Analyze results of strut 1 measurements

test-bench-apa300ml.org

@@ -1881,7 +1881,7 @@ for i = 1:length(apa_nums)
 end
 #+end_src
 
-The coherence is shown in Figure [[fig:frf_dvf_plant_coh]].
+The coherence is shown in Figure [[fig:apa_frf_dvf_plant_coh]].
 It is clear that the Sweep sine gives good coherence up to 400Hz and that the high frequency noise excitation signal helps increasing a little bit the coherence at high frequency.
 
 #+begin_src matlab :exports none
@@ -1905,13 +1905,13 @@ legend('location', 'southeast');
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/apa_frf_dvf_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:frf_dvf_plant_coh
+#+name: fig:apa_frf_dvf_plant_coh
 #+caption: Obtained coherence for the plant from $V_a$ to $d_e$
 #+RESULTS:
-[[file:figs/frf_dvf_plant_coh.png]]
+[[file:figs/apa_frf_dvf_plant_coh.png]]
 
 
 Then, the transfer function from the DAC output voltage $V_a$ to the measured displacement by the encoders is computed:
@@ -1930,7 +1930,7 @@ for i = 1:length(apa_nums)
 end
 #+end_src
 
-The obtained transfer functions are shown in Figure [[fig:frf_dvf_plant_tf]].
+The obtained transfer functions are shown in Figure [[fig:apa_frf_dvf_plant_tf]].
 They are all superimposed except for the APA7.
 
 #+begin_question
@@ -1978,15 +1978,15 @@ xlim([10, 2e3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/apa_frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_dvf_plant_tf
+#+name: fig:apa_frf_dvf_plant_tf
 #+caption: Estimated FRF for the DVF plant (transfer function from $V_a$ to the encoder $d_e$)
 #+RESULTS:
-[[file:figs/frf_dvf_plant_tf.png]]
+[[file:figs/apa_frf_dvf_plant_tf.png]]
 
-A zoom on the main resonance is shown in Figure [[fig:frf_dvf_zoom_res_plant_tf]].
+A zoom on the main resonance is shown in Figure [[fig:apa_frf_dvf_zoom_res_plant_tf]].
 It is clear that expect for the APA 7, the response around the resonances are well matching for all the APA.
 
 It is also clear that there is not a single resonance but two resonances, a first one at 95Hz and a second one at 105Hz.
@@ -2029,18 +2029,18 @@ xlim([80, 120]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_zoom_res_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/apa_frf_dvf_zoom_res_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_dvf_zoom_res_plant_tf
+#+name: fig:apa_frf_dvf_zoom_res_plant_tf
 #+caption: Estimated FRF for the DVF plant (transfer function from $V_a$ to the encoder $d_e$) - Zoom on the main resonance
 #+RESULTS:
-[[file:figs/frf_dvf_zoom_res_plant_tf.png]]
+[[file:figs/apa_frf_dvf_zoom_res_plant_tf.png]]
 
 *** FRF Identification - IFF
 In this section, the dynamics from $V_a$ to $V_s$ is identified.
 
-First the coherence is computed and shown in Figure [[fig:frf_iff_plant_coh]].
+First the coherence is computed and shown in Figure [[fig:apa_frf_iff_plant_coh]].
 The coherence is very nice from 10Hz to 2kHz.
 It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
 
@@ -2080,15 +2080,15 @@ legend('location', 'southeast');
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_iff_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/apa_frf_iff_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:frf_iff_plant_coh
+#+name: fig:apa_frf_iff_plant_coh
 #+caption: Obtained coherence for the IFF plant
 #+RESULTS:
-[[file:figs/frf_iff_plant_coh.png]]
+[[file:figs/apa_frf_iff_plant_coh.png]]
 
