From 7b472d199cb2763158f65d8c89dbd549d89d480e Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 15 Oct 2019 11:01:28 +0200 Subject: [PATCH] Add analysis with LPF --- figs/IMG_20190916_160550.jpg | Bin 0 -> 3804538 bytes figs/IMG_20190916_160600.jpg | Bin 0 -> 3501416 bytes figs/error_4qd_half.pdf | Bin 0 -> 246168 bytes figs/error_4qd_half.png | Bin 0 -> 53193 bytes figs/huddle_test_Va.pdf | Bin 88252 -> 122751 bytes figs/huddle_test_Va.png | Bin 88549 -> 124949 bytes figs/huddle_test_Va_half.pdf | Bin 0 -> 60822 bytes figs/huddle_test_Va_half.png | Bin 0 -> 56089 bytes figs/non-repeatability-parts-half.pdf | Bin 0 -> 4215246 bytes figs/non-repeatability-parts-half.png | Bin 0 -> 71526 bytes figs/repeat_plot_lpf.pdf | Bin 0 -> 1012338 bytes figs/repeat_plot_lpf.png | Bin 0 -> 63374 bytes figs/repeat_plot_raw_half.pdf | Bin 0 -> 1572150 bytes figs/repeat_plot_raw_half.png | Bin 0 -> 35655 bytes figs/repeat_plot_subtract_mean_half.pdf | Bin 0 -> 1617581 bytes 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    -
    -

    10.1 Load Plant

    +
    +

    10.1 Load Plant

    -
    load('mat/plant.mat', 'Gn', 'Gd');
    +
    load('mat/plant.mat', 'Gn', 'Gd');
     
    -
    -

    10.2 Analysis

    +
    +

    10.2 Analysis

    The plant is basically a constant until frequencies up to the required bandwidth. @@ -3142,7 +3166,7 @@ Knv = 1

    -
    +

    loop_gain_newport.png

    Figure 43: Diagonal Loop Gain for the Newport (png, pdf)

    @@ -3150,8 +3174,8 @@ Knv = 1
    -
    -

    10.3 Save

    +
    +

    10.3 Save

    Kn = blkdiag(Knh, Knv);
    @@ -3165,43 +3189,43 @@ The controllers can be downloaded here.
     

    -
    save('mat/K_newport.mat', 'Kn', 'Knd');
    +
    save('mat/K_newport.mat', 'Kn', 'Knd');
     
    -
    -

    11 Measurement of the non-repeatability

    +
    +

    11 Measurement of the non-repeatability

    - +

    The goal here is the measure the non-repeatability of the setup.

    -All sources of error (detailed in the budget error in Section 4) will contribute to the non-repeatability of the system. +All sources of error (detailed in the budget error in Section 4) will contribute to the non-repeatability of the system.

    -
    -

    11.1 Data Load and pre-processing

    +
    +

    11.1 Data Load and pre-processing

    -
    uh = load('mat/data_rep_h.mat', ...
    -     't', 'Uch', 'Ucv', ...
    -     'Unh', 'Unv', ...
    -     'Vph', 'Vpv', ...
    -     'Vnh', 'Vnv', ...
    +
    uh = load('mat/data_rep_h.mat', ...
    +     't', 'Uch', 'Ucv', ...
    +     'Unh', 'Unv', ...
    +     'Vph', 'Vpv', ...
    +     'Vnh', 'Vnv', ...
          'Va');
     
    -uv = load('mat/data_rep_v.mat', ...
    -     't', 'Uch', 'Ucv', ...
    -     'Unh', 'Unv', ...
    -     'Vph', 'Vpv', ...
    -     'Vnh', 'Vnv', ...
    +uv = load('mat/data_rep_v.mat', ...
    +     't', 'Uch', 'Ucv', ...
    +     'Unh', 'Unv', ...
    +     'Vph', 'Vpv', ...
    +     'Vnh', 'Vnv', ...
          'Va');
     
    @@ -3250,11 +3274,11 @@ uv.t = uv.t - uv.t -

    11.2 Some Time domain plots

    +
    +

    11.2 Some Time domain plots

    -
    +

    repeat_time_signals.png

    Figure 44: Time domain Signals for the repeatability measurement (png, pdf)

    @@ -3262,20 +3286,20 @@ uv.t = uv.t - uv.t -

    11.3 Verify Tracking Angle Error

    +
    +

    11.3 Verify Tracking Angle Error

    Let's verify that the positioning error of the beam is small and what could be the effect on the distance measured by the intereferometer.

