Update huddle test analysis
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@ -1791,73 +1791,27 @@ The file =mat/plant.mat= is accessible [[./mat/plant.mat][here]].
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save('mat/plant.mat', 'sys', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
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#+end_src
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* Active Damping
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab
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freqs = logspace(1, 3, 1000);
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#+end_src
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** Load Plant
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#+begin_src matlab
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load('mat/plant.mat', 'sys', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
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#+end_src
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** Test
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#+begin_src matlab
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bode(sys({'Vch', 'Vcv'}, {'Uch', 'Ucv'}));
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#+end_src
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#+begin_src matlab
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Kppf = blkdiag(-10000/s, tf(0));
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Kppf.InputName = {'Vch', 'Vcv'};
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Kppf.OutputName = {'Uch', 'Ucv'};
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#+end_src
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#+begin_src matlab :exports none
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figure;
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% Magnitude
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ax1 = subaxis(2,1,1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'k-');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]);
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ylabel('Magnitude [dB]');
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hold off;
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% Phase
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ax2 = subaxis(2,1,2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(G, freqs, 'Hz'))), 'k-');
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set(gca,'xscale','log');
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yticks(-360:90:180);
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ylim([-360 0]);
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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#+begin_src matlab
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inputs = {'Uch', 'Ucv', 'Unh', 'Unv'};
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outputs = {'Ich', 'Icv', 'Rh', 'Rv', 'Vph', 'Vpv'};
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sys_cl = connect(sys, Kppf, inputs, outputs);
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figure; bode(sys_cl({'Vph', 'Vpv'}, {'Uch', 'Ucv'}), sys({'Vph', 'Vpv'}, {'Uch', 'Ucv'}))
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#+end_src
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* Huddle Test
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/huddle_test.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:huddle_test>>
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** Introduction :ignore:
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The goal is to determine the noise of the photodiodes as well as the noise of the Attocube interferometer.
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Multiple measurements are done with different experimental configuration as follow:
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#+name: tab:huddle_tests
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#+caption: Experimental Configuration for the various Huddle test
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| Number | OL/CL | Compensation Unit | Aluminum |
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|--------+-------------+-------------------+----------|
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| 1 | Open Loop | | |
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| 2 | Open Loop | Compensation Unit | |
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| 3 | Closed Loop | Compensation Unit | |
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| 4 | Open Loop | Compensation Unit | Aluminum |
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| 5 | Closed Loop | Compensation Unit | Aluminum |
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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@ -1867,103 +1821,227 @@ The file =mat/plant.mat= is accessible [[./mat/plant.mat][here]].
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<<matlab-init>>
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#+end_src
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** Load data
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We load the data taken during the Huddle Test.
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** Load Data
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#+begin_src matlab
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load('mat/data_huddle_test.mat', ...
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't', 'Uch', 'Ucv', ...
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'Unh', 'Unv', ...
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'Vph', 'Vpv', ...
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'Vch', 'Vcv', ...
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'Vnh', 'Vnv', ...
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'Va');
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ht_1 = load('./mat/data_huddle_test_1.mat', 't', 'Vph', 'Vpv', 'Va');
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ht_2 = load('./mat/data_huddle_test_2.mat', 't', 'Vph', 'Vpv', 'Va');
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ht_3 = load('./mat/data_huddle_test_3.mat', 't', 'Uch', 'Ucv', 'Vph', 'Vpv', 'Va');
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ht_4 = load('./mat/data_huddle_test_4.mat', 't', 'Vph', 'Vpv', 'Va');
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% ht_5 = load('./mat/data_huddle_test_5.mat', 't', 'Uch', 'Ucv', 'Vph', 'Vpv', 'Va');
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#+end_src
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#+begin_src matlab
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fs = 1e4;
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#+end_src
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** Pre-processing
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We remove the first second of data where everything is settling down.
