From 30177e48092d9d38f8e0bfb00ade1c0443d0bb08 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 4 Feb 2021 20:23:22 +0100 Subject: [PATCH 1/2] Update with last measured encoder --- figs/vionic_noise_asd.pdf | Bin 541953 -> 628262 bytes figs/vionic_noise_asd.png | Bin 85396 -> 88795 bytes figs/vionic_noise_asd_model.pdf | Bin 626862 -> 713001 bytes figs/vionic_noise_asd_model.png | Bin 87082 -> 88002 bytes figs/vionic_noise_raw_lpf.pdf | Bin 73552 -> 73552 bytes figs/vionic_noise_time.pdf | Bin 283481 -> 325385 bytes figs/vionic_noise_time.png | Bin 53877 -> 58469 bytes test-bench-vionic.html | 119 ++++++++++++++------------------ test-bench-vionic.org | 69 ++++++++---------- test-bench-vionic.pdf | Bin 1435951 -> 2811902 bytes 10 files changed, 83 insertions(+), 105 deletions(-) diff --git a/figs/vionic_noise_asd.pdf b/figs/vionic_noise_asd.pdf index a5b8ffda35763a35af42fc84e64760fd92c6cab3..caf57193694cdace445065cbefe2fa222b416462 100644 GIT binary patch delta 263030 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zsfc)}HDcgw{q{n1?v4tqb6iU`;));42H|bt<`vg_@pMvw_CsZOr0oLAS*omCODlD%@}N3YlbLOOany4R;7?{-q}HnWsek~5=; zjx&zaA|SmeHq^8_P3VSTEH7s9TB_G2o}m7P-$Ln{a}QB|CtA$odx?HEqyDVK<{S(5 zz1t&jI{D*z@c7GCFjgh@N`$h+nVta)JWy)XtgIMBl23((08tC5(e#L@D`Z=zxE{?a zVFVMly3|F;LPKD-FI)%=n^j=@X=zbxcL8nvM`F$&VwjjhWh+F7{PF|&9j%5K@XLKeko~Y_!=P1R5s^o4 zrh_j)w?sIj51I3D1VbFD5mzgHo0+9$1l*tyUOu;eW()WyK`hncV2V_=r#phzu@Ocg z{`&5CwWN3&j&nf5sRqjQXUT>`elqa)P|m2W+2xUboEjR9 -
+

encoder_vionic.png

Figure 1: Picture of the Vionic Encoder

@@ -106,8 +106,8 @@ In particular, we would like to measure:
  • 7: 2YJ313
  • -
    -

    1 Encoder Model

    +
    +

    1 Encoder Model

    The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\). @@ -119,27 +119,27 @@ It is also characterized by its measurement noise \(n\) that can be described by

    -The model of the encoder is shown in Figure 2. +The model of the encoder is shown in Figure 2.

    -
    +

    encoder-model-schematic.png

    Figure 2: Model of the Encoder

    -We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure 4. +We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure 4.

    -
    +

    encoder-model-schematic-with-asd.png

    - +
    @@ -184,7 +184,7 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
    Table 1: Characteristics of the Vionic Encoder
    -
    +

    vionic_expected_noise.png

    Figure 4: Expected interpolation errors for the Vionic Encoder

    @@ -193,15 +193,15 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
    -
    -

    2 Noise Measurement

    +
    +

    2 Noise Measurement

    - +

    -
    -

    2.1 Test Bench

    +
    +

    2.1 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. @@ -210,48 +210,35 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\).

    -
    -

    2.2 Results

    +
    +

    2.2 Results

    First we load the data. -

    -
    -
    %% Load Data
    -enc1 = load('noise_meas_100s_20kHz_1.mat', 't', 'x');
    -enc2 = load('noise_meas_100s_20kHz_2.mat', 't', 'x');
    -enc3 = load('noise_meas_100s_20kHz_3.mat', 't', 'x');
    -enc4 = load('noise_meas_100s_20kHz_4.mat', 't', 'x');
    -enc6 = load('noise_meas_100s_20kHz_6.mat', 't', 'x');
    -enc7 = load('noise_meas_100s_20kHz_7.mat', 't', 'x');
    -
    -
    - -

    -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 5. +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 5.

