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Thomas Dehaeze 2025-02-04 15:30:07 +01:00
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@ -139,9 +139,9 @@ In this report, a uniaxial model of the acrfull:nass is developed and used to ob
Note that in this study, only the vertical direction is considered (which is the most stiff), but other directions were considered as well, yielding to similar conclusions.
The model is schematically shown in Figure ref:fig:uniaxial_overview_model_sections where the colors represent the parts studied in different sections.
To have a relevant model, the micro-station dynamics is first identified and its model is tuned to match the measurements (Section ref:sec:micro_station_model).
To have a relevant model, the micro-station dynamics is first identified and its model is tuned to match the measurements (Section ref:sec:uniaxial_micro_station_model).
Then, a model of the nano-hexapod is added on top of the micro-station.
With the added sample and sensors, this gives a uniaxial dynamical model of the acrshort:nass that will be used for further analysis (Section ref:sec:nano_station_model).
With the added sample and sensors, this gives a uniaxial dynamical model of the acrshort:nass that will be used for further analysis (Section ref:sec:uniaxial_nano_station_model).
The disturbances affecting position stability are identified experimentally (Section ref:sec:uniaxial_disturbances) and included in the model for dynamical noise budgeting (Section ref:sec:uniaxial_noise_budgeting).
In all the following analysis, three nano-hexapod stiffnesses are considered to better understand the trade-offs and to find the most adequate nano-hexapod design.
@ -301,7 +301,7 @@ Two key effects that may limit that positioning performances are then considered
#+end_src
#+name: fig:uniaxial_overview_model_sections
#+caption: Uniaxial Micro-Station model in blue (Section ref:sec:micro_station_model), Nano-Hexapod models in red (Section ref:sec:nano_station_model), Disturbances in yellow (Section ref:sec:uniaxial_disturbances), Active Damping in green (Section ref:sec:uniaxial_active_damping), Position control in purple (Section ref:sec:uniaxial_position_control) and Sample dynamics in cyan (Section ref:sec:uniaxial_payload_dynamics)
#+caption: Uniaxial Micro-Station model in blue (Section ref:sec:uniaxial_micro_station_model), Nano-Hexapod models in red (Section ref:sec:uniaxial_nano_station_model), Disturbances in yellow (Section ref:sec:uniaxial_disturbances), Active Damping in green (Section ref:sec:uniaxial_active_damping), Position control in purple (Section ref:sec:uniaxial_position_control) and Sample dynamics in cyan (Section ref:sec:uniaxial_payload_dynamics)
#+RESULTS:
[[file:figs/uniaxial_overview_model_sections.png]]
@ -309,11 +309,11 @@ Two key effects that may limit that positioning performances are then considered
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/uniaxial_1_micro_station_model.m
:END:
<<sec:micro_station_model>>
<<sec:uniaxial_micro_station_model>>
** Introduction :ignore:
In this section, a uniaxial model of the micro-station is tuned to match measurements made on the micro-station.
The measurement setup is shown in Figure ref:fig:uniaxial_ustation_first_meas_dynamics where several geophones[fn:1] are fixed to the micro-station and an instrumented hammer is used to inject forces on different stages of the micro-station.
The measurement setup is shown in Figure ref:fig:uniaxial_ustation_first_meas_dynamics where several geophones[fn:uniaxial_1] are fixed to the micro-station and an instrumented hammer is used to inject forces on different stages of the micro-station.
From the measured frequency response functions (FRF), the model can be tuned to approximate the uniaxial dynamics of the micro-station.
@ -756,7 +756,7 @@ exportFig('figs/uniaxial_comp_frf_meas_model.pdf', 'width', 'wide', 'height', 't
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/uniaxial_2_nano_hexapod_model.m
:END:
<<sec:nano_station_model>>
<<sec:uniaxial_nano_station_model>>
** Introduction :ignore:
A model of the nano-hexapod and sample is now added on top of the uniaxial model of the micro-station (Figure ref:fig:uniaxial_model_micro_station_nass).
@ -1193,7 +1193,7 @@ save('./mat/uniaxial_plants.mat', 'G_vc_light', 'G_md_light', 'G_pz_light', ...
:END:
<<sec:uniaxial_disturbances>>
** Introduction :ignore:
To quantify disturbances (red signals in Figure ref:fig:uniaxial_model_micro_station_nass), three geophones[fn:2] are used.