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#+begin_src matlab
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t0 = 1;
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t0 = 1; % [s]
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Uch(t<t0) = [];
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Ucv(t<t0) = [];
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Unh(t<t0) = [];
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Unv(t<t0) = [];
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Vph(t<t0) = [];
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Vpv(t<t0) = [];
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Vch(t<t0) = [];
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Vcv(t<t0) = [];
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Vnh(t<t0) = [];
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Vnv(t<t0) = [];
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Va(t<t0) = [];
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t(t<t0) = [];
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tend = 100; % [s]
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t = t - t(1); % We start at t=0
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ht_s = {ht_1 ht_2 ht_3 ht_4}
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for i = 1:length(ht_s)
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ht_s{i}.Vph(ht_s{i}.t<t0) = [];
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ht_s{i}.Vpv(ht_s{i}.t<t0) = [];
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ht_s{i}.Va(ht_s{i}.t<t0) = [];
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ht_s{i}.t(ht_s{i}.t<t0) = [];
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ht_s{i}.t = ht_s{i}.t - ht_s{i}.t(1); % We start at t=0
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ht_s{i}.Vph(tend*fs+1:end) = [];
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ht_s{i}.Vpv(tend*fs+1:end) = [];
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ht_s{i}.Va(tend*fs+1:end) = [];
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ht_s{i}.t(tend*fs+1:end) = [];
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ht_s{i}.Va = ht_s{i}.Va - mean(ht_s{i}.Va);
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end
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ht_1 = ht_s{1};
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ht_2 = ht_s{2};
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ht_3 = ht_s{3};
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ht_4 = ht_s{4};
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#+end_src
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** Time Domain Data
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** Time domain plots
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#+begin_src matlab :exports none
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figure;
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ax1 = subaxis(2, 2, 1)
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hold on;
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plot(t, Uch, 'DisplayName', '$Vp_h$');
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plot(t, Ucv, 'DisplayName', '$Vp_v$');
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plot(ht_1.t, 1e9*ht_1.Va);
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hold off;
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ylabel('Displacement [nm]');
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set(gca, 'XTickLabel',[]);
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title('OL');
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ax2 = subaxis(2, 2, 2)
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hold on;
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plot(ht_2.t, 1e9*ht_2.Va);
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hold off;
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set(gca, 'XTickLabel',[]);
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set(gca, 'YTickLabel',[]);
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title('OL + CU');
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ax3 = subaxis(2, 2, 3)
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hold on;
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plot(ht_3.t, 1e9*ht_3.Va);
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hold off;
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xlabel('Time [s]');
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ylabel('Amplitude [V]');
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xlim([t(1), t(end)]);
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legend();
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ylabel('Displacement [nm]');
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title('CL + CU');
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ax4 = subaxis(2, 2, 4)
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hold on;
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plot(ht_4.t, 1e9*ht_4.Va);
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hold off;
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xlabel('Time [s]');
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set(gca, 'YTickLabel',[]);
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title('OL + CU + AL');
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linkaxes([ax1 ax2 ax3 ax4], 'xy');
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#+end_src
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We compute the Power Spectral Density of the horizontal and vertical positions of the beam as measured by the 4 quadrant diode.
