Add all before first review

matlab/test_struts_1_flexible_modes.m

@@ -12,7 +12,7 @@ addpath('./src/'); % Path for functions
 colors = colororder;
 
 % Measured results
-% The obtained frequency response functions are shown in Figure ref:fig:test_struts_spur_res_frf.
+% The obtained frequency response functions for the three configurations (X-bending, Y-bending and Z-torsion) are shown in Figure ref:fig:test_struts_spur_res_frf_no_enc when the encoder is not fixed to the strut and in Figure ref:fig:test_struts_spur_res_frf_enc when the encoder is fixed to the strut.
 
 
 %% Load Data (without the encoder)
@@ -41,6 +41,7 @@ hold off;
 set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
 xlabel('Frequency [Hz]'); ylabel('Amplitude');
 xlim([50, 8e2]); ylim([5e-7, 3e-4])
+xticks([50, 100, 500]);
 legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
 
 %% Plot the responses (with the encoder)
@@ -59,4 +60,5 @@ hold off;
 set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
 xlabel('Frequency [Hz]'); ylabel('Amplitude');
 xlim([50, 8e2]); ylim([5e-7, 3e-4])
+xticks([50, 100, 500]);
 legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);

matlab/test_struts_2_dynamical_meas.m

@@ -63,11 +63,33 @@ enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF
 
 
 
-% Figure ref:fig:test_struts_effect_encoder_int
-% Same goes for the transfer function from excitation voltage $u$ to the axial motion of the strut $d_a$ as measured by the interferometer ().
+% System identification is performed in two cases:
+% - no encoder is fixed to the strut (Figure ref:fig:test_struts_bench_leg_front)
+% - one encoder is fixed to the strut (Figure ref:fig:test_struts_bench_leg_coder)
 
-% The transfer function from the excitation voltage $u$ to the generated voltage $V_s$ by the sensor stack is not influence by the fixation of the encoder (Figure ref:fig:test_struts_effect_encoder_iff).
-% This means that the IFF control strategy should be as effective whether or not the encoders are fixed to the struts.
+% #+name: fig:test_struts_bench_leg_with_without_enc
+% #+caption: Struts fixed to the test bench with clamped flexible joints. The coder can be fixed to the struts (\subref{fig:test_struts_bench_leg_coder}) or removed (\subref{fig:test_struts_bench_leg_front})
+% #+attr_latex: :options [htbp]
+% #+begin_figure
+% #+attr_latex: :caption \subcaption{\label{fig:test_struts_bench_leg_coder}Strut with encoder}
+% #+attr_latex: :options {0.5\textwidth}
+% #+begin_subfigure
+% #+attr_latex: :height 6cm
+% [[file:figs/test_struts_bench_leg_coder.jpg]]
+% #+end_subfigure
+% #+attr_latex: :caption \subcaption{\label{fig:test_struts_bench_leg_front}Strut without encoder}
+% #+attr_latex: :options {0.5\textwidth}
+% #+begin_subfigure
+% #+attr_latex: :height 6cm
+% [[file:figs/test_struts_bench_leg_front.jpg]]
+% #+end_subfigure
+% #+end_figure
+
+% The obtained frequency response functions are compared in Figure ref:fig:test_struts_effect_encoder.
+% It is found that the encoder has very little effect on the transfer function from excitation voltage $u$ to the axial motion of the strut $d_a$ as measured by the interferometer (Figure ref:fig:test_struts_effect_encoder_int).
+% This means that the axial motion of the strut is unaffected by the presence of the encoder.
+% Similarly, it has very little effect on the transfer function from $u$ to the sensor stack voltage $V_s$ (Figure ref:fig:test_struts_effect_encoder_iff).
+% This means that the integral force feedback control strategy should be as effective whether the encoders are fixed to the struts.
 
 
 %% Plot the FRF from u to da with and without the encoder
@@ -131,17 +153,12 @@ xlim([10, 2e3]);
 
 % The dynamics as measured by the encoder and by the interferometers are compared in Figure ref:fig:test_struts_comp_enc_int.
 
-% The dynamics from the excitation voltage $u$ to the measured displacement by the encoder $d_e$ presents much more complicated behavior than the transfer function to the displacement as measured by the Interferometer (compared in Figure ref:fig:test_struts_comp_enc_int).
-% It will be further investigated why the two dynamics as so different and what are causing all these resonances.
+% The dynamics from the excitation voltage $u$ to the measured displacement by the encoder $d_e$ presents a behavior that is much more complex than the dynamics to the displacement as measured by the interferometer (comparison made in Figure ref:fig:test_struts_comp_enc_int).
+% Three additional resonance frequencies can be observed at 197Hz, 290Hz and 376Hz.
+% These resonance frequencies correspond to flexible modes of the strut that were studied in Section ref:sec:test_struts_flexible_modes.
 
