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Reword pictures and make subfigure
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Before Width: | Height: | Size: 5.1 MiB After Width: | Height: | Size: 5.3 MiB |
Binary file not shown.
Binary file not shown.
+156
-130
@@ -104,13 +104,23 @@ To integrate:
|
||||
- [X] [[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-apa300ml/test-bench-apa300ml.org][test-bench-apa300ml]]
|
||||
- [X] Dynamical measurements (Section 5)
|
||||
- [X] Simscape model (Section 6)
|
||||
- [ ] Check what are the used Matlab functions
|
||||
- [X] Check what are the used Matlab functions
|
||||
- [X] check [[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-apa300ml/test-bench-apa300ml.org::*Compare with the FEM/Simscape Model][Compare with the FEM/Simscape Model]]
|
||||
*no, it is only for the APA and not the strut*
|
||||
- [X] Check [[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-apa300ml/test-bench-apa300ml.org::*New Measurements - IFF Root Locus][New Measurements - IFF Root Locus]]
|
||||
*no, it is only for the APA and not the strut*
|
||||
|
||||
** TODO [#B] Make the simscape model work
|
||||
** TODO [#A] Rework mounting procedure section
|
||||
|
||||
- [X] Use smaller images, maybe one subfigure for all the steps
|
||||
- [ ] Explain clearly the mounting goals (coaxiality, etc.)
|
||||
|
||||
** TODO [#B] Rework flexible mode measurements
|
||||
|
||||
- [ ] Use smaller images, one subfigure for all measurements
|
||||
|
||||
** DONE [#B] Make the simscape model work
|
||||
CLOSED: [2024-03-25 Mon 15:09]
|
||||
|
||||
* Introduction :ignore:
|
||||
|
||||
@@ -146,7 +156,7 @@ The final goal of the work presented in this document is to have an accurate Sim
|
||||
|--------------------------------------------+----------------------------------|
|
||||
| Section ref:sec:test_struts_flexible_modes | =test_struts_1_flexible_modes.m= |
|
||||
| Section ref:sec:test_struts_dynamical_meas | =test_struts_2_dynamical_meas.m= |
|
||||
| Section ref:sec:test_struts_mounting | =test_struts_3_simscape_model.m= |
|
||||
| Section ref:sec:test_struts_simscape | =test_struts_3_simscape_model.m= |
|
||||
|
||||
* Mounting Procedure
|
||||
<<sec:test_struts_mounting>>
|
||||
@@ -158,76 +168,104 @@ This is very important in order to not loose any stroke when the struts will be
|
||||
|
||||
A CAD view of the mounting bench is shown in Figure ref:fig:test_struts_mounting_bench_first_concept.
|
||||
|
||||
- [ ] Add some notes to the figure
|
||||
|
||||
#+name: fig:test_struts_mounting_bench_first_concept
|
||||
#+caption: CAD view of the mounting bench
|
||||
#+attr_latex: :width \linewidth
|
||||
#+attr_latex: :width 0.6\linewidth
|
||||
[[file:figs/test_struts_mounting_bench_first_concept.png]]
|
||||
|
||||
The main part of the bench is here to ensure both the correct strut length and strut coaxiality as shown in Figure ref:fig:test_struts_mounting_step_0.
|
||||
|
||||
#+name: fig:test_struts_mounting_step_0
|
||||
#+caption: Useful features of the main mounting element
|
||||
#+attr_latex: :width \linewidth
|
||||
#+name: fig:test_struts_mounting_base_part
|
||||
#+caption: Caption..., add foot note with Faro arm
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mounting_step_0}Useful features of the main mounting element}
|
||||
#+attr_latex: :options {0.56\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :height 4.5cm
|
||||
[[file:figs/test_struts_mounting_step_0.jpg]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_check_dimensions_bench}Dimensional check}
|
||||
#+attr_latex: :options {0.43\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :height 4.5cm
|
||||
[[file:figs/test_struts_check_dimensions_bench.jpg]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
|
||||
The tight tolerances of this element has been verified as shown in Figure ref:fig:test_struts_mounting_bench_first_concept and were found to comply with the requirements.
|
||||
The tight tolerances of this element has been verified as shown in Figure ref:fig:test_struts_check_dimensions_bench and were found to comply with the requirements.
|
||||
|
||||
#+name: fig:test_struts_mounting_bench_first_concept
|
||||
#+caption: Dimensional verifications of the mounting bench tolerances
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/check_dimensions_bench.jpg]]
|
||||
|
||||
The flexible joints are rigidly fixed to cylindrical tools shown in Figure ref:fig:cylindrical_mounting_part which are then mounted on the mounting tool shown in Figure ref:fig:test_struts_mounting_step_0.
|
||||
The flexible joints are rigidly fixed to cylindrical tools shown in Figures ref:fig:test_struts_cylindrical_mounting_part_top and ref:fig:test_struts_cylindrical_mounting_part_bot which are then mounted on the mounting tool shown in Figure ref:fig:test_struts_mounting_step_0.
|
||||
This cylindrical tool is here to protect the flexible joints when tightening the screws and therefore applying large torque.
|
||||
|
||||
#+name: fig:cylindrical_mounting_part
|
||||
#+caption: Cylindrical mounting elements
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/cylindrical_mounting_part.jpg]]
|
||||
|
||||
** Mounting Procedure
|
||||
|
||||
The mounting procedure is as follows:
|
||||
1. Screw flexible joints inside the cylindrical interface element shown in Figure ref:fig:cylindrical_mounting_part (Figure ref:fig:test_struts_mounting_step_1)
|
||||
1. Screw flexible joints inside the cylindrical interface element shown in Figure ref:fig:test_struts_cylindrical_mounting
|
||||
2. Fix the two interface elements. One of the two should be clamped, the other one should have its axial rotation free.
|
||||
Visually align the clamped one horizontally. (Figure ref:fig:test_struts_mounting_step_2)
|
||||
3. Put cylindrical washers, APA and interface pieces on top of the flexible joints (Figure ref:fig:test_struts_mounting_step_3)
|
||||
Visually align the clamped one horizontally. (Figure ref:fig:test_struts_mounting_step_1)
|
||||
3. Put cylindrical washers, APA and interface pieces on top of the flexible joints (Figure ref:fig:test_struts_mounting_step_2)
|
||||
4. Put the 4 screws just in contact such that everything is correctly positioned and such that the "free" flexible joint is correctly oriented
|
||||
5. Put the 8 lateral screws in contact
|
||||
6. Tighten the 4 screws to fix the APA on the two flexible joints (using a torque screwdriver)
|
||||
7. Remove the 4 laterals screws
|
||||
8. (optional) Put the APA horizontally and fix the encoder and align it to maximize the contrast (Figure ref:fig:test_struts_mounting_step_4)
|
||||
8. (optional) Put the APA horizontally and fix the encoder and align it to maximize the contrast (Figure ref:fig:test_struts_mounting_step_3)
|
||||
9. Disassemble to have an properly mounted strut (Figure ref:fig:test_struts_mounting_step_4) for which the coaxiality between the two flexible joint's interfaces is good
|
||||
|
||||
#+name: fig:test_struts_mounting_step_1
|
||||
#+caption: Step 1 - Flexible joints fixed on the cylindrical interface elements
|
||||
#+attr_latex: :width 0.5\linewidth
|
||||
#+name: fig:test_struts_cylindrical_mounting
|
||||
#+caption: Preparation of the flexible joints by fixing them in their cylindrical interface
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_cylindrical_mounting_part_top}Cylindral Interface (Top)}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :height 4.5cm
|
||||
[[file:figs/test_struts_cylindrical_mounting_part_top.jpg]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_cylindrical_mounting_part_bot}Cylindrlcal Interface (Bottom)}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :height 4.5cm
|
||||
[[file:figs/test_struts_cylindrical_mounting_part_bot.jpg]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mounting_joints}Mounted flexible joints}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :height 4.5cm
|
||||
[[file:figs/test_struts_mounting_joints.jpg]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
|
||||
#+name: fig:test_struts_mounting_steps
|
||||
#+caption: Steps for mounting the struts.