-Then the FRF are estimated and shown in Figure [[fig:frf_iff_plant_tf]]
+Then the FRF are estimated and shown in Figure [[fig:apa_frf_iff_plant_tf]]
 #+begin_src matlab
 %% FRF estimation of the transfer function from Va to Vs
 iff_sweep = zeros(length(f), length(apa_nums));
@@ -2140,42 +2140,42 @@ xlim([10, 2e3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/apa_frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_iff_plant_tf
+#+name: fig:apa_frf_iff_plant_tf
 #+caption:Identified IFF Plant
 #+RESULTS:
-[[file:figs/frf_iff_plant_tf.png]]
+[[file:figs/apa_frf_iff_plant_tf.png]]
 
 * Dynamical measurements - Struts
 <<sec:dynamical_meas_struts>>
 ** Introduction                                                      :ignore:
 
+The same bench used in Section [[sec:dynamical_meas_apa]] is here used with the strut instead of only the APA.
+
+The bench is shown in Figure [[fig:test_bench_leg_overview]].
+Measurements are performed either when no encoder is fixed to the strut (Figure [[fig:test_bench_leg_front]]) or when one encoder is fixed to the strut (Figure [[fig:test_bench_leg_overview]]).
+
 #+name: fig:test_bench_leg_overview
 #+caption: Test Bench with Strut - Overview
+#+attr_latex: :width 0.5\linewidth
 [[file:figs/test_bench_leg_overview.png]]
 
 #+name: fig:test_bench_leg_front
 #+caption: Test Bench with Strut - Zoom on the strut
+#+attr_latex: :width 0.5\linewidth
 [[file:figs/test_bench_leg_front.png]]
 
 #+name: fig:test_bench_leg_overview
 #+caption: Test Bench with Strut - Zoom on the strut with the encoder
+#+attr_latex: :width 0.5\linewidth
 [[file:figs/test_bench_leg_coder.png]]
 
-
-| Variable |                              | Unit | Hardware                      |
-|----------+------------------------------+------+-------------------------------|
-| =Va=     | Output DAC voltage           | [V]  | DAC - Ch. 1 => PD200 => APA   |
-| =Vs=     | Measured stack voltage (ADC) | [V]  | APA => ADC - Ch. 1            |
-| =de=     | Encoder Measurement          | [m]  | PEPU Ch. 1 - IO318(1) - Ch. 1 |
-| =da=     | Attocube Measurement         | [m]  | PEPU Ch. 2 - IO318(1) - Ch. 2 |
-| =t=      | Time                         | [s]  |                               |
-
 ** Measurement on Strut 1
+<<sec:meas_strut_1>>
 *** Introduction                                                    :ignore:
-Measurements are first performed on the strut number 1 with:
+Measurements are first performed on the strut 1 that contains:
 - APA 1
 - flex 1 and flex 2
 
@@ -2204,6 +2204,7 @@ addpath('./src/');
 #+end_src
 
 *** Without Encoder
+<<sec:meas_strut_1_no_encoder>>
 **** FRF Identification - Setup
 The identification is performed in three steps:
 1. White noise excitation with small amplitude.
@@ -2241,8 +2242,8 @@ We get the frequency vector that will be the same for all the frequency domain a
 [~, f] = tfestimate(leg_sweep.Va, leg_sweep.de, win, [], [], 1/Ts);
 #+end_src
 
-**** TODO FRF Identification - DVF
-In this section, the dynamics from $V_a$ to $d_e$ is identified.
+**** FRF Identification - Displacement
+In this section, the dynamics from the excitation voltage $V_a$ to the interferometer $d_a$ is identified.
 
