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After Width: | Height: | Size: 27 KiB |
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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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<!-- 2021-02-02 mar. 18:24 -->
|
||||
<!-- 2021-02-02 mar. 18:44 -->
|
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Encoder Renishaw Vionic - Test Bench</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@ -39,19 +39,33 @@
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgd4a4664">1. Encoder Model</a></li>
|
||||
<li><a href="#org8e70edd">2. Test-Bench Description</a></li>
|
||||
<li><a href="#orge118b0f">3. Measurement procedure</a></li>
|
||||
<li><a href="#org8e44240">4. Measurement Results</a>
|
||||
<li><a href="#orgad23dda">1. Encoder Model</a></li>
|
||||
<li><a href="#org6337f06">2. Noise Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#org7e465e7">4.1. Noise Measurement</a></li>
|
||||
<li><a href="#orgc20e5d1">2.1. Test Bench</a></li>
|
||||
<li><a href="#org818aa3a">2.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgfb293f3">3. Linearity Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#orgee55e64">3.1. Test Bench</a></li>
|
||||
<li><a href="#org53d1667">3.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org1f03c19">4. Dynamical Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#org2650123">4.1. Test Bench</a></li>
|
||||
<li><a href="#org26f79d3">4.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<hr>
|
||||
<p>This report is also available as a <a href="./index.pdf">pdf</a>.</p>
|
||||
<hr>
|
||||
|
||||
<div class="note" id="org4c0c9be">
|
||||
<div class="note" id="org7fbf5f9">
|
||||
<p>
|
||||
You can find below the document of:
|
||||
</p>
|
||||
@ -76,14 +90,14 @@ In particular, we would like to measure:
|
||||
</ul>
|
||||
|
||||
|
||||
<div id="org13fff85" class="figure">
|
||||
<div id="org136f1cc" class="figure">
|
||||
<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd4a4664" class="outline-2">
|
||||
<h2 id="orgd4a4664"><span class="section-number-2">1</span> Encoder Model</h2>
|
||||
<div id="outline-container-orgad23dda" class="outline-2">
|
||||
<h2 id="orgad23dda"><span class="section-number-2">1</span> Encoder Model</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\).
|
||||
@ -95,18 +109,27 @@ It is also characterized by its measurement noise \(n\) that can be described by
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The model of the encoder is shown in Figure <a href="#org08a4e7a">2</a>.
|
||||
The model of the encoder is shown in Figure <a href="#orgb95c9f6">2</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org08a4e7a" class="figure">
|
||||
<div id="orgb95c9f6" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
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="#org9d20614">4</a>.
|
||||
</p>
|
||||
|
||||
<table id="org20ed9a5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
<div id="org985a473" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<table id="orgcd45716" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -151,104 +174,57 @@ The model of the encoder is shown in Figure <a href="#org08a4e7a">2</a>.
|
||||
</table>
|
||||
|
||||
|
||||
<div id="org2068d11" class="figure">
|
||||
<div id="org9d20614" class="figure">
|
||||
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Expected interpolation errors for the Vionic Encoder</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Expected interpolation errors for the Vionic Encoder</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org8e70edd" class="outline-2">
|
||||
<h2 id="org8e70edd"><span class="section-number-2">2</span> Test-Bench Description</h2>
|
||||
<div id="outline-container-org6337f06" class="outline-2">
|
||||
<h2 id="org6337f06"><span class="section-number-2">2</span> Noise Measurement</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org93db977"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgc20e5d1" class="outline-3">
|
||||
<h3 id="orgc20e5d1"><span class="section-number-3">2.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
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.
|
||||
Then, the measured signal \(y_m\) corresponds to the noise \(n\).
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org818aa3a" class="outline-3">
|
||||
<h3 id="org818aa3a"><span class="section-number-3">2.2</span> Results</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
|
||||
An interferometer or capacitive sensor should work fine.
|
||||
An actuator should also be there so impose a displacement.
|
||||
First we load the data.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
One idea is to use the test-bench shown in Figure <a href="#orgfefda93">4</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The APA300ML is used to excite the mass in a broad bandwidth.
|
||||
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder is it is less than the Nyquist frequency (~ 5kHz).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgfefda93" class="figure">
|
||||
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Schematic of the test bench</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
To measure the noise of the sensor, we can also simply measure the output signal when the relative motion between the encoder and the ruler is null.