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/huddle_test_Va.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:huddle_test_Va
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#+CAPTION: Measurement of the Attocube during Huddle Test ([[./figs/huddle_test_Va.png][png]], [[./figs/huddle_test_Va.pdf][pdf]])
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[[file:figs/huddle_test_Va.png]]
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#+begin_src matlab :exports none
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figure;
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ax1 = subaxis(2, 2, 1)
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hold on;
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plot(ht_1.t, ht_1.Vph);
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plot(ht_1.t, ht_1.Vpv);
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hold off;
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ylabel('Voltage [V]');
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set(gca, 'XTickLabel',[]);
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title('OL');
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ax2 = subaxis(2, 2, 2)
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hold on;
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plot(ht_2.t, ht_2.Vph);
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plot(ht_2.t, ht_2.Vpv);
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hold off;
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set(gca, 'XTickLabel',[]);
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set(gca, 'YTickLabel',[]);
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title('OL + CU');
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ax3 = subaxis(2, 2, 3)
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hold on;
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plot(ht_3.t, ht_3.Vph);
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plot(ht_3.t, ht_3.Vpv);
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hold off;
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xlabel('Time [s]');
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ylabel('Voltage [V]');
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title('CL + CU');
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ax4 = subaxis(2, 2, 4)
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hold on;
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plot(ht_4.t, ht_4.Vph);
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plot(ht_4.t, ht_4.Vpv);
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hold off;
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xlabel('Time [s]');
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set(gca, 'YTickLabel',[]);
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title('OL + CU + AL');
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linkaxes([ax1 ax2 ax3 ax4], 'xy');
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/huddle_test_4qd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:huddle_test_4qd
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#+CAPTION: Measurement of the 4QD during the Huddle tests ([[./figs/huddle_test_4qd.png][png]], [[./figs/huddle_test_4qd.pdf][pdf]])
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[[file:figs/huddle_test_4qd.png]]
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** Power Spectral Density
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#+begin_src matlab
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[psd_Vph, f] = pwelch(Vph, hanning(ceil(1*fs)), [], [], fs);
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[psd_Vpv, ~] = pwelch(Vpv, hanning(ceil(1*fs)), [], [], fs);
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win = hanning(ceil(1*fs));
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#+end_src
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#+begin_src matlab
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[psd_Va1, f] = pwelch(ht_1.Va, win, [], [], fs);
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[psd_Va2, ~] = pwelch(ht_2.Va, win, [], [], fs);
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[psd_Va3, ~] = pwelch(ht_3.Va, win, [], [], fs);
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[psd_Va4, ~] = pwelch(ht_4.Va, win, [], [], fs);
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#+end_src
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#+begin_src matlab
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[psd_Vph1, ~] = pwelch(ht_1.Vph, win, [], [], fs);
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[psd_Vph2, ~] = pwelch(ht_2.Vph, win, [], [], fs);
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[psd_Vph3, ~] = pwelch(ht_3.Vph, win, [], [], fs);
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[psd_Vph4, ~] = pwelch(ht_4.Vph, win, [], [], fs);
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#+end_src
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#+begin_src matlab
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[psd_Vpv1, ~] = pwelch(ht_1.Vpv, win, [], [], fs);
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[psd_Vpv2, ~] = pwelch(ht_2.Vpv, win, [], [], fs);
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[psd_Vpv3, ~] = pwelch(ht_3.Vpv, win, [], [], fs);
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[psd_Vpv4, ~] = pwelch(ht_4.Vpv, win, [], [], fs);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(f, sqrt(psd_Vph), 'DisplayName', '$\Gamma_{Vp_h}$');
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plot(f, sqrt(psd_Vpv), 'DisplayName', '$\Gamma_{Vp_v}$');
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plot(f, sqrt(psd_Va1), 'DisplayName', 'OL');
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plot(f, sqrt(psd_Va2), 'DisplayName', 'OL + CU');
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plot(f, sqrt(psd_Va3), 'DisplayName', 'CL + CU');
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plot(f, sqrt(psd_Va4), 'DisplayName', 'OL + CU + AL');
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlabel('Frequency [Hz]');
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ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$');
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legend('location', 'northeast');
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xlim([1, 1000]);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(t, Vch, 'DisplayName', '$Vc_h$');
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plot(t, Vcv, 'DisplayName', '$Vc_v$');
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hold off;
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xlabel('Time [s]');
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ylabel('Amplitude [V]');
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xlim([t(1), t(end)]);
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legend();
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/huddle_test_psd_va.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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We compute the Power Spectral Density of the voltage across the inductance used for horizontal and vertical positioning of the Cercalo.