 We compute the coherence for 2nd and 3rd identification:
 #+begin_src matlab
@@ -2253,57 +2254,40 @@ We compute the coherence for 2nd and 3rd identification:
 #+begin_src matlab :exports none
 figure;
 hold on;
-plot(f, coh_noise_hf(:, 1), 'color', [colors(1, :), 0.5], ...
+plot(f, coh_noise_hf(:, 1), 'color', colors(1, :), ...
      'DisplayName', 'HF Noise');
-plot(f, coh_sweep(:, 1), 'color', [colors(2, :), 0.5], ...
+plot(f, coh_sweep(:, 1), 'color', colors(2, :), ...
      'DisplayName', 'Sweep');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
-% xlim([5, 5e3]); ylim([0, 1]);
+xlim([5, 5e3]); ylim([0, 1]);
 legend('location', 'southeast');
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/strut_1_frf_dvf_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:frf_dvf_plant_coh
-#+caption: Obtained coherence for the plant from $V_a$ to $d_e$
+#+name: fig:strut_1_frf_dvf_plant_coh
+#+caption: Obtained coherence for the plant from $V_a$ to $d_a$
 #+RESULTS:
-[[file:figs/frf_dvf_plant_coh.png]]
-
+[[file:figs/strut_1_frf_dvf_plant_coh.png]]
 
+The transfer function from $V_a$ to the interferometer measured displacement $d_a$ is estimated and shown in Figure [[fig:strut_1_frf_dvf_plant_tf]].
 #+begin_src matlab
 [dvf_sweep, ~]    = tfestimate(leg_sweep.Va,    leg_sweep.da,    win, [], [], 1/Ts);
 [dvf_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.da, win, [], [], 1/Ts);
 #+end_src
 
-The obtained transfer functions are shown in Figure [[fig:frf_dvf_plant_tf]].
-
-They are all superimposed except for the APA7.
-
-#+begin_question
-Why is the APA7 off?
-We could think that the APA7 is stiffer, but also the mass line is off.
-
-It seems that there is a "gain" problem.
-The encoder seems fine (it measured the same as the Interferometer).
-Maybe it could be due to the amplifier?
-#+end_question
-
-#+begin_question
-Why is there a double resonance at around 94Hz?
-#+end_question
-
 #+begin_src matlab :exports none
 figure;
-tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
 
-ax1 = nexttile;
+ax1 = nexttile([2,1]);
 hold on;
-plot(f(f> 350), abs(dvf_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), abs(dvf_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), abs(dvf_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), abs(dvf_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
 ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
@@ -2312,31 +2296,31 @@ ylim([1e-9, 1e-3]);
 
 ax2 = nexttile;
 hold on;
-plot(f(f> 350), 180/pi*angle(dvf_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), 180/pi*angle(dvf_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), 180/pi*angle(dvf_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), 180/pi*angle(dvf_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:90:360);
+yticks(-360:90:360); ylim([-180, 180]);
 
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/strut_1_frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_dvf_plant_tf
-#+caption: Estimated FRF for the DVF plant (transfer function from $V_a$ to the encoder $d_e$)
+#+name: fig:strut_1_frf_dvf_plant_tf
+#+caption: Estimated FRF for the DVF plant (transfer function from $V_a$ to the interferometer $d_a$)
 #+RESULTS:
-[[file:figs/frf_dvf_plant_tf.png]]
+[[file:figs/strut_1_frf_dvf_plant_tf.png]]
 
-**** TODO FRF Identification - IFF
+**** FRF Identification - IFF
 In this section, the dynamics from $V_a$ to $V_s$ is identified.
 
-First the coherence is computed and shown in Figure [[fig:frf_iff_plant_coh]].
+First the coherence is computed and shown in Figure [[fig:strut_1_frf_iff_plant_coh]].
 The coherence is very nice from 10Hz to 2kHz.
 It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
 
@@ -2360,15 +2344,15 @@ legend('location', 'southeast');
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_iff_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/strut_1_frf_iff_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:frf_iff_plant_coh
+#+name: fig:strut_1_frf_iff_plant_coh
 #+caption: Obtained coherence for the IFF plant
 #+RESULTS:
-[[file:figs/frf_iff_plant_coh.png]]
+[[file:figs/strut_1_frf_iff_plant_coh.png]]
 