|
||||
This can be done by clamping the two as done in the mounting strut tool (Figure <a href="#org742c647">5</a>).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org742c647" class="figure">
|
||||
<p><img src="figs/test_bench_measure_noise.png" alt="test_bench_measure_noise.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Mounting Strut test bench as a clamping method to measure the encoder noise.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge118b0f" class="outline-2">
|
||||
<h2 id="orge118b0f"><span class="section-number-2">3</span> Measurement procedure</h2>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8e44240" class="outline-2">
|
||||
<h2 id="org8e44240"><span class="section-number-2">4</span> Measurement Results</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org7e465e7" class="outline-3">
|
||||
<h3 id="org7e465e7"><span class="section-number-3">4.1</span> Noise Measurement</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">'noise_meas_100s_20kHz.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
|
||||
x = x <span class="org-type">-</span> mean(x);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
hold on;
|
||||
plot(t, 1e9<span class="org-type">*</span>x, <span class="org-string">'.'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Raw'</span>);
|
||||
plot(t, 1e9<span class="org-type">*</span>lsim(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>500), x, t), <span class="org-string">'DisplayName'</span>, <span class="org-string">'LPF - 500Hz'</span>)
|
||||
hold off;
|
||||
xlabel(<span class="org-string">'Time [s]'</span>);
|
||||
ylabel(<span class="org-string">'Displacement [nm]'</span>);
|
||||
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org3070d03" class="figure">
|
||||
<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
|
||||
<p>
|
||||
The time domain data are shown in Figure <a href="#orgb5a687f">4</a>.
|
||||
</p>
|
||||
<p>
|
||||
<img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
|
||||
The amplitude spectral density is computed and shown in Figure <a href="#org5702aa0">5</a>.
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Time domain measurement (raw data and low pass filtered data)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd593081" class="figure">
|
||||
<div id="org5702aa0" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the measured signal</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signal</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@ -259,19 +235,81 @@ Let’s create a transfer function that approximate the measured noise of th
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#orgbbcd196">6</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgd1f9fd9" class="figure">
|
||||
|
||||
<div id="orgbbcd196" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Measured ASD of the noise and modelled one</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Measured ASD of the noise and modelled one</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgfb293f3" class="outline-2">
|
||||
<h2 id="orgfb293f3"><span class="section-number-2">3</span> Linearity Measurement</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org0812023"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgee55e64" class="outline-3">
|
||||
<h3 id="orgee55e64"><span class="section-number-3">3.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
|
||||
An interferometer or capacitive sensor should work fine.
|
||||
An actuator should also be there so impose a displacement.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
One idea is to use the test-bench shown in Figure <a href="#org00b4ff5">7</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The APA300ML is used to excite the mass in a broad bandwidth.
|
||||
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
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.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org00b4ff5" class="figure">
|
||||
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Schematic of the test bench</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org53d1667" class="outline-3">
|
||||
<h3 id="org53d1667"><span class="section-number-3">3.2</span> Results</h3>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1f03c19" class="outline-2">
|
||||
<h2 id="org1f03c19"><span class="section-number-2">4</span> Dynamical Measurement</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="org02907d6"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org2650123" class="outline-3">
|
||||
<h3 id="org2650123"><span class="section-number-3">4.1</span> Test Bench</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org26f79d3" class="outline-3">
|
||||
<h3 id="org26f79d3"><span class="section-number-3">4.2</span> Results</h3>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-02-02 mar. 18:24</p>
|
||||
<p class="date">Created: 2021-02-02 mar. 18:44</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
134
index.org
134
index.org
@ -16,6 +16,7 @@
|
||||
#+LaTeX_CLASS: scrreprt
|
||||
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
|
||||
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
|
||||
#+EXPORT_FILE_NAME: test-bench-vionic.tex
|
||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||
#+PROPERTY: header-args:matlab+ :comments org
|
||||
@ -40,6 +41,12 @@
|
||||
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
|
||||
:END:
|
||||
|
||||
#+begin_export html
|
||||
<hr>
|
||||
<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
|
||||
<hr>
|
||||
#+end_export
|
||||
|
||||
* Introduction :ignore:
|
||||
|
||||
#+begin_note
|
||||
@ -57,6 +64,7 @@ In particular, we would like to measure:
|
||||
|
||||
#+name: fig:encoder_vionic
|
||||
#+caption: Picture of the Vionic Encoder
|
||||
#+attr_latex: :width 0.6\linewidth
|
||||
[[file:figs/encoder_vionic.png]]
|
||||
|
||||
* Encoder Model
|
||||
@ -89,6 +97,29 @@ The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
|
||||
#+RESULTS:
|
||||
[[file:figs/encoder-model-schematic.png]]
|
||||
|
||||
We can also use a transfer function $G_n(s)$ to shape a noise $\tilde{n}$ with unity ASD as shown in Figure [[fig:vionic_expected_noise]].