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mounting_step_1}Step 1}
|
||||
#+attr_latex: :options {0.5\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.99\linewidth
|
||||
[[file:figs/test_struts_mounting_step_1.jpg]]
|
||||
|
||||
#+name: fig:test_struts_mounting_step_2
|
||||
#+caption: Step 2 - Cylindrical elements fixed on the bench
|
||||
#+attr_latex: :width \linewidth
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mounting_step_2}Step 2}
|
||||
#+attr_latex: :options {0.5\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.99\linewidth
|
||||
[[file:figs/test_struts_mounting_step_2.jpg]]
|
||||
|
||||
#+name: fig:test_struts_mounting_step_3
|
||||
#+caption: Step 3 - Mount the nuts, washers and APA
|
||||
#+attr_latex: :width \linewidth
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mounting_step_3}Step 3}
|
||||
#+attr_latex: :options {0.5\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.99\linewidth
|
||||
[[file:figs/test_struts_mounting_step_3.jpg]]
|
||||
|
||||
#+name: fig:test_struts_mounting_step_4
|
||||
#+caption: Last step - Align the encoder on the strut
|
||||
#+attr_latex: :width \linewidth
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mounting_step_4}Step 4}
|
||||
#+attr_latex: :options {0.5\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.99\linewidth
|
||||
[[file:figs/test_struts_mounting_step_4.jpg]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
|
||||
** Mounted Struts
|
||||
|
||||
After removing the strut from the mounting bench, we obtain a strut with ensured coaxiality between the two flexible joint's interfaces (Figure ref:fig:test_struts_mounted_strut).
|
||||
|
||||
#+name: fig:test_struts_mounted_strut
|
||||
#+caption: Mounted Strut with ensured coaxiality
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/test_struts_mounted_strut.jpg]]
|
||||
|
||||
* Spurious resonances
|
||||
* Measurement of flexible modes
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/test_struts_1_flexible_modes.m
|
||||
:END:
|
||||
@@ -244,9 +282,27 @@ From a Finite Element Model of the struts, it have been found that three main re
|
||||
- Mode in Z-torsion at 400Hz
|
||||
|
||||
#+name: fig:test_struts_mode_shapes
|
||||
#+caption: Spurious resonances of the struts estimated from a Finite Element Model. a) X-bending mode at 189Hz. b) Y-bending mode at 285Hz. c) Z-torsion mode at 400Hz
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/test_struts_mode_shapes.png]]
|
||||
#+caption: Spurious resonances of the struts estimated from a Finite Element Model
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mode_shapes_3}X-bending mode (189Hz)}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/test_struts_mode_shapes_1.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mode_shapes_3}Y-bending mode (285Hz)}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/test_struts_mode_shapes_2.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_mode_shapes_3}Z-torsion mode (400Hz)}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/test_struts_mode_shapes_3.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
@@ -271,38 +327,37 @@ From a Finite Element Model of the struts, it have been found that three main re
|
||||
|
||||
** Measurement Setup
|
||||
|
||||
A Laser vibrometer is measuring the difference of motion between two points (Figure ref:fig:test_struts_meas_spur_res_struts_1_enc).
|
||||
The APA is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
|
||||
A Laser vibrometer is measuring the difference of motion between two beam path (red points in Figure ref:fig:test_struts_meas_modes).
|
||||
The strut is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
|
||||
|
||||
#+begin_note
|
||||
The instrumentation used are:
|
||||
- Laser Doppler Vibrometer Polytec OFV512
|
||||
- Instrumented hammer
|
||||
#+end_note
|
||||
The "X-bending" mode is measured as shown in Figure ref:fig:test_struts_meas_x_bending.
|
||||
The "Y-bending" mode is measured as shown in Figure ref:fig:test_struts_meas_y_bending.
|
||||
Finally, the "Z-torsion" is measured as shown in Figure ref:fig:test_struts_meas_z_torsion.
|
||||
|
||||
The "X-bending" mode is measured as shown in Figure ref:fig:test_struts_meas_spur_res_struts_1_enc.
|
||||
The "Y-bending" mode is measured as shown in Figure ref:fig:test_struts_meas_spur_res_struts_2 with the encoder and in Figure ref:fig:test_struts_meas_spur_res_struts_2_encoder with the encoder.
|
||||
Finally, the "Z-torsion" is measured as shown in Figure ref:fig:test_struts_meas_spur_res_struts_3.
|
||||
This is done with and without the encoder fixed to the strut.
|
||||
|
||||
#+name: fig:test_struts_meas_spur_res_struts_1_enc
|
||||
#+caption: Measurement setup for the X-Bending measurement (with the encoder)
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/test_struts_meas_spur_res_struts_1_enc.jpg]]
|
||||
|
||||
#+name: fig:test_struts_meas_spur_res_struts_2
|
||||
#+caption: Measurement setup for the Y-Bending measurement
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/test_struts_meas_spur_res_struts_2.jpg]]
|
||||
|
||||
#+name: fig:test_struts_meas_spur_res_struts_2_encoder
|
||||
#+caption: Measurement setup for the Y-Bending measurement (with the encoder)
|
||||
#+attr_latex: :width \linewidth
|
||||
[[file:figs/test_struts_meas_spur_res_struts_2_encoder.jpg]]
|
||||
|
||||
#+name: fig:test_struts_meas_spur_res_struts_3
|
||||
#+caption: Measurement setup for the Z-Torsion measurement
|
||||
#+attr_latex: :width 0.8\linewidth
|
||||
[[file:figs/test_struts_meas_spur_res_struts_3.jpg]]
|
||||
#+name: fig:test_struts_meas_modes
|
||||
#+caption: Measurement of strut flexible modes
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_meas_x_bending}X-bending mode}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/test_struts_meas_x_bending.jpg]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_meas_y_bending}Y-bending mode}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/test_struts_meas_y_bending.jpg]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:test_struts_meas_z_torsion}Z-torsion mode}
|
||||
#+attr_latex: :options {0.33\textwidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
[[file:figs/test_struts_meas_z_torsion.jpg]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
|
||||
** Without Encoder
|
||||
When the encoder is not fixed to the strut, the obtained FRF are shown in Figure ref:fig:test_struts_spur_res_frf.
|
||||
@@ -381,7 +436,7 @@ exportFig('figs/test_struts_spur_res_frf_enc.pdf', 'width', 'wide', 'height', 'n
|
||||
#+RESULTS:
|
||||
[[file:figs/test_struts_spur_res_frf_enc.png]]
|
||||
|
||||
** Conclusion
|
||||
** Conclusion :ignore:
|
||||
|
||||
Table ref:tab:test_struts_spur_mode_freqs summarizes the measured resonance frequencies as well as the computed ones using the Finite Element Model.
|
||||
|
||||
@@ -393,7 +448,7 @@ From the values in Table ref:tab:test_struts_spur_mode_freqs, it is shown that:
|
||||
|
||||
#+name: tab:test_struts_spur_mode_freqs
|
||||
#+caption: Measured frequency of the strut spurious modes
|
||||
#+attr_latex: :environment tabularx :width 0.45\linewidth :align cccc
|
||||
#+attr_latex: :environment tabularx :width 0.7\linewidth :align Xccc
|
||||
#+attr_latex: :center t :booktabs t :float t
|
||||
| *Mode* | *Struts (FEM)* | *Struts (exp)* | *Plates (exp)* |
|
||||
|-----------+----------------+----------------+----------------|
|
||||
@@ -459,16 +514,13 @@ First, only one strut is measured in details (Section ref:ssec:test_struts_meas_
|
||||
** Measurement on Strut 1
|
||||
<<ssec:test_struts_meas_strut_1>>
|
||||
*** Introduction :ignore:
|
||||
Measurements are first performed on one of the strut that contains:
|
||||
- the Amplified Piezoelectric Actuator (APA) number 1
|
||||
- flexible joints 1 and 2
|
||||
Measurements are first performed on one of the strut.
|
||||
|
||||
In Section ref:sec:meas_strut_1_no_encoder, the dynamics of the strut is measured without the encoder attached to it.
|
||||
Then in Section ref:sec:meas_strut_1_encoder, the encoder is attached to the struts, and the dynamic is identified.
|
||||
|
||||
*** Without Encoder
|
||||
<<sec:meas_strut_1_no_encoder>>
|
||||
**** FRF Identification - Setup
|
||||
Similarly to what was done for the identification of the APA, 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.
|
||||
@@ -480,11 +532,11 @@ Similarly to what was done for the identification of the APA, the identification
|
||||
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.
|
||||
|
||||
#+begin_src matlab
|
||||
%% Sampling frequency/time
|
||||
%% Parameters for Frequency Analysis
|
||||
Ts = 1e-4; % Sampling Time [s]
|
||||
Nfft = floor(1/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
Nfft = floor(1/Ts); % Number of points for the FFT computation
|
||||
win = hanning(Nfft); % Hanning window
|
||||
Noverlap = floor(Nfft/2); % Overlap between frequency analysis
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
@@ -497,10 +549,9 @@ leg_noise_hf = load('frf_data_leg_1_noise_hf.mat', 'u', 'Vs', 'de', 'da');
|
||||
%% We get the frequency vector that will be the same for all the frequency domain analysis.
|
||||
[~, f] = tfestimate(leg_sweep.u, leg_sweep.de, win, Noverlap, Nfft, 1/Ts);
|
||||
i_lf = f <= 350; % Indices used for the low frequency
|
||||
i_hf = f > 350; % Indices used for the low frequency
|
||||
i_hf = f > 350; % Indices used for the high frequency
|
||||
#+end_src
|
||||
|
||||
**** FRF Identification - Interferometer
|
||||
In this section, the dynamics from the excitation voltage $u$ to the interferometer $d_a$ is identified.
|
||||
The transfer function from $u$ to the interferometer measured displacement $d_a$ is estimated and shown in Figure ref:fig:strut_1_frf_dvf_plant_tf.
|
||||
#+begin_src matlab
|
||||
@@ -548,7 +599,6 @@ exportFig('figs/strut_1_frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 'tall'
|
||||
#+RESULTS:
|
||||
[[file:figs/strut_1_frf_dvf_plant_tf.png]]
|
||||
|
||||
**** FRF Identification - IFF
|
||||
In this section, the dynamics from $u$ to $V_s$ is identified.
