Update huddle test analysis

index.org

@@ -1791,73 +1791,27 @@ The file =mat/plant.mat= is accessible [[./mat/plant.mat][here]].
   save('mat/plant.mat', 'sys', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
 #+end_src
 
-* Active Damping
-** 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
-
-** Test
-#+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
-
 * Huddle Test
+:PROPERTIES:
+:header-args:matlab+: :tangle matlab/huddle_test.m
+:header-args:matlab+: :comments org :mkdirp yes
+:END:
+<<sec:huddle_test>>
 ** Introduction                                                     :ignore:
+The goal is to determine the noise of the photodiodes as well as the noise of the Attocube interferometer.
+
+Multiple measurements are done with different experimental configuration as follow:
+
+#+name: tab:huddle_tests
+#+caption: Experimental Configuration for the various Huddle test
+| Number | OL/CL       | Compensation Unit | Aluminum |
+|--------+-------------+-------------------+----------|
+|      1 | Open Loop   |                   |          |
+|      2 | Open Loop   | Compensation Unit |          |
+|      3 | Closed Loop | Compensation Unit |          |
+|      4 | Open Loop   | Compensation Unit | Aluminum |
+|      5 | Closed Loop | Compensation Unit | Aluminum |
+
 ** 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>>
@@ -1867,103 +1821,227 @@ The file =mat/plant.mat= is accessible [[./mat/plant.mat][here]].
   <<matlab-init>>
 #+end_src
 
-** Load data
+** Load Data
-We load the data taken during the Huddle Test.
 #+begin_src matlab
-  load('mat/data_huddle_test.mat', ...
+  ht_1 = load('./mat/data_huddle_test_1.mat', 't', 'Vph', 'Vpv', 'Va');
-       't', 'Uch', 'Ucv', ...
+  ht_2 = load('./mat/data_huddle_test_2.mat', 't', 'Vph', 'Vpv', 'Va');
-       'Unh', 'Unv', ...
+  ht_3 = load('./mat/data_huddle_test_3.mat', 't', 'Uch', 'Ucv', 'Vph', 'Vpv', 'Va');
-       'Vph', 'Vpv', ...
+  ht_4 = load('./mat/data_huddle_test_4.mat', 't', 'Vph', 'Vpv', 'Va');
-       'Vch', 'Vcv', ...
+  % ht_5 = load('./mat/data_huddle_test_5.mat', 't', 'Uch', 'Ucv', 'Vph', 'Vpv', 'Va');
-       'Vnh', 'Vnv', ...
+#+end_src
-       'Va');
+
+#+begin_src matlab
+  fs = 1e4;
 #+end_src
 
 ** Pre-processing
-We remove the first second of data where everything is settling down.
 #+begin_src matlab
-  t0 = 1;
+  t0 = 1; % [s]
 
-  Uch(t<t0) = [];
+  tend = 100; % [s]
-  Ucv(t<t0) = [];
-  Unh(t<t0) = [];
-  Unv(t<t0) = [];
-  Vph(t<t0) = [];
-  Vpv(t<t0) = [];
-  Vch(t<t0) = [];
-  Vcv(t<t0) = [];
-  Vnh(t<t0) = [];
-  Vnv(t<t0) = [];
-  Va(t<t0)  = [];
-  t(t<t0)   = [];
 
-  t = t - t(1); % We start at t=0
+  ht_s = {ht_1 ht_2 ht_3 ht_4}
+
+  for i = 1:length(ht_s)
+    ht_s{i}.Vph(ht_s{i}.t<t0) = [];
+    ht_s{i}.Vpv(ht_s{i}.t<t0) = [];
+    ht_s{i}.Va(ht_s{i}.t<t0)  = [];
+    ht_s{i}.t(ht_s{i}.t<t0)   = [];
+
+    ht_s{i}.t = ht_s{i}.t - ht_s{i}.t(1); % We start at t=0
+
+    ht_s{i}.Vph(tend*fs+1:end) = [];
+    ht_s{i}.Vpv(tend*fs+1:end) = [];
+    ht_s{i}.Va(tend*fs+1:end)  = [];
+    ht_s{i}.t(tend*fs+1:end)   = [];
+
+    ht_s{i}.Va = ht_s{i}.Va - mean(ht_s{i}.Va);
+  end
+
+  ht_1 = ht_s{1};
+  ht_2 = ht_s{2};
+  ht_3 = ht_s{3};
+  ht_4 = ht_s{4};
 #+end_src
 