|
||||
|
||||
#+begin_src latex :file encoder-model-schematic-with-asd.pdf
|
||||
\begin{tikzpicture}
|
||||
\node[block] (G) at (0,0){$G_m(s)$};
|
||||
\node[addb, left=0.8 of G] (add){};
|
||||
\node[block, above=0.5 of add] (Gn) {$G_n(s)$};
|
||||
|
||||
\draw[<-] (add.west) -- ++(-1.0, 0) node[above right]{$y$};
|
||||
\draw[->] (add.east) -- (G.west);
|
||||
\draw[->] (G.east) -- ++(1.0, 0) node[above left]{$y_m$};
|
||||
\draw[->] (Gn.south) -- (add.north) node[above right]{$n$};
|
||||
\draw[<-] (Gn.north) -- ++(0, 0.6) node[below right](n){$\tilde{n}$};
|
||||
|
||||
\begin{scope}[on background layer]
|
||||
\node[fit={(Gn.west|-G.south) (n.north-|G.east)}, inner sep=8pt, draw, dashed, fill=black!20!white] (P) {};
|
||||
\node[below left] at (P.north east) {Encoder};
|
||||
\end{scope}
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
[[file:figs/encoder-model-schematic-with-asd.png]]
|
||||
|
||||
#+name: tab:vionic_characteristics_manual
|
||||
#+caption: Characteristics of the Vionic Encoder
|
||||
@ -103,42 +134,19 @@ The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
|
||||
| Bandwidth | To be checked | > 5 [kHz] |
|
||||
|
||||
#+name: fig:vionic_expected_noise
|
||||
#+attr_latex: :width \linewidth
|
||||
#+caption: Expected interpolation errors for the Vionic Encoder
|
||||
[[file:./figs/vionic_expected_noise.png]]
|
||||
|
||||
|
||||
* Test-Bench Description
|
||||
* Noise Measurement
|
||||
<<sec:noise_measurement>>
|
||||
** Test Bench
|
||||
|
||||
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.
|
||||
Then, the measured signal $y_m$ corresponds to the noise $n$.
|
||||
|
||||
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
|
||||
An interferometer or capacitive sensor should work fine.
|
||||
An actuator should also be there so impose a displacement.
|
||||
|
||||
One idea is to use the test-bench shown in Figure [[fig:test_bench_encoder_calibration]].
|
||||
|
||||
The APA300ML is used to excite the mass in a broad bandwidth.
|
||||
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
|
||||
|
||||
As the interferometer has a very large bandwidth, we should be able to estimate the bandwidth of the encoder is it is less than the Nyquist frequency (~ 5kHz).
|
||||
|
||||
#+name: fig:test_bench_encoder_calibration
|
||||
#+caption: Schematic of the test bench
|
||||
[[file:figs/test_bench_encoder_calibration.png]]
|
||||
|
||||
To measure the noise of the sensor, we can also simply measure the output signal when the relative motion between the encoder and the ruler is null.
|
||||
This can be done by clamping the two as done in the mounting strut tool (Figure [[fig:test_bench_measure_noise]]).
|
||||
|
||||
#+name: fig:test_bench_measure_noise
|
||||
#+caption: Mounting Strut test bench as a clamping method to measure the encoder noise.
|
||||
[[file:figs/test_bench_measure_noise.png]]
|
||||
|
||||
* Measurement procedure
|
||||
|
||||
* Measurement Results
|
||||
** Noise Measurement
|
||||
*** Matlab Init :noexport:ignore:
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
@ -156,13 +164,15 @@ addpath('./matlab/');
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
*** Analysis :ignore:
|
||||
** Results
|
||||
First we load the data.
|
||||
#+begin_src matlab
|
||||
load('noise_meas_100s_20kHz.mat', 't', 'x');
|
||||
x = x - mean(x);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
The time domain data are shown in Figure [[fig:vionic_noise_time]].
