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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="#org3c3af3a">1. Experimental Setup</a></li>
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<li><a href="#orgdb3277a">2. Noise Spectral Density of the Encoder</a>
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<li><a href="#org4f09976">1. Experimental Setup</a></li>
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<li><a href="#org5bbb12a">2. Noise Spectral Density of the Encoder</a>
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<ul>
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<li><a href="#org81a5e5f">2.1. Load Data</a></li>
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<li><a href="#orgbed7f20">2.2. Time Domain Results</a></li>
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<li><a href="#org319de75">2.3. Frequency Domain Noise</a></li>
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<li><a href="#org91e2f9a">2.1. Load Data</a></li>
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<li><a href="#org9392d29">2.2. Time Domain Results</a></li>
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<li><a href="#org998b458">2.3. Frequency Domain Noise</a></li>
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</ul>
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</li>
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<li><a href="#orgb1ca2cf">3. Dynamics from Actuator to Encoder</a>
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<li><a href="#org3ede191">3. Dynamics from Actuator to Encoder</a>
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<ul>
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<li><a href="#orgfa505d1">3.1. Load Data</a></li>
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<li><a href="#org3f21900">3.2. Excitation and Measured Signals</a></li>
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<li><a href="#org0b79009">3.3. Identification</a></li>
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<li><a href="#org0c30c61">3.1. Load Data</a></li>
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<li><a href="#org0975d17">3.2. Excitation and Measured Signals</a></li>
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<li><a href="#org516cfff">3.3. Identification</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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<hr>
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<p>This report is also available as a <a href="./test-bench-encoder.pdf">pdf</a>.</p>
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<hr>
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<p>
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In this document, we wish to study the use of an encoder in parallel with an Amplified Piezoelectric Actuator.
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@ -49,23 +52,23 @@ In this document, we wish to study the use of an encoder in parallel with an Amp
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The document is divided into the following Sections:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org4c85aef">1</a>: the test-bench used is described</li>
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<li>Section <a href="#org088f993">2</a>: the noise spectral density of the encoder is estimated</li>
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<li>Section <a href="#org077ed39">3</a>: the dynamics from the amplified piezoelectric actuator to the encoder measured displacement is identified</li>
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<li>Section <a href="#org3940fb3">1</a>: the test-bench used is described</li>
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<li>Section <a href="#orgdef31f1">2</a>: the noise spectral density of the encoder is estimated</li>
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<li>Section <a href="#orgb7d0942">3</a>: the dynamics from the amplified piezoelectric actuator to the encoder measured displacement is identified</li>
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</ul>
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<div id="outline-container-org3c3af3a" class="outline-2">
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<h2 id="org3c3af3a"><span class="section-number-2">1</span> Experimental Setup</h2>
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<div id="outline-container-org4f09976" class="outline-2">
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<h2 id="org4f09976"><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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<a id="org4c85aef"></a>
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<a id="org3940fb3"></a>
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</p>
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<p>
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The experimental Setup is schematically represented in Figure <a href="#org87d981b">1</a>.
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The experimental Setup is schematically represented in Figure <a href="#org124732f">1</a>.
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</p>
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<div class="note" id="org217bb34">
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<div class="note" id="org5402283">
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<p>
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Here are the equipment used in the test bench:
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</p>
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@ -85,21 +88,21 @@ The displacement of the mass (relative to the mechanical frame) is measured both
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</p>
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<div id="org87d981b" class="figure">
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<div id="org124732f" 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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<div id="org4703eda" class="figure">
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<div id="org88b06b0" 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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<div id="orgd6a1cee" class="figure">
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<div id="orga02fdc7" 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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@ -107,11 +110,11 @@ 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-orgdb3277a" class="outline-2">
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<h2 id="orgdb3277a"><span class="section-number-2">2</span> Noise Spectral Density of the Encoder</h2>
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<div id="outline-container-org5bbb12a" class="outline-2">
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<h2 id="org5bbb12a"><span class="section-number-2">2</span> Noise Spectral Density of the Encoder</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org088f993"></a>
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<a id="orgdef31f1"></a>
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</p>
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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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@ -123,8 +126,8 @@ 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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<div id="outline-container-org81a5e5f" class="outline-3">
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<h3 id="org81a5e5f"><span class="section-number-3">2.1</span> Load Data</h3>
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<div id="outline-container-org91e2f9a" class="outline-3">
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<h3 id="org91e2f9a"><span class="section-number-3">2.1</span> Load Data</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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The measurement data are loaded and the offset are removed using the <code>detrend</code> command.