|
||||
Then the FRF are estimated and shown in Figure ref:fig:strut_1_frf_iff_plant_tf
|
||||
#+begin_src matlab
|
||||
@@ -598,19 +648,15 @@ exportFig('figs/strut_1_frf_iff_plant_tf.pdf', 'width', 'wide', 'height', 'tall'
|
||||
|
||||
*** With Encoder
|
||||
<<sec:meas_strut_1_encoder>>
|
||||
**** Introduction :ignore:
|
||||
Now the encoder is fixed to the strut and the identification is performed.
|
||||
|
||||
**** Measurement Data
|
||||
The measurements are loaded.
|
||||
#+begin_src matlab
|
||||
%% Load data
|
||||
leg_enc_sweep = load('frf_data_leg_coder_1_noise.mat', 'u', 'Vs', 'de', 'da');
|
||||
leg_enc_noise_hf = load('frf_data_leg_coder_1_noise_hf.mat', 'u', 'Vs', 'de', 'da');
|
||||
#+end_src
|
||||
|
||||
**** FRF Identification - Interferometer
|
||||
In this section, the dynamics from $u$ to $d_a$ is identified.
|
||||
The dynamics from $u$ to $d_a$ is identified.
|
||||
#+begin_src matlab
|
||||
%% Compute FRF function from u to da
|
||||
[frf_sweep, ~] = tfestimate(leg_enc_sweep.u, leg_enc_sweep.da, win, Noverlap, Nfft, 1/Ts);
|
||||
@@ -660,9 +706,6 @@ exportFig('figs/strut_leg_compare_int_frf.pdf', 'width', 'wide', 'height', 'tall
|
||||
#+RESULTS:
|
||||
[[file:figs/strut_leg_compare_int_frf.png]]
|
||||
|
||||
**** FRF Identification - Encoder
|
||||
In this section, the dynamics from $u$ to $d_e$ (encoder) is identified.
|
||||
|
||||
The FRF from $u$ to the encoder measured displacement $d_e$ is computed and shown in Figure ref:fig:strut_1_enc_frf_dvf_plant_tf.
|
||||
#+begin_src matlab
|
||||
%% Compute FRF function from u to da
|
||||
@@ -710,7 +753,6 @@ exportFig('figs/strut_1_enc_frf_dvf_plant_tf.pdf', 'width', 'wide', 'height', 't
|
||||
[[file:figs/strut_1_enc_frf_dvf_plant_tf.png]]
|
||||
|
||||
The transfer functions from $u$ to $d_e$ (encoder) and to $d_a$ (interferometer) are compared in Figure ref:fig:strut_1_comp_enc_int.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
@@ -754,7 +796,6 @@ The dynamics from the excitation voltage $u$ to the measured displacement by the
|
||||
It will be further investigated why the two dynamics as so different and what are causing all these resonances.
|
||||
#+end_important
|
||||
|
||||
**** APA Resonances Frequency
|
||||
As shown in Figure ref:fig:strut_1_spurious_resonances, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
@@ -794,8 +835,7 @@ They are very close to what was estimated using a finite element model of the st
|
||||
The resonances seen by the encoder in Figure ref:fig:strut_1_spurious_resonances are indeed corresponding to the modes of the strut as shown in Figure ref:fig:test_struts_mode_shapes.
|
||||
#+end_important
|
||||
|
||||
**** FRF Identification - Force Sensor
|
||||
In this section, the dynamics from $u$ to $V_s$ is identified.
|
||||
Let's now compare the IFF plants (dynamics from $u$ to $V_s$) whether the encoders are fixed to the APA or not (Figure ref:fig:strut_1_frf_iff_comp_enc).
|
||||
|
||||
#+begin_src matlab
|
||||
%% Compute FRF function from u to da
|
||||
@@ -806,7 +846,6 @@ In this section, the dynamics from $u$ to $V_s$ is identified.
|
||||
iff_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)];
|
||||
#+end_src
|
||||
|
||||
Let's now compare the IFF plants whether the encoders are fixed to the APA or not (Figure ref:fig:strut_1_frf_iff_comp_enc).
|
||||
#+begin_src matlab :exports none
|
||||
%% Compare the IFF plant with and without the encoders
|
||||
figure;
|
||||
@@ -851,8 +890,6 @@ The transfer function from the excitation voltage $u$ to the generated voltage $
|
||||
This means that the IFF control strategy should be as effective whether or not the encoders are fixed to the struts.
|
||||
#+end_important
|
||||
|
||||
**** Non-Minimum phase zero?
|
||||
|
||||
In order to determine if the complex conjugate zero of Figure ref:fig:strut_1_enc_frf_iff_plant_tf is minimum phase or non-minimum phase, longer measurements are performed.
|
||||
|
||||
#+begin_src matlab
|
||||
@@ -902,7 +939,7 @@ xlim([38, 45]);
|
||||
*** Introduction :ignore:
|
||||
Now all struts are measured using the same procedure and test bench as in Section ref:sec:meas_strut_1.
|
||||
|
||||
*** FRF Identification - Setup
|
||||
*** FRF Identification
|
||||
The identification of the struts dynamics is performed in two steps:
|
||||
1. The excitation signal is a white noise with small amplitude.
|
||||
This is used to estimate the low frequency dynamics.
|
||||
@@ -916,7 +953,6 @@ Here are the leg numbers that have been measured.
|
||||
strut_nums = [1 2 3 4 5];
|
||||
#+end_src
|
||||
|
||||
The data are loaded for both the first and second identification:
|
||||
#+begin_src matlab
|
||||
%% First identification (low frequency noise)
|
||||
leg_noise = {};
|
||||
@@ -938,7 +974,6 @@ win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
#+end_src
|
||||
|
||||
We get the frequency vector that will be the same for all the frequency domain analysis.
|
||||
#+begin_src matlab
|
||||
% Only used to have the frequency vector "f"
|
||||
[~, f] = tfestimate(leg_noise{1}.u, leg_noise{1}.de, win, Noverlap, Nfft, 1/Ts);
|
||||
@@ -946,10 +981,9 @@ i_lf = f <= 350;
|
||||
i_hf = f > 350;
|
||||
#+end_src
|
||||
|
||||
*** FRF Identification - Encoder
|
||||
In this section, the dynamics from $u$ to $d_e$ (encoder) is identified.
|
||||
The transfer function from the DAC output voltage $u$ to the measured displacement by the encoder $d_e$ is computed.
|
||||
The obtained transfer functions are shown in Figure ref:fig:struts_frf_dvf_plant_tf.
|
||||
|
||||
Then, the transfer function from the DAC output voltage $u$ to the measured displacement by the encoder $d_e$ is computed:
|
||||
#+begin_src matlab
|
||||
%% Transfer function estimation
|
||||
enc_frf = zeros(length(f), length(strut_nums));
|
||||
@@ -961,7 +995,6 @@ for i = 1:length(strut_nums)
|
||||
end
|
||||
#+end_src
|
||||
|
||||
The obtained transfer functions are shown in Figure ref:fig:struts_frf_dvf_plant_tf.
|
||||
#+begin_src matlab :exports none
|
||||
%% Bode plot of the FRF from u to de
|
||||
figure;
|
||||
@@ -1012,11 +1045,9 @@ Moreover, the location or even the presence of complex conjugate zeros is changi
|
||||
All of this will be explained in Section ref:sec:simscape_bench_struts thanks to the Simscape model.
|
||||
#+end_important
|
||||
|
||||
*** FRF Identification - Interferometer
|
||||
In this section, the dynamics from $u$ to $d_a$ (interferometer) is identified.
|
||||
|
||||
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:struts_frf_int_plant_tf.
|
||||
All the struts are giving very similar FRF.
|
||||
|
||||
#+begin_src matlab
|
||||
%% Transfer function estimation
|
||||
int_frf = zeros(length(f), length(strut_nums));
|
||||
@@ -1069,7 +1100,6 @@ exportFig('figs/struts_frf_int_plant_tf.pdf', 'width', 'wide', 'height', 'tall')
|
||||
#+RESULTS:
|
||||
[[file:figs/struts_frf_int_plant_tf.png]]
|
||||
|
||||
*** FRF Identification - Force Sensor
|
||||
In this section, the dynamics from $u$ to $V_s$ is identified.
|
||||
Then the FRF are estimated and shown in Figure ref:fig:struts_frf_iff_plant_tf.
|
||||
They are also shown all to be very similar.
|
||||
@@ -1227,6 +1257,8 @@ save('./mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_n
|
||||
|
||||
** TODO Comparison of all the (re-aligned) Struts
|
||||
<<sec:test_struts_meas_all_aligned_struts>>
|
||||
- [ ] Should this be included here?
|
||||
|
||||
*** Introduction :ignore:
|
||||
The struts are re-aligned and measured using the same test bench.
|
||||
|
||||
@@ -1415,6 +1447,8 @@ Having the struts well aligned does not change significantly the obtained dynami
|
||||
The measured FRF are now saved for further use.
|
||||
|
||||
** TODO Noise measurement :noexport:
|
||||
- [ ] Is it interesting and should this be included here?