-Then the FRF are estimated and shown in Figure [[fig:frf_iff_plant_tf]]
+Then the FRF are estimated and shown in Figure [[fig:strut_1_frf_iff_plant_tf]]
 #+begin_src matlab
 [iff_sweep, ~] = tfestimate(leg_sweep.Va, leg_sweep.Vs, win, [], [], 1/Ts);
 [iff_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.Vs, win, [], [], 1/Ts);
@@ -2376,60 +2360,50 @@ Then the FRF are estimated and shown in Figure [[fig:frf_iff_plant_tf]]
 
 #+begin_src matlab :exports none
 figure;
-tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
 
-ax1 = nexttile;
+ax1 = nexttile([2,1]);
 hold on;
-plot(f(f> 350), abs(iff_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), abs(iff_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), abs(iff_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), abs(iff_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
 ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
 hold off;
 ylim([1e-2, 1e2]);
-legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
 
 ax2 = nexttile;
 hold on;
-plot(f(f> 350), 180/pi*angle(iff_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), 180/pi*angle(iff_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), 180/pi*angle(iff_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), 180/pi*angle(iff_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:90:360);
+yticks(-360:90:360); ylim([-180, 180]);
 
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/strut_1_frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_iff_plant_tf
-#+caption:Identified IFF Plant
+#+name: fig:strut_1_frf_iff_plant_tf
+#+caption:Identified IFF Plant for the Strut 1
 #+RESULTS:
-[[file:figs/frf_iff_plant_tf.png]]
+[[file:figs/strut_1_frf_iff_plant_tf.png]]
 
 *** With Encoder
-**** FRF Identification - Setup
-The identification is performed in three steps:
-1. White noise excitation with small amplitude.
-   This is used to determine the main resonance of the system.
-2. Sweep sine excitation with the amplitude lowered around the resonance.
-   The sweep sine is from 10Hz to 400Hz.
-3. High frequency noise.
-   The noise is band-passed between 300Hz and 2kHz.
-
-Then, the result of the second identification is used between 10Hz and 350Hz and the result of the third identification if used between 350Hz and 2kHz.
-
+<<sec:meas_strut_1_encoder>>
+**** Measurement Data
 #+begin_src matlab
 leg_enc_sweep    = load(sprintf('frf_data_leg_coder_badly_align_%i_noise.mat',    1), 't', 'Va', 'Vs', 'de', 'da');
 leg_enc_noise_hf = load(sprintf('frf_data_leg_coder_badly_align_%i_noise_hf.mat', 1), 't', 'Va', 'Vs', 'de', 'da');
 #+end_src
 
-**** TODO FRF Identification - DVF
+**** FRF Identification - DVF
 In this section, the dynamics from $V_a$ to $d_e$ is identified.
 
 We compute the coherence for 2nd and 3rd identification:
@@ -2443,9 +2417,9 @@ colors = get(gca,'colororder');
 
 figure;
 hold on;
-plot(f, coh_enc_noise_hf(:, 1), 'color', [colors(1, :), 0.5], ...
+plot(f, coh_enc_noise_hf(:, 1), 'color', colors(1, :), ...
      'DisplayName', 'HF Noise');
-plot(f, coh_enc_sweep(:, 1), 'color', [colors(2, :), 0.5], ...
+plot(f, coh_enc_sweep(:, 1), 'color', colors(2, :), ...
      'DisplayName', 'Sweep');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
@@ -2455,21 +2429,25 @@ legend('location', 'southeast');
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/strut_1_enc_frf_dvf_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:frf_dvf_plant_coh
+#+name: fig:strut_1_enc_frf_dvf_plant_coh
 #+caption: Obtained coherence for the plant from $V_a$ to $d_e$
 #+RESULTS:
-[[file:figs/frf_dvf_plant_coh.png]]
-
+[[file:figs/strut_1_enc_frf_dvf_plant_coh.png]]
 
 #+begin_src matlab
 [dvf_enc_sweep, ~]    = tfestimate(leg_enc_sweep.Va,    leg_enc_sweep.de,    win, [], [], 1/Ts);
 [dvf_enc_noise_hf, ~] = tfestimate(leg_enc_noise_hf.Va, leg_enc_noise_hf.de, win, [], [], 1/Ts);
 #+end_src
 
