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Add analysis of the repeatability test

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Thomas Dehaeze 2019-09-18 16:02:14 +02:00
parent 8af81d3558
commit b0333f3917
2 changed files with 308 additions and 23 deletions
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@ -1856,7 +1856,17 @@ The file =mat/plant.mat= is accessible [[./mat/plant.mat][here]].
figure; bode(sys_cl({'Vph', 'Vpv'}, {'Uch', 'Ucv'}), sys({'Vph', 'Vpv'}, {'Uch', 'Ucv'})) figure; bode(sys_cl({'Vph', 'Vpv'}, {'Uch', 'Ucv'}), sys({'Vph', 'Vpv'}, {'Uch', 'Ucv'}))
#+end_src #+end_src
* TODO Huddle Test * Huddle Test
** 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
** Load data
We load the data taken during the Huddle Test. We load the data taken during the Huddle Test.
#+begin_src matlab #+begin_src matlab
load('mat/data_huddle_test.mat', ... load('mat/data_huddle_test.mat', ...
@ -1868,6 +1878,7 @@ We load the data taken during the Huddle Test.
'Va'); 'Va');
#+end_src #+end_src
** Pre-processing
We remove the first second of data where everything is settling down. We remove the first second of data where everything is settling down.
#+begin_src matlab #+begin_src matlab
t0 = 1; t0 = 1;
@ -1888,11 +1899,12 @@ We remove the first second of data where everything is settling down.
t = t - t(1); % We start at t=0 t = t - t(1); % We start at t=0
#+end_src #+end_src
** Time Domain Data
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(t, Vph, 'DisplayName', '$Vp_h$'); plot(t, Uch, 'DisplayName', '$Vp_h$');
plot(t, Vpv, 'DisplayName', '$Vp_v$'); plot(t, Ucv, 'DisplayName', '$Vp_v$');
hold off; hold off;
xlabel('Time [s]'); xlabel('Time [s]');
ylabel('Amplitude [V]'); ylabel('Amplitude [V]');
@ -1906,7 +1918,7 @@ We compute the Power Spectral Density of the horizontal and vertical positions o
[psd_Vpv, ~] = pwelch(Vpv, hanning(ceil(1*fs)), [], [], fs); [psd_Vpv, ~] = pwelch(Vpv, hanning(ceil(1*fs)), [], [], fs);
#+end_src #+end_src
#+begin_src matlab :results none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(f, sqrt(psd_Vph), 'DisplayName', '$\Gamma_{Vp_h}$'); plot(f, sqrt(psd_Vph), 'DisplayName', '$\Gamma_{Vp_h}$');
@ -1936,7 +1948,7 @@ We compute the Power Spectral Density of the voltage across the inductance used
[psd_Vcv, ~] = pwelch(Vcv, hanning(ceil(1*fs)), [], [], fs); [psd_Vcv, ~] = pwelch(Vcv, hanning(ceil(1*fs)), [], [], fs);
#+end_src #+end_src
#+begin_src matlab :results none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(f, sqrt(psd_Vch), 'DisplayName', '$\Gamma_{Vc_h}$'); plot(f, sqrt(psd_Vch), 'DisplayName', '$\Gamma_{Vc_h}$');
@ -2237,7 +2249,12 @@ The controllers can be downloaded [[./mat/K_newport.mat][here]].
save('mat/K_newport.mat', 'Kn', 'Knd'); save('mat/K_newport.mat', 'Kn', 'Knd');
#+end_src #+end_src
* Measurement of the non-repeatability * Measuement of the non-repeatability
** Introduction :ignore:
- Explanation of the procedure
- List all sources of error and their effects on the Attocube measurement
- Think about how to determine the value of the individual sources of error
** 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) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
@ -2247,37 +2264,305 @@ The controllers can be downloaded [[./mat/K_newport.mat][here]].
<<matlab-init>> <<matlab-init>>
#+end_src #+end_src
#+begin_src matlab
fs = 1e4;
#+end_src
** Data Load ** Data Load
#+begin_src matlab #+begin_src matlab
load('mat/data_rep_1.mat', ... 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', ... 't', 'Uch', 'Ucv', ...
'Unh', 'Unv', ... 'Unh', 'Unv', ...
'Vph', 'Vpv', ... 'Vph', 'Vpv', ...
'Vch', 'Vcv', ...
'Vnh', 'Vnv', ... 'Vnh', 'Vnv', ...
