Add analysis of the effect of added resistor
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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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<!-- 2020-10-29 jeu. 10:08 -->
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<!-- 2020-11-04 mer. 20:38 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Encoder - Test Bench</title>
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<meta name="generator" content="Org mode" />
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@@ -35,49 +35,50 @@
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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="#orgfe3d6c5">1. Experimental Setup</a></li>
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||||
<li><a href="#org85c4a97">2. Huddle Test</a>
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||||
<li><a href="#org2b2f049">1. Experimental Setup</a></li>
|
||||
<li><a href="#org9ae614e">2. Huddle Test</a>
|
||||
<ul>
|
||||
<li><a href="#org6f9e775">2.1. Load Data</a></li>
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||||
<li><a href="#orgd27ba42">2.2. Time Domain Results</a></li>
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||||
<li><a href="#org963a243">2.3. Frequency Domain Noise</a></li>
|
||||
<li><a href="#orgc034802">2.1. Load Data</a></li>
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||||
<li><a href="#orgd8ae4ae">2.2. Time Domain Results</a></li>
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||||
<li><a href="#org864c60c">2.3. Frequency Domain Noise</a></li>
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||||
</ul>
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||||
</li>
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||||
<li><a href="#org0e0c48a">3. Comparison Interferometer / Encoder</a>
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||||
<li><a href="#org96539c5">3. Comparison Interferometer / Encoder</a>
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||||
<ul>
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||||
<li><a href="#orgc15a506">3.1. Load Data</a></li>
|
||||
<li><a href="#orgc509698">3.2. Time Domain Results</a></li>
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||||
<li><a href="#org1b5953a">3.3. Difference between Encoder and Interferometer as a function of time</a></li>
|
||||
<li><a href="#orgcb56769">3.4. Difference between Encoder and Interferometer as a function of position</a></li>
|
||||
<li><a href="#orgc6453b2">3.1. Load Data</a></li>
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||||
<li><a href="#orgc362641">3.2. Time Domain Results</a></li>
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||||
<li><a href="#orgb50503c">3.3. Difference between Encoder and Interferometer as a function of time</a></li>
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||||
<li><a href="#org5ec03aa">3.4. Difference between Encoder and Interferometer as a function of position</a></li>
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||||
</ul>
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||||
</li>
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||||
<li><a href="#org8399536">4. Identification</a>
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||||
<li><a href="#org6b73303">4. Identification</a>
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||||
<ul>
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||||
<li><a href="#org4b364a5">4.1. Load Data</a></li>
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||||
<li><a href="#org0dd3820">4.2. Identification</a></li>
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||||
<li><a href="#orga15e9e2">4.1. Load Data</a></li>
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||||
<li><a href="#org6974653">4.2. Identification</a></li>
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||||
</ul>
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||||
</li>
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||||
<li><a href="#org4a7e08f">5. Change of Stiffness due to Sensors stack being open/closed circuit</a>
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||||
<li><a href="#org5be1a0f">5. Change of Stiffness due to Sensors stack being open/closed circuit</a>
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||||
<ul>
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||||
<li><a href="#orgba85fb9">5.1. Load Data</a></li>
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<li><a href="#org2876c52">5.2. Transfer Functions</a></li>
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||||
<li><a href="#org00fc76c">5.1. Load Data</a></li>
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||||
<li><a href="#org757917f">5.2. Transfer Functions</a></li>
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||||
</ul>
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||||
</li>
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||||
<li><a href="#org1abff1f">6. Generated Number of Charge / Voltage</a>
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<li><a href="#org8dab16f">6. Generated Number of Charge / Voltage</a>
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||||
<ul>
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||||
<li><a href="#org65e8206">6.1. Steps</a></li>
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<li><a href="#org4df253f">6.2. Sinus</a></li>
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||||
<li><a href="#org28149b5">6.1. Steps</a></li>
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||||
<li><a href="#org900387e">6.2. Add Parallel Resistor</a></li>
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||||
<li><a href="#org7cfe5a8">6.3. Sinus</a></li>
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||||
</ul>
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||||
</li>
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||||
</ul>
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||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-orgfe3d6c5" class="outline-2">
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||||
<h2 id="orgfe3d6c5"><span class="section-number-2">1</span> Experimental Setup</h2>
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||||
<div id="outline-container-org2b2f049" class="outline-2">
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||||
<h2 id="org2b2f049"><span class="section-number-2">1</span> Experimental Setup</h2>
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||||
<div class="outline-text-2" id="text-1">
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||||
<p>
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||||
The experimental Setup is schematically represented in Figure <a href="#orgb535f32">1</a>.
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||||
The experimental Setup is schematically represented in Figure <a href="#orgff06236">1</a>.