    -
    +

    vionic_noise_raw_lpf.png

    Figure 5: Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)

    -The time domain data for all the encoders are compared in Figure 6. +The time domain data for all the encoders are compared in Figure 6.

    -
    +

    vionic_noise_time.png

    Figure 6: Comparison of the time domain measurement

    -The amplitude spectral density is computed and shown in Figure 7. +The amplitude spectral density is computed and shown in Figure 7.

    -
    +

    vionic_noise_asd.png

    Figure 7: Amplitude Spectral Density of the measured signal

    @@ -266,11 +253,11 @@ Let’s create a transfer function that approximate the measured noise of th

    -The amplitude of the transfer function and the measured ASD are shown in Figure 8. +The amplitude of the transfer function and the measured ASD are shown in Figure 8.

    -
    +

    vionic_noise_asd_model.png

    Figure 8: Measured ASD of the noise and modelled one

    @@ -279,15 +266,15 @@ The amplitude of the transfer function and the measured ASD are shown in Figure
    -
    -

    3 Linearity Measurement

    +
    +

    3 Linearity Measurement

    - +

    -
    -

    3.1 Test Bench

    +
    +

    3.1 Test Bench

    In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity. @@ -296,7 +283,7 @@ An actuator should also be there so impose a displacement.

    -One idea is to use the test-bench shown in Figure 9. +One idea is to use the test-bench shown in Figure 9.

    @@ -309,7 +296,7 @@ As the interferometer has a very large bandwidth, we should be able to estimate

    -
    +

    test_bench_encoder_calibration.png

    Figure 9: Schematic of the test bench

    @@ -317,30 +304,30 @@ As the interferometer has a very large bandwidth, we should be able to estimate
    -
    -

