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511 lines
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<title>Encoder Renishaw Vionic - Test Bench</title>
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Encoder Renishaw Vionic - Test Bench</h1>
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<div id="table-of-contents">
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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="#orgfa3d11e">1. Expected Performances</a></li>
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<li><a href="#orgf23b21b">2. Encoder Model</a></li>
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<li><a href="#org9c17913">3. Noise Measurement</a>
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<ul>
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<li><a href="#orgb9429ef">3.1. Test Bench</a></li>
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<li><a href="#orgd9c9c77">3.2. Thermal drifts</a></li>
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<li><a href="#org8ec1ba2">3.3. Time Domain signals</a></li>
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<li><a href="#org833451c">3.4. Noise Spectral Density</a></li>
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<li><a href="#org71a7d07">3.5. Noise Model</a></li>
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</ul>
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</li>
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<li><a href="#org61522ff">4. Linearity Measurement</a>
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<ul>
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<li><a href="#orge455e25">4.1. Test Bench</a></li>
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<li><a href="#orgc6e5044">4.2. Results</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-vionic.pdf">pdf</a>.</p>
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<hr>
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<div class="note" id="orge01a92a">
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<p>
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You can find below the documentation of:
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</p>
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<ul class="org-ul">
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<li><a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Vionic Encoder</a></li>
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<li><a href="doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf">Linear Scale</a></li>
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</ul>
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</div>
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<p>
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In this document, we wish to characterize the performances of the encoder measurement system.
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In particular, we would like to measure:
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</p>
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<ul class="org-ul">
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<li>the measurement noise</li>
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<li>the linearity of the sensor</li>
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<li>the bandwidth of the sensor</li>
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</ul>
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<p>
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This document is structured as follow:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org5ddac7d">1</a>: the expected performance of the Vionic encoder system are described</li>
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<li>Section <a href="#org55cdc69">2</a>: a simple model of the encoder is developed</li>
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<li>Section <a href="#orgb828c8d">3</a>: the noise of the encoder is measured and a model of the noise is identified</li>
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<li>Section <a href="#org49975c3">4</a>: the linearity of the sensor is estimated</li>
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</ul>
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<div id="outline-container-orgfa3d11e" class="outline-2">
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<h2 id="orgfa3d11e"><span class="section-number-2">1</span> Expected Performances</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org5ddac7d"></a>
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</p>
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<p>
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The Vionic encoder is shown in Figure <a href="#orga0ecb6c">1</a>.
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</p>
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<div id="orga0ecb6c" class="figure">
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<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
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</div>
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<p>
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From the Renishaw <a href="https://www.renishaw.com/en/how-optical-encoders-work--36979">website</a>:
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</p>
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<blockquote>
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<p>
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The VIONiC encoder features the third generation of Renishaw’s unique filtering optics that average the contributions from many scale periods and effectively filter out non-periodic features such as dirt.
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The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector.
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Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals.
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These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining <b>bandwidth to beyond 500 kHz</b>.
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</p>
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<p>
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Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure <b>ultra-low Sub-Divisional Error (SDE) of typically</b> \(<\pm 15\, nm\).
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</p>
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<p>
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This evolution of filtering optics, combined with carefully-selected electronics, provide incremental signals with wide bandwidth achieving a maximum speed of 12 m/s with the lowest positional jitter (noise) of any encoder in its class.
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Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve <b>jitter of just 1.6 nm RMS</b>.
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</p>
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</blockquote>
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<p>
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The expected interpolation errors (non-linearity) is shown in Figure <a href="#orgc38e53f">2</a>.
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</p>
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<div id="orgc38e53f" class="figure">
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<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Expected interpolation errors for the Vionic Encoder</p>
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</div>
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<p>
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The characteristics as advertise in the manual as well as our specifications are shown in Table <a href="#org091f419">1</a>.
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</p>
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<table id="org091f419" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic compared with the specifications</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-center" />
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<col class="org-center" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"><b>Characteristics</b></th>
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<th scope="col" class="org-center"><b>Manual</b></th>
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<th scope="col" class="org-center"><b>Specification</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Time Delay</td>
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<td class="org-center">< 10 ns</td>
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<td class="org-center">< 0.5 ms</td>
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</tr>
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<tr>
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<td class="org-left">Bandwidth</td>
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<td class="org-center">> 500 kHz</td>
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<td class="org-center">> 5 kHz</td>
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</tr>
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<tr>
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<td class="org-left">Noise</td>
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<td class="org-center">< 1.6 nm rms</td>
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<td class="org-center">< 50 nm rms</td>
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</tr>
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<tr>
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<td class="org-left">Linearity</td>
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<td class="org-center">< +/- 15 nm</td>
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<td class="org-center"> </td>
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</tr>
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<tr>
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<td class="org-left">Range</td>
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<td class="org-center">Ruler length</td>
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<td class="org-center">> 200 um</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-orgf23b21b" class="outline-2">
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<h2 id="orgf23b21b"><span class="section-number-2">2</span> Encoder Model</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org55cdc69"></a>
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</p>
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<p>
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The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\).
