Add analysis with LPF

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")
+  <<plt-matlab>>
+#+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")
+  <<plt-matlab>>
+#+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")
+  <<plt-matlab>>
+#+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]]