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</p>
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||||
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||||
<p>
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@@ -86,21 +87,21 @@ The displacement of the mass (relative to the mechanical frame) is measured both
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</p>
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<div id="orgb535f32" class="figure">
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<div id="orgff06236" class="figure">
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||||
<p><img src="figs/exp_setup_schematic.png" alt="exp_setup_schematic.png" />
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||||
</p>
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||||
<p><span class="figure-number">Figure 1: </span>Schematic of the Experiment</p>
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</div>
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||||
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||||
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||||
<div id="org7c9d65a" class="figure">
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<div id="orgc6b5ad5" class="figure">
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||||
<p><img src="figs/IMG_20201023_153905.jpg" alt="IMG_20201023_153905.jpg" />
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||||
</p>
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<p><span class="figure-number">Figure 2: </span>Side View of the encoder</p>
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</div>
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||||
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||||
<div id="org6ecf3f2" class="figure">
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<div id="orgcf538be" class="figure">
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||||
<p><img src="figs/IMG_20201023_153914.jpg" alt="IMG_20201023_153914.jpg" />
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||||
</p>
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||||
<p><span class="figure-number">Figure 3: </span>Front View of the encoder</p>
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@@ -108,8 +109,8 @@ The displacement of the mass (relative to the mechanical frame) is measured both
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</div>
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||||
</div>
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||||
|
||||
<div id="outline-container-org85c4a97" class="outline-2">
|
||||
<h2 id="org85c4a97"><span class="section-number-2">2</span> Huddle Test</h2>
|
||||
<div id="outline-container-org9ae614e" class="outline-2">
|
||||
<h2 id="org9ae614e"><span class="section-number-2">2</span> Huddle Test</h2>
|
||||
<div class="outline-text-2" id="text-2">
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||||
<p>
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||||
The goal in this section is the estimate the noise of both the encoder and the intereferometer.
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||||
@@ -121,8 +122,8 @@ Ideally, a mechanical part would clamp the two together, we here suppose that th
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||||
</p>
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||||
</div>
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||||
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||||
<div id="outline-container-org6f9e775" class="outline-3">
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||||
<h3 id="org6f9e775"><span class="section-number-3">2.1</span> Load Data</h3>
|
||||
<div id="outline-container-orgc034802" class="outline-3">
|
||||
<h3 id="orgc034802"><span class="section-number-3">2.1</span> Load Data</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
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||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_huddle_test.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'t'</span>);
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||||
@@ -137,11 +138,11 @@ encoder = detrend(encoder, 0);
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||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-orgd27ba42" class="outline-3">
|
||||
<h3 id="orgd27ba42"><span class="section-number-3">2.2</span> Time Domain Results</h3>
|
||||
<div id="outline-container-orgd8ae4ae" class="outline-3">
|
||||
<h3 id="orgd8ae4ae"><span class="section-number-3">2.2</span> Time Domain Results</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
|
||||
<div id="orgbec33e3" class="figure">
|
||||
<div id="orgff47510" class="figure">
|
||||
<p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Huddle test - Time domain signals</p>
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||||
@@ -153,7 +154,7 @@ encoder = detrend(encoder, 0);
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||||
</div>
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||||
|
||||
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||||
<div id="org19de732" class="figure">
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||||
<div id="org21436f3" class="figure">
|
||||
<p><img src="figs/huddle_test_time_domain_filtered.png" alt="huddle_test_time_domain_filtered.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Huddle test - Time domain signals filtered with a LPF at 10Hz</p>
|
||||
@@ -161,8 +162,8 @@ encoder = detrend(encoder, 0);
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||||
</div>
|
||||
</div>
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||||
|
||||
<div id="outline-container-org963a243" class="outline-3">
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||||
<h3 id="org963a243"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
|
||||
<div id="outline-container-org864c60c" class="outline-3">
|
||||
<h3 id="org864c60c"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
|
||||
@@ -174,7 +175,7 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgb6a29d5" class="figure">
|
||||
<div id="org63bcf43" class="figure">
|
||||
<p><img src="figs/huddle_test_asd.png" alt="huddle_test_asd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signals during the Huddle test</p>
|
||||
@@ -183,8 +184,8 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||
</div>
|
||||
</div>
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||||
|
||||
<div id="outline-container-org0e0c48a" class="outline-2">
|
||||
<h2 id="org0e0c48a"><span class="section-number-2">3</span> Comparison Interferometer / Encoder</h2>
|
||||
<div id="outline-container-org96539c5" class="outline-2">
|
||||
<h2 id="org96539c5"><span class="section-number-2">3</span> Comparison Interferometer / Encoder</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
The goal here is to make sure that the interferometer and encoder measurements are coherent.
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||||
@@ -192,8 +193,8 @@ We may see non-linearity in the interferometric measurement.