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Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
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</p>
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<p>
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It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD) \(\Gamma_n(\omega)\).
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</p>
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<p>
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The model of the encoder is shown in Figure <a href="#org4fdb73a">3</a>.
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</p>
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<div id="org4fdb73a" class="figure">
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<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Model of the Encoder</p>
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</div>
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<p>
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We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure <a href="#orgc38e53f">2</a>.
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</p>
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<div id="org793433f" class="figure">
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<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
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</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org9c17913" class="outline-2">
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<h2 id="org9c17913"><span class="section-number-2">3</span> Noise Measurement</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="orgb828c8d"></a>
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</p>
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<p>
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This part is structured as follow:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org8cfb922">3.1</a>: the measurement bench is described</li>
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<li>Section <a href="#orgfd5ce06">3.2</a>: long measurement is performed to estimate the low frequency drifts in the measurement</li>
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<li>Section <a href="#org4df45c5">3.3</a>: high frequency measurements are performed to estimate the high frequency noise</li>
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<li>Section <a href="#orgd464562">3.4</a>: the Spectral density of the measurement noise is estimated</li>
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<li>Section <a href="#orgd6ec52a">3.5</a>: finally, the measured noise is modeled</li>
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</ul>
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</div>
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<div id="outline-container-orgb9429ef" class="outline-3">
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<h3 id="orgb9429ef"><span class="section-number-3">3.1</span> Test Bench</h3>
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<div class="outline-text-3" id="text-3-1">
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<p>
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<a id="org8cfb922"></a>
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</p>
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<p>
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To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
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Then, the measured signal \(y_m\) corresponds to the noise \(n\).
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</p>
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<p>
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The measurement bench is shown in Figures <a href="#org4037996">5</a> and <a href="#org06e2754">6</a>.
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Note that the bench is then covered with a “plastic bubble sheet” in order to keep disturbances as small as possible.
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</p>
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<div id="org4037996" class="figure">
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<p><img src="figs/IMG_20210211_170554.jpg" alt="IMG_20210211_170554.jpg" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Top view picture of the measurement bench</p>
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</div>
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<div id="org06e2754" class="figure">
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<p><img src="figs/IMG_20210211_170607.jpg" alt="IMG_20210211_170607.jpg" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Side view picture of the measurement bench</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgd9c9c77" class="outline-3">
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<h3 id="orgd9c9c77"><span class="section-number-3">3.2</span> Thermal drifts</h3>
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<div class="outline-text-3" id="text-3-2">
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<p>
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<a id="orgfd5ce06"></a>
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Measured displacement were recording during approximately 40 hours with a sample frequency of 100Hz.
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A first order low pass filter with a corner frequency of 1Hz
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">enc_l = load(<span class="org-string">'mat/noise_meas_40h_100Hz_1.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
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</pre>
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</div>
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<p>
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The measured time domain data are shown in Figure <a href="#org1454db4">7</a>.
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</p>
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<div id="org1454db4" class="figure">
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<p><img src="figs/vionic_drifts_time.png" alt="vionic_drifts_time.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Measured thermal drifts</p>
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</div>
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<p>
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The measured data seems to experience a constant drift after approximately 20 hour.
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Let’s estimate this drift.
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</p>
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<pre class="example">
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The mean drift is approximately 60.9 [nm/hour] or 1.0 [nm/min]
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</pre>
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<p>
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Comparison between the data and the linear fit is shown in Figure <a href="#orgfbe5f53">8</a>.
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</p>
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<div id="orgfbe5f53" class="figure">
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<p><img src="figs/vionic_drifts_linear_fit.png" alt="vionic_drifts_linear_fit.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>Measured drift and linear fit</p>
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</div>
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<p>
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Let’s now estimate the Power Spectral Density of the measured displacement.
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The obtained low frequency ASD is shown in Figure <a href="#org42f3fad">9</a>.