    3.2 Results

    +
    +

    3.2 Results

    -
    -

    4 Dynamical Measurement

    +
    +

    4 Dynamical Measurement

    - +

    -
    -

    4.1 Test Bench

    +
    +

    4.1 Test Bench

    -
    -

    4.2 Results

    +
    +

    4.2 Results

    Author: Dehaeze Thomas

    -

    Created: 2021-02-03 mer. 11:20

    +

    Created: 2021-02-04 jeu. 20:23

    diff --git a/test-bench-vionic.org b/test-bench-vionic.org index bb6fed7..8c11682 100644 --- a/test-bench-vionic.org +++ b/test-bench-vionic.org @@ -173,32 +173,27 @@ addpath('./mat/'); ** Results First we load the data. -#+begin_src matlab -%% Load Data -enc1 = load('noise_meas_100s_20kHz_1.mat', 't', 'x'); -enc2 = load('noise_meas_100s_20kHz_2.mat', 't', 'x'); -enc3 = load('noise_meas_100s_20kHz_3.mat', 't', 'x'); -enc4 = load('noise_meas_100s_20kHz_4.mat', 't', 'x'); -enc6 = load('noise_meas_100s_20kHz_6.mat', 't', 'x'); -enc7 = load('noise_meas_100s_20kHz_7.mat', 't', 'x'); +#+begin_src matlab :exports none +%% Load all the measurements +enc = {}; +for i = 1:7 + enc(i) = {load(['mat/noise_meas_100s_20kHz_' num2str(i) '.mat'], 't', 'x')}; +end #+end_src #+begin_src matlab :exports none %% Remove initial offset -enc1.x = enc1.x - mean(enc1.x(1:1000)); -enc2.x = enc2.x - mean(enc2.x(1:1000)); -enc3.x = enc3.x - mean(enc3.x(1:1000)); -enc4.x = enc4.x - mean(enc4.x(1:1000)); -enc6.x = enc6.x - mean(enc6.x(1:1000)); -enc7.x = enc7.x - mean(enc7.x(1:1000)); +for i = 1:7 + enc{i}.x = enc{i}.x - mean(enc{i}.x(1:1000)); +end #+end_src 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 [[fig:vionic_noise_raw_lpf]]. #+begin_src matlab :exports none figure; hold on; -plot(enc1.t, 1e9*enc1.x, '.', 'DisplayName', 'Enc 1 - Raw'); -plot(enc1.t, 1e9*lsim(1/(1 + s/2/pi/10), enc1.x, enc1.t), '-', 'DisplayName', 'Enc 1 - LPF'); +plot(enc{1}.t, 1e9*enc{1}.x, '.', 'DisplayName', 'Enc 1 - Raw'); +plot(enc{1}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{1}.x, enc{1}.t), '-', 'DisplayName', 'Enc 1 - LPF'); hold off; xlabel('Time [s]'); ylabel('Displacement [nm]'); @@ -218,12 +213,10 @@ The time domain data for all the encoders are compared in Figure [[fig:vionic_no #+begin_src matlab :exports none figure; hold on; -plot(enc1.t, 1e9*lsim(1/(1 + s/2/pi/10), enc1.x, enc1.t), '.', 'DisplayName', 'Enc 1'); -plot(enc2.t, 1e9*lsim(1/(1 + s/2/pi/10), enc2.x, enc2.t), '.', 'DisplayName', 'Enc 2'); -plot(enc3.t, 1e9*lsim(1/(1 + s/2/pi/10), enc3.x, enc3.t), '.', 'DisplayName', 'Enc 3'); -plot(enc4.t, 1e9*lsim(1/(1 + s/2/pi/10), enc4.x, enc4.t), '.', 'DisplayName', 'Enc 4'); -plot(enc6.t, 1e9*lsim(1/(1 + s/2/pi/10), enc6.x, enc6.t), '.', 'DisplayName', 'Enc 6'); -plot(enc7.t, 1e9*lsim(1/(1 + s/2/pi/10), enc7.x, enc7.t), '.', 'DisplayName', 'Enc 7'); +for i=1:7 + plot(enc{i}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{i}.x, enc{i}.t), '.', ... + 'DisplayName', sprintf('Enc %i', i)); +end hold off; xlabel('Time [s]'); ylabel('Displacement [nm]'); @@ -248,23 +241,22 @@ Fs = 1/Ts; % Hannning Windows win = hanning(ceil(0.5/Ts)); -[p1, f] = pwelch(enc1.x, win, [], [], Fs); -[p2, ~] = pwelch(enc2.x, win, [], [], Fs); -[p3, ~] = pwelch(enc3.x, win, [], [], Fs); -[p4, ~] = pwelch(enc4.x, win, [], [], Fs); -[p6, ~] = pwelch(enc6.x, win, [], [], Fs); -[p7, ~] = pwelch(enc7.x, win, [], [], Fs); +[pxx, f] = pwelch(enc{1}.x, win, [], [], Fs); +enc{1}.pxx = pxx; + +for i=2:7 + [pxx, ~] = pwelch(enc{i}.x, win, [], [], Fs); + enc{i}.pxx = pxx; +end #+end_src #+begin_src matlab :exports none figure; hold on; -plot(f, sqrt(p1), 'DisplayName', 'Enc 1'); -plot(f, sqrt(p2), 'DisplayName', 'Enc 2'); -plot(f, sqrt(p3), 'DisplayName', 'Enc 3'); -plot(f, sqrt(p4), 'DisplayName', 'Enc 4'); -plot(f, sqrt(p6), 'DisplayName', 'Enc 6'); -plot(f, sqrt(p7), 'DisplayName', 'Enc 7'); +for i=1:7 + plot(f, sqrt(enc{i}.pxx), ... + 'DisplayName', sprintf('Enc %i', i)); +end set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]'); xlim([10, Fs/2]); @@ -292,11 +284,10 @@ The amplitude of the transfer function and the measured ASD are shown in Figure figure; hold on; plot(f, sqrt(p1), 'color', [0, 0, 0, 0.5], 'DisplayName', '$\Gamma_n(\omega)$'); -plot(f, sqrt(p2), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off'); -plot(f, sqrt(p3), 'color', [0, 0, 0, 0.5], 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z%$GP04dM zdvnT(U*0T%u}52V-?^`1rsH&=_BhotK7zJbm>;8Zyo~Y=iEX7jn(a>KVM-c|LR>r!CjsD)}<^_Y42-V*$%KhM_D~sHjsc0`=#Cw9>sI INu!|u0mUNO?*IS* literal 0 HcmV?d00001 diff --git a/test-bench-vionic.html b/test-bench-vionic.html index 5596bad..3b934bf 100644 --- a/test-bench-vionic.html +++ b/test-bench-vionic.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Encoder Renishaw Vionic - Test Bench @@ -39,23 +39,22 @@