To quantify disturbances (red signals in Figure ref:fig:uniaxial_model_micro_station_nass), three geophones[fn:uniaxial_2] are used.
One is located on the floor, another one on the granite, and the last one on the micro-hexapod's top platform (see Figure ref:fig:uniaxial_ustation_meas_disturbances).
The geophone located on the floor was used to measure the floor motion $x_f$ while the other two geophones were used to measure vibrations introduced by scanning of the $T_y$ stage and $R_z$ stage (see Figure ref:fig:uniaxial_ustation_dynamical_id_setup).
@ -1389,7 +1389,7 @@ load('uniaxial_micro_station_parameters.mat');
** Ground Motion
To acquire the geophone signals, the measurement setup shown in Figure ref:fig:uniaxial_geophone_meas_chain is used.
The voltage generated by the geophone is amplified using a low noise voltage amplifier[fn:3] with a gain of 60dB before going to the ADC.
The voltage generated by the geophone is amplified using a low noise voltage amplifier[fn:uniaxial_3] with a gain of 60dB before going to the ADC.
This is done to improve the signal-to-noise ratio.
To reconstruct the displacement $x_f$ from the measured voltage $\hat{V}_{x_f}$, the transfer function of the measurement chain from $x_f$ to $\hat{V}_{x_f}$ needs to be estimated.
@ -1601,7 +1601,7 @@ save('./mat/uniaxial_disturbance_psd.mat', 'f', 'psd_ft', 'psd_xf');
:END:
<<sec:uniaxial_noise_budgeting>>
** Introduction :ignore:
Now that a model of the acrshort:nass has been obtained (see section ref:sec:nano_station_model) and that the disturbances have been estimated (see section ref:sec:uniaxial_disturbances), it is possible to perform an /open-loop dynamic noise budgeting/.
Now that a model of the acrshort:nass has been obtained (see section ref:sec:uniaxial_nano_station_model) and that the disturbances have been estimated (see section ref:sec:uniaxial_disturbances), it is possible to perform an /open-loop dynamic noise budgeting/.
To perform such noise budgeting, the disturbances need to be modeled by their spectral densities (done in section ref:sec:uniaxial_disturbances).
Then, the transfer functions from disturbances to the performance metric (here the distance $d$) are computed (Section ref:ssec:uniaxial_noise_budget_sensitivity).
@ -6147,7 +6147,7 @@ Therefore, it is important to take special care when designing sampling environm
# TODO - Make a table summarizing the findings
In this study, a uniaxial model of the nano-active-stabilization-system was tuned from both dynamical measurements (Section ref:sec:micro_station_model) and from disturbances measurements (Section ref:sec:uniaxial_disturbances).
In this study, a uniaxial model of the nano-active-stabilization-system was tuned from both dynamical measurements (Section ref:sec:uniaxial_micro_station_model) and from disturbances measurements (Section ref:sec:uniaxial_disturbances).
Three active damping techniques can be used to critically damp the nano-hexapod resonances (Section ref:sec:uniaxial_active_damping).
However, this model does not allow the determination of which one is most suited to this application (a comparison of the three active damping techniques is done in Table ref:tab:comp_active_damping).
@ -6192,6 +6192,6 @@ colors = colororder;
* Footnotes
[fn:3]DLPVA-100-B from Femto with a voltage input noise is $2.4\,nV/\sqrt{\text{Hz}}$
[fn:2]Mark Product L-22D geophones are used with a sensitivity of $88\,\frac{V}{m/s}$ and a natural frequency of $\approx 2\,\text{Hz}$
[fn:1]Mark Product L4-C geophones are used with a sensitivity of $171\,\frac{V}{m/s}$ and a natural frequency of $\approx 1\,\text{Hz}$
[fn:uniaxial_3]DLPVA-100-B from Femto with a voltage input noise is $2.4\,nV/\sqrt{\text{Hz}}$
[fn:uniaxial_2]Mark Product L-22D geophones are used with a sensitivity of $88\,\frac{V}{m/s}$ and a natural frequency of $\approx 2\,\text{Hz}$
[fn:uniaxial_1]Mark Product L4-C geophones are used with a sensitivity of $171\,\frac{V}{m/s}$ and a natural frequency of $\approx 1\,\text{Hz}$