    -
    load('./mat/plant.mat', 'Gd');
    +
    load('./mat/plant.mat', 'Gd');
     
    -
    +

    repeat_tracking_errors.png

    Figure 45: Tracking errors during the repeatability measurement (png, pdf)

    @@ -3294,7 +3318,7 @@ Let's compute the PSD of the error to see the frequency content.
    -
    +

    psd_tracking_error_rad.png

    Figure 46: Power Spectral Density of the tracking errors (png, pdf)

    @@ -3329,7 +3353,7 @@ with

    -Now, compare that with the PSD of the measured distance by the interferometer (Fig. 47). +Now, compare that with the PSD of the measured distance by the interferometer (Fig. 47).

    [psd_Lh, f] = pwelch(uh.Va, hanning(ceil(1*fs)), [], [], fs);
    @@ -3338,7 +3362,7 @@ Now, compare that with the PSD of the measured distance by the interferometer (F
     
    -
    +

    compare_tracking_error_attocube_meas.png

    Figure 47: Comparison of the effect of tracking error on the measured distance and the measured distance by the Attocube (png, pdf)

    @@ -3353,8 +3377,8 @@ The tracking errors are a limiting factor.
    -
    -

    11.4 Processing

    +
    +

    11.4 Processing

    First, we get the mean value as measured by the interferometer for each value of the Newport angle. @@ -3394,15 +3418,14 @@ And we can compute the RMS value of the non-repeatable part: -

    +

    repeat_plot_raw.png

    Figure 48: Repeatability of the measurement (png, pdf)

    - -
    +

    repeat_plot_subtract_mean.png

    Figure 49: Repeatability of the measurement after subtracting the mean value (png, pdf)

    @@ -3410,8 +3433,8 @@ And we can compute the RMS value of the non-repeatable part:
    -
    -

    11.5 Analysis of the non-repeatable contributions

    +
    +

    11.5 Analysis of the non-repeatable contributions

    Let's know try to determine where does the non-repeatability comes from. @@ -3430,22 +3453,96 @@ We also plot the displacement measured during the huddle test.

    -All the signals are shown on Fig. 50. +All the signals are shown on Fig. 50.

    -
    +

    non-repeatability-parts.png

    Figure 50: Non repeatabilities (png, pdf)

    +
    +

    11.6 Results with a low pass filter

    +
    +

    +We filter the data with a first order low pass filter with a crossover frequency of \(\omega_0\). +

    + +
    +
    w0 = 10; % [Hz]
    +
    +G_lpf = 1/(1 + s/2/pi/w0);
    +
    +uh.Vaf = lsim(G_lpf, uh.Va, uh.t);
    +uv.Vaf = lsim(G_lpf, uv.Va, uv.t);
    +
    +
    +
    +
    + +
    +

    11.7 Processing

    +
    +

    +First, we get the mean value as measured by the interferometer for each value of the Newport angle. +

    +
    +
    Vahm = mean(reshape(uh.Vaf, [fs floor(length(uh.t)/fs)]),2);
    +Unhm = mean(reshape(uh.Unh, [fs floor(length(uh.t)/fs)]),2);
    +
    +Vavm = mean(reshape(uv.Vaf, [fs floor(length(uv.t)/fs)]),2);
    +Unvm = mean(reshape(uv.Unv, [fs floor(length(uv.t)/fs)]),2);
    +
    +
    + +

    +And we can compute the RMS value of the non-repeatable part: +

    + + + +++ ++ + + + + + + + + + + + + +
    Va - Horizontal [nm rms]Va - Vertical [nm rms]
    22.913.9
    + + +
    +

    repeat_plot_lpf.png +

    +

    Figure 51: Repeatability of the measurement (png, pdf)

    +
    + + +
    +

    repeat_plot_subtract_mean_lpf.png +

    +

    Figure 52: Repeatability of the measurement after subtracting the mean value (png, pdf)