|
||||
|
||||
#+begin_src matlab
|
||||
%% Nothing connected to the actuator stacks
|
||||
open_circuit = load('frf_struts_align_3_huddle_open_circuit.mat', 't', 'Vs', 'de');
|
||||
@@ -1478,6 +1512,7 @@ legend('location', 'northeast');
|
||||
xlim([1, 5e3])
|
||||
#+end_src
|
||||
|
||||
** Conclusion :ignore:
|
||||
* Simscape Model
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/test_struts_3_simscape_model.m
|
||||
@@ -1489,7 +1524,7 @@ However, now the full strut is put instead of only the APA (see Figure ref:fig:t
|
||||
|
||||
#+name: fig:test_struts_simscape_model
|
||||
#+caption: Screenshot of the Simscape model of the strut fixed to the bench
|
||||
#+attr_latex: :width \linewidth
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/test_struts_simscape_model.png]]
|
||||
|
||||
This Simscape model is used to:
|
||||
@@ -2637,16 +2672,7 @@ exportFig('figs/effect_enc_bending_damp.pdf', 'width', 'wide', 'height', 'tall')
|
||||
#+RESULTS:
|
||||
[[file:figs/effect_enc_bending_damp.png]]
|
||||
|
||||
#+begin_important
|
||||
Adding damping in bending for the flexible joints could be a nice way to reduce the effects of the spurious resonances of the struts.
|
||||
#+end_important
|
||||
|
||||
#+begin_question
|
||||
How to effectively add damping to the flexible joints?
|
||||
|
||||
One idea would be to introduce a sheet of damping material inside the flexible joint.
|
||||
Not sure is would be effect though.
|
||||
#+end_question
|
||||
** Conclusion :ignore:
|
||||
|
||||
* Conclusion
|
||||
<<sec:test_struts_conclusion>>
|
||||
|
||||
Binary file not shown.
+183
-302
@@ -1,4 +1,4 @@
|
||||
% Created 2024-03-25 Mon 10:54
|
||||
% Created 2024-03-25 Mon 16:32
|
||||
% Intended LaTeX compiler: pdflatex
|
||||
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
|
||||
|
||||
@@ -62,7 +62,7 @@ The final goal of the work presented in this document is to have an accurate Sim
|
||||
\midrule
|
||||
Section \ref{sec:test_struts_flexible_modes} & \texttt{test\_struts\_1\_flexible\_modes.m}\\
|
||||
Section \ref{sec:test_struts_dynamical_meas} & \texttt{test\_struts\_2\_dynamical\_meas.m}\\
|
||||
Section \ref{sec:test_struts_mounting} & \texttt{test\_struts\_3\_simscape\_model.m}\\
|
||||
Section \ref{sec:test_struts_simscape} & \texttt{test\_struts\_3\_simscape\_model.m}\\
|
||||
\bottomrule
|
||||
\end{tabularx}
|
||||
\end{table}
|
||||
@@ -75,84 +75,104 @@ This is very important in order to not loose any stroke when the struts will be
|
||||
|
||||
A CAD view of the mounting bench is shown in Figure \ref{fig:test_struts_mounting_bench_first_concept}.
|
||||
|
||||
\begin{itemize}
|
||||
\item[{$\square$}] Add some notes to the figure
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mounting_bench_first_concept.png}
|
||||
\includegraphics[scale=1,width=0.6\linewidth]{figs/test_struts_mounting_bench_first_concept.png}
|
||||
\caption{\label{fig:test_struts_mounting_bench_first_concept}CAD view of the mounting bench}
|
||||
\end{figure}
|
||||
|
||||
The main part of the bench is here to ensure both the correct strut length and strut coaxiality as shown in Figure \ref{fig:test_struts_mounting_step_0}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mounting_step_0.jpg}
|
||||
\caption{\label{fig:test_struts_mounting_step_0}Useful features of the main mounting element}
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.56\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,height=4.5cm]{figs/test_struts_mounting_step_0.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mounting_step_0}Useful features of the main mounting element}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.43\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,height=4.5cm]{figs/test_struts_check_dimensions_bench.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_check_dimensions_bench}Dimensional check}
|
||||
\end{subfigure}
|
||||
\caption{\label{fig:test_struts_mounting_base_part}Caption\ldots{}, add foot note with Faro arm}
|
||||
\end{figure}
|
||||
|
||||
The tight tolerances of this element has been verified as shown in Figure \ref{fig:test_struts_mounting_bench_first_concept} and were found to comply with the requirements.
|
||||
The tight tolerances of this element has been verified as shown in Figure \ref{fig:test_struts_check_dimensions_bench} and were found to comply with the requirements.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/check_dimensions_bench.jpg}
|
||||
\caption{\label{fig:test_struts_mounting_bench_first_concept}Dimensional verifications of the mounting bench tolerances}
|
||||
\end{figure}
|
||||
|
||||
The flexible joints are rigidly fixed to cylindrical tools shown in Figure \ref{fig:cylindrical_mounting_part} which are then mounted on the mounting tool shown in Figure \ref{fig:test_struts_mounting_step_0}.
|
||||
The flexible joints are rigidly fixed to cylindrical tools shown in Figures \ref{fig:test_struts_cylindrical_mounting_part_top} and \ref{fig:test_struts_cylindrical_mounting_part_bot} which are then mounted on the mounting tool shown in Figure \ref{fig:test_struts_mounting_step_0}.
|
||||
This cylindrical tool is here to protect the flexible joints when tightening the screws and therefore applying large torque.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/cylindrical_mounting_part.jpg}
|
||||
\caption{\label{fig:cylindrical_mounting_part}Cylindrical mounting elements}
|
||||
\end{figure}
|
||||
\section{Mounting Procedure}
|
||||
|
||||
The mounting procedure is as follows:
|
||||
\begin{enumerate}
|
||||
\item Screw flexible joints inside the cylindrical interface element shown in Figure \ref{fig:cylindrical_mounting_part} (Figure \ref{fig:test_struts_mounting_step_1})
|
||||
\item Screw flexible joints inside the cylindrical interface element shown in Figure \ref{fig:test_struts_cylindrical_mounting}
|
||||
\item Fix the two interface elements. One of the two should be clamped, the other one should have its axial rotation free.
|
||||
Visually align the clamped one horizontally. (Figure \ref{fig:test_struts_mounting_step_2})
|
||||
\item Put cylindrical washers, APA and interface pieces on top of the flexible joints (Figure \ref{fig:test_struts_mounting_step_3})
|
||||
Visually align the clamped one horizontally. (Figure \ref{fig:test_struts_mounting_step_1})
|
||||
\item Put cylindrical washers, APA and interface pieces on top of the flexible joints (Figure \ref{fig:test_struts_mounting_step_2})
|
||||
\item Put the 4 screws just in contact such that everything is correctly positioned and such that the ``free'' flexible joint is correctly oriented
|
||||
\item Put the 8 lateral screws in contact
|
||||
\item Tighten the 4 screws to fix the APA on the two flexible joints (using a torque screwdriver)
|
||||
\item Remove the 4 laterals screws
|
||||
\item (optional) Put the APA horizontally and fix the encoder and align it to maximize the contrast (Figure \ref{fig:test_struts_mounting_step_4})
|
||||
\item (optional) Put the APA horizontally and fix the encoder and align it to maximize the contrast (Figure \ref{fig:test_struts_mounting_step_3})
|
||||
\item Disassemble to have an properly mounted strut (Figure \ref{fig:test_struts_mounting_step_4}) for which the coaxiality between the two flexible joint's interfaces is good
|
||||
\end{enumerate}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=0.5\linewidth]{figs/test_struts_mounting_step_1.jpg}
|
||||
\caption{\label{fig:test_struts_mounting_step_1}Step 1 - Flexible joints fixed on the cylindrical interface elements}
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,height=4.5cm]{figs/test_struts_cylindrical_mounting_part_top.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_cylindrical_mounting_part_top}Cylindral Interface (Top)}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,height=4.5cm]{figs/test_struts_cylindrical_mounting_part_bot.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_cylindrical_mounting_part_bot}Cylindrlcal Interface (Bottom)}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,height=4.5cm]{figs/test_struts_mounting_joints.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mounting_joints}Mounted flexible joints}
|
||||
\end{subfigure}
|
||||
\caption{\label{fig:test_struts_cylindrical_mounting}Preparation of the flexible joints by fixing them in their cylindrical interface}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mounting_step_2.jpg}
|
||||
\caption{\label{fig:test_struts_mounting_step_2}Step 2 - Cylindrical elements fixed on the bench}
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.99\linewidth]{figs/test_struts_mounting_step_1.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mounting_step_1}Step 1}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.99\linewidth]{figs/test_struts_mounting_step_2.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mounting_step_2}Step 2}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.99\linewidth]{figs/test_struts_mounting_step_3.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mounting_step_3}Step 3}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.99\linewidth]{figs/test_struts_mounting_step_4.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mounting_step_4}Step 4}
|
||||
\end{subfigure}
|
||||
\caption{\label{fig:test_struts_mounting_steps}Steps for mounting the struts.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mounting_step_3.jpg}
|
||||
\caption{\label{fig:test_struts_mounting_step_3}Step 3 - Mount the nuts, washers and APA}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mounting_step_4.jpg}
|
||||
\caption{\label{fig:test_struts_mounting_step_4}Last step - Align the encoder on the strut}
|
||||
\end{figure}
|
||||
\section{Mounted Struts}
|
||||
|
||||
After removing the strut from the mounting bench, we obtain a strut with ensured coaxiality between the two flexible joint's interfaces (Figure \ref{fig:test_struts_mounted_strut}).