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||||
</p>
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||||
</div>
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||||
|
||||
<div id="outline-container-orgc15a506" class="outline-3">
|
||||
<h3 id="orgc15a506"><span class="section-number-3">3.1</span> Load Data</h3>
|
||||
<div id="outline-container-orgc6453b2" class="outline-3">
|
||||
<h3 id="orgc6453b2"><span class="section-number-3">3.1</span> Load Data</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_comp.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>);
|
||||
@@ -209,18 +210,18 @@ u = detrend(u, 0);
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||||
</div>
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||||
</div>
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||||
|
||||
<div id="outline-container-orgc509698" class="outline-3">
|
||||
<h3 id="orgc509698"><span class="section-number-3">3.2</span> Time Domain Results</h3>
|
||||
<div id="outline-container-orgc362641" class="outline-3">
|
||||
<h3 id="orgc362641"><span class="section-number-3">3.2</span> Time Domain Results</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
|
||||
<div id="orgdf791be" class="figure">
|
||||
<div id="orgfd33423" class="figure">
|
||||
<p><img src="figs/int_enc_one_cycle.png" alt="int_enc_one_cycle.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>One cycle measurement</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7e30f32" class="figure">
|
||||
<div id="orgf82fd3e" class="figure">
|
||||
<p><img src="figs/int_enc_one_cycle_error.png" alt="int_enc_one_cycle_error.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Difference between the Encoder and the interferometer during one cycle</p>
|
||||
@@ -228,8 +229,8 @@ u = detrend(u, 0);
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||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1b5953a" class="outline-3">
|
||||
<h3 id="org1b5953a"><span class="section-number-3">3.3</span> Difference between Encoder and Interferometer as a function of time</h3>
|
||||
<div id="outline-container-orgb50503c" class="outline-3">
|
||||
<h3 id="orgb50503c"><span class="section-number-3">3.3</span> Difference between Encoder and Interferometer as a function of time</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
|
||||
@@ -250,7 +251,7 @@ d_err_mean = d_err_mean <span class="org-type">-</span> mean(d_err_mean);
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org95838e4" class="figure">
|
||||
<div id="org6eb78a0" class="figure">
|
||||
<p><img src="figs/int_enc_error_mean_time.png" alt="int_enc_error_mean_time.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Difference between the two measurement in the time domain, averaged for all the cycles</p>
|
||||
@@ -258,8 +259,8 @@ d_err_mean = d_err_mean <span class="org-type">-</span> mean(d_err_mean);
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcb56769" class="outline-3">
|
||||
<h3 id="orgcb56769"><span class="section-number-3">3.4</span> Difference between Encoder and Interferometer as a function of position</h3>
|
||||
<div id="outline-container-org5ec03aa" class="outline-3">
|
||||
<h3 id="org5ec03aa"><span class="section-number-3">3.4</span> Difference between Encoder and Interferometer as a function of position</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
Compute the mean of the interferometer measurement corresponding to each of the encoder measurement.
|
||||
@@ -278,7 +279,7 @@ i_mean_error = (i_mean <span class="org-type">-</span> e_sorted);
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orga34e36f" class="figure">
|
||||
<div id="org2aecb58" class="figure">
|
||||
<p><img src="figs/int_enc_error_mean_position.png" alt="int_enc_error_mean_position.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles</p>
|
||||
@@ -299,7 +300,7 @@ e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init<span class="org-typ
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org064a7da" class="figure">
|
||||
<div id="orgd0cea4e" class="figure">
|
||||
<p><img src="figs/int_non_linearity_period_wavelength.png" alt="int_non_linearity_period_wavelength.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Non-Linearity of the Interferometer over the period of the wavelength</p>
|
||||
@@ -308,12 +309,12 @@ e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init<span class="org-typ
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8399536" class="outline-2">
|
||||
<h2 id="org8399536"><span class="section-number-2">4</span> Identification</h2>
|
||||
<div id="outline-container-org6b73303" class="outline-2">
|
||||
<h2 id="org6b73303"><span class="section-number-2">4</span> Identification</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org4b364a5" class="outline-3">
|
||||
<h3 id="org4b364a5"><span class="section-number-3">4.1</span> Load Data</h3>
|
||||
<div id="outline-container-orga15e9e2" class="outline-3">
|
||||
