Tangle Matlab files without comments

matlab/test_struts_1_flexible_modes.m

@@ -11,10 +11,6 @@ addpath('./src/'); % Path for functions
 %% Colors for the figures
 colors = colororder;
 
-% Measured results
-% 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)
 bending_X = load('strut_spur_res_x_bending.mat');
 bending_Y = load('strut_spur_res_y_bending.mat');

matlab/test_struts_2_dynamical_meas.m

@@ -11,10 +11,6 @@ addpath('./src/'); % Path for functions
 %% Colors for the figures
 colors = colororder;
 
-% Effect of the Encoder on the measured dynamics
-% <<ssec:test_struts_effect_encoder>>
-
-
 %% Parameters for Frequency Analysis
 Ts = 1e-4; % Sampling Time [s]
 Nfft = floor(1/Ts); % Number of points for the FFT computation
@@ -61,35 +57,6 @@ iff_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF
 [frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.de, win, Noverlap, Nfft, 1/Ts);
 enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF
 
-
-
-% System identification is performed without the encoder fixed to the strut (Figure ref:fig:test_struts_bench_leg_front) and with one encoder fixed to the strut (Figure ref:fig:test_struts_bench_leg_coder).
-
-% #+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 or not.
-
-
 %% Plot the FRF from u to da with and without the encoder
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
@@ -150,18 +117,6 @@ linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Comparison of the encoder and interferometer
-% <<ssec:test_struts_comp_enc_int>>
-
-% The dynamics as measured by the encoder (i.e. $d_e/u$) and by the interferometers (i.e. $d_a/u$) 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 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 are matching the frequencies of the flexible modes that were studied in Section ref:sec:test_struts_flexible_modes.
-
-% The good news is that these resonances are 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 from a control perspective.
-
-
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
 
@@ -195,10 +150,6 @@ linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Comparison of all the Struts
-% <<ssec:test_struts_comp_all_struts>>
-
-
 %% Numbers of the measured legs
 strut_nums = [1 2 3 4 5];
 
@@ -240,13 +191,6 @@ for i = 1:length(strut_nums)
     iff_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
 end
 
-
-
-% Then, the dynamics of all the mounted struts (only 5 at the time of the experiment) were 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)
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

matlab/test_struts_3_simscape_model.m

@@ -31,10 +31,6 @@ io(io_i) = linio([mdl, '/da'], 1, 'openoutput'); io_i = io_i + 1; % Interferomet
 %% Frequency vector [Hz]
 freqs = logspace(1, log10(2000), 1000);
 
-% Model dynamics
-% <<ssec:test_struts_comp_model>>
-
-
 %% Load measured FRF for comparison
 load('meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums');
 
@@ -64,20 +60,6 @@ Gs_flex = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
 Gs_flex.InputName  = {'u'};
 Gs_flex.OutputName = {'Vs', 'de', 'da'};
 