    +
    +
    +

    Author: Dehaeze Thomas

    -

    Created: 2019-10-08 mar. 16:18

    +

    Created: 2019-10-15 mar. 11:01

    Validate

    diff --git a/index.org b/index.org index 556f5ef..123b8f7 100644 --- a/index.org +++ b/index.org @@ -18,7 +18,7 @@ #+LATEX_CLASS_OPTIONS: [] #+LATEX_HEADER: \usepackage{minted} -#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/These/LaTeX/}{config.tex}") +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/thesis/latex/}{config.tex}") #+PROPERTY: header-args:latex+ :imagemagick t :fit yes #+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 #+PROPERTY: header-args:latex+ :imoutoptions -quality 100 @@ -1868,36 +1868,54 @@ Multiple measurements are done with different experimental configuration as foll ht_4 = ht_s{4}; #+end_src +** Filter data with low pass filter +We filter the data with a first order low pass filter with a crossover frequency of $\omega_0$. + +#+begin_src matlab + w0 = 50; % [Hz] + + G_lpf = 1/(1 + s/2/pi/w0); + + ht_1.Vaf = lsim(G_lpf, ht_1.Va, ht_1.t); + ht_2.Vaf = lsim(G_lpf, ht_2.Va, ht_2.t); + ht_3.Vaf = lsim(G_lpf, ht_3.Va, ht_3.t); + ht_4.Vaf = lsim(G_lpf, ht_4.Va, ht_4.t); +#+end_src + ** Time domain plots #+begin_src matlab :exports none figure; - ax1 = subaxis(2, 2, 1) + ax1 = subplot(2, 2, 1); hold on; plot(ht_1.t, 1e9*ht_1.Va); + plot(ht_1.t, 1e9*ht_1.Vaf); hold off; ylabel('Displacement [nm]'); set(gca, 'XTickLabel',[]); title('OL'); - ax2 = subaxis(2, 2, 2) + ax2 = subplot(2, 2, 2); hold on; plot(ht_2.t, 1e9*ht_2.Va); + plot(ht_2.t, 1e9*ht_2.Vaf); hold off; set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]); title('OL + CU'); - ax3 = subaxis(2, 2, 3) + ax3 = subplot(2, 2, 3); hold on; plot(ht_3.t, 1e9*ht_3.Va); + plot(ht_3.t, 1e9*ht_3.Vaf); hold off; xlabel('Time [s]'); ylabel('Displacement [nm]'); title('CL + CU'); - ax4 = subaxis(2, 2, 4) + ax4 = subplot(2, 2, 4); hold on; plot(ht_4.t, 1e9*ht_4.Va); + plot(ht_4.t, 1e9*ht_4.Vaf); hold off; xlabel('Time [s]'); set(gca, 'YTickLabel',[]); @@ -1917,7 +1935,7 @@ Multiple measurements are done with different experimental configuration as foll #+begin_src matlab :exports none figure; - ax1 = subaxis(2, 2, 1) + ax1 = subplot(2, 2, 1) hold on; plot(ht_1.t, ht_1.Vph); plot(ht_1.t, ht_1.Vpv); @@ -1926,7 +1944,7 @@ Multiple measurements are done with different experimental configuration as foll set(gca, 'XTickLabel',[]); title('OL'); - ax2 = subaxis(2, 2, 2) + ax2 = subplot(2, 2, 2) hold on; plot(ht_2.t, ht_2.Vph); plot(ht_2.t, ht_2.Vpv); @@ -1935,7 +1953,7 @@ Multiple measurements are done with different experimental configuration as foll set(gca, 'YTickLabel',[]); title('OL + CU'); - ax3 = subaxis(2, 2, 3) + ax3 = subplot(2, 2, 3) hold on; plot(ht_3.t, ht_3.Vph); plot(ht_3.t, ht_3.Vpv); @@ -1944,7 +1962,7 @@ Multiple measurements are done with different experimental configuration as foll ylabel('Voltage [V]'); title('CL + CU'); - ax4 = subaxis(2, 2, 4) + ax4 = subplot(2, 2, 4) hold on; plot(ht_4.t, ht_4.Vph); plot(ht_4.t, ht_4.Vpv); @@ -2784,7 +2802,7 @@ The plant is put in a general configuration as shown in Fig. [[fig:general_contr #+begin_src matlab :exports none figure; % Magnitude - ax1 = subaxis(2,1,1); + ax1 = subplot(2,1,1); hold on; plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'k-'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); @@ -2793,7 +2811,7 @@ The plant is put in a general configuration as shown in Fig. [[fig:general_contr hold off; % Phase - ax2 = subaxis(2,1,2); + ax2 = subplot(2,1,2); hold on; plot(freqs, 180/pi*angle(squeeze(freqresp(G, freqs, 'Hz'))), 'k-'); set(gca,'xscale','log'); @@ -2875,7 +2893,7 @@ The two SISO loop gains are shown in Fig. [[fig:diag_contr_loop_gain]]. #+begin_src matlab :exports none figure; % Magnitude - ax1 = subaxis(2,1,1); + ax1 = subplot(2,1,1); hold on; plot(freqs, abs(squeeze(freqresp(Kh*sys('Rh', 'Uch'), freqs, 'Hz'))), 'DisplayName', '$L_h = K_h G_{d,h}^{-1} G_{\frac{V_{p,h}}{\tilde{U}_{c,h}}} G_{i,h} $'); plot(freqs, abs(squeeze(freqresp(Kv*sys('Rv', 'Ucv'), freqs, 'Hz'))), 'DisplayName', '$L_v = K_v G_{d,v}^{-1} G_{\frac{V_{p,v}}{\tilde{U}_{c,v}}} G_{i,v} $'); @@ -2886,7 +2904,7 @@ The two SISO loop gains are shown in Fig. [[fig:diag_contr_loop_gain]]. legend('location', 'northeast'); % Phase - ax2 = subaxis(2,1,2); + ax2 = subplot(2,1,2); hold on; plot(freqs, 180/pi*angle(squeeze(freqresp(Kh*sys('Rh', 'Uch'), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(Kv*sys('Rv', 'Ucv'), freqs, 'Hz')))); @@ -3329,14 +3347,14 @@ And we can compute the RMS value of the non-repeatable part: figure; ax1 = subplot(1, 2, 1); hold on; - plot(uh.Unh, uh.Va); + plot(uh.Unh, uh.Vaf); plot(Unhm, Vahm) hold off; xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]'); ax2 = subplot(1, 2, 2); hold on; - plot(uv.Unv, uv.Va); + plot(uv.Unv, uv.Vaf); plot(Unvm, Vavm) hold off; xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]'); @@ -3353,18 +3371,17 @@ And we can compute the RMS value of the non-repeatable part: #+CAPTION: Repeatability of the measurement ([[./figs/repeat_plot_raw.png][png]], [[./figs/repeat_plot_raw.pdf][pdf]]) [[file:figs/repeat_plot_raw.png]] - #+begin_src matlab :exports none figure; ax1 = subplot(1, 2, 1); hold on; - plot(uh.Unh, 1e9*(uh.Va - repmat(Vahm, length(uh.t)/length(Vahm),1))); + plot(uh.Unh, 1e9*(uh.Vaf - repmat(Vahm, length(uh.t)/length(Vahm),1))); hold off; xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [nm]'); ax2 = subplot(1, 2, 2); hold on; - plot(uv.Unv, 1e9*(uv.Va - repmat(Vavm, length(uv.t)/length(Vavm),1))); + plot(uv.Unv, 1e9*(uv.Vaf - repmat(Vavm, length(uv.t)/length(Vavm),1))); hold off; xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [nm]'); @@ -3418,6 +3435,24 @@ All the signals are shown on Fig. [[fig:non-repeatability-parts]]. htm = 1e9*ht.Va(1:length(Vaheq)) - repmat(mean(1e9*ht.Va(1:length(Vaheq))), length(uh.t)/length(Vaheq),1); #+end_src +#+begin_src matlab :exports none + figure; + hold on; + plot(uh.Unh, 1e9*(uh.Va - repmat(Vahm, length(uh.t)/length(Vahm),1)), 'DisplayName', 'Measured Non-Repeatability'); + plot(uh.Unh, 1e9*ht.Va(1:length(Vaheq))-mean(1e9*ht.Va(1:length(Vaheq))), 'DisplayName', 'Huddle Test'); + plot(uh.Unh, 1e9*Vaheq, 'DisplayName', 'Due to Sercalo Angle Error'); + hold off; + xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [nm]'); + ylim([-100 100]); + legend(); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/non-repeatability-parts-half.pdf" :var