_relation.png" alt="force_sensor_linear_relation.png" /> <p><img src="figs/force_sensor_linear_relation.png" alt="force_sensor_linear_relation.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Almost linear relation between the relative displacement and the generated voltage</p> <p><span class="figure-number">Figure 14: </span>Almost linear relation between the relative displacement and the generated voltage</p>
@ -735,7 +734,7 @@ With a 16bits ADC, the resolution will then be equals to (in [nm]):
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-10 mar. 13:41</p> <p class="date">Created: 2020-11-10 mar. 13:46</p>
</div> </div>
</body> </body>
</html> </html>

33
index.org
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@ -128,12 +128,11 @@ The equipment used in the test bench are:
#+RESULTS: #+RESULTS:
[[file:figs/stiffness_force_sensor_coherence.png]] [[file:figs/stiffness_force_sensor_coherence.png]]
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None'); tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
ax1 = nexttile; ax1 = nexttile([2,1]);
hold on; hold on;
plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit') plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit')
plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit') plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit')
@ -166,9 +165,33 @@ The equipment used in the test bench are:
#+RESULTS: #+RESULTS:
[[file:figs/stiffness_force_sensor_bode.png]] [[file:figs/stiffness_force_sensor_bode.png]]
#+begin_src matlab :exports none
figure;
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
ax1 = nexttile;
hold on;
plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit')
plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
xlim([200, 280]);
legend('location', 'southwest');
ax3 = nexttile;
hold on;
plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit')
plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
xlim([800, 950]);
legend('location', 'southwest');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace #+begin_src matlab :tangle no :exports results :results file replace
xlim([180, 280]); exportFig('figs/stiffness_force_sensor_bode_zoom.pdf', 'width', 'wide', 'height', 'normal');
exportFig('figs/stiffness_force_sensor_bode_zoom.pdf', 'width', 'small', 'height', 'tall');
#+end_src #+end_src
#+name: fig:stiffness_force_sensor_bode_zoom #+name: fig:stiffness_force_sensor_bode_zoom