'Va'); 'Va');
#+end_src #+end_src
#+begin_src matlab #+begin_src matlab
t0 = 5; % Let's start one second after the first command in the system
i0 = find(uh.Unh ~= 0, 1) + fs;
iend = i0+fs*floor((length(uh.t)-i0)/fs);
Uch(t<t0) = []; uh.Uch([1:i0-1, iend:end]) = [];
Ucv(t<t0) = []; uh.Ucv([1:i0-1, iend:end]) = [];
Unh(t<t0) = []; uh.Unh([1:i0-1, iend:end]) = [];
Unv(t<t0) = []; uh.Unv([1:i0-1, iend:end]) = [];
Vph(t<t0) = []; uh.Vph([1:i0-1, iend:end]) = [];
Vpv(t<t0) = []; uh.Vpv([1:i0-1, iend:end]) = [];
Vch(t<t0) = []; uh.Vnh([1:i0-1, iend:end]) = [];
Vcv(t<t0) = []; uh.Vnv([1:i0-1, iend:end]) = [];
Vnh(t<t0) = []; uh.Va ([1:i0-1, iend:end]) = [];
Vnv(t<t0) = []; uh.t ([1:i0-1, iend:end]) = [];
Va(t<t0) = [];
t(t<t0) = [];
t = t - t(1); % We start at t=0 % We reset the time t
uh.t = uh.t - uh.t(1);
#+end_src #+end_src
** TODO Some Plots #+begin_src matlab
% Let's start one second after the first command in the system
i0 = find(uv.Unv ~= 0, 1) + fs;
iend = i0+fs*floor((length(uv.t)-i0)/fs);
uv.Uch([1:i0-1, iend:end]) = [];
uv.Ucv([1:i0-1, iend:end]) = [];
uv.Unh([1:i0-1, iend:end]) = [];
uv.Unv([1:i0-1, iend:end]) = [];
uv.Vph([1:i0-1, iend:end]) = [];
uv.Vpv([1:i0-1, iend:end]) = [];
uv.Vnh([1:i0-1, iend:end]) = [];
uv.Vnv([1:i0-1, iend:end]) = [];
uv.Va ([1:i0-1, iend:end]) = [];
uv.t ([1:i0-1, iend:end]) = [];
% We reset the time t
uv.t = uv.t - uv.t(1);
#+end_src
** 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.
#+begin_src matlab
load('./mat/plant.mat', 'Gd');
#+end_src
#+begin_src matlab
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(uh.t(1:2*fs), 1e6*uh.Vph(1:2*fs)/freqresp(Gd(1,1), 0), 'DisplayName', '$\theta_{h}$');
plot(uh.t(1:2*fs), 1e6*uh.Vpv(1:2*fs)/freqresp(Gd(2,2), 0), 'DisplayName', '$\theta_{v}$');
hold off;
xlabel('Time [s]'); ylabel('$\theta$ [$\mu$ rad]');
title('Newport Tilt - Horizontal Direction');
legend();
ax2 = subplot(1, 2, 2);
hold on;
plot(uv.t(1:2*fs), 1e6*uv.Vph(1:2*fs)/freqresp(Gd(1,1), 0), 'DisplayName', '$\theta_{h}$');
plot(uv.t(1:2*fs), 1e6*uv.Vpv(1:2*fs)/freqresp(Gd(2,2), 0), 'DisplayName', '$\theta_{v}$');
hold off;
xlabel('Time [s]'); ylabel('$\theta$ [$\mu$ rad]');
title('Newport Tilt - Vertical Direction');
legend();
linkaxes([ax1,ax2],'xy');
#+end_src
Let's compute the PSD of the error to see the frequency content.
#+begin_src matlab
[psd_UhRh, f] = pwelch(uh.Vph/freqresp(Gd(1,1), 0), hanning(ceil(1*fs)), [], [], fs);
[psd_UhRv, ~] = pwelch(uh.Vpv/freqresp(Gd(2,2), 0), hanning(ceil(1*fs)), [], [], fs);
[psd_UvRh, ~] = pwelch(uv.Vph/freqresp(Gd(1,1), 0), hanning(ceil(1*fs)), [], [], fs);
[psd_UvRv, ~] = pwelch(uv.Vpv/freqresp(Gd(2,2), 0), hanning(ceil(1*fs)), [], [], fs);
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(f, sqrt(psd_UhRh), 'DisplayName', '$\Gamma_{\theta_h}$');
plot(f, sqrt(psd_UhRv), 'DisplayName', '$\Gamma_{\theta_v}$');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{rad}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
title('Newport Tilt - Horizontal Direction');
ax2 = subplot(1, 2, 2);
hold on;
plot(f, sqrt(psd_UvRh), 'DisplayName', '$\Gamma_{\theta_h}$');
plot(f, sqrt(psd_UvRv), 'DisplayName', '$\Gamma_{\theta_v}$');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{rad}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
title('Newport Tilt - Vertical Direction');
linkaxes([ax1,ax2],'xy');
xlim([1, 1000]);
#+end_src
Let's convert that to errors in distance
\[ \Delta L = L^\prime - L = \frac{L}{\cos(\alpha)} - L \approx \frac{L \alpha^2}{2} \]
with
- $L$ is the nominal distance traveled by the beam
- $L^\prime$ is the distance traveled by the beam with an angle error
- $\alpha$ is the angle error