-
-
-% Two models of the APA300ML are used here: a simple two degrees of freedom model and a model using a super element extracted from a finite element model.
-% These two models of the APA300ML were tuned to best match measured frequency response functions of the APA alone.
-% The flexible joints are here modelled with the 4DoF model (axial stiffness, two bending stiffnesses and one torsion stiffness).
-% These two models are compared with the measured frequency responses in Figure ref:fig:test_struts_comp_frf_flexible_model.
-
-% The model dynamics from DAC voltage $u$ to the axial motion of the strut $d_a$ (Figure ref:fig:test_struts_comp_frf_flexible_model_int) and from DAC voltage $u$ to the force sensor voltage $V_s$ (Figure ref:fig:test_struts_comp_frf_flexible_model_iff) are well matching the experimental identification.
-
-% 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 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
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
@@ -202,36 +184,6 @@ linkaxes([ax1a,ax2a],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Effect of strut misalignment
-% <<ssec:test_struts_effect_misalignment>>
-
-% As was shown in Figure ref:fig:test_struts_comp_enc_plants, the identified dynamics from DAC voltage $u$ to encoder measured displacement $d_e$ are very different from one strut to the other.
-% In this section, it is investigated whether poor alignment of the strut (flexible joints with respect to the APA) can explain such dynamics.
-% For instance, consider Figure ref:fig:test_struts_misalign_schematic where there is a misalignment in the $y$ direction between the two flexible joints (well aligned thanks to the mounting procedure in Section ref:sec:test_struts_mounting) and the APA300ML.
-% In such case, the "x-bending" mode at 200Hz (see Figure ref:fig:test_struts_meas_x_bending) can be expected to have more impact on the dynamics from the actuator to the encoder.
-
-% #+name: fig:test_struts_misalign_schematic
-% #+caption: Mis-alignement between the joints and the APA
-% #+attr_latex: :width 0.8\linewidth
-% [[file:figs/test_struts_misalign_schematic.png]]
-
-% To verify this assumption, the dynamics from output DAC voltage $u$ to the measured displacement by the encoder $d_e$ is computed using the flexible APA Simscape model for several misalignment in the $y$ direction.
-% Obtained dynamics are shown in Figure ref:fig:test_struts_effect_misalignment_y.
-% The alignment of the APA with the flexible joints as a large influence on the dynamics from actuator voltage to measured displacement by the encoder.
-% 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
-% - 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.
-% The obtained dynamics (Figure ref:fig:test_struts_effect_misalignment_x) are showing that misalignment in the $x$ direction mostly influences the presence of the flexible mode at 300Hz (see mode shape in Figure ref:fig:test_struts_mode_shapes_2).
-
-% Comparing the experimental frequency response functions for all the APA in Figure ref:fig:test_struts_comp_enc_plants with the model dynamics for several $y$ misalignments in Figure ref:fig:test_struts_effect_misalignment_y indicates a clear similarity.
-% This similarity suggests that the identified differences in dynamics are caused by the misalignment.
-
-
 %% Effect of a misalignment in Y-Direction
 % Considered misalignment in the Y direction
 dy_aligns = [-0.5, -0.1, 0.1, 0.5]*1e-3; % [m]
@@ -338,23 +290,6 @@ linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Measured strut misalignment
-% <<ssec:test_struts_meas_misalignment>>
-
-% During the initial mounting of the struts as presented in Section ref:sec:test_struts_mounting, the positioning pins that are used to position the APA with respect to the flexible joints in the $y$ directions were not used (not received at the time).
-% Therefore, large $y$ misalignments is expected.
-
-% In order to estimate the misalignments between the two flexible joints and the APA:
-% - the struts are fixed horizontally on the mounting bench as shown in Figure ref:fig:test_struts_mounting_step_3 but without the encoder
-% - using a length gauge[fn:2], the height difference from the flexible joints surface and the APA shell surface is measured both for the top and bottom joints and for both sides
-% - as the thickness of the flexible joint is $21\,mm$ and the thickness of the APA shell is $20\,mm$, $0.5\,mm$ of height different should be measured if the two are perfectly aligned
-
-% Large variations in the $y$ misalignment are found from one strut to the other (results are summarized in Table ref:tab:test_struts_meas_y_misalignment).
-
-% To check the validity of the measurement, it can be verified that sum of the measured thickness difference on each side is $1\,mm$ (equal to the thickness difference between the flexible joint and the APA).
-% This thickness differences for all the struts were found to be between $0.94\,mm$ and $1.00\,mm$ which indicate low errors as compared to the misalignments found in Table ref:tab:test_struts_meas_y_misalignment.
-
-
 %% Measurement of the y misalignment between the APA and the flexible joints
 % Mesured struts
 strut_nums = [1, 2, 3, 4, 5];
@@ -376,31 +311,6 @@ thichness_diff_bot = strut_align(:,1) + strut_align(:,2); % [mm]
 dy_bot = (strut_align(:,1) - strut_align(:,2))/2; % [mm]
 dy_top = (strut_align(:,3) - strut_align(:,4))/2; % [mm]
 