-The obtained transfer functions are shown in Figure [[fig:frf_dvf_plant_tf]].
+#+begin_src matlab
+[dvf_int_sweep, ~]    = tfestimate(leg_enc_sweep.Va,    leg_enc_sweep.da,    win, [], [], 1/Ts);
+[dvf_int_noise_hf, ~] = tfestimate(leg_enc_noise_hf.Va, leg_enc_noise_hf.da, win, [], [], 1/Ts);
+#+end_src
+
+The obtained transfer functions are shown in Figure [[fig:strut_1_enc_frf_dvf_plant_tf]].
 
 They are all superimposed except for the APA7.
 
@@ -2488,53 +2466,51 @@ Why is there a double resonance at around 94Hz?
 
 #+begin_src matlab :exports none
 figure;
-tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
 
-ax1 = nexttile;
+ax1 = nexttile([2,1]);
 hold on;
-plot(f(f> 350), abs(dvf_enc_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), abs(dvf_enc_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), abs(dvf_enc_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), abs(dvf_enc_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
 ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
 hold off;
-ylim([1e-9, 1e-3]);
+ylim([1e-7, 1e-3]);
 
 ax2 = nexttile;
 hold on;
-plot(f(f> 350), 180/pi*angle(dvf_enc_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), 180/pi*angle(dvf_enc_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), 180/pi*angle(dvf_enc_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), 180/pi*angle(dvf_enc_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:90:360);
+yticks(-360:90:360); ylim([-180, 180]);
 
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/strut_1_enc_frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_dvf_plant_tf
+#+name: fig:strut_1_enc_frf_dvf_plant_tf
 #+caption: Estimated FRF for the DVF plant (transfer function from $V_a$ to the encoder $d_e$)
 #+RESULTS:
-[[file:figs/frf_dvf_plant_tf.png]]
+[[file:figs/strut_1_enc_frf_dvf_plant_tf.png]]
 
-**** Comparison with Interferometer
+**** Comparison of the Encoder and Interferometer
+The interferometer could here represent the case where the encoders are fixed to the plates and not the APA.
 
-#+begin_src matlab
-[dvf_int_sweep, ~]    = tfestimate(leg_enc_sweep.Va,    leg_enc_sweep.da,    win, [], [], 1/Ts);
-[dvf_int_noise_hf, ~] = tfestimate(leg_enc_noise_hf.Va, leg_enc_noise_hf.da, win, [], [], 1/Ts);
-#+end_src
+The dynamics from $V_a$ to $d_e$ and from $V_a$ to $d_a$ are compared in Figure [[fig:strut_1_comp_enc_int]].
 
 #+begin_src matlab :exports none
 figure;
-tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
 
-ax1 = nexttile;
+ax1 = nexttile([2,1]);
 hold on;
 plot(f(f> 350), abs(dvf_enc_noise_hf(f> 350)), 'color', colors(1, :), ...
      'DisplayName', 'Encoder');
@@ -2546,10 +2522,10 @@ plot(f(f<=350), abs(dvf_int_sweep(   f<=350)), 'color', colors(2, :), ...
      'HandleVisibility', 'off');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
+ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
 hold off;
 legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
-ylim([1e-9, 1e-3]);
+ylim([1e-8, 1e-3]);
 
 ax2 = nexttile;
 hold on;
@@ -2561,19 +2537,27 @@ hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:90:360);
+yticks(-360:90:360); ylim([-180, 180]);
 
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 #+end_src
 
-#+begin_important
-Clearly using the encoder like this will not be useful.
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/strut_1_comp_enc_int.pdf', 'width', 'wide', 'height', 'tall');
+#+end_src
 