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mounted_strut.jpg}
|
||||
\caption{\label{fig:test_struts_mounted_strut}Mounted Strut with ensured coaxiality}
|
||||
\end{figure}
|
||||
\chapter{Spurious resonances}
|
||||
\chapter{Measurement of flexible modes}
|
||||
\label{sec:test_struts_flexible_modes}
|
||||
\section{Introduction}
|
||||
|
||||
@@ -167,50 +187,58 @@ From a Finite Element Model of the struts, it have been found that three main re
|
||||
\item Mode in Z-torsion at 400Hz
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_mode_shapes.png}
|
||||
\caption{\label{fig:test_struts_mode_shapes}Spurious resonances of the struts estimated from a Finite Element Model. a) X-bending mode at 189Hz. b) Y-bending mode at 285Hz. c) Z-torsion mode at 400Hz}
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.9\linewidth]{figs/test_struts_mode_shapes_1.png}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mode_shapes_3}X-bending mode (189Hz)}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.9\linewidth]{figs/test_struts_mode_shapes_2.png}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mode_shapes_3}Y-bending mode (285Hz)}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.9\linewidth]{figs/test_struts_mode_shapes_3.png}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_mode_shapes_3}Z-torsion mode (400Hz)}
|
||||
\end{subfigure}
|
||||
\caption{\label{fig:test_struts_mode_shapes}Spurious resonances of the struts estimated from a Finite Element Model}
|
||||
\end{figure}
|
||||
\section{Measurement Setup}
|
||||
|
||||
A Laser vibrometer is measuring the difference of motion between two points (Figure \ref{fig:test_struts_meas_spur_res_struts_1_enc}).
|
||||
The APA is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
|
||||
A Laser vibrometer is measuring the difference of motion between two beam path (red points in Figure \ref{fig:test_struts_meas_modes}).
|
||||
The strut is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
|
||||
|
||||
\begin{note}
|
||||
The instrumentation used are:
|
||||
\begin{itemize}
|
||||
\item Laser Doppler Vibrometer Polytec OFV512
|
||||
\item Instrumented hammer
|
||||
\end{itemize}
|
||||
\end{note}
|
||||
The ``X-bending'' mode is measured as shown in Figure \ref{fig:test_struts_meas_x_bending}.
|
||||
The ``Y-bending'' mode is measured as shown in Figure \ref{fig:test_struts_meas_y_bending}.
|
||||
Finally, the ``Z-torsion'' is measured as shown in Figure \ref{fig:test_struts_meas_z_torsion}.
|
||||
|
||||
The ``X-bending'' mode is measured as shown in Figure \ref{fig:test_struts_meas_spur_res_struts_1_enc}.
|
||||
The ``Y-bending'' mode is measured as shown in Figure \ref{fig:test_struts_meas_spur_res_struts_2} with the encoder and in Figure \ref{fig:test_struts_meas_spur_res_struts_2_encoder} with the encoder.
|
||||
Finally, the ``Z-torsion'' is measured as shown in Figure \ref{fig:test_struts_meas_spur_res_struts_3}.
|
||||
This is done with and without the encoder fixed to the strut.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_meas_spur_res_struts_1_enc.jpg}
|
||||
\caption{\label{fig:test_struts_meas_spur_res_struts_1_enc}Measurement setup for the X-Bending measurement (with the encoder)}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_meas_spur_res_struts_2.jpg}
|
||||
\caption{\label{fig:test_struts_meas_spur_res_struts_2}Measurement setup for the Y-Bending measurement}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_meas_spur_res_struts_2_encoder.jpg}
|
||||
\caption{\label{fig:test_struts_meas_spur_res_struts_2_encoder}Measurement setup for the Y-Bending measurement (with the encoder)}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=0.8\linewidth]{figs/test_struts_meas_spur_res_struts_3.jpg}
|
||||
\caption{\label{fig:test_struts_meas_spur_res_struts_3}Measurement setup for the Z-Torsion measurement}
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.9\linewidth]{figs/test_struts_meas_x_bending.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_meas_x_bending}X-bending mode}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.9\linewidth]{figs/test_struts_meas_y_bending.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_meas_y_bending}Y-bending mode}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}{0.33\textwidth}
|
||||
\begin{center}
|
||||
\includegraphics[scale=1,width=0.9\linewidth]{figs/test_struts_meas_z_torsion.jpg}
|
||||
\end{center}
|
||||
\subcaption{\label{fig:test_struts_meas_z_torsion}Z-torsion mode}
|
||||
\end{subfigure}
|
||||
\caption{\label{fig:test_struts_meas_modes}Measurement of strut flexible modes}
|
||||
\end{figure}
|
||||
\section{Without Encoder}
|
||||
When the encoder is not fixed to the strut, the obtained FRF are shown in Figure \ref{fig:test_struts_spur_res_frf}.
|
||||
@@ -242,7 +270,7 @@ From the values in Table \ref{tab:test_struts_spur_mode_freqs}, it is shown that
|
||||
\begin{table}[htbp]
|
||||
\caption{\label{tab:test_struts_spur_mode_freqs}Measured frequency of the strut spurious modes}
|
||||
\centering
|
||||
\begin{tabularx}{0.45\linewidth}{cccc}
|
||||
\begin{tabularx}{0.7\linewidth}{Xccc}
|
||||
\toprule
|
||||
\textbf{Mode} & \textbf{Struts (FEM)} & \textbf{Struts (exp)} & \textbf{Plates (exp)}\\
|
||||
\midrule
|
||||
@@ -282,17 +310,12 @@ Measurements are performed either when no encoder is fixed to the strut (Figure
|
||||
First, only one strut is measured in details (Section \ref{ssec:test_struts_meas_strut_1}), and then all the struts are measured and compared (Section \ref{ssec:test_struts_meas_all_struts}).
|
||||
\section{Measurement on Strut 1}
|
||||
\label{ssec:test_struts_meas_strut_1}
|
||||
Measurements are first performed on one of the strut that contains:
|
||||
\begin{itemize}
|
||||
\item the Amplified Piezoelectric Actuator (APA) number 1
|
||||
\item flexible joints 1 and 2
|
||||
\end{itemize}
|
||||
Measurements are first performed on one of the strut.
|
||||
|
||||
In Section \ref{sec:meas_strut_1_no_encoder}, the dynamics of the strut is measured without the encoder attached to it.
|
||||
Then in Section \ref{sec:meas_strut_1_encoder}, the encoder is attached to the struts, and the dynamic is identified.
|
||||
\subsection{Without Encoder}
|
||||
\label{sec:meas_strut_1_no_encoder}
|
||||
\paragraph{FRF Identification - Setup}
|
||||
Similarly to what was done for the identification of the APA, the identification is performed in three steps:
|
||||
\begin{enumerate}
|
||||
\item White noise excitation with small amplitude.
|
||||
@@ -305,39 +328,15 @@ 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.
|
||||
|
||||
The time is the same for all measurements.
|
||||
We get the frequency vector that will be the same for all the frequency domain analysis.
|
||||
\paragraph{FRF Identification - Interferometer}
|
||||
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 and combine them.
|
||||
The combined coherence is shown in Figure \ref{fig:strut_1_frf_dvf_plant_coh}, and is found to be very good up to at least 1kHz.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_frf_dvf_plant_coh.png}
|
||||
\caption{\label{fig:strut_1_frf_dvf_plant_coh}Obtained coherence for the plant from \(V_a\) to \(d_a\)}
|
||||
\end{figure}
|
||||
|
||||
The transfer function from \(V_a\) to the interferometer measured displacement \(d_a\) is estimated and shown in Figure \ref{fig:strut_1_frf_dvf_plant_tf}.
|
||||
In this section, the dynamics from the excitation voltage \(u\) to the interferometer \(d_a\) is identified.
|
||||
The transfer function from \(u\) to the interferometer measured displacement \(d_a\) is estimated and shown in Figure \ref{fig:strut_1_frf_dvf_plant_tf}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_frf_dvf_plant_tf.png}
|
||||
\caption{\label{fig:strut_1_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(V_a\) to the interferometer \(d_a\))}
|
||||
\end{figure}
|
||||
\paragraph{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 \ref{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).