#+begin_src matlab
L = 0.1; % [m]
#+end_src
#+begin_src matlab
[psd_UhLh, f] = pwelch(0.5*L*(uh.Vph/freqresp(Gd(1,1), 0)).^2, hanning(ceil(1*fs)), [], [], fs);
[psd_UhLv, ~] = pwelch(0.5*L*(uh.Vpv/freqresp(Gd(2,2), 0)).^2, hanning(ceil(1*fs)), [], [], fs);
[psd_UvLh, ~] = pwelch(0.5*L*(uv.Vph/freqresp(Gd(1,1), 0)).^2, hanning(ceil(1*fs)), [], [], fs);
[psd_UvLv, ~] = pwelch(0.5*L*(uv.Vpv/freqresp(Gd(2,2), 0)).^2, hanning(ceil(1*fs)), [], [], fs);
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(f, sqrt(psd_UhLh), 'DisplayName', '$\Gamma_{L_h}$');
plot(f, sqrt(psd_UhLv), 'DisplayName', '$\Gamma_{L_v}$');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
title('Newport Tilt - Horizontal Direction');
ax2 = subplot(1, 2, 2);
hold on;
plot(f, sqrt(psd_UvLh), 'DisplayName', '$\Gamma_{L_h}$');
plot(f, sqrt(psd_UvLv), 'DisplayName', '$\Gamma_{L_v}$');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
title('Newport Tilt - Vertical Direction');
linkaxes([ax1,ax2],'xy');
xlim([1, 1000]);
#+end_src
Now, compare that with the PSD of the measured distance by the interferometer.
#+begin_src matlab
[psd_Lh, f] = pwelch(uh.Va, hanning(ceil(1*fs)), [], [], fs);
[psd_Lv, ~] = pwelch(uv.Va, hanning(ceil(1*fs)), [], [], fs);
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(f, sqrt(psd_UhLh), 'DisplayName', '$\Gamma_{L_h}$');
plot(f, sqrt(psd_UhLv), 'DisplayName', '$\Gamma_{L_v}$');
plot(f, sqrt(psd_Lh), '--k', 'DisplayName', '$\Gamma_{L_h}$');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
title('Newport Tilt - Horizontal Direction');
ax2 = subplot(1, 2, 2);
hold on;
plot(f, sqrt(psd_UvLh), 'DisplayName', '$\Gamma_{L_h}$');
plot(f, sqrt(psd_UvLv), 'DisplayName', '$\Gamma_{L_v}$');
plot(f, sqrt(psd_Lv), '--k', 'DisplayName', '$\Gamma_{L_h}$');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
title('Newport Tilt - Vertical Direction');
linkaxes([ax1,ax2],'xy');
xlim([1, 1000]);
#+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.Va, [fs floor(length(uh.t)/fs)]),2);
Unhm = mean(reshape(uh.Unh, [fs floor(length(uh.t)/fs)]),2);
Vavm = mean(reshape(uv.Va, [fs floor(length(uv.t)/fs)]),2);
Unvm = mean(reshape(uv.Unv, [fs floor(length(uv.t)/fs)]),2);
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(uh.Unh, uh.Va);
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(Unvm, Vavm)
hold off;
xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
#+end_src
#+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)));
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)));
hold off;
xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [nm]');
linkaxes([ax1,ax2],'xy');
ylim([-100 100]);
#+end_src
We then subtract
#+begin_src matlab
figure;
hold on;
plot(uh.Unh, 1e9*(uh.Va - repmat(Vam, length(uh.t)/length(Vam),1)))
hold off;
xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [nm]');
#+end_src
** Some Plots
#+begin_src matlab
figure;
hold on;
plot(uh.Unh, uh.Va);
plot(Unhm, Vam)
hold off;
xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(uh.Vnh(1:fs/2), uh.Va(1:fs/2));
hold off;
xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
ax2 = subplot(1, 2, 2);
hold on;
plot(uv.Vnv, uv.Va);
hold off;
xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(1, 2, 1);
hold on;
plot(uh.Vnh, uh.Va);
hold off;
xlabel('$V_{n,h}$ [V]'); ylabel('$V_a$ [m]');
ax2 = subplot(1, 2, 2);
hold on;
plot(uv.Vnv, uv.Va);
hold off;
xlabel('$V_{n,v}$ [V]'); ylabel('$V_a$ [m]');
#+end_src
** Repeatability ** Repeatability
#+begin_src matlab :exports none #+begin_src matlab :exports none

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matlab/test_cercalo.slx
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