<h3 id="orga15e9e2"><span class="section-number-3">4.1</span> Load Data</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_id_noise_bis.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>);
|
||||
@@ -329,8 +330,8 @@ u = detrend(u, 0);
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0dd3820" class="outline-3">
|
||||
<h3 id="org0dd3820"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div id="outline-container-org6974653" class="outline-3">
|
||||
<h3 id="org6974653"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<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>
|
||||
@@ -348,14 +349,14 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||
</div>
|
||||
|
||||
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||||
<div id="org4e10071" class="figure">
|
||||
<div id="org37fcd05" class="figure">
|
||||
<p><img src="figs/identification_dynamics_coherence.png" alt="identification_dynamics_coherence.png" />
|
||||
</p>
|
||||
</div>
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||||
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||||
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||||
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||||
<div id="orgfa48d56" class="figure">
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||||
<div id="orge65c21c" class="figure">
|
||||
<p><img src="figs/identification_dynamics_bode.png" alt="identification_dynamics_bode.png" />
|
||||
</p>
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||||
</div>
|
||||
@@ -363,12 +364,12 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4a7e08f" class="outline-2">
|
||||
<h2 id="org4a7e08f"><span class="section-number-2">5</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2>
|
||||
<div id="outline-container-org5be1a0f" class="outline-2">
|
||||
<h2 id="org5be1a0f"><span class="section-number-2">5</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
</div>
|
||||
<div id="outline-container-orgba85fb9" class="outline-3">
|
||||
<h3 id="orgba85fb9"><span class="section-number-3">5.1</span> Load Data</h3>
|
||||
<div id="outline-container-org00fc76c" class="outline-3">
|
||||
<h3 id="org00fc76c"><span class="section-number-3">5.1</span> Load Data</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">oc = load(<span class="org-string">'./mat/identification_open_circuit.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>);
|
||||
@@ -378,8 +379,8 @@ sc = load(<span class="org-string">'./mat/identification_short_circuit.mat'</spa
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2876c52" class="outline-3">
|
||||
<h3 id="org2876c52"><span class="section-number-3">5.2</span> Transfer Functions</h3>
|
||||
<div id="outline-container-org757917f" class="outline-3">
|
||||
<h3 id="org757917f"><span class="section-number-3">5.2</span> Transfer Functions</h3>
|
||||
<div class="outline-text-3" id="text-5-2">
|
||||
<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>
|
||||
@@ -397,26 +398,26 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org525ff65" class="figure">
|
||||
<div id="orgcba7c3a" class="figure">
|
||||
<p><img src="figs/stiffness_force_sensor_coherence.png" alt="stiffness_force_sensor_coherence.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="orge72a5de" class="figure">
|
||||
<div id="orgfdef3b4" class="figure">
|
||||
<p><img src="figs/stiffness_force_sensor_bode.png" alt="stiffness_force_sensor_bode.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd8a00e8" class="figure">
|
||||
<div id="org655038d" class="figure">
|
||||
<p><img src="figs/stiffness_force_sensor_bode_zoom.png" alt="stiffness_force_sensor_bode_zoom.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Zoom on the change of resonance</p>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org5981596">
|
||||
<div class="important" id="orga5e301b">
|
||||
<p>
|
||||
The change of resonance frequency / stiffness is very small and is not important here.
|
||||
</p>
|
||||
@@ -426,8 +427,8 @@ The change of resonance frequency / stiffness is very small and is not important
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1abff1f" class="outline-2">
|
||||
<h2 id="org1abff1f"><span class="section-number-2">6</span> Generated Number of Charge / Voltage</h2>
|
||||
<div id="outline-container-org8dab16f" class="outline-2">
|
||||
<h2 id="org8dab16f"><span class="section-number-2">6</span> Generated Number of Charge / Voltage</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<p>
|
||||
Two stacks are used as actuator (in parallel) and one stack is used as sensor.
|
||||
@@ -438,8 +439,8 @@ The amplifier gain is 20V/V (Cedrat LA75B).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org65e8206" class="outline-3">
|
||||
<h3 id="org65e8206"><span class="section-number-3">6.1</span> Steps</h3>
|
||||
<div id="outline-container-org28149b5" class="outline-3">
|
||||
<h3 id="org28149b5"><span class="section-number-3">6.1</span> Steps</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'./mat/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>);
|
||||
@@ -459,7 +460,7 @@ xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-stri