-** Time Domain Data
+** Time domain plots
 #+begin_src matlab :exports none
   figure;
+  ax1 = subaxis(2, 2, 1)
   hold on;
-  plot(t, Uch, 'DisplayName', '$Vp_h$');
+  plot(ht_1.t, 1e9*ht_1.Va);
-  plot(t, Ucv, 'DisplayName', '$Vp_v$');
+  hold off;
+  ylabel('Displacement [nm]');
+  set(gca, 'XTickLabel',[]);
+  title('OL');
+
+  ax2 = subaxis(2, 2, 2)
+  hold on;
+  plot(ht_2.t, 1e9*ht_2.Va);
+  hold off;
+  set(gca, 'XTickLabel',[]);
+  set(gca, 'YTickLabel',[]);
+  title('OL + CU');
+
+  ax3 = subaxis(2, 2, 3)
+  hold on;
+  plot(ht_3.t, 1e9*ht_3.Va);
   hold off;
   xlabel('Time [s]');
-  ylabel('Amplitude [V]');
+  ylabel('Displacement [nm]');
-  xlim([t(1), t(end)]);
+  title('CL + CU');
-  legend();
+
+  ax4 = subaxis(2, 2, 4)
+  hold on;
+  plot(ht_4.t, 1e9*ht_4.Va);
+  hold off;
+  xlabel('Time [s]');
+  set(gca, 'YTickLabel',[]);
+  title('OL + CU + AL');
+
+  linkaxes([ax1 ax2 ax3 ax4], 'xy');
 #+end_src
 
-We compute the Power Spectral Density of the horizontal and vertical positions of the beam as measured by the 4 quadrant diode.
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/huddle_test_Va.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:huddle_test_Va
+#+CAPTION: Measurement of the Attocube during Huddle Test ([[./figs/huddle_test_Va.png][png]], [[./figs/huddle_test_Va.pdf][pdf]])
+[[file:figs/huddle_test_Va.png]]
+
+#+begin_src matlab :exports none
+  figure;
+  ax1 = subaxis(2, 2, 1)
+  hold on;
+  plot(ht_1.t, ht_1.Vph);
+  plot(ht_1.t, ht_1.Vpv);
+  hold off;
+  ylabel('Voltage [V]');
+  set(gca, 'XTickLabel',[]);
+  title('OL');
+
+  ax2 = subaxis(2, 2, 2)
+  hold on;
+  plot(ht_2.t, ht_2.Vph);
+  plot(ht_2.t, ht_2.Vpv);
+  hold off;
+  set(gca, 'XTickLabel',[]);
+  set(gca, 'YTickLabel',[]);
+  title('OL + CU');
+
+  ax3 = subaxis(2, 2, 3)
+  hold on;
+  plot(ht_3.t, ht_3.Vph);
+  plot(ht_3.t, ht_3.Vpv);
+  hold off;
+  xlabel('Time [s]');
+  ylabel('Voltage [V]');
+  title('CL + CU');
+
+  ax4 = subaxis(2, 2, 4)
+  hold on;
+  plot(ht_4.t, ht_4.Vph);
+  plot(ht_4.t, ht_4.Vpv);
+  hold off;
+  xlabel('Time [s]');
+  set(gca, 'YTickLabel',[]);
+  title('OL + CU + AL');
+
+  linkaxes([ax1 ax2 ax3 ax4], 'xy');
+#+end_src
+
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/huddle_test_4qd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:huddle_test_4qd
+#+CAPTION: Measurement of the 4QD during the Huddle tests ([[./figs/huddle_test_4qd.png][png]], [[./figs/huddle_test_4qd.pdf][pdf]])
+[[file:figs/huddle_test_4qd.png]]
+
+** Power Spectral Density
 #+begin_src matlab
-  [psd_Vph, f] = pwelch(Vph, hanning(ceil(1*fs)), [], [], fs);
+  win = hanning(ceil(1*fs));
-  [psd_Vpv, ~] = pwelch(Vpv, hanning(ceil(1*fs)), [], [], fs);
+#+end_src
+
+#+begin_src matlab
+  [psd_Va1, f] = pwelch(ht_1.Va, win, [], [], fs);
+  [psd_Va2, ~] = pwelch(ht_2.Va, win, [], [], fs);
+  [psd_Va3, ~] = pwelch(ht_3.Va, win, [], [], fs);
+  [psd_Va4, ~] = pwelch(ht_4.Va, win, [], [], fs);
+#+end_src
+
+#+begin_src matlab
+  [psd_Vph1, ~] = pwelch(ht_1.Vph, win, [], [], fs);
+  [psd_Vph2, ~] = pwelch(ht_2.Vph, win, [], [], fs);
+  [psd_Vph3, ~] = pwelch(ht_3.Vph, win, [], [], fs);
+  [psd_Vph4, ~] = pwelch(ht_4.Vph, win, [], [], fs);
+#+end_src
+
+#+begin_src matlab
+  [psd_Vpv1, ~] = pwelch(ht_1.Vpv, win, [], [], fs);
+  [psd_Vpv2, ~] = pwelch(ht_2.Vpv, win, [], [], fs);
+  [psd_Vpv3, ~] = pwelch(ht_3.Vpv, win, [], [], fs);
+  [psd_Vpv4, ~] = pwelch(ht_4.Vpv, win, [], [], fs);
 #+end_src
 
