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Thomas Dehaeze 2021-02-02 18:46:58 +01:00
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commit 9e38f0bd14
8 changed files with 710 additions and 118 deletions
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2021-02-02 mar. 18:24 --> <!-- 2021-02-02 mar. 18:44 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Encoder Renishaw Vionic - Test Bench</title> <title>Encoder Renishaw Vionic - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -39,19 +39,33 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgd4a4664">1. Encoder Model</a></li> <li><a href="#orgad23dda">1. Encoder Model</a></li>
<li><a href="#org8e70edd">2. Test-Bench Description</a></li> <li><a href="#org6337f06">2. Noise Measurement</a>
<li><a href="#orge118b0f">3. Measurement procedure</a></li>
<li><a href="#org8e44240">4. Measurement Results</a>
<ul> <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> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</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> <p>
You can find below the document of: You can find below the document of:
</p> </p>
@ -76,14 +90,14 @@ In particular, we would like to measure:
</ul> </ul>
<div id="org13fff85" class="figure"> <div id="org136f1cc" class="figure">
<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" /> <p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p> <p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
</div> </div>
<div id="outline-container-orgd4a4664" class="outline-2"> <div id="outline-container-orgad23dda" class="outline-2">
<h2 id="orgd4a4664"><span class="section-number-2">1</span> Encoder Model</h2> <h2 id="orgad23dda"><span class="section-number-2">1</span> Encoder Model</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; displacement \(y\) to measured displacement \(y_m\). The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; 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>
<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> </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><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p> <p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
</div> </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> <caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption>
<colgroup> <colgroup>
@ -151,104 +174,57 @@ The model of the encoder is shown in Figure <a href="#org08a4e7a">2</a>.
</table> </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><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
</p> </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>
</div> </div>
<div id="outline-container-org8e70edd" class="outline-2"> <div id="outline-container-org6337f06" class="outline-2">
<h2 id="org8e70edd"><span class="section-number-2">2</span> Test-Bench Description</h2> <h2 id="org6337f06"><span class="section-number-2">2</span> Noise Measurement</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <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. 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 \(n\). Then, the measured signal \(y_m\) corresponds to the noise \(n\).
</p> </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> <p>
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity. First we load the data.
An interferometer or capacitive sensor should work fine.
An actuator should also be there so impose a displacement.
</p> </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"> <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>); <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); x = x <span class="org-type">-</span> mean(x);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <p>
<pre class="src src-matlab"><span class="org-type">figure</span>; The time domain data are shown in Figure <a href="#orgb5a687f">4</a>.
hold on; </p>
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>); <p>
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>) <img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
hold off; The amplitude spectral density is computed and shown in Figure <a href="#org5702aa0">5</a>.
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> </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><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
</p> </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> </div>
<p> <p>
@ -259,19 +235,81 @@ Let&rsquo;s create a transfer function that approximate the measured noise of th
</pre> </pre>
</div> </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><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
</p> </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> </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>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-02-02 mar. 18:24</p> <p class="date">Created: 2021-02-02 mar. 18:44</p>
</div> </div>
</body> </body>
</html> </html>

134
index.org
View File

@ -16,6 +16,7 @@
#+LaTeX_CLASS: scrreprt #+LaTeX_CLASS: scrreprt
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full] #+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
#+LaTeX_HEADER_EXTRA: \input{preamble.tex} #+LaTeX_HEADER_EXTRA: \input{preamble.tex}
#+EXPORT_FILE_NAME: test-bench-vionic.tex
#+PROPERTY: header-args:matlab :session *MATLAB* #+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org #+PROPERTY: header-args:matlab+ :comments org
@ -40,6 +41,12 @@
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") #+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END: :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: * Introduction :ignore:
#+begin_note #+begin_note
@ -57,6 +64,7 @@ In particular, we would like to measure:
#+name: fig:encoder_vionic #+name: fig:encoder_vionic
#+caption: Picture of the Vionic Encoder #+caption: Picture of the Vionic Encoder
#+attr_latex: :width 0.6\linewidth
[[file:figs/encoder_vionic.png]] [[file:figs/encoder_vionic.png]]
* Encoder Model * Encoder Model
@ -89,6 +97,29 @@ The model of the encoder is shown in Figure [[fig:encoder-model-schematic]].
#+RESULTS: #+RESULTS:
[[file:figs/encoder-model-schematic.png]] [[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 #+name: tab:vionic_characteristics_manual
#+caption: Characteristics of the Vionic Encoder #+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] | | Bandwidth | To be checked | > 5 [kHz] |
#+name: fig:vionic_expected_noise #+name: fig:vionic_expected_noise
#+attr_latex: :width \linewidth
#+caption: Expected interpolation errors for the Vionic Encoder #+caption: Expected interpolation errors for the Vionic Encoder
[[file:./figs/vionic_expected_noise.png]] [[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. 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 $n$. 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. ** Matlab Init :noexport:ignore:
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:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
#+end_src #+end_src
@ -156,13 +164,15 @@ addpath('./matlab/');
addpath('./mat/'); addpath('./mat/');
#+end_src #+end_src
*** Analysis :ignore: ** Results
First we load the data.
#+begin_src matlab #+begin_src matlab
load('noise_meas_100s_20kHz.mat', 't', 'x'); load('noise_meas_100s_20kHz.mat', 't', 'x');
x = x - mean(x); x = x - mean(x);
#+end_src #+end_src
#+begin_src matlab The time domain data are shown in Figure [[fig:vionic_noise_time]].
#+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(t, 1e9*x, '.', 'DisplayName', 'Raw'); 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) #+caption: Time domain measurement (raw data and low pass filtered data)
#+RESULTS: #+RESULTS:
[[file:figs/vionic_noise_time.png]] [[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 #+begin_src matlab :exports none
% Compute sampling Frequency % 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); Gn_e = 1.8e-11/(1 + s/2/pi/5e3);
#+end_src #+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 #+begin_src matlab :exports none
figure; figure;
hold on; 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 #+caption: Measured ASD of the noise and modelled one
#+RESULTS: #+RESULTS:
[[file:figs/vionic_noise_asd_model.png]] [[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
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<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 &ldquo;true&rdquo; 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">&gt; 200 [um]</td>
</tr>
<tr>
<td class="org-left">Resolution</td>
<td class="org-center">2.5 [nm]</td>
<td class="org-center">&lt; 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">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Bandwidth</td>
<td class="org-center">To be checked</td>
<td class="org-center">&gt; 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&rsquo;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>
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