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0233cf4" class="figure">
|
||||
<div id="org0c7c950" class="figure">
|
||||
<p><img src="figs/force_sen_steps_time_domain.png" alt="force_sen_steps_time_domain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Time domain signal during the 3 actuator voltage steps</p>
|
||||
@@ -468,11 +469,12 @@ xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-stri
|
||||
<p>
|
||||
Three steps are performed at the following time intervals:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>2.5, 23</li>
|
||||
<li>23.8, 35</li>
|
||||
<li>35.8, 50</li>
|
||||
</ul>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">t_s = [ 2.5, 23;
|
||||
23.8, 35;
|
||||
35.8, 50];
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Fit function:
|
||||
@@ -485,52 +487,25 @@ Fit function:
|
||||
<p>
|
||||
We are interested by the <code>b(2)</code> term, which is the time constant of the exponential.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">tau = zeros(3,1);
|
||||
V0 = zeros(3,1);
|
||||
<pre class="src src-matlab">tau = zeros(size(t_s, 1),1);
|
||||
V0 = zeros(size(t_s, 1),1);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">t_cur = t(2.5 <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> 23);
|
||||
t_cur = t_cur <span class="org-type">-</span> t_cur(1);
|
||||
y_cur = v(2.5 <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> 23);
|
||||
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name">t_i</span> = <span class="org-constant">1:size(t_s, 1)</span>
|
||||
t_cur = t(t_s(t_i, 1) <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> t_s(t_i, 2));
|
||||
t_cur = t_cur <span class="org-type">-</span> t_cur(1);
|
||||
y_cur = v(t_s(t_i, 1) <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> t_s(t_i, 2));
|
||||
|
||||
nrmrsd = @(b) norm(y_cur <span class="org-type">-</span> f(b,t_cur)); <span class="org-comment">% Residual Norm Cost Function</span>
|
||||
B0 = [0.5, <span class="org-type">-</span>0.15, 2.2]; <span class="org-comment">% Choose Appropriate Initial Estimates</span>
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); <span class="org-comment">% Estimate Parameters ‘B’</span>
|
||||
nrmrsd = @(b) norm(y_cur <span class="org-type">-</span> f(b,t_cur)); <span class="org-comment">% Residual Norm Cost Function</span>
|
||||
B0 = [0.5, <span class="org-type">-</span>0.15, 2.2]; <span class="org-comment">% Choose Appropriate Initial Estimates</span>
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); <span class="org-comment">% Estimate Parameters ‘B’</span>
|
||||
|
||||
tau<span class="org-type">(1) </span>= 1<span class="org-type">/</span>B(2);
|
||||
V0<span class="org-type">(1) </span>= B(3);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">t_cur = t(23.8 <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> 35);
|
||||
t_cur = t_cur <span class="org-type">-</span> t_cur(1);
|
||||
y_cur = v(23.8 <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> 35);
|
||||
|
||||
nrmrsd = @(b) norm(y_cur <span class="org-type">-</span> f(b,t_cur)); <span class="org-comment">% Residual Norm Cost Function</span>
|
||||
B0 = [0.5, <span class="org-type">-</span>0.15, 2.2]; <span class="org-comment">% Choose Appropriate Initial Estimates</span>
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); <span class="org-comment">% Estimate Parameters ‘B’</span>
|
||||
|
||||
tau<span class="org-type">(2) </span>= 1<span class="org-type">/</span>B(2);
|
||||
V0<span class="org-type">(2) </span>= B(3);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">t_cur = t(35.8 <span class="org-type"><</span> t);
|
||||
t_cur = t_cur <span class="org-type">-</span> t_cur(1);
|
||||
y_cur = v(35.8 <span class="org-type"><</span> t);
|
||||
|
||||
nrmrsd = @(b) norm(y_cur <span class="org-type">-</span> f(b,t_cur)); <span class="org-comment">% Residual Norm Cost Function</span>
|
||||
B0 = [0.5, <span class="org-type">-</span>0.15, 2.2]; <span class="org-comment">% Choose Appropriate Initial Estimates</span>
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); <span class="org-comment">% Estimate Parameters ‘B’</span>
|
||||
|
||||
tau<span class="org-type">(3) </span>= 1<span class="org-type">/</span>B(2);
|
||||
V0<span class="org-type">(3) </span>= B(3);
|
||||
tau(t_i) = 1<span class="org-type">/</span>B(2);
|
||||
V0(t_i) = B(3);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -584,7 +559,7 @@ Rin = abs(mean(tau))<span class="org-type">/</span>Cp;
|
||||
The input impedance of the Speedgoat’s ADC should then be close to \(1.5\,M\Omega\) (specified at \(1\,M\Omega\)).
|
||||
</p>
|
||||
|
||||
<div class="important" id="org8ca234e">
|
||||
<div class="important" id="org60ccf75">
|
||||
<p>
|
||||
How can we explain the voltage offset?
|
||||
</p>
|
||||
@@ -592,11 +567,11 @@ How can we explain the voltage offset?
|
||||
</div>
|
||||
|
||||
<p>
|
||||
As shown in Figure <a href="#org6a0d23a">18</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 \(i_n\).