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_frf_iff_plant_coh.png}
|
||||
\caption{\label{fig:strut_1_frf_iff_plant_coh}Obtained coherence for the IFF plant}
|
||||
\caption{\label{fig:strut_1_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(u\) to the interferometer \(d_a\))}
|
||||
\end{figure}
|
||||
|
||||
In this section, the dynamics from \(u\) to \(V_s\) is identified.
|
||||
Then the FRF are estimated and shown in Figure \ref{fig:strut_1_frf_iff_plant_tf}
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
@@ -347,68 +346,40 @@ Then the FRF are estimated and shown in Figure \ref{fig:strut_1_frf_iff_plant_tf
|
||||
\subsection{With Encoder}
|
||||
\label{sec:meas_strut_1_encoder}
|
||||
Now the encoder is fixed to the strut and the identification is performed.
|
||||
\paragraph{Measurement Data}
|
||||
The measurements are loaded.
|
||||
\paragraph{FRF Identification - Interferometer}
|
||||
In this section, the dynamics from \(V_a\) to \(d_a\) is identified.
|
||||
|
||||
First, the coherence is computed and shown in Figure \ref{fig:strut_1_int_with_enc_frf_dvf_plant_coh}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_int_with_enc_frf_dvf_plant_coh.png}
|
||||
\caption{\label{fig:strut_1_int_with_enc_frf_dvf_plant_coh}Obtained coherence for the plant from \(V_a\) to \(d_a\)}
|
||||
\end{figure}
|
||||
|
||||
Then the FRF are computed and shown in Figure \ref{fig:strut_1_int_with_enc_frf_dvf_plant_tf}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_int_with_enc_frf_dvf_plant_tf.png}
|
||||
\caption{\label{fig:strut_1_int_with_enc_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))}
|
||||
\end{figure}
|
||||
|
||||
The dynamics from \(u\) to \(d_a\) is identified.
|
||||
The obtained FRF is very close to the one that was obtained when no encoder was fixed to the struts as shown in Figure \ref{fig:strut_leg_compare_int_frf}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_leg_compare_int_frf.png}
|
||||
\caption{\label{fig:strut_leg_compare_int_frf}Comparison of the measured FRF from \(V_a\) to \(d_a\) with and without the encoders fixed to the struts}
|
||||
\end{figure}
|
||||
\paragraph{FRF Identification - Encoder}
|
||||
In this section, the dynamics from \(V_a\) to \(d_e\) (encoder) is identified.
|
||||
|
||||
The coherence is computed and shown in Figure \ref{fig:strut_1_enc_frf_dvf_plant_coh}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_enc_frf_dvf_plant_coh.png}
|
||||
\caption{\label{fig:strut_1_enc_frf_dvf_plant_coh}Obtained coherence for the plant from \(V_a\) to \(d_e\) and from \(V_a\) to \(d_a\)}
|
||||
\caption{\label{fig:strut_leg_compare_int_frf}Comparison of the measured FRF from \(u\) to \(d_a\) with and without the encoders fixed to the struts}
|
||||
\end{figure}
|
||||
|
||||
The FRF from \(V_a\) to the encoder measured displacement \(d_e\) is computed and shown in Figure \ref{fig:strut_1_enc_frf_dvf_plant_tf}.
|
||||
The FRF from \(u\) to the encoder measured displacement \(d_e\) is computed and shown in Figure \ref{fig:strut_1_enc_frf_dvf_plant_tf}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_enc_frf_dvf_plant_tf.png}
|
||||
\caption{\label{fig:strut_1_enc_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))}
|
||||
\caption{\label{fig:strut_1_enc_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(u\) to the encoder \(d_e\))}
|
||||
\end{figure}
|
||||
|
||||
The transfer functions from \(V_a\) to \(d_e\) (encoder) and to \(d_a\) (interferometer) are compared in Figure \ref{fig:strut_1_comp_enc_int}.
|
||||
|
||||
The transfer functions from \(u\) to \(d_e\) (encoder) and to \(d_a\) (interferometer) are compared in Figure \ref{fig:strut_1_comp_enc_int}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_comp_enc_int.png}
|
||||
\caption{\label{fig:strut_1_comp_enc_int}Comparison of the transfer functions from excitation voltage \(V_a\) to either the encoder \(d_e\) or the interferometer \(d_a\)}
|
||||
\caption{\label{fig:strut_1_comp_enc_int}Comparison of the transfer functions from excitation voltage \(u\) to either the encoder \(d_e\) or the interferometer \(d_a\)}
|
||||
\end{figure}
|
||||
|
||||
\begin{important}
|
||||
The dynamics from the excitation voltage \(V_a\) 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:strut_1_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:strut_1_comp_enc_int}).
|
||||
It will be further investigated why the two dynamics as so different and what are causing all these resonances.
|
||||
\end{important}
|
||||
\paragraph{APA Resonances Frequency}
|
||||
|
||||
As shown in Figure \ref{fig:strut_1_spurious_resonances}, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_spurious_resonances.png}
|
||||
\caption{\label{fig:strut_1_spurious_resonances}Magnitude of the transfer function from excitation voltage \(V_a\) to encoder measurement \(d_e\). The frequency of the resonances are noted.}
|
||||
\caption{\label{fig:strut_1_spurious_resonances}Magnitude of the transfer function from excitation voltage \(u\) to encoder measurement \(d_e\). The frequency of the resonances are noted.}
|
||||
\end{figure}
|
||||
|
||||
|
||||
@@ -424,27 +395,9 @@ They are very close to what was estimated using a finite element model of the st
|
||||
\begin{important}
|
||||
The resonances seen by the encoder in Figure \ref{fig:strut_1_spurious_resonances} are indeed corresponding to the modes of the strut as shown in Figure \ref{fig:test_struts_mode_shapes}.
|
||||
\end{important}
|
||||
\paragraph{FRF Identification - Force Sensor}
|
||||
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
|
||||
|
||||
First the coherence is computed and shown in Figure \ref{fig:strut_1_frf_iff_with_enc_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).
|
||||
Let's now compare the IFF plants (dynamics from \(u\) to \(V_s\)) whether the encoders are fixed to the APA or not (Figure \ref{fig:strut_1_frf_iff_comp_enc}).
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_frf_iff_with_enc_plant_coh.png}
|
||||
\caption{\label{fig:strut_1_frf_iff_with_enc_plant_coh}Obtained coherence for the IFF plant}
|
||||
\end{figure}
|
||||
|
||||
Then the FRF are estimated and shown in Figure \ref{fig:strut_1_enc_frf_iff_plant_tf}
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_enc_frf_iff_plant_tf.png}
|
||||
\caption{\label{fig:strut_1_enc_frf_iff_plant_tf}Identified IFF Plant}
|
||||
\end{figure}
|
||||
|
||||
Let's now compare the IFF plants whether the encoders are fixed to the APA or not (Figure \ref{fig:strut_1_frf_iff_comp_enc}).
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_1_frf_iff_effect_enc.png}
|
||||
@@ -452,18 +405,15 @@ Let's now compare the IFF plants whether the encoders are fixed to the APA or no
|
||||
\end{figure}
|
||||
|
||||
\begin{important}
|
||||
The transfer function from the excitation voltage \(V_a\) to the generated voltage \(V_s\) by the sensor stack is not influence by the fixation of the encoder.
|
||||
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.
|
||||
This means that the IFF control strategy should be as effective whether or not the encoders are fixed to the struts.
|
||||
\end{important}
|
||||
\paragraph{Non-Minimum phase zero?}
|
||||
|
||||
In order to determine if the complex conjugate zero of Figure \ref{fig:strut_1_enc_frf_iff_plant_tf} is minimum phase or non-minimum phase, longer measurements are performed.
|
||||
|
||||
Remove time delay
|
||||
\section{Comparison of all the Struts}
|
||||
\label{ssec:test_struts_meas_all_struts}
|
||||
Now all struts are measured using the same procedure and test bench as in Section \ref{sec:meas_strut_1}.
|
||||
\subsection{FRF Identification - Setup}
|
||||
\subsection{FRF Identification}
|
||||
The identification of the struts dynamics is performed in two steps:
|
||||
\begin{enumerate}
|
||||
\item The excitation signal is a white noise with small amplitude.
|
||||
@@ -474,27 +424,13 @@ This is used to estimate the low frequency dynamics.
|
||||
Then, the result of the first identification is used between 10Hz and 350Hz and the result of the second identification if used between 350Hz and 2kHz.
|
||||
|
||||
Here are the leg numbers that have been measured.
|
||||
The data are loaded for both the first and second identification:
|
||||
The time is the same for all measurements.
|
||||
Then we defined a ``Hanning'' windows that will be used for the spectral analysis:
|
||||
We get the frequency vector that will be the same for all the frequency domain analysis.
|
||||
\subsection{FRF Identification - Encoder}
|
||||
In this section, the dynamics from \(V_a\) to \(d_e\) (encoder) is identified.
|
||||
|
||||
The coherence is computed and shown in Figure \ref{fig:struts_frf_dvf_plant_coh} for all the measured struts.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_frf_dvf_plant_coh.png}
|
||||
\caption{\label{fig:struts_frf_dvf_plant_coh}Obtained coherence for the plant from \(V_a\) to \(d_e\)}
|
||||
\end{figure}
|
||||
|
||||
|
||||
Then, the transfer function from the DAC output voltage \(V_a\) to the measured displacement by the encoder \(d_e\) is computed:
|
||||
The transfer function from the DAC output voltage \(u\) to the measured displacement by the encoder \(d_e\) is computed.
|
||||
The obtained transfer functions are shown in Figure \ref{fig:struts_frf_dvf_plant_tf}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_frf_dvf_plant_tf.png}
|
||||
\caption{\label{fig:struts_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))}
|
||||
\caption{\label{fig:struts_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(u\) to the encoder \(d_e\))}
|
||||
\end{figure}
|
||||
|
||||
\begin{important}
|
||||
@@ -504,33 +440,17 @@ Moreover, the location or even the presence of complex conjugate zeros is changi
|
||||
|
||||
All of this will be explained in Section \ref{sec:simscape_bench_struts} thanks to the Simscape model.