 #+begin_src matlab :exports none
   figure;
   hold on;
-  plot(f, sqrt(psd_Vph), 'DisplayName', '$\Gamma_{Vp_h}$');
+  plot(f, sqrt(psd_Va1), 'DisplayName', 'OL');
-  plot(f, sqrt(psd_Vpv), 'DisplayName', '$\Gamma_{Vp_v}$');
+  plot(f, sqrt(psd_Va2), 'DisplayName', 'OL + CU');
+  plot(f, sqrt(psd_Va3), 'DisplayName', 'CL + CU');
+  plot(f, sqrt(psd_Va4), 'DisplayName', 'OL + CU + AL');
   hold off;
   set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{V}{\sqrt{Hz}}\right]$')
+  xlabel('Frequency [Hz]');
-  legend('Location', 'southwest');
+  ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$');
+  legend('location', 'northeast');
   xlim([1, 1000]);
 #+end_src
 
-#+begin_src matlab :exports none
+#+HEADER: :tangle no :exports results :results none :noweb yes
-  figure;
+#+begin_src matlab :var filepath="figs/huddle_test_psd_va.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
-  hold on;
+  <<plt-matlab>>
-  plot(t, Vch, 'DisplayName', '$Vc_h$');
-  plot(t, Vcv, 'DisplayName', '$Vc_v$');
-  hold off;
-  xlabel('Time [s]');
-  ylabel('Amplitude [V]');
-  xlim([t(1), t(end)]);
-  legend();
 #+end_src
 
-We compute the Power Spectral Density of the voltage across the inductance used for horizontal and vertical positioning of the Cercalo.
+#+NAME: fig:huddle_test_psd_va
-#+begin_src matlab
+#+CAPTION: PSD of the Interferometer measurement during Huddle tests ([[./figs/huddle_test_psd_va.png][png]], [[./figs/huddle_test_psd_va.pdf][pdf]])
-  [psd_Vch, f] = pwelch(Vch, hanning(ceil(1*fs)), [], [], fs);
+[[file:figs/huddle_test_psd_va.png]]
-  [psd_Vcv, ~] = pwelch(Vcv, hanning(ceil(1*fs)), [], [], fs);
+
-#+end_src
 
 #+begin_src matlab :exports none
   figure;
   hold on;
-  plot(f, sqrt(psd_Vch), 'DisplayName', '$\Gamma_{Vc_h}$');
+  plot(f, sqrt(psd_Vph1), 'DisplayName', 'OL');
-  plot(f, sqrt(psd_Vcv), 'DisplayName', '$\Gamma_{Vc_v}$');
+  plot(f, sqrt(psd_Vph2), 'DisplayName', 'OL + CU');
+  plot(f, sqrt(psd_Vph3), 'DisplayName', 'CL + CU');
+  plot(f, sqrt(psd_Vph4), 'DisplayName', 'OL + CU + AL');
   hold off;
   set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{V}{\sqrt{Hz}}\right]$')
+  xlabel('Frequency [Hz]');
-  legend('Location', 'southwest');
+  ylabel('ASD $\left[\frac{m}{\sqrt{Hz}}\right]$');
+  legend('location', 'northeast');
   xlim([1, 1000]);
 #+end_src
 
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/huddle_test_4qd_psd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:huddle_test_4qd_psd
+#+CAPTION: PSD of the 4QD signal during Huddle tests ([[./figs/huddle_test_4qd_psd.png][png]], [[./figs/huddle_test_4qd_psd.pdf][pdf]])
+[[file:figs/huddle_test_4qd_psd.png]]
+
+
+** Conclusion
+The Attocube's "Environmental Compensation Unit" does not have a significant effect on the stability of the measurement.
+
 * Budget Error
 <<sec:budget_error>>
-
 ** Introduction                                                     :ignore:
 *Goals*:
 - List all sources of error and compute their effects on the Attocube measurement
@@ -2039,7 +2117,7 @@ The geometrical parameters of the setup are defined below.
 #+end_src
 
 #+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        |          |
+<<sec:plant_scaling>>
-|------------------------+-------+-------------+----------|
+** Introduction                                                     :ignore:
-| Expected perturbations |     1 | [V]         | $U_n$    |
+The goal is the scale the plant prior to control synthesis.
-| Maximum input usage    |    10 | [V]         | $U_c$    |
+This will simplify the choice of weighting functions and will yield useful insight on the controllability of the plant.
-| Maximum wanted error   |    10 | [$\mu rad$] | $\theta$ |
-| Measured noise         |     5 | [$\mu rad$] |          |
 
-** 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