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(t, 1e9*x, '.', 'DisplayName', 'Raw');
|
||||
@ -181,6 +191,7 @@ exportFig('figs/vionic_noise_time.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+caption: Time domain measurement (raw data and low pass filtered data)
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_time.png]]
|
||||
The amplitude spectral density is computed and shown in Figure [[fig:vionic_noise_asd]].
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
% Compute sampling Frequency
|
||||
@ -218,6 +229,8 @@ Let's create a transfer function that approximate the measured noise of the enco
|
||||
Gn_e = 1.8e-11/(1 + s/2/pi/5e3);
|
||||
#+end_src
|
||||
|
||||
The amplitude of the transfer function and the measured ASD are shown in Figure [[fig:vionic_noise_asd_model]].
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
@ -238,3 +251,64 @@ exportFig('figs/vionic_noise_asd_model.pdf', 'width', 'wide', 'height', 'normal'
|
||||
#+caption: Measured ASD of the noise and modelled one
|
||||
#+RESULTS:
|
||||
[[file:figs/vionic_noise_asd_model.png]]
|
||||
* Linearity Measurement
|
||||
<<sec:linearity_measurement>>
|
||||
** Test Bench
|
||||
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
|
||||
An interferometer or capacitive sensor should work fine.
|
||||
An actuator should also be there so impose a displacement.
|
||||
|
||||
One idea is to use the test-bench shown in Figure [[fig:test_bench_encoder_calibration]].
|
||||
|
||||
The APA300ML is used to excite the mass in a broad bandwidth.
|
||||
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
|
||||
|
||||
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.
|
||||
|
||||
#+name: fig:test_bench_encoder_calibration
|
||||
#+caption: Schematic of the test bench
|
||||
[[file:figs/test_bench_encoder_calibration.png]]
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('./matlab/mat/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
** Results
|
||||
|
||||
* Dynamical Measurement
|
||||
<<sec:dynamical_measurement>>
|
||||
** Test Bench
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('./matlab/mat/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
** Results
|
||||
|
||||
315
test-bench-vionic.html
Normal file
315
test-bench-vionic.html
Normal file
@ -0,0 +1,315 @@
|
||||
<?xml version="1.0" encoding="utf-8"?>
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2021-02-02 mar. 18:46 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Encoder Renishaw Vionic - Test Bench</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
<meta name="author" content="Dehaeze Thomas" />
|
||||
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||||
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||||
<script>
|
||||
MathJax = {
|
||||
svg: {
|
||||
scale: 1,
|
||||
fontCache: "global"
|
||||
},
|
||||
tex: {
|
||||
tags: "ams",
|
||||
multlineWidth: "%MULTLINEWIDTH",
|
||||
tagSide: "right",
|
||||
macros: {bm: ["\\boldsymbol{#1}",1],},
|
||||
tagIndent: ".8em"
|
||||
}
|
||||
};
|
||||
</script>
|
||||
<script id="MathJax-script" async
|
||||
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
|
||||
</head>
|
||||
<body>
|
||||
<div id="org-div-home-and-up">
|
||||
<a accesskey="h" href="../index.html"> UP </a>
|
||||
|
|
||||
<a accesskey="H" href="../index.html"> HOME </a>
|
||||
</div><div id="content">
|
||||
<h1 class="title">Encoder Renishaw Vionic - Test Bench</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#org3a55927">1. Encoder Model</a></li>
|
||||
<li><a href="#orgde74ebc">2. Noise Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#org835e359">2.1. Test Bench</a></li>
|
||||
<li><a href="#org52a3f6f">2.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orge941dff">3. Linearity Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#orga2e857a">3.1. Test Bench</a></li>
|
||||
<li><a href="#orgc7f59c3">3.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org42e063d">4. Dynamical Measurement</a>
|
||||
<ul>
|
||||
<li><a href="#org4e0f29a">4.1. Test Bench</a></li>
|
||||
<li><a href="#orgb2f1f77">4.2. Results</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
<hr>
|
||||
<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
|
||||
<hr>
|
||||
|
||||
<div class="note" id="orgf92d65f">
|
||||
<p>
|
||||
You can find below the document of:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li><a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Vionic Encoder</a></li>
|
||||
<li><a href="doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf">Linear Scale</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We would like to characterize the encoder measurement system.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In particular, we would like to measure:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Power Spectral Density of the measurement noise</li>
|
||||
<li>Bandwidth of the sensor</li>
|
||||
<li>Linearity of the sensor</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<div id="orgddb4738" class="figure">
|
||||
<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3a55927" class="outline-2">
|
||||
<h2 id="org3a55927"><span class="section-number-2">1</span> Encoder Model</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\).