|
||||
\end{important}
|
||||
\subsection{FRF Identification - Interferometer}
|
||||
In this section, the dynamics from \(V_a\) to \(d_a\) (interferometer) is identified.
|
||||
|
||||
The coherence is computed and shown in Figure \ref{fig:struts_frf_int_plant_coh}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_frf_int_plant_coh.png}
|
||||
\caption{\label{fig:struts_frf_int_plant_coh}Obtained coherence for the plant from \(V_a\) to \(d_e\)}
|
||||
\end{figure}
|
||||
|
||||
Then, the transfer function from the DAC output voltage \(V_a\) to the measured displacement by the Attocube is computed for all the struts and shown in Figure \ref{fig:struts_frf_int_plant_tf}.
|
||||
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:struts_frf_int_plant_tf}.
|
||||
All the struts are giving very similar FRF.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_frf_int_plant_tf.png}
|
||||
\caption{\label{fig:struts_frf_int_plant_tf}Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))}
|
||||
\end{figure}
|
||||
\subsection{FRF Identification - Force Sensor}
|
||||
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
|
||||
|
||||
First the coherence is computed and shown in Figure \ref{fig:struts_frf_iff_plant_coh}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_frf_iff_plant_coh.png}
|
||||
\caption{\label{fig:struts_frf_iff_plant_coh}Obtained coherence for the IFF plant}
|
||||
\caption{\label{fig:struts_frf_int_plant_tf}Estimated FRF for the DVF plant (transfer function from \(u\) to the encoder \(d_e\))}
|
||||
\end{figure}
|
||||
|
||||
In this section, the dynamics from \(u\) to \(V_s\) is identified.
|
||||
Then the FRF are estimated and shown in Figure \ref{fig:struts_frf_iff_plant_tf}.
|
||||
They are also shown all to be very similar.
|
||||
\begin{figure}[htbp]
|
||||
@@ -610,13 +530,17 @@ The misalignment of the APA and flexible joints is quite large and variable from
|
||||
\subsection{Conclusion}
|
||||
|
||||
\begin{important}
|
||||
All the struts are giving very consistent behavior from the excitation voltage \(V_a\) to the force sensor generated voltage \(V_s\) and to the interferometer measured displacement \(d_a\).
|
||||
However, the dynamics from \(V_a\) to the encoder measurement \(d_e\) is much more complex and variable from one strut to the other most likely due to poor alignment of the APA with respect to the flexible joints.
|
||||
All the struts are giving very consistent behavior from the excitation voltage \(u\) to the force sensor generated voltage \(V_s\) and to the interferometer measured displacement \(d_a\).
|
||||
However, the dynamics from \(u\) to the encoder measurement \(d_e\) is much more complex and variable from one strut to the other most likely due to poor alignment of the APA with respect to the flexible joints.
|
||||
\end{important}
|
||||
|
||||
The measured FRF are now saved for further use.
|
||||
\section{Comparison of all the (re-aligned) Struts}
|
||||
\label{sec:test_struts_meas_all_aligned_struts}
|
||||
\begin{itemize}
|
||||
\item[{$\square$}] Should this be included here?
|
||||
\end{itemize}
|
||||
|
||||
The struts are re-aligned and measured using the same test bench.
|
||||
\subsection{Measured misalignment of the APA and flexible joints}
|
||||
The misalignment between the APA and the flexible joints are measured.
|
||||
@@ -687,48 +611,21 @@ The excitation signal is a low pass filtered white noise.
|
||||
Both the encoder and the force sensor voltage are measured.
|
||||
|
||||
Here are the leg numbers that have been measured.
|
||||
The time is the same for all measurements.
|
||||
Then we defined a ``Hanning'' windows that will be used for the spectral analysis:
|
||||
We get the frequency vector that will be the same for all the frequency domain analysis.
|
||||
\subsection{FRF Identification - Encoder}
|
||||
In this section, the dynamics from \(V_a\) to \(d_e\) (encoder) is identified.
|
||||
In this section, the dynamics from \(u\) to \(d_e\) (encoder) is identified.
|
||||
|
||||
The coherence is computed and shown in Figure \ref{fig:struts_align_frf_dvf_plant_coh} for all the measured struts.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_align_frf_dvf_plant_coh.png}
|
||||
\caption{\label{fig:struts_align_frf_dvf_plant_coh}Obtained coherence for the plant from \(V_a\) to \(d_e\)}
|
||||
\end{figure}
|
||||
|
||||
|
||||
Then, the transfer function from the DAC output voltage \(V_a\) to the measured displacement by the encoder \(d_e\) is computed:
|
||||
Then, the transfer function from the DAC output voltage \(u\) to the measured displacement by the encoder \(d_e\) is computed:
|
||||
The obtained transfer functions are shown in Figure \ref{fig:struts_align_frf_dvf_plant_tf}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_align_frf_dvf_plant_tf.png}
|
||||
\caption{\label{fig:struts_align_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))}
|
||||
\caption{\label{fig:struts_align_frf_dvf_plant_tf}Estimated FRF for the DVF plant (transfer function from \(u\) to the encoder \(d_e\))}
|
||||
\end{figure}
|
||||
|
||||
\begin{important}
|
||||
Even though the struts are much better aligned, we still observe high variability between the struts for the transfer function from \(V_a\) to \(d_e\).
|
||||
Even though the struts are much better aligned, we still observe high variability between the struts for the transfer function from \(u\) to \(d_e\).
|
||||
\end{important}
|
||||
\subsection{FRF Identification - Force Sensor}
|
||||
In this section, the dynamics from \(V_a\) to \(V_s\) is identified.
|
||||
|
||||
First the coherence is computed and shown in Figure \ref{fig:struts_frf_iff_plant_coh}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_align_frf_iff_plant_coh.png}
|
||||
\caption{\label{fig:struts_align_frf_iff_plant_coh}Obtained coherence for the IFF plant}
|
||||
\end{figure}
|
||||
|
||||
Then the FRF are estimated and shown in Figure \ref{fig:struts_frf_iff_plant_tf}.
|
||||
They are also shown all to be very similar.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/struts_align_frf_iff_plant_tf.png}
|
||||
\caption{\label{fig:struts_align_frf_iff_plant_tf}Identified IFF Plant}
|
||||
\end{figure}
|
||||
\subsection{Conclusion}
|
||||
|
||||
\begin{important}
|
||||
@@ -742,7 +639,7 @@ However, now the full strut is put instead of only the APA (see Figure \ref{fig:
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=\linewidth]{figs/test_struts_simscape_model.png}
|
||||
\includegraphics[scale=1,width=0.7\linewidth]{figs/test_struts_simscape_model.png}
|
||||
\caption{\label{fig:test_struts_simscape_model}Screenshot of the Simscape model of the strut fixed to the bench}
|
||||
\end{figure}
|
||||
|
||||
@@ -755,27 +652,25 @@ This Simscape model is used to:
|
||||
|
||||
This study is structured as follow:
|
||||
\begin{itemize}
|
||||
\item Section \ref{sec:struts_comp_2dof}: the measured FRF are compared with the 2DoF APA model.
|
||||
\item Section \ref{sec:struts_effect_misalignment}: the flexible APA model is used, and the effect of a misalignment of the APA and flexible joints is studied.
|
||||
It is found that the misalignment has a large impact on the dynamics from \(V_a\) to \(d_e\).
|
||||
\item Section \ref{sec:struts_effect_joint_stiffness}: the effect of the flexible joint's stiffness on the dynamics is studied.
|
||||
\item Section \ref{ssec:test_struts_comp_model}: the measured FRF are compared with the Simscape model.
|
||||
\item Section \ref{ssec:test_struts_effect_misalignment}: the flexible APA model is used, and the effect of a misalignment of the APA and flexible joints is studied.
|
||||
It is found that the misalignment has a large impact on the dynamics from \(u\) to \(d_e\).
|
||||
\item Section \ref{ssec:test_struts_effect_joint_stiffness}: the effect of the flexible joint's stiffness on the dynamics is studied.
|
||||
It is found that the axial stiffness of the joints has a large impact on the location of the zeros on the transfer function from \(V_s\) to \(d_e\).
|
||||
\end{itemize}
|
||||
\section{Comparison with the 2-DoF Model}
|
||||
\label{sec:struts_comp_2dof}
|
||||
\subsection{First Identification}
|
||||
\section{Comparison with the Model}
|
||||
\label{ssec:test_struts_comp_model}
|
||||
\subsection{2Dof model}
|
||||
The strut is initialized with default parameters (optimized parameters identified from previous experiments).
|
||||
|
||||
The inputs and outputs of the model are defined.
|
||||
The dynamics is identified and shown in Figure \ref{fig:strut_bench_model_bode}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/strut_bench_model_bode.png}
|
||||
\caption{\label{fig:strut_bench_model_bode}Identified transfer function from \(V_a\) to \(V_s\) and from \(V_a\) to \(d_e,d_a\) using the simple 2DoF model for the APA}
|
||||
\caption{\label{fig:strut_bench_model_bode}Identified transfer function from \(u\) to \(V_s\) and from \(u\) to \(d_e,d_a\) using the simple 2DoF model for the APA}
|
||||
\end{figure}
|
||||
\subsection{Comparison with the experimental Data}
|
||||
|
||||
The experimentally measured FRF are loaded.