-Probably, the encoders will have to be fixed on the plates so that the resonances of the APA are not a problem anymore.
+#+name: fig:strut_1_comp_enc_int
+#+caption:
+#+RESULTS:
+[[file:figs/strut_1_comp_enc_int.png]]
+
+#+begin_important
+It will clearly be difficult to do something (except some low frequency positioning) with the encoders fixed to the APA.
 #+end_important
 
 **** APA Resonances Frequency
+As shown in Figure [[fig:strut_1_spurious_resonances]], we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
 
 #+begin_src matlab :exports none
 figure;
@@ -2592,19 +2576,33 @@ hold off;
 ylim([1e-7, 1e-3]); xlim([10, 2e3]);
 #+end_src
 
-This is very close to what was estimated using the FEM.
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/strut_1_spurious_resonances.pdf', 'width', 'wide', 'height', 'tall');
+#+end_src
 
-#+name: fig:mode_bending_x
+#+name: fig:strut_1_spurious_resonances
+#+caption:
+#+RESULTS:
+[[file:figs/strut_1_spurious_resonances.png]]
+
+
+These resonances correspond to parasitic resonances of the APA itself.
+They are very close to what was estimated using the FEM:
+- X-bending mode at ~190Hz (Figure [[fig:mode_bending_x_bis]])
+- Y-bending mode at ~290Hz (Figure [[fig:mode_bending_y_bis]])
+- Z-torsion mode at ~400Hz (Figure [[fig:mode_torsion_z_bis]])
+
+#+name: fig:mode_bending_x_bis
 #+caption: X-bending mode (189Hz)
 #+attr_latex: :width 0.9\linewidth
 [[file:figs/mode_bending_x.gif]]
 
-#+name: fig:mode_bending_y
+#+name: fig:mode_bending_y_bis
 #+caption: Y-bending mode (285Hz)
 #+attr_latex: :width 0.9\linewidth
 [[file:figs/mode_bending_y.gif]]
 
-#+name: fig:mode_torsion_z
+#+name: fig:mode_torsion_z_bis
 #+caption: Z-torsion mode (400Hz)
 #+attr_latex: :width 0.9\linewidth
 [[file:figs/mode_torsion_z.gif]]
@@ -2613,10 +2611,11 @@ This is very close to what was estimated using the FEM.
 The resonances are indeed due to limited stiffness of the APA.
 #+end_important
 
+**** TODO Estimated Flexible Joint axial stiffness
 **** FRF Identification - IFF
 In this section, the dynamics from $V_a$ to $V_s$ is identified.
 
-First the coherence is computed and shown in Figure [[fig:frf_iff_plant_coh]].
+First the coherence is computed and shown in Figure [[fig:strut_1_frf_iff_plant_coh]].
 The coherence is very nice from 10Hz to 2kHz.
 It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).
 
@@ -2630,8 +2629,8 @@ colors = get(gca,'colororder');
 
 figure;
 hold on;
-plot(f, coh_enc_noise_hf, 'color', [colors(1, :), 0.5], 'DisplayName', 'HF Noise');
-plot(f, coh_enc_sweep,    'color', [colors(2, :), 0.5], 'DisplayName', 'Sweep');
+plot(f, coh_enc_noise_hf, 'color', colors(1, :), 'DisplayName', 'HF Noise');
+plot(f, coh_enc_sweep,    'color', colors(2, :), 'DisplayName', 'Sweep');
 hold off;
 xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
@@ -2640,15 +2639,15 @@ legend('location', 'southeast');
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_iff_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/strut_1_frf_iff_plant_coh.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:frf_iff_plant_coh
+#+name: fig:strut_1_frf_iff_plant_coh
 #+caption: Obtained coherence for the IFF plant
 #+RESULTS:
-[[file:figs/frf_iff_plant_coh.png]]
+[[file:figs/strut_1_frf_iff_plant_coh.png]]
 