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</p>
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<div id="org42f3fad" class="figure">
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<p><img src="figs/vionic_noise_asd_low_freq.png" alt="vionic_noise_asd_low_freq.png" />
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</p>
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<p><span class="figure-number">Figure 9: </span>Amplitude Spectral density of the measured displacement</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org8ec1ba2" class="outline-3">
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<h3 id="org8ec1ba2"><span class="section-number-3">3.3</span> Time Domain signals</h3>
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<div class="outline-text-3" id="text-3-3">
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<p>
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<a id="org4df45c5"></a>
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</p>
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<p>
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Then, and for all the 7 encoders, we record the measured motion during 100s with a sampling frequency of 20kHz.
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</p>
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<p>
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The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure <a href="#org28ad5da">10</a>.
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</p>
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<div id="org28ad5da" class="figure">
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<p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" />
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</p>
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<p><span class="figure-number">Figure 10: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</p>
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</div>
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<p>
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The time domain data for all the encoders are compared in Figure <a href="#org1656541">11</a>.
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</p>
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<p>
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We can see some drifts that are in the order of few nm to 20nm per minute.
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As shown in Section <a href="#orgfd5ce06">3.2</a>, these drifts should diminish over time down to 1nm/min.
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</p>
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<div id="org1656541" class="figure">
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<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
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</p>
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<p><span class="figure-number">Figure 11: </span>Comparison of the time domain measurement</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org833451c" class="outline-3">
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<h3 id="org833451c"><span class="section-number-3">3.4</span> Noise Spectral Density</h3>
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<div class="outline-text-3" id="text-3-4">
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<p>
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<a id="orgd464562"></a>
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</p>
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<p>
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The amplitude spectral densities for all the encoder are computed and shown in Figure <a href="#org7e93bb1">12</a>.
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</p>
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<div id="org7e93bb1" class="figure">
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<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
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</p>
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<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the measured signal</p>
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</div>
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<p>
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We can combine these measurements with the low frequency noise computed in Section <a href="#orgfd5ce06">3.2</a>.
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The obtained ASD is shown in Figure <a href="#org7e54160">13</a>.
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</p>
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<div id="org7e54160" class="figure">
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<p><img src="figs/vionic_noise_asd_combined.png" alt="vionic_noise_asd_combined.png" />
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</p>
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<p><span class="figure-number">Figure 13: </span>Combined low frequency and high frequency noise measurements</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org71a7d07" class="outline-3">
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<h3 id="org71a7d07"><span class="section-number-3">3.5</span> Noise Model</h3>
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<div class="outline-text-3" id="text-3-5">
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<p>
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<a id="orgd6ec52a"></a>
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</p>
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<p>
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Let’s create a transfer function that approximate the measured noise of the encoder.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Gn_e = 1.8e<span class="org-type">-</span>11<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>1e4);
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</pre>
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</div>
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<p>
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The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org5d39757">14</a>.
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</p>
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<div id="org5d39757" class="figure">
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<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
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</p>
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<p><span class="figure-number">Figure 14: </span>Measured ASD of the noise and modeled one</p>
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</div>
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<p>
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The cumulative amplitude spectrum is now computed and shown in Figure <a href="#org05b258c">15</a>.
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</p>
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<p>
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We can see that the Root Mean Square value of the measurement noise is \(\approx 1.6 \, nm\) as advertise in the datasheet.
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</p>
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<div id="org05b258c" class="figure">
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<p><img src="figs/vionic_noise_cas_model.png" alt="vionic_noise_cas_model.png" />
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</p>
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<p><span class="figure-number">Figure 15: </span>Meassured CAS of the noise and modeled one</p>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org61522ff" class="outline-2">
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<h2 id="org61522ff"><span class="section-number-2">4</span> Linearity Measurement</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="org49975c3"></a>
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</p>
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</div>
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|
<div id="outline-container-orge455e25" class="outline-3">
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<h3 id="orge455e25"><span class="section-number-3">4.1</span> Test Bench</h3>
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<div class="outline-text-3" id="text-4-1">
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<p>
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|
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
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An interferometer or capacitive sensor should work fine.
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An actuator should also be there so impose a displacement.
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</p>
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<p>
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One idea is to use the test-bench shown in Figure <a href="#org177aa2c">16</a>.
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</p>
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<p>
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|
The APA300ML is used to excite the mass in a broad bandwidth.
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|
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
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</p>
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<p>
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As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder if it is less than the Nyquist frequency that can be around 10kHz.
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</p>
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<div id="org177aa2c" class="figure">
|
|
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
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|
</p>
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|
<p><span class="figure-number">Figure 16: </span>Schematic of the test bench</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgc6e5044" class="outline-3">
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<h3 id="orgc6e5044"><span class="section-number-3">4.2</span> Results</h3>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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|
<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2021-02-12 ven. 18:26</p>
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</div>
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</body>
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</html>
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