|
||||
The FRF from \(V_a\) to \(d_a\) as well as from \(V_a\) to \(V_s\) are shown in Figure \ref{fig:comp_strut_plant_after_opt} and compared with the model.
|
||||
The FRF from \(u\) to \(d_a\) as well as from \(u\) to \(V_s\) are shown in Figure \ref{fig:comp_strut_plant_after_opt} and compared with the model.
|
||||
They are both found to match quite well with the model.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
@@ -783,7 +678,7 @@ They are both found to match quite well with the model.
|
||||
\caption{\label{fig:comp_strut_plant_after_opt}Comparison of the measured FRF and the optimized model}
|
||||
\end{figure}
|
||||
|
||||
The measured FRF from \(V_a\) to \(d_e\) (encoder) is compared with the model in Figure \ref{fig:comp_strut_plant_iff_after_opt}.
|
||||
The measured FRF from \(u\) to \(d_e\) (encoder) is compared with the model in Figure \ref{fig:comp_strut_plant_iff_after_opt}.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/comp_strut_plant_iff_after_opt.png}
|
||||
@@ -796,16 +691,15 @@ But it is not effective in modeling the transfer function from actuator to encod
|
||||
This is due to the fact that resonances greatly affecting the encoder reading are not modelled.
|
||||
In the next section, flexible model of the APA will be used to model such resonances.
|
||||
\end{important}
|
||||
\section{Comparison with the Flexible Model}
|
||||
\label{sec:struts_comp_flexible}
|
||||
\subsection{First Identification}
|
||||
\subsection{Comparison with the Flexible Model}
|
||||
The strut is initialized with default parameters (optimized parameters identified from previous experiments).
|
||||
|
||||
The inputs and outputs of the model are defined.
|
||||
The dynamics is identified and shown in Figure \ref{fig:strut_bench_model_bode}.
|
||||
\subsection{Comparison with the experimental Data}
|
||||
The experimentally measured FRF are loaded.
|
||||
The FRF from \(V_a\) to \(d_a\) as well as from \(V_a\) to \(V_s\) are shown in Figure \ref{fig:comp_strut_plant_after_opt} and compared with the model.
|
||||
\begin{itemize}
|
||||
\item[{$\square$}] Add encoder plot
|
||||
\end{itemize}
|
||||
|
||||
The FRF from \(u\) to \(d_a\) as well as from \(u\) to \(V_s\) are shown in Figure \ref{fig:comp_strut_plant_after_opt} and compared with the model.
|
||||
They are both found to match quite well with the model.
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
@@ -813,27 +707,25 @@ They are both found to match quite well with the model.
|
||||
\label{fig:strut_meas_frf_model_int_force}
|
||||
\end{figure}
|
||||
\section{Effect of a misalignment of the APA and flexible joints on the transfer function from actuator to encoder}
|
||||
\label{sec:struts_effect_misalignment}
|
||||
\label{ssec:test_struts_effect_misalignment}
|
||||
As shown in Figure \ref{fig:struts_frf_dvf_plant_tf}, the dynamics from actuator to encoder for all the struts is very different.
|
||||
|
||||
This could be explained by a large variability in the alignment of the flexible joints and the APA (at the time, the alignment pins were not used).
|
||||
|
||||
Depending on the alignment, the spurious resonances of the struts (Figure \ref{fig:test_struts_mode_shapes}) can be excited differently.
|
||||
|
||||
For instance, consider Figure \ref{fig:strut_misalign_schematic} where there is a misalignment in the \(y\) direction.
|
||||
For instance, consider Figure \ref{fig:test_struts_misalign_schematic} where there is a misalignment in the \(y\) direction.
|
||||
In such case, the mode at 200Hz is foreseen to be more excited as the misalignment \(d_y\) increases and therefore the dynamics from the actuator to the encoder should also change around 200Hz.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,width=0.8\linewidth]{figs/strut_misalign_schematic.png}
|
||||
\caption{\label{fig:strut_misalign_schematic}Mis-alignement between the joints and the APA}
|
||||
\includegraphics[scale=1,width=0.8\linewidth]{figs/test_struts_misalign_schematic.png}
|
||||
\caption{\label{fig:test_struts_misalign_schematic}Mis-alignement between the joints and the APA}
|
||||
\end{figure}
|
||||
|
||||
If the misalignment is in the \(x\) direction, the mode at 285Hz should be more affected whereas a misalignment in the \(z\) direction should not affect these resonances.
|
||||
|
||||
Such statement is studied in this section.
|
||||
|
||||
But first, the measured FRF of the struts are loaded.
|
||||
\subsection{Perfectly aligned APA}
|
||||
Let's first consider that the strut is perfectly mounted such that the two flexible joints and the APA are aligned.
|
||||
And define the inputs and outputs of the models:
|
||||
@@ -841,6 +733,7 @@ And define the inputs and outputs of the models:
|
||||
\item Input: voltage generated by the DAC
|
||||
\item Output: measured displacement by the encoder
|
||||
\end{itemize}
|
||||
|
||||
The transfer function is identified and shown in Figure \ref{fig:comp_enc_frf_align_perfect}.
|
||||
From Figure \ref{fig:comp_enc_frf_align_perfect}, it is clear that:
|
||||
\begin{enumerate}
|
||||
@@ -871,7 +764,6 @@ The obtained dynamics are shown in Figure \ref{fig:effect_misalignment_y}.
|
||||
\caption{\label{fig:effect_misalignment_y}Effect of a misalignement in the \(y\) direction}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\begin{important}
|
||||
The alignment of the APA with the flexible joints as a \textbf{huge} influence on the dynamics from actuator voltage to measured displacement by the encoder.
|
||||
The misalignment in the \(y\) direction mostly influences:
|
||||
@@ -897,6 +789,7 @@ The obtained dynamics are shown in Figure \ref{fig:effect_misalignment_x}.
|
||||
\begin{important}
|
||||
The misalignment in the \(x\) direction mostly influences the presence of the flexible mode at 300Hz.
|
||||
\end{important}
|
||||
\subsection{Comparison with identified misalignment}
|
||||
\subsection{Find the misalignment of each strut}
|
||||
From the previous analysis on the effect of a \(x\) and \(y\) misalignment, it is possible to estimate the \(x,y\) misalignment of the measured struts.
|
||||
|
||||
@@ -918,7 +811,7 @@ In the future, a ``pin'' will be used to better align the APA with the flexible
|
||||
We can expect the amplitude of the spurious resonances to decrease.
|
||||
\end{important}
|
||||
\section{Effect of flexible joint's characteristics}
|
||||
\label{sec:struts_effect_joint_stiffness}
|
||||
\label{ssec:test_struts_effect_joint_stiffness}
|
||||
As the struts are composed of one APA and two flexible joints, it is obvious that the flexible joint characteristics will change the dynamic behavior of the struts.
|
||||
|
||||
Using the Simscape model, the effect of the flexible joint's characteristics on the dynamics as measured on the test bench are studied:
|
||||
@@ -928,7 +821,7 @@ Using the Simscape model, the effect of the flexible joint's characteristics on
|
||||
\item Section \ref{sec:struts_effect_bending_damping_joints}: the effects of a change of bending damping is studied
|
||||
\end{itemize}
|
||||
|
||||
The studied dynamics is between \(V_a\) and the encoder displacement \(d_e\).
|
||||
The studied dynamics is between \(u\) and the encoder displacement \(d_e\).
|
||||
\subsection{Effect of bending stiffness of the flexible joints}
|
||||
\label{sec:struts_effect_bending_stiff_joints}
|
||||
|
||||
@@ -943,7 +836,7 @@ The obtained dynamics from DAC voltage to encoder measurements are compared in F
|
||||
\end{figure}
|
||||
|
||||
\begin{important}
|
||||
The bending stiffness of the joints has little impact on the transfer function from \(V_a\) to \(d_e\).
|
||||
The bending stiffness of the joints has little impact on the transfer function from \(u\) to \(d_e\).
|
||||
\end{important}
|
||||
\subsection{Effect of axial stiffness of the flexible joints}
|
||||
\label{sec:struts_effect_axial_stiff_joints}
|
||||
@@ -977,18 +870,6 @@ The results are shown in Figure \ref{fig:effect_enc_bending_damp}.
|
||||
\includegraphics[scale=1]{figs/effect_enc_bending_damp.png}
|
||||
\caption{\label{fig:effect_enc_bending_damp}Dynamics from DAC output to encoder for several bending damping}
|
||||
\end{figure}
|
||||
|
||||
\begin{important}
|
||||
Adding damping in bending for the flexible joints could be a nice way to reduce the effects of the spurious resonances of the struts.
|
||||
\end{important}
|
||||
|
||||
\begin{question}
|
||||
How to effectively add damping to the flexible joints?
|
||||
|
||||
One idea would be to introduce a sheet of damping material inside the flexible joint.
|
||||
Not sure is would be effect though.
|
||||
\end{question}
|
||||
\section{Comparison with identified misalignment}
|
||||
\chapter{Conclusion}
|
||||
\label{sec:test_struts_conclusion}
|
||||
\printbibliography[heading=bibintoc,title={Bibliography}]
|
||||
|
||||
Reference in new issue
Block a user