-
-
-% #+name: tab:test_struts_meas_y_misalignment
-% #+caption: Measured $y$ misalignment at the top and bottom of the APA. Measurements are in $mm$
-% #+attr_latex: :environment tabularx :width 0.25\linewidth :align ccc
-% #+attr_latex: :center t :booktabs t
-% #+RESULTS:
-% | *Strut* | *Bot* | *Top* |
-% |---------+-------+-------|
-% |       1 |   0.1 |  0.33 |
-% |       2 | -0.19 |  0.14 |
-% |       3 |  0.41 |  0.32 |
-% |       4 | -0.01 |  0.54 |
-% |       5 |  0.15 |  0.02 |
-
-% By using the measured $y$ misalignment in the Simscape model with the flexible APA model, the model dynamics from $u$ to $d_e$ is closer to the measured one as shown in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc.
-% Better match in the dynamics can be obtained by fine tuning both the $x$ and $y$ misalignments (yellow curves in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc).
-
-% This confirms that the misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and is inducing large variations in the dynamics from DAC voltage $u$ to encoder measured displacement $d_e$.
-% If encoders are fixed to the struts, it is important to precisely align the APA and the flexible joints when mounting the struts.
-
-% In the next section, the struts are re-assembled with a "positioning pin" to better align the APA with the flexible joints.
-% With a better alignment, the amplitude of the spurious resonances are expected to decrease as was shown in Figure ref:fig:test_struts_effect_misalignment_y.
-
-
 %% Idenfity the dynamics from u to de - misalignement estimated from measurement
 Gs_y_align = {zeros(size(strut_align,1), 1)};
 
@@ -496,16 +406,6 @@ xticks([1e1, 1e2, 1e3]);
 linkaxes([ax1,ax2,ax3],'xy');
 xlim([10, 2e3]); ylim([1e-8, 1e-3]);
 
-% Proper struts alignment
-% <<sec:test_struts_meas_all_aligned_struts>>
-
-% After the positioning pins had been received, the struts were mounted again with the positioning pins.
-% This should make the APA better aligned with the two flexible joints.
-
-% This alignment is then estimated using a length gauge as in the previous sections.
-% Measured $y$ alignments are summarized in Table ref:tab:test_struts_meas_y_misalignment_with_pin and are found to be bellow $55\mu m$ for all the struts which is much better than before (see Table ref:tab:test_struts_meas_y_misalignment).
-
-
 %% Measurement of the y misalignment between the APA and the flexible joints after strut better alignment
 
 % Numbers of the measured legs
@@ -529,31 +429,6 @@ thichness_diff_bot = strut_align(:,1) + strut_align(:,2); % [mm]
 dy_bot = (strut_align(:,1) - strut_align(:,2))/2; % [mm]
 dy_top = (strut_align(:,3) - strut_align(:,4))/2; % [mm]
 
-
-
-% #+name: tab:test_struts_meas_y_misalignment_with_pin
-% #+caption: Measured $y$ misalignment at the top and bottom of the APA after realigning the struts using a positioning pin. Measurements are in $mm$.
-% #+attr_latex: :environment tabularx :width 0.25\linewidth :align ccc
-% #+attr_latex: :center t :booktabs t
-% #+RESULTS:
-% | *Strut* |  *Bot* | *Top* |
-% |---------+--------+-------|
-% |       1 |  -0.02 |  0.01 |
-% |       2 |  0.055 |   0.0 |
-% |       3 |   0.01 | -0.02 |
-% |       4 |   0.03 | -0.03 |
-% |       5 |    0.0 |   0.0 |
-% |       6 | -0.005 | 0.055 |
-
-% The dynamics of the re-aligned struts are then measured using the same test bench (Figure ref:fig:test_struts_bench_leg).
-% The comparison of the initial strut dynamics and the dynamics of the re-aligned struts (i.e. with the positioning pin) is made in Figure ref:fig:test_struts_comp_enc_frf_realign.
-% Even though the struts are now much better aligned, not much improvement can be observed.
-% Also, the dynamics of the six aligned struts are quite different from one another.
-
-% Having the encoders fixed to the struts are making the control more challenging.
-% Therefore, the encoders may be fixed to the nano-hexapod plates instead.
-
-
 %% New dynamical identified with re-aligned struts
 % Load the identification data
 leg_noise = {};

test-bench-struts.org

@@ -22,7 +22,7 @@
 # #+BIND: org-latex-bib-compiler "biber"
 
 #+PROPERTY: header-args:matlab  :session *MATLAB*
-#+PROPERTY: header-args:matlab+ :comments org
+#+PROPERTY: header-args:matlab+ :comments no
 #+PROPERTY: header-args:matlab+ :exports none
 #+PROPERTY: header-args:matlab+ :results none
 #+PROPERTY: header-args:matlab+ :eval no-export