|
||||
As shown in Figure <a href="#org39e1694">18</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 \(i_n\).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org6a0d23a" class="figure">
|
||||
<div id="org39e1694" class="figure">
|
||||
<p><img src="figs/piezo_sensor_model_instrumentation.png" alt="piezo_sensor_model_instrumentation.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right)</p>
|
||||
@@ -632,7 +607,7 @@ If we allow the high pass corner frequency to be equals to 3Hz:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">fc = 3;
|
||||
Ra = Rin<span class="org-type">/</span>(fc<span class="org-type">*</span>C<span class="org-type">*</span>Rin <span class="org-type">-</span> 1);
|
||||
Ra = Rin<span class="org-type">/</span>(fc<span class="org-type">*</span>Cp<span class="org-type">*</span>Rin <span class="org-type">-</span> 1);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -660,9 +635,178 @@ Which is much more acceptable.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4df253f" class="outline-3">
|
||||
<h3 id="org4df253f"><span class="section-number-3">6.2</span> Sinus</h3>
|
||||
<div id="outline-container-org900387e" class="outline-3">
|
||||
<h3 id="org900387e"><span class="section-number-3">6.2</span> Add Parallel Resistor</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
<p>
|
||||
A resistor of \(\approx 100\,k\Omega\) is added in parallel with the force sensor and the same kin.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'./mat/force_sensor_steps_R_82k7.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>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
tiledlayout(2, 1, <span class="org-string">'TileSpacing'</span>, <span class="org-string">'None'</span>, <span class="org-string">'Padding'</span>, <span class="org-string">'None'</span>);
|
||||
nexttile;
|
||||
plot(t, v);
|
||||
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Measured voltage [V]'</span>);
|
||||
nexttile;
|
||||
plot(t, u);
|
||||
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Actuator Voltage [V]'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgaee44e2" class="figure">
|
||||
<p><img src="figs/force_sen_steps_time_domain_par_R.png" alt="force_sen_steps_time_domain_par_R.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Time domain signal during the actuator voltage steps</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Three steps are performed at the following time intervals:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">t_s = [1.9, 6;
|
||||
8.5, 13;
|
||||
15.5, 21;
|
||||
22.6, 26;
|
||||
30.0, 36;
|
||||
37.5, 41;
|
||||
46.2, 49.5]
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Fit function:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">f = @(b,x) b(1)<span class="org-type">.*</span>exp(b(2)<span class="org-type">.*</span>x) <span class="org-type">+</span> b(3);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We are interested by the <code>b(2)</code> term, which is the time constant of the exponential.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">tau = zeros(size(t_s, 1),1);
|
||||
V0 = zeros(size(t_s, 1),1);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name">t_i</span> = <span class="org-constant">1:size(t_s, 1)</span>
|
||||
t_cur = t(t_s(t_i, 1) <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> t_s(t_i, 2));
|
||||
t_cur = t_cur <span class="org-type">-</span> t_cur(1);
|
||||
y_cur = v(t_s(t_i, 1) <span class="org-type"><</span> t <span class="org-type">&</span> t <span class="org-type"><</span> t_s(t_i, 2));
|
||||
|
||||
nrmrsd = @(b) norm(y_cur <span class="org-type">-</span> f(b,t_cur)); <span class="org-comment">% Residual Norm Cost Function</span>
|
||||
B0 = [0.5, <span class="org-type">-</span>0.2, 0.2]; <span class="org-comment">% Choose Appropriate Initial Estimates</span>
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); <span class="org-comment">% Estimate Parameters ‘B’</span>
|
||||
|
||||
tau(t_i) = 1<span class="org-type">/</span>B(2);
|
||||
V0(t_i) = B(3);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
And indeed, we obtain a much smaller offset voltage and a much faster time constant.
|
||||
</p>
|
||||
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
|
||||
<colgroup>
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
</colgroup>
|
||||
<thead>
|
||||
<tr>
|
||||
<th scope="col" class="org-right">\(tau\) [s]</th>
|
||||
<th scope="col" class="org-right">\(V_0\) [V]</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-right">0.43</td>
|
||||
<td class="org-right">0.15</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.45</td>
|
||||
<td class="org-right">0.16</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.43</td>
|
||||
<td class="org-right">0.15</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.43</td>
|
||||
<td class="org-right">0.15</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.45</td>
|
||||
<td class="org-right">0.15</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.46</td>
|
||||
<td class="org-right">0.16</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.48</td>
|
||||
<td class="org-right">0.16</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<p>
|
||||
Knowing the capacitance value, we can estimate the value of the added resistor (neglecting the input impedance of \(\approx 1\,M\Omega\)):
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Cp = 4.4e<span class="org-type">-</span>6; <span class="org-comment">% [F]</span>
|
||||
Rin = abs(mean(tau))<span class="org-type">/</span>Cp;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example">
|
||||
101200.0
|
||||
</pre>
|
||||
|
||||
|
||||
<p>
|
||||
And we can verify that the bias current estimation stays the same:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">in = mean(V0)<span class="org-type">/</span>Rin;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example">
|
||||
1.5305e-06
|
||||
</pre>
|
||||
|
||||
|
||||
<p>
|
||||
This validates the model of the ADC and the effectiveness of the added resistor.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7cfe5a8" class="outline-3">
|
||||
<h3 id="org7cfe5a8"><span class="section-number-3">6.3</span> Sinus</h3>
|
||||
<div class="outline-text-3" id="text-6-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'./mat/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>);
|
||||
|
||||
@@ -674,14 +818,14 @@ t = t(t<span class="org-type">></span>25);
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#orga819354">19</a>).