      Table of Contents

      @@ -65,9 +64,9 @@

      This report is also available as a pdf.


      -
      +

      -You can find below the document of: +You can find below the documentation of:

      • Vionic Encoder
      • @@ -77,70 +76,81 @@ You can find below the document of:

      -We would like to characterize the encoder measurement system. -

      - -

      +In this document, we wish to characterize the performances of the encoder measurement system. In particular, we would like to measure:

        -
      • Power Spectral Density of the measurement noise
      • -
      • Bandwidth of the sensor
      • -
      • Linearity of the sensor
      • +
      • the measurement noise
      • +
      • the linearity of the sensor
      • +
      • the bandwidth of the sensor
      +

      +This document is structured as follow: +

      +
        +
      • Section 1: the expected performance of the Vionic encoder system are described
      • +
      • Section 2: a simple model of the encoder is developed
      • +
      • Section 3: the noise of the encoder is measured and a model of the noise is identified
      • +
      • Section 4: the linearity of the sensor is estimated
      • +
      -
      +
      +

      1 Expected Performances

      +
      +

      + +

      + +

      +The Vionic encoder is shown in Figure 1. +

      + + +

      encoder_vionic.png

      Figure 1: Picture of the Vionic Encoder

      -
        -
      • 1: 2YA275
      • -
      • 2: 2YA274
      • -
      • 3: 2YA273
      • -
      • 4: 2YA270
      • -
      • 5: 2YA272
      • -
      • 6: 2YA271
      • -
      • 7: 2YJ313
      • -
      - -
      -

      1 Encoder Model

      -

      -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. +From the Renishaw website: +

      +
      +

      +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. +The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector. +Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals. +These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining bandwidth to beyond 500 kHz.

      -It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD). +Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure ultra-low Sub-Divisional Error (SDE) of typically \(<\pm 15\, nm\).

      -The model of the encoder is shown in Figure 2. +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. +Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve jitter of just 1.6 nm RMS. +

      +
      + +

      +The expected interpolation errors (non-linearity) is shown in Figure 2.

      -
      -

      encoder-model-schematic.png +

      +

      vionic_expected_noise.png

      -

      Figure 2: Model of the Encoder

      +

      Figure 2: Expected interpolation errors for the Vionic Encoder

      -We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure 4. +The characteristics as advertise in the manual as well as our specifications are shown in Table 1.