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#+begin_src matlab
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[psd_Vch, f] = pwelch(Vch, hanning(ceil(1*fs)), [], [], fs);
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[psd_Vcv, ~] = pwelch(Vcv, hanning(ceil(1*fs)), [], [], fs);
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#+end_src
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#+NAME: fig:huddle_test_psd_va
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#+CAPTION: PSD of the Interferometer measurement during Huddle tests ([[./figs/huddle_test_psd_va.png][png]], [[./figs/huddle_test_psd_va.pdf][pdf]])
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[[file:figs/huddle_test_psd_va.png]]
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(f, sqrt(psd_Vch), 'DisplayName', '$\Gamma_{Vc_h}$');
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plot(f, sqrt(psd_Vcv), 'DisplayName', '$\Gamma_{Vc_v}$');
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plot(f, sqrt(psd_Vph1), 'DisplayName', 'OL');
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plot(f, sqrt(psd_Vph2), 'DisplayName', 'OL + CU');
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plot(f, sqrt(psd_Vph3), 'DisplayName', 'CL + CU');
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plot(f, sqrt(psd_Vph4), 'DisplayName', 'OL + CU + AL');
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlabel('Frequency [Hz]');
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ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$');
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legend('location', 'northeast');
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xlim([1, 1000]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/huddle_test_4qd_psd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:huddle_test_4qd_psd
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#+CAPTION: PSD of the 4QD signal during Huddle tests ([[./figs/huddle_test_4qd_psd.png][png]], [[./figs/huddle_test_4qd_psd.pdf][pdf]])
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[[file:figs/huddle_test_4qd_psd.png]]
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** Conclusion
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The Attocube's "Environmental Compensation Unit" does not have a significant effect on the stability of the measurement.
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* Budget Error
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<<sec:budget_error>>
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** Introduction :ignore:
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*Goals*:
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- List all sources of error and compute their effects on the Attocube measurement
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@ -2039,7 +2117,7 @@ The geometrical parameters of the setup are defined below.
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#+end_src
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#+NAME: fig:angle_error_schematic_cercalo
|
||||
#+CAPTION: Caption
|
||||
#+CAPTION: Schematic of the geometry used to evaluate the effect of $\delta \theta_c$ on the measured distance $\delta L$
|
||||
#+RESULTS:
|
||||
[[file:figs/angle_error_schematic_cercalo.png]]
|
||||
|
||||
@ -2554,16 +2632,21 @@ This corresponds to a measurement error of the Attocube equals to (in [m])
|
||||
#+end_important
|
||||
|
||||
* Plant Scaling
|
||||
| | Value | Unit | |
|
||||
|------------------------+-------+-------------+----------|
|
||||
| Expected perturbations | 1 | [V] | $U_n$ |
|
||||
| Maximum input usage | 10 | [V] | $U_c$ |
|
||||
| Maximum wanted error | 10 | [$\mu rad$] | $\theta$ |
|
||||
| Measured noise | 5 | [$\mu rad$] | |
|
||||
<<sec:plant_scaling>>
|
||||
** Introduction :ignore:
|
||||
The goal is the scale the plant prior to control synthesis.
|
||||
This will simplify the choice of weighting functions and will yield useful insight on the controllability of the plant.
|
||||
|
||||
** General Configuration
|
||||
#+name: tab:plant_scaling_values
|
||||
#+caption: Maximum wanted values for various signals
|
||||
| | Value | Unit | Variable Name |
|
||||
|------------------------+-------+-------------+---------------|
|
||||
| Expected perturbations | 1 | [V] | $U_n$ |
|
||||
| Maximum input usage | 10 | [V] | $U_c$ |
|
||||
| Maximum wanted error | 10 | [$\mu rad$] | $\theta$ |
|
||||
| Measured noise | 5 | [$\mu rad$] | |
|
||||
|
||||
* Control Objective
|
||||
** Control Objective
|
||||
The maximum expected stroke is $y_\text{max} = 3mm \approx 5e^{-2} rad$ at $1Hz$.
|
||||
The maximum wanted error is $e_\text{max} = 10 \mu rad$.
|
||||
|
||||
@ -2576,8 +2659,17 @@ Thus, we require the sensitivity function at $\omega_0 = 1\text{ Hz}$:
|
||||
In terms of loop gain, this is equivalent to:
|
||||
\[ |L(j\omega_0)| > 5 \cdot 10^{3} \]
|
||||
|
||||
** General Configuration
|
||||
The plant is put in a general configuration as shown in Fig. [[fig:general_control_names]].