|
||||
The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#orga42b4f8">20</a>).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga819354" class="figure">
|
||||
<div id="orga42b4f8" class="figure">
|
||||
<p><img src="figs/force_sensor_sin_u.png" alt="force_sensor_sin_u.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Driving Voltage</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Driving Voltage</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@@ -698,14 +842,14 @@ The full stroke as measured by the encoder is:
|
||||
|
||||
|
||||
<p>
|
||||
Its signal is shown in Figure <a href="#orgde5c100">20</a>.
|
||||
Its signal is shown in Figure <a href="#orgcda82ea">21</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgde5c100" class="figure">
|
||||
<div id="orgcda82ea" class="figure">
|
||||
<p><img src="figs/force_sensor_sin_encoder.png" alt="force_sensor_sin_encoder.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Encoder measurement</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Encoder measurement</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@@ -713,10 +857,10 @@ The generated voltage by the stack is shown in Figure
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org1f6aabd" class="figure">
|
||||
<div id="orgdd5fd9b" class="figure">
|
||||
<p><img src="figs/force_sensor_sin_stack.png" alt="force_sensor_sin_stack.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Voltage measured on the stack used as a sensor</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Voltage measured on the stack used as a sensor</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@@ -728,18 +872,18 @@ The capacitance of the stack is
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The corresponding generated charge is then shown in Figure <a href="#orgcfb4c95">22</a>.
|
||||
The corresponding generated charge is then shown in Figure <a href="#org15cf433">23</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgcfb4c95" class="figure">
|
||||
<div id="org15cf433" class="figure">
|
||||
<p><img src="figs/force_sensor_sin_charge.png" alt="force_sensor_sin_charge.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Generated Charge</p>
|
||||
<p><span class="figure-number">Figure 23: </span>Generated Charge</p>
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#orgd584dd5">23</a>.
|
||||
The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#orge276186">24</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@@ -748,10 +892,10 @@ The relation between the generated voltage and the measured displacement is almo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd584dd5" class="figure">
|
||||
<div id="orge276186" class="figure">
|
||||
<p><img src="figs/force_sensor_linear_relation.png" alt="force_sensor_linear_relation.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 23: </span>Almost linear relation between the relative displacement and the generated voltage</p>
|
||||
<p><span class="figure-number">Figure 24: </span>Almost linear relation between the relative displacement and the generated voltage</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@@ -777,7 +921,7 @@ With a 16bits ADC, the resolution will then be equals to (in [nm]):
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-10-29 jeu. 10:08</p>
|
||||
<p class="date">Created: 2020-11-04 mer. 20:38</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
161
index.org
161
index.org
@@ -551,9 +551,11 @@ The amplifier gain is 20V/V (Cedrat LA75B).
|
||||
[[file:figs/force_sen_steps_time_domain.png]]
|
||||
|
||||
Three steps are performed at the following time intervals:
|
||||
- 2.5, 23
|
||||
- 23.8, 35
|
||||
- 35.8, 50
|
||||
#+begin_src matlab
|
||||
t_s = [ 2.5, 23;
|
||||
23.8, 35;
|
||||
35.8, 50];
|
||||
#+end_src
|
||||
|
||||
Fit function:
|
||||
#+begin_src matlab
|
||||
@@ -561,49 +563,24 @@ Fit function:
|
||||
#+end_src
|
||||
|
||||
We are interested by the =b(2)= term, which is the time constant of the exponential.
|
||||
|
||||
#+begin_src matlab
|
||||
tau = zeros(3,1);
|
||||
V0 = zeros(3,1);
|
||||
tau = zeros(size(t_s, 1),1);
|
||||
V0 = zeros(size(t_s, 1),1);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
t_cur = t(2.5 < t & t < 23);
|
||||
for t_i = 1:size(t_s, 1)
|
||||
t_cur = t(t_s(t_i, 1) < t & t < t_s(t_i, 2));
|
||||
t_cur = t_cur - t_cur(1);
|
||||
y_cur = v(2.5 < t & t < 23);
|
||||
y_cur = v(t_s(t_i, 1) < t & t < t_s(t_i, 2));
|
||||
|
||||
nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
|
||||
B0 = [0.5, -0.15, 2.2]; % Choose Appropriate Initial Estimates
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
|
||||
|
||||
tau(1) = 1/B(2);
|
||||
V0(1) = B(3);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
t_cur = t(23.8 < t & t < 35);
|
||||
t_cur = t_cur - t_cur(1);
|
||||
y_cur = v(23.8 < t & t < 35);
|
||||
|
||||
nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
|
||||
B0 = [0.5, -0.15, 2.2]; % Choose Appropriate Initial Estimates
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
|
||||
|
||||
tau(2) = 1/B(2);
|
||||
V0(2) = B(3);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
t_cur = t(35.8 < t);
|
||||
t_cur = t_cur - t_cur(1);
|
||||
y_cur = v(35.8 < t);
|
||||
|
||||
nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
|
||||
B0 = [0.5, -0.15, 2.2]; % Choose Appropriate Initial Estimates
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
|
||||
|
||||
tau(3) = 1/B(2);
|
||||
V0(3) = B(3);
|
||||
tau(t_i) = 1/B(2);
|
||||
V0(t_i) = B(3);
|
||||
end
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||
@@ -665,7 +642,7 @@ An additional resistor in parallel with $R_{in}$ would have two effects:
|
||||
If we allow the high pass corner frequency to be equals to 3Hz:
|
||||
#+begin_src matlab
|
||||
fc = 3;
|
||||
Ra = Rin/(fc*C*Rin - 1);
|
||||
Ra = Rin/(fc*Cp*Rin - 1);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
@@ -689,6 +666,116 @@ With this parallel resistance value, the voltage offset would be:
|
||||
|
||||
Which is much more acceptable.