      - -
      -

      encoder-model-schematic-with-asd.png -

      -
      - - - +
      Table 1: Characteristics of the Vionic Encoder
      +@@ -153,56 +163,93 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi - + - - - - - - - - - - - - - - + + - - + + + + + + + + + + + + + + + + + + + +
      Table 1: Characteristics of the Vionic compared with the specifications
      Characteristics ManualSpecificationsSpecification
      RangeRuler length> 200 [um]
      Resolution2.5 [nm]< 50 [nm rms]
      Sub-Divisional Error\(< \pm 15\,nm\)Time Delay  < 0.5 ms
      BandwidthTo be checked> 5 [kHz]> 500 kHz> 5 kHz
      Noise< 1.6 nm rms< 50 nm rms
      Linearity< +/- 15 nm 
      RangeRuler length> 200 um
      - - -
      -

      vionic_expected_noise.png -

      -

      Figure 4: Expected interpolation errors for the Vionic Encoder

      -
      - -
      -

      2 Noise Measurement

      +
      +

      2 Encoder Model

      - + +

      + +

      +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. +

      + +

      +It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD) \(\Gamma_n(\omega)\). +

      + +

      +The model of the encoder is shown in Figure 3. +

      + + +
      +

      encoder-model-schematic.png +

      +

      Figure 3: Model of the Encoder

      +
      + +

      +We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure 2. +

      + + +
      +

      encoder-model-schematic-with-asd.png

      -
      -

      2.1 Test Bench

      -
      +
      +
      + +
      +

      3 Noise Measurement

      +
      +

      + +

      +
      +
      +

      3.1 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 \(n\). @@ -210,40 +257,62 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\).

      -
      -

      2.2 Results

      -
      +
      +

      3.2 Thermal drifts

      +
      +
        +
      • [ ] picture of the setup
      • +
      • [ ] long thermal drifts
      • +
      • [ ] once stabilize, look at the noise
      • +
      • [ ] compute low frequency ASD (may still be thermal drifts of the mechanics and not noise)
      • +
      +
      +
      + +
      +

      3.3 Time Domain signals

      +

      First we load the data. -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 5. +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 5.

      -
      +

      vionic_noise_raw_lpf.png

      Figure 5: Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)

      -The time domain data for all the encoders are compared in Figure 6. +The time domain data for all the encoders are compared in Figure 6.

      -
      +

      vionic_noise_time.png

      Figure 6: Comparison of the time domain measurement

      +
      +
      +
      +

      3.4 Noise Spectral Density

      +

      -The amplitude spectral density is computed and shown in Figure 7. +The amplitude spectral density is computed and shown in Figure 7.

      -
      +

      vionic_noise_asd.png

      Figure 7: Amplitude Spectral Density of the measured signal

      +
      +
      +
      +

      3.5 Noise Model

      +

      Let’s create a transfer function that approximate the measured noise of the encoder.

      @@ -253,29 +322,49 @@ Let’s create a transfer function that approximate the measured noise of th

      -The amplitude of the transfer function and the measured ASD are shown in Figure 8. +The amplitude of the transfer function and the measured ASD are shown in Figure 8.

      -
      +

      vionic_noise_asd_model.png

      -

      Figure 8: Measured ASD of the noise and modelled one

      +

      Figure 8: Measured ASD of the noise and modeled one

      +
      +
      +
      + +
      +

      3.6 Validity of the noise model

      +
      +

      +The cumulative amplitude spectrum is now computed and shown in Figure 9. +

      + +

      +We can see that the Root Mean Square value of the measurement noise is \(\approx 1.6 \, nm\) as advertise in the datasheet. +

      + + +
      +

      vionic_noise_cas_model.png +

      +

      Figure 9: Meassured CAS of the noise and modeled one

      -
      -

      3 Linearity Measurement

      -
      +
      +

      4 Linearity Measurement

      +

      - +

      -
      -

      3.1 Test Bench

      -
      +
      +

      4.1 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. @@ -283,7 +372,7 @@ An actuator should also be there so impose a displacement.

      -One idea is to use the test-bench shown in Figure 9. +One idea is to use the test-bench shown in Figure 10.