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@ -143,22 +146,22 @@ The measurement data are loaded and the offset are removed using the <code>detre
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</div>
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</div>
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<div id="outline-container-orgbed7f20" class="outline-3">
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<h3 id="orgbed7f20"><span class="section-number-3">2.2</span> Time Domain Results</h3>
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<div id="outline-container-org9392d29" class="outline-3">
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<h3 id="org9392d29"><span class="section-number-3">2.2</span> Time Domain Results</h3>
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<div class="outline-text-3" id="text-2-2">
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<p>
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The measurement of both the encoder and interferometer are shown in Figure <a href="#orgad4a9af">4</a>.
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The measurement of both the encoder and interferometer are shown in Figure <a href="#orgcdebd06">4</a>.
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</p>
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<div id="orgad4a9af" class="figure">
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<div id="orgcdebd06" class="figure">
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<p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Huddle test - Time domain signals</p>
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</div>
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<p>
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The raw signals are filtered with a Low Pass filter (defined below) such that we can see the low frequency motion (Figure <a href="#orgc981fe9">5</a>).
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The raw signals are filtered with a Low Pass filter (defined below) such that we can see the low frequency motion (Figure <a href="#org53d6d3d">5</a>).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"> G_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10);
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@ -166,7 +169,7 @@ The raw signals are filtered with a Low Pass filter (defined below) such that we
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</div>
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<div id="orgc981fe9" class="figure">
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<div id="org53d6d3d" class="figure">
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<p><img src="figs/huddle_test_time_domain_filtered.png" alt="huddle_test_time_domain_filtered.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Huddle test - Time domain signals filtered with a LPF at 10Hz</p>
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@ -174,8 +177,8 @@ The raw signals are filtered with a Low Pass filter (defined below) such that we
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</div>
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</div>
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<div id="outline-container-org319de75" class="outline-3">
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<h3 id="org319de75"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
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<div id="outline-container-org998b458" class="outline-3">
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<h3 id="org998b458"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
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<div class="outline-text-3" id="text-2-3">
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<p>
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The noise of the measurement (supposing there is no motion) is now translated in the frequency domain by computed the Amplitude Spectral Density.
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@ -191,7 +194,7 @@ The noise of the measurement (supposing there is no motion) is now translated in
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</div>
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<p>
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The comparison of the ASD of the encoder and interferometer are shown in Figure <a href="#orgeae7d8d">6</a>.
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The comparison of the ASD of the encoder and interferometer are shown in Figure <a href="#orgcb0713e">6</a>.
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</p>
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<p>
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@ -199,7 +202,7 @@ It is clear that although the encoder exhibit higher frequency noise, is it more
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</p>
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<div id="orgeae7d8d" class="figure">
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<div id="orgcb0713e" class="figure">
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<p><img src="figs/huddle_test_asd.png" alt="huddle_test_asd.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signals during the Huddle test</p>
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@ -208,19 +211,19 @@ It is clear that although the encoder exhibit higher frequency noise, is it more
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</div>
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</div>
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<div id="outline-container-orgb1ca2cf" class="outline-2">
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<h2 id="orgb1ca2cf"><span class="section-number-2">3</span> Dynamics from Actuator to Encoder</h2>
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<div id="outline-container-org3ede191" class="outline-2">
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<h2 id="org3ede191"><span class="section-number-2">3</span> Dynamics from Actuator to Encoder</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org077ed39"></a>
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<a id="orgb7d0942"></a>
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</p>
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<p>
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Now the dynamics from the force actuator to the measurement by the encoder is identified.
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</p>
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</div>
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<div id="outline-container-orgfa505d1" class="outline-3">
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<h3 id="orgfa505d1"><span class="section-number-3">3.1</span> Load Data</h3>
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<div id="outline-container-org0c30c61" class="outline-3">
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<h3 id="org0c30c61"><span class="section-number-3">3.1</span> Load Data</h3>
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<div class="outline-text-3" id="text-3-1">
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<p>
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As usual, the measurement data are loaded.