-Then the FRF are estimated and shown in Figure [[fig:frf_iff_plant_tf]]
+Then the FRF are estimated and shown in Figure [[fig:strut_1_enc_frf_iff_plant_tf]]
 #+begin_src matlab
 [iff_enc_sweep,    ~] = tfestimate(leg_enc_sweep.Va,    leg_enc_sweep.Vs,    win, [], [], 1/Ts);
 [iff_enc_noise_hf, ~] = tfestimate(leg_enc_noise_hf.Va, leg_enc_noise_hf.Vs, win, [], [], 1/Ts);
@@ -2656,61 +2655,54 @@ Then the FRF are estimated and shown in Figure [[fig:frf_iff_plant_tf]]
 
 #+begin_src matlab :exports none
 figure;
-tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
 
-ax1 = nexttile;
+ax1 = nexttile([2,1]);
 hold on;
-plot(f(f> 350), abs(iff_enc_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), abs(iff_enc_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), abs(iff_enc_noise_hf(f> 350)), 'k-');
+plot(f(f<=350), abs(iff_enc_sweep(   f<=350)), 'k-');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
 ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
 hold off;
 ylim([1e-2, 1e2]);
-legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
 
 ax2 = nexttile;
 hold on;
-plot(f(f> 350), 180/pi*angle(iff_enc_noise_hf(f> 350)), 'color', colors(1, :));
-plot(f(f<=350), 180/pi*angle(iff_enc_sweep(   f<=350)), 'color', colors(1, :));
+plot(f(f> 350), 180/pi*angle(iff_enc_noise_hf(f> 350)), 'k');
+plot(f(f<=350), 180/pi*angle(iff_enc_sweep(   f<=350)), 'k');
 hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:90:360);
+yticks(-360:90:360); ylim([-180, 180]);
 
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
+exportFig('figs/strut_1_enc_frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall');
 #+end_src
 
-#+name: fig:frf_iff_plant_tf
+#+name: fig:strut_1_enc_frf_iff_plant_tf
 #+caption:Identified IFF Plant
 #+RESULTS:
-[[file:figs/frf_iff_plant_tf.png]]
-
-**** Comparison to when the encoder is not fixed
-
-#+begin_src matlab
-[iff_sweep, ~]    = tfestimate(leg_sweep.Va,    leg_sweep.Vs,    win, [], [], 1/Ts);
-[iff_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.Vs, win, [], [], 1/Ts);
-#+end_src
+[[file:figs/strut_1_enc_frf_iff_plant_tf.png]]
 
+Let's now compare the IFF plants whether the encoders are fixed to the APA or not (Figure [[fig:strut_1_frf_iff_comp_enc]]).
 #+begin_src matlab :exports none
 figure;
-tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
 
-ax1 = nexttile;
+ax1 = nexttile([2,1]);
 hold on;
 plot(f(f> 350), abs(iff_enc_noise_hf(f> 350)), 'color', colors(1, :), ...
      'DisplayName', 'Encoder');
 plot(f(f<=350), abs(iff_enc_sweep(   f<=350)), 'color', colors(1, :), ...
      'HandleVisibility', 'off');
 plot(f(f> 350), abs(iff_noise_hf(f> 350)), 'color', colors(2, :), ...
-     'DisplayName', 'Withotu Encoder');
+     'DisplayName', 'Without Encoder');
 plot(f(f<=350), abs(iff_sweep(   f<=350)), 'color', colors(2, :), ...
      'HandleVisibility', 'off');
 hold off;
@@ -2730,12 +2722,21 @@ hold off;
 set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
 xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
 hold off;
-yticks(-360:90:360);
+yticks(-360:90:360); ylim([-180, 180]);
 
 linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 #+end_src
 
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/strut_1_frf_iff_effect_enc.pdf', 'width', 'wide', 'height', 'tall');
+#+end_src
+
+#+name: fig:strut_1_frf_iff_comp_enc
+#+caption: Effect of the encoder on the IFF plant
+#+RESULTS:
+[[file:figs/strut_1_frf_iff_effect_enc.png]]
+
 #+begin_important
 We can see that the IFF does not change whether of not the encoder are fixed to the struts.
 #+end_important