|
||||
Ideally, this dynamics is constant over a wide frequency band with very small phase drop.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The model of the encoder is shown in Figure <a href="#orga0a431c">2</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga0a431c" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
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="#org70392dd">4</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org27d4d98" class="figure">
|
||||
<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<table id="org212ba69" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption>
|
||||
|
||||
<colgroup>
|
||||
<col class="org-left" />
|
||||
|
||||
<col class="org-center" />
|
||||
|
||||
<col class="org-center" />
|
||||
</colgroup>
|
||||
<thead>
|
||||
<tr>
|
||||
<th scope="col" class="org-left"><b>Characteristics</b></th>
|
||||
<th scope="col" class="org-center"><b>Manual</b></th>
|
||||
<th scope="col" class="org-center"><b>Specifications</b></th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-left">Range</td>
|
||||
<td class="org-center">Ruler length</td>
|
||||
<td class="org-center">> 200 [um]</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Resolution</td>
|
||||
<td class="org-center">2.5 [nm]</td>
|
||||
<td class="org-center">< 50 [nm rms]</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Sub-Divisional Error</td>
|
||||
<td class="org-center">\(< \pm 15\,nm\)</td>
|
||||
<td class="org-center"> </td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Bandwidth</td>
|
||||
<td class="org-center">To be checked</td>
|
||||
<td class="org-center">> 5 [kHz]</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
|
||||
<div id="org70392dd" class="figure">
|
||||
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Expected interpolation errors for the Vionic Encoder</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-orgde74ebc" class="outline-2">
|
||||
<h2 id="orgde74ebc"><span class="section-number-2">2</span> Noise Measurement</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="orgcac09c5"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org835e359" class="outline-3">
|
||||
<h3 id="org835e359"><span class="section-number-3">2.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
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.
|
||||
Then, the measured signal \(y_m\) corresponds to the noise \(n\).
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org52a3f6f" class="outline-3">
|
||||
<h3 id="org52a3f6f"><span class="section-number-3">2.2</span> Results</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
First we load the data.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'noise_meas_100s_20kHz.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
|
||||
x = x <span class="org-type">-</span> mean(x);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The time domain data are shown in Figure <a href="#orgc55250e">4</a>.
|
||||
</p>
|
||||
<p>
|
||||
<img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
|
||||
The amplitude spectral density is computed and shown in Figure <a href="#orgfb661b7">5</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgfb661b7" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signal</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Let’s create a transfer function that approximate the measured noise of the encoder.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<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>5e3);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org6d60818">6</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org6d60818" class="figure">
|
||||
<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Measured ASD of the noise and modelled one</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orge941dff" class="outline-2">
|
||||
<h2 id="orge941dff"><span class="section-number-2">3</span> Linearity Measurement</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org0c843ed"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orga2e857a" class="outline-3">
|
||||
<h3 id="orga2e857a"><span class="section-number-3">3.1</span> Test Bench</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
|
||||
An interferometer or capacitive sensor should work fine.
|
||||
An actuator should also be there so impose a displacement.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
One idea is to use the test-bench shown in Figure <a href="#org793dd45">7</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The APA300ML is used to excite the mass in a broad bandwidth.
|
||||
The motion is measured at the same time by the Vionic Encoder and by an interferometer (most likely an Attocube).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
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.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org793dd45" class="figure">
|
||||
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Schematic of the test bench</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc7f59c3" class="outline-3">
|
||||
<h3 id="orgc7f59c3"><span class="section-number-3">3.2</span> Results</h3>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org42e063d" class="outline-2">
|
||||
<h2 id="org42e063d"><span class="section-number-2">4</span> Dynamical Measurement</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="org2b52f4b"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org4e0f29a" class="outline-3">
|
||||
<h3 id="org4e0f29a"><span class="section-number-3">4.1</span> Test Bench</h3>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb2f1f77" class="outline-3">
|
||||
<h3 id="orgb2f1f77"><span class="section-number-3">4.2</span> Results</h3>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-02-02 mar. 18:46</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
BIN
test-bench-vionic.pdf
Normal file
BIN
test-bench-vionic.pdf
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user