|
||||
|
||||
** Add Parallel Resistor
|
||||
A resistor of $\approx 100\,k\Omega$ is added in parallel with the force sensor and the same kin.
|
||||
|
||||
#+begin_src matlab
|
||||
load('./mat/force_sensor_steps_R_82k7.mat', 't', 'encoder', 'u', 'v');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
nexttile;
|
||||
plot(t, v);
|
||||
xlabel('Time [s]'); ylabel('Measured voltage [V]');
|
||||
nexttile;
|
||||
plot(t, u);
|
||||
xlabel('Time [s]'); ylabel('Actuator Voltage [V]');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/force_sen_steps_time_domain_par_R.pdf', 'width', 'wide', 'height', 'tall');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:force_sen_steps_time_domain_par_R
|
||||
#+caption: Time domain signal during the actuator voltage steps
|
||||
#+RESULTS:
|
||||
[[file:figs/force_sen_steps_time_domain_par_R.png]]
|
||||
|
||||
Three steps are performed at the following time intervals:
|
||||
#+begin_src matlab
|
||||
t_s = [1.9, 6;
|
||||
8.5, 13;
|
||||
15.5, 21;
|
||||
22.6, 26;
|
||||
30.0, 36;
|
||||
37.5, 41;
|
||||
46.2, 49.5]
|
||||
#+end_src
|
||||
|
||||
Fit function:
|
||||
#+begin_src matlab
|
||||
f = @(b,x) b(1).*exp(b(2).*x) + b(3);
|
||||
#+end_src
|
||||
|
||||
We are interested by the =b(2)= term, which is the time constant of the exponential.
|
||||
|
||||
#+begin_src matlab
|
||||
tau = zeros(size(t_s, 1),1);
|
||||
V0 = zeros(size(t_s, 1),1);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
for t_i = 1:size(t_s, 1)
|
||||
t_cur = t(t_s(t_i, 1) < t & t < t_s(t_i, 2));
|
||||
t_cur = t_cur - t_cur(1);
|
||||
y_cur = v(t_s(t_i, 1) < t & t < t_s(t_i, 2));
|
||||
|
||||
nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
|
||||
B0 = [0.5, -0.2, 0.2]; % Choose Appropriate Initial Estimates
|
||||
[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
|
||||
|
||||
tau(t_i) = 1/B(2);
|
||||
V0(t_i) = B(3);
|
||||
end
|
||||
#+end_src
|
||||
|
||||
And indeed, we obtain a much smaller offset voltage and a much faster time constant.
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||
data2orgtable([abs(tau), V0], {}, {'$tau$ [s]', '$V_0$ [V]'}, ' %.2f ');
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
| $tau$ [s] | $V_0$ [V] |
|
||||
|-----------+-----------|
|
||||
| 0.43 | 0.15 |
|
||||
| 0.45 | 0.16 |
|
||||
| 0.43 | 0.15 |
|
||||
| 0.43 | 0.15 |
|
||||
| 0.45 | 0.15 |
|
||||
| 0.46 | 0.16 |
|
||||
| 0.48 | 0.16 |
|
||||
|
||||
Knowing the capacitance value, we can estimate the value of the added resistor (neglecting the input impedance of $\approx 1\,M\Omega$):
|
||||
|
||||
#+begin_src matlab
|
||||
Cp = 4.4e-6; % [F]
|
||||
Rin = abs(mean(tau))/Cp;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
ans = Rin
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: 101200.0
|
||||
|
||||
And we can verify that the bias current estimation stays the same:
|
||||
#+begin_src matlab
|
||||
in = mean(V0)/Rin;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
ans = in
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: 1.5305e-06
|
||||
|
||||
This validates the model of the ADC and the effectiveness of the added resistor.
|
||||
|
||||
** Sinus
|
||||
#+begin_src matlab
|
||||
load('./mat/force_sensor_sin.mat', 't', 'encoder', 'u', 'v');
|
||||
|
||||
Reference in New Issue
Block a user