figsize="normal-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + + #+begin_src matlab :exports none figure; ax1 = subplot(1, 2, 1); @@ -3449,3 +3484,89 @@ All the signals are shown on Fig. [[fig:non-repeatability-parts]]. #+NAME: fig:non-repeatability-parts #+CAPTION: Non repeatabilities ([[./figs/non-repeatability-parts.png][png]], [[./figs/non-repeatability-parts.pdf][pdf]]) [[file:figs/non-repeatability-parts.png]] +** Results with a low pass filter +We filter the data with a first order low pass filter with a crossover frequency of $\omega_0$. + +#+begin_src matlab + w0 = 10; % [Hz] + + G_lpf = 1/(1 + s/2/pi/w0); + + uh.Vaf = lsim(G_lpf, uh.Va, uh.t); + uv.Vaf = lsim(G_lpf, uv.Va, uv.t); +#+end_src + +** Processing +First, we get the mean value as measured by the interferometer for each value of the Newport angle. +#+begin_src matlab + Vahm = mean(reshape(uh.Vaf, [fs floor(length(uh.t)/fs)]),2); + Unhm = mean(reshape(uh.Unh, [fs floor(length(uh.t)/fs)]),2); + + Vavm = mean(reshape(uv.Vaf, [fs floor(length(uv.t)/fs)]),2); + Unvm = mean(reshape(uv.Unv, [fs floor(length(uv.t)/fs)]),2); +#+end_src + +And we can compute the RMS value of the non-repeatable part: +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([rms(1e9*(uh.Vaf - repmat(Vahm, length(uh.t)/length(Vahm),1))), rms(1e9*(uv.Vaf - repmat(Vavm, length(uv.t)/length(Vavm),1)))], {}, {'Va - Horizontal [nm rms]', 'Va - Vertical [nm rms]'}, ' %.1f '); +#+end_src + +#+RESULTS: +| Va - Horizontal [nm rms] | Va - Vertical [nm rms] | +|--------------------------+------------------------| +| 22.9 | 13.9 | + +#+begin_src matlab :exports none + figure; + ax1 = subplot(1, 2, 1); + hold on; + plot(uh.Unh, uh.Vaf); + plot(Unhm, Vahm) + hold off; + xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]'); + + ax2 = subplot(1, 2, 2); + hold on; + plot(uv.Unv, uv.Vaf); + plot(Unvm, Vavm) + hold off; + xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]'); + + linkaxes([ax1,ax2],'xy'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/repeat_plot_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:repeat_plot_raw +#+CAPTION: Repeatability of the measurement ([[./figs/repeat_plot_lpf.png][png]], [[./figs/repeat_plot_lpf.pdf][pdf]]) +[[file:figs/repeat_plot_lpf.png]] + +#+begin_src matlab :exports none + figure; + ax1 = subplot(1, 2, 1); + hold on; + plot(uh.Unh, 1e9*(uh.Vaf - repmat(Vahm, length(uh.t)/length(Vahm),1))); + hold off; + xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [nm]'); + + ax2 = subplot(1, 2, 2); + hold on; + plot(uv.Unv, 1e9*(uv.Vaf - repmat(Vavm, length(uv.t)/length(Vavm),1))); + hold off; + xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [nm]'); + + linkaxes([ax1,ax2],'xy'); + ylim([-60 60]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/repeat_plot_subtract_mean_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:repeat_plot_subtract_mean_lpf +#+CAPTION: Repeatability of the measurement after subtracting the mean value ([[./figs/repeat_plot_subtract_mean_lpf.png][png]], [[./figs/repeat_plot_subtract_mean_lpf.pdf][pdf]]) +[[file:figs/repeat_plot_subtract_mean_lpf.png]]

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