      @@ -296,38 +385,22 @@ As the interferometer has a very large bandwidth, we should be able to estimate

      -
      +

      test_bench_encoder_calibration.png

      -

      Figure 9: Schematic of the test bench

      +

      Figure 10: Schematic of the test bench

      -
      -

      3.2 Results

      -
      -
      - -
      -

      4 Dynamical Measurement

      -
      -

      - -

      -
      -
      -

      4.1 Test Bench

      -
      - -
      -

      4.2 Results

      +
      +

      4.2 Results

      Author: Dehaeze Thomas

      -

      Created: 2021-02-04 jeu. 20:23

      +

      Created: 2021-02-10 mer. 15:14

      diff --git a/test-bench-vionic.org b/test-bench-vionic.org index 8c11682..6332d4c 100644 --- a/test-bench-vionic.org +++ b/test-bench-vionic.org @@ -49,36 +49,75 @@ * Introduction :ignore: #+begin_note -You can find below the document of: +You can find below the documentation of: - [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic Encoder]] - [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Linear Scale]] #+end_note -We would like to characterize the encoder measurement system. - +In this document, we wish to characterize the performances of the encoder measurement system. In particular, we would like to measure: -- Power Spectral Density of the measurement noise -- Bandwidth of the sensor -- Linearity of the sensor +- the measurement noise +- the linearity of the sensor +- the bandwidth of the sensor + +This document is structured as follow: +- Section [[sec:vionic_expected_performances]]: the expected performance of the Vionic encoder system are described +- Section [[sec:encoder_model]]: a simple model of the encoder is developed +- Section [[sec:noise_measurement]]: the noise of the encoder is measured and a model of the noise is identified +- Section [[sec:linearity_measurement]]: the linearity of the sensor is estimated + +* Expected Performances +<> + +The Vionic encoder is shown in Figure [[fig:encoder_vionic]]. #+name: fig:encoder_vionic #+caption: Picture of the Vionic Encoder #+attr_latex: :width 0.6\linewidth [[file:figs/encoder_vionic.png]] -- 1: 2YA275 -- 2: 2YA274 -- 3: 2YA273 -- 4: 2YA270 -- 5: 2YA272 -- 6: 2YA271 -- 7: 2YJ313 +From the Renishaw [[https://www.renishaw.com/en/how-optical-encoders-work--36979][website]]: +#+begin_quote +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. +The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector. +Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals. +These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining *bandwidth to beyond 500 kHz*. + +Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure *ultra-low Sub-Divisional Error (SDE) of typically* $<\pm 15\, nm$. + +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. +Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve *jitter of just 1.6 nm RMS*. +#+end_quote + +The expected interpolation errors (non-linearity) is shown in Figure [[fig:vionic_expected_noise]]. + +#+name: fig:vionic_expected_noise +#+attr_latex: :width \linewidth +#+caption: Expected interpolation errors for the Vionic Encoder +[[file:./figs/vionic_expected_noise.png]] + +The characteristics as advertise in the manual as well as our specifications are shown in Table [[tab:vionic_characteristics]]. + +#+name: tab:vionic_characteristics +#+caption: Characteristics of the Vionic compared with the specifications +#+attr_latex: :environment tabularx :width 0.6\linewidth :align lcc +#+attr_latex: :center t :booktabs t :float t +| | | | +| *Characteristics* | *Manual* | *Specification* | +|-------------------+--------------+-----------------| +| Time Delay | | < 0.5 ms | +| Bandwidth | > 500 kHz | > 5 kHz | +| Noise | < 1.6 nm rms | < 50 nm rms | +| Linearity | < +/- 15 nm | | +| Range | Ruler length | > 200 um | * Encoder Model +<> + 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. -It is also characterized by