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@ -253,18 +256,18 @@ Finally the offset are removed using the <code>detrend</code> command.
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</div>
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</div>
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<div id="outline-container-org3f21900" class="outline-3">
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<h3 id="org3f21900"><span class="section-number-3">3.2</span> Excitation and Measured Signals</h3>
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<div id="outline-container-org0975d17" class="outline-3">
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<h3 id="org0975d17"><span class="section-number-3">3.2</span> Excitation and Measured Signals</h3>
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<div class="outline-text-3" id="text-3-2">
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<p>
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The excitation signal is a white noise filtered by a low pass filter to not excite too much the high frequency modes.
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</p>
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<p>
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The excitation signal is shown in Figure <a href="#orgf417c0d">7</a>.
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The excitation signal is shown in Figure <a href="#org2a39907">7</a>.
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</p>
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<div id="orgf417c0d" class="figure">
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<div id="org2a39907" class="figure">
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<p><img src="figs/encoder_identification_excitation_time.png" alt="encoder_identification_excitation_time.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Excitation Voltage</p>
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@ -274,7 +277,7 @@ The excitation signal is shown in Figure <a href="#orgf417c0d">7</a>.
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The measured motion by the interferometer and encoder is shown in Figure
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</p>
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<div id="orgb870b1e" class="figure">
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<div id="org928216c" class="figure">
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<p><img src="figs/encoder_identification_motion.png" alt="encoder_identification_motion.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>Measured displacement by the encoder and interferometer</p>
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@ -282,8 +285,8 @@ The measured motion by the interferometer and encoder is shown in Figure
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</div>
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</div>
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<div id="outline-container-org0b79009" class="outline-3">
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<h3 id="org0b79009"><span class="section-number-3">3.3</span> Identification</h3>
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<div id="outline-container-org516cfff" class="outline-3">
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<h3 id="org516cfff"><span class="section-number-3">3.3</span> Identification</h3>
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<div class="outline-text-3" id="text-3-3">
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<p>
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Now the dynamics from the voltage sent to the voltage amplitude driving the APA95ML to the measured displacement by both the encoder and interferometer are computed.
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@ -302,23 +305,23 @@ Now the dynamics from the voltage sent to the voltage amplitude driving the APA9
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</div>
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<p>
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The obtained coherence is shown in Figure <a href="#orgd2811d2">9</a>.
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The obtained coherence is shown in Figure <a href="#org5941eaf">9</a>.
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It is shown that the identification is good until 500Hz for the interferometer and until 1kHz for the encoder.
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</p>
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<div id="orgd2811d2" class="figure">
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<div id="org5941eaf" class="figure">
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<p><img src="figs/identification_dynamics_coherence.png" alt="identification_dynamics_coherence.png" />
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</p>
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<p><span class="figure-number">Figure 9: </span>Obtained coherence for both the encoder and interferometer</p>
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</div>
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<p>
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The compared dynamics as measured by the intereferometer and encoder are shown in Figure <a href="#org7032434">10</a>.
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The compared dynamics as measured by the intereferometer and encoder are shown in Figure <a href="#orgae9e5a6">10</a>.
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</p>
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<div id="org7032434" class="figure">
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<div id="orgae9e5a6" class="figure">
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<p><img src="figs/identification_dynamics_bode.png" alt="identification_dynamics_bode.png" />
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</p>
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<p><span class="figure-number">Figure 10: </span>Obtained dynamics from actuator voltage to displacement as measured by the interferometer and by the encoder</p>
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@ -16,7 +16,6 @@
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#+LaTeX_CLASS: scrreprt
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#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
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#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
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#+EXPORT_FILE_NAME: test-bench-pd200.tex
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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:END:
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#+begin_export html
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<hr>
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<p>This report is also available as a <a href="./test-bench-encoder.pdf">pdf</a>.</p>
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<hr>
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#+end_export
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* Introduction :ignore:
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In this document, we wish to study the use of an encoder in parallel with an Amplified Piezoelectric Actuator.
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