-% As shown in Figure ref:fig:test_struts_comp_enc_int, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
-% These resonances correspond to parasitic resonances of the strut itself that was estimated using a finite element model of the strut (Figure ref:fig:test_struts_mode_shapes):
-% - Mode in X-bending at 189Hz
-% - Mode in Y-bending at 285Hz
-% - Mode in Z-torsion at 400Hz
-
-% The good news is that these resonances are not seen on the interferometer (they are therefore not impacting the axial motion of the strut).
-% But these resonances are making the use of encoder fixed to the strut difficult.
+% The good news is that these resonances are not seen on the interferometer and are therefore not impacting the axial motion of the strut (which is what is important for the hexapod positioning).
+% However, these resonances are making the use of encoder fixed to the strut difficult.
 
 
 figure;
@@ -222,8 +239,9 @@ end
 
 
 
-% Then, the transfer function from the DAC output voltage $u$ to the measured displacement by the Attocube is computed for all the struts and shown in Figure ref:fig:test_struts_comp_interf_plants.
-% All the struts are giving very similar FRF.
+% Then, the dynamics of all the mounted struts (only 5 at the time of the experiment) are all measured using the same test bench.
+% The obtained dynamics from $u$ to $d_a$ are compared in Figure ref:fig:test_struts_comp_interf_plants while is dynamics from $u$ to $V_s$ are compared in Figure ref:fig:test_struts_comp_iff_plants.
+% Very good match can be observed between all the struts.
 
 
 %% Plot the FRF from u to de (interferometer)
@@ -308,11 +326,12 @@ xlim([10, 2e3]);
 % #+end_subfigure
 % #+end_figure
 
-% There is a very large variability of the dynamics as measured by the encoder as shown in Figure ref:fig:test_struts_comp_enc_plants.
+% The same comparison is made for the transfer function from $u$ to $d_e$ (encoder output) in Figure ref:fig:test_struts_comp_enc_plants.
+% This time, large dynamics differences are observed between the 5 struts.
 % Even-though the same peaks are seen for all of the struts (95Hz, 200Hz, 300Hz, 400Hz), the amplitude of the peaks are not the same.
 % Moreover, the location or even the presence of complex conjugate zeros is changing from one strut to the other.
 
-% All of this will be studied in Section ref:sec:test_struts_simscape using the Simscape model.
+% It will be further investigated why such differences are observed (see Section ref:ssec:test_struts_effect_misalignment).
 
 
 %% Bode plot of the FRF from u to de

matlab/test_struts_3_simscape_model.m

@@ -78,7 +78,7 @@ Gs_flex.OutputName = {'Vs', 'de', 'da'};
 
 % However, the transfer function from $u$ to encoder displacement $d_e$ are not well matching for both models.
 % For the 2DoF model, this is normal as the resonances affecting the dynamics are not modelled at all (the APA300ML is modelled as infinitely rigid in all directions except the translation along it's actuation axis).
-% For the flexible model, it will be shown in the next section that by adding some misalignment betwen the flexible joints and the APA300ML, this model can better represent the observed dynamics.
+% For the flexible model, it will be shown in the next section that by adding some misalignment between the flexible joints and the APA300ML, this model can better represent the observed dynamics.
 
 
 %% Compare the FRF and identified dynamics from u to Vs and da
@@ -222,8 +222,8 @@ xlim([10, 2e3]);
 % The misalignment in the $y$ direction mostly influences:
 % - the presence of the flexible mode at 200Hz (see mode shape in Figure ref:fig:test_struts_mode_shapes_1)
 % - the location of the complex conjugate zero between the first two resonances:
-%   - if $d_y < 0$: there is no zero between the two resonances and possibly not even between the second and third ones
-%   - if $d_y > 0$: there is a complex conjugate zero between the first two resonances
+%   - if $d_{y} < 0$: there is no zero between the two resonances and possibly not even between the second and third ones
+%   - if $d_{y} > 0$: there is a complex conjugate zero between the first two resonances
 % - the location of the high frequency complex conjugate zeros at 500Hz (secondary effect, as the axial stiffness of the joint also has large effect on the position of this zero)
 
 % The same can be done for a misalignment in the $x$ direction.