|
||||
|
||||
#+name: fig:general_control_names
|
||||
#+caption: General Control Configuration
|
||||
[[file:figs/general_control_names.png]]
|
||||
|
||||
* Plant Analysis
|
||||
** Matlab Init :noexport:ignore:
|
||||
<<sec:plant_analysis>>
|
||||
** Introduction :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
|
||||
@ -2629,17 +2721,90 @@ In terms of loop gain, this is equivalent to:
|
||||
G0 = freqresp(G, 0);
|
||||
#+end_src
|
||||
|
||||
* Active Damping
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/active_damping.m
|
||||
:header-args:matlab+: :comments org :mkdirp yes
|
||||
:END:
|
||||
<<sec:active_damping>>
|
||||
** Introduction :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
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
freqs = logspace(1, 3, 1000);
|
||||
#+end_src
|
||||
|
||||
** Load Plant
|
||||
#+begin_src matlab
|
||||
load('mat/plant.mat', 'sys', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
|
||||
#+end_src
|
||||
|
||||
** Integral Force Feedback
|
||||
#+begin_src matlab
|
||||
bode(sys({'Vch', 'Vcv'}, {'Uch', 'Ucv'}));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Kppf = blkdiag(-10000/s, tf(0));
|
||||
|
||||
Kppf.InputName = {'Vch', 'Vcv'};
|
||||
Kppf.OutputName = {'Uch', 'Ucv'};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
% Magnitude
|
||||
ax1 = subaxis(2,1,1);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('Magnitude [dB]');
|
||||
hold off;
|
||||
|
||||
% Phase
|
||||
ax2 = subaxis(2,1,2);
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G, freqs, 'Hz'))), 'k-');
|
||||
set(gca,'xscale','log');
|
||||
yticks(-360:90:180);
|
||||
ylim([-360 0]);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
inputs = {'Uch', 'Ucv', 'Unh', 'Unv'};
|
||||
outputs = {'Ich', 'Icv', 'Rh', 'Rv', 'Vph', 'Vpv'};
|
||||
|
||||
sys_cl = connect(sys, Kppf, inputs, outputs);
|
||||
|
||||
figure; bode(sys_cl({'Vph', 'Vpv'}, {'Uch', 'Ucv'}), sys({'Vph', 'Vpv'}, {'Uch', 'Ucv'}))
|
||||
#+end_src
|
||||
|
||||
** Conclusion
|
||||
Active damping does not seems to be applicable here.
|
||||
|
||||
* Decentralized Control of the Cercalo
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/decentralized_control.m
|
||||
:header-args:matlab+: :comments org :mkdirp yes
|
||||
:END:
|
||||
<<sec:decentralized_control>>
|
||||
|
||||
** Introduction :ignore:
|
||||
In this section, we try to implement a simple decentralized controller.
|
||||
|
||||
** ZIP file containing the data and matlab files :ignore:
|
||||
** ZIP file containing the data and matlab files :ignore:
|
||||
#+begin_src bash :exports none :results none
|
||||
if [ matlab/decentralized_control.m -nt data/decentralized_control.zip ]; then
|
||||
cp matlab/decentralized_control.m decentralized_control.m;
|
||||
@ -2767,6 +2932,7 @@ The diagonal controller is accessible [[./mat/K_diag.mat][here]].
|
||||
#+end_src
|
||||
|
||||
* Newport Control
|
||||
<<sec:newport_control>>
|
||||
** Introduction :ignore:
|
||||
In this section, we try to implement a simple decentralized controller for the Newport.
|
||||
This can be used to align the 4QD:
|
||||
@ -2843,6 +3009,7 @@ The controllers can be downloaded [[./mat/K_newport.mat][here]].
|
||||
#+end_src
|
||||
|
||||
* Measurement of the non-repeatability
|
||||
<<sec:non_rep_meas>>
|
||||
** Introduction :ignore:
|
||||
- Explanation of the procedure
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user