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