its measurement noise $n$ that can be described by its Power Spectral Density (PSD). +It is also characterized by its measurement noise $n$ that can be described by its Power Spectral Density (PSD) $\Gamma_n(\omega)$. The model of the encoder is shown in Figure [[fig:encoder-model-schematic]]. @@ -128,24 +167,6 @@ We can also use a transfer function $G_n(s)$ to shape a noise $\tilde{n}$ with u #+RESULTS: [[file:figs/encoder-model-schematic-with-asd.png]] -#+name: tab:vionic_characteristics_manual -#+caption: Characteristics of the Vionic Encoder -#+attr_latex: :environment tabularx :width \linewidth :align lXX -#+attr_latex: :center t :booktabs t :float t -| | | | -| *Characteristics* | *Manual* | *Specifications* | -|----------------------+----------------+------------------| -| Range | Ruler length | > 200 [um] | -| Resolution | 2.5 [nm] | < 50 [nm rms] | -| Sub-Divisional Error | $< \pm 15\,nm$ | | -| 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]] - - * Noise Measurement <> ** Test Bench @@ -171,7 +192,13 @@ addpath('./matlab/'); addpath('./mat/'); #+end_src -** Results +** TODO Thermal drifts +- [ ] picture of the setup +- [ ] long thermal drifts +- [ ] once stabilize, look at the noise +- [ ] compute low frequency ASD (may still be thermal drifts of the mechanics and not noise) + +** Time Domain signals First we load the data. #+begin_src matlab :exports none %% Load all the measurements @@ -232,10 +259,11 @@ exportFig('figs/vionic_noise_time.pdf', 'width', 'wide', 'height', 'normal'); #+RESULTS: [[file:figs/vionic_noise_time.png]] +** Noise Spectral Density The amplitude spectral density is computed and shown in Figure [[fig:vionic_noise_asd]]. #+begin_src matlab :exports none % Compute sampling Frequency -Ts = (enc1.t(end) - enc1.t(1))/(length(enc1.t)-1); +Ts = (enc{1}.t(end) - enc{1}.t(1))/(length(enc{1}.t)-1); Fs = 1/Ts; % Hannning Windows @@ -273,6 +301,8 @@ exportFig('figs/vionic_noise_asd.pdf', 'width', 'wide', 'height', 'normal'); #+RESULTS: [[file:figs/vionic_noise_asd.png]] +** Noise Model + Let's create a transfer function that approximate the measured noise of the encoder. #+begin_src matlab Gn_e = 1.8e-11/(1 + s/2/pi/1e4); @@ -302,10 +332,48 @@ exportFig('figs/vionic_noise_asd_model.pdf', 'width', 'wide', 'height', 'normal' #+end_src #+name: fig:vionic_noise_asd_model -#+caption: Measured ASD of the noise and modelled one +#+caption: Measured ASD of the noise and modeled one #+RESULTS: [[file:figs/vionic_noise_asd_model.png]] +** Validity of the noise model +The cumulative amplitude spectrum is now computed and shown in Figure [[fig:vionic_noise_cas_model]]. + +We can see that the Root Mean Square value of the measurement noise is $\approx 1.6 \, nm$ as advertise in the datasheet. + +#+begin_src matlab :exports none +for i = 1:7 + enc{i}.CPS = flip(-cumtrapz(flip(f), flip(enc{i}.pxx))); +end + +CAS_Gn = flip(-cumtrapz(flip(f), flip(abs(squeeze(freqresp(Gn_e, f, 'Hz'))).^2))); +#+end_src + +#+begin_src matlab :exports none +figure; +hold on; +plot(f, sqrt(enc{1}.CPS), 'color', [0, 0, 0, 0.5], 'DisplayName', '$CAS_n(\omega)$'); +for i=2:7 + plot(f, sqrt(enc{i}.CPS), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off'); +end +plot(f, sqrt(CAS_Gn), 'r-', 'DisplayName', 'model'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('CPS [$m$]'); +xlim([10, Fs/2]); +ylim([1e-10, 1e-8]); +legend('location', 'northeast'); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/vionic_noise_cas_model.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:vionic_noise_cas_model +#+caption: Meassured CAS of the noise and modeled one +#+RESULTS: +[[file:figs/vionic_noise_cas_model.png]] + * Linearity Measurement <> ** Test Bench @@ -344,26 +412,3 @@ addpath('./mat/'); ** Results -* Dynamical Measurement -<> -** Test Bench - -** Matlab Init :noexport:ignore: -#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var 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