Update text about disturbances

figs/nohup.out

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+(termite:48779): GLib-WARNING **: 10:35:19.170: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

index.org

@@ -371,15 +371,22 @@ To estimate the PSD of the position error $\epsilon$ and thus the RMS residual m
 <<sec:micro_station_dynamics>>
 
 ** Introduction                                                      :ignore:
+As explained before, it is very important to have a good estimation of the micro-station dynamics as it will be coupled with the dynamics of the nano-hexapod and thus is very important for both the design of the nano-hexapod and the controller.
+The estimated dynamics will also be used to tune the developed multi-body model of the micro-station with which the simulations will be performed.
 
-https://tdehaeze.github.io/meas-analysis/
+All the measurements performed on the micro-station are detailed in [[https://tdehaeze.github.io/meas-analysis/][this]] document and summarized in the following sections.
 
-Modal Analysis: https://tdehaeze.github.io/meas-analysis/modal-analysis/index.html
-
-The obtained dynamics will allows us to compare the dynamics of the model.
 
 ** Setup
-In order to perform to *Modal Analysis* and to obtain first a response model, the following devices were used:
+<<sec:id_setup>>
+
+To measure the dynamics of such complicated system, it as been chosen to perform a full modal analysis.
+
+To limit the number of degrees of freedom to be measured, we suppose that in the frequency range of interest (DC-300Hz), each of the positioning stage is behaving as a solid body.
+Thus, to fully describe the dynamics of the station, we (only) need to measure 6 degrees of freedom on each of the positioning stage (that is 36 degrees of freedom for the 6 solid bodies).
+
+
+In order to perform the *Modal Analysis*, the following devices were used:
 - An *acquisition system* (OROS) with 24bits ADCs
 - 3 tri-axis *Accelerometers*
 - An *Instrumented Hammer*
@@ -395,103 +402,208 @@ The measurement thus consists of:
   - 3 on top of the spindle
   - 4 on top of the hexapod
 
-In total, 69 degrees of freedom are measured (23 tri axis accelerometers).
-
-#+name: fig:accelerometers_ty_overview
-#+caption: Figure caption
-[[file:figs/accelerometers_ty_overview.jpg]]
+In total, 69 degrees of freedom are measured (23 tri axis accelerometers) which is way more that what was required.
 
+We chose to have some redundancy in the measurement to be able to verify that the solid-body assumption was correct for each of the stage.
 
 #+name: fig:hammer_z
-#+caption: Figure caption
+#+caption: Example of one hammer impact
 [[file:figs/hammer_z.gif]]
 
-** Results
-From the measurements, we obtain
+#+name: fig:accelerometers_ty_overview
+#+caption: 3 tri axis accelerometers fixed to the translation stage
+[[file:figs/accelerometers_ty_overview.jpg]]
 
-- Reduction of the
-- solid body assumption
-- verification of the assumption => ok
+** Results
+<<sec:id_results>>
+
+From the measurements, we obtain all the transfer functions from forces applied at the location of the hammer impacts to the x-y-z acceleration of each solid body at the location of each accelerometer.
+
+Modal shapes and natural frequencies are then computed. Example of mode shapes are shown in Figures [[fig:mode1]] [[fig:mode6]].
 
 #+name: fig:mode1
-#+caption: Figure caption
+#+caption: First mode
 [[file:figs/mode1.gif]]
 
 #+name: fig:mode6
-#+caption: Figure caption
+#+caption: Sixth mode
 [[file:figs/mode6.gif]]
 
-** Conclusion
-The reduction of the number of degrees of freedom from 69 (23 accelerometers with each 3DOF) to 36 (6 solid bodies with 6 DOF) seems to work well.
 
-This confirms the fact that the stages are indeed behaving as a solid body in the frequency band of interest. This valid the fact that a multi-body model can be used to represent the dynamics of the micro-station.
+We then reduce the number of degrees of freedom from 69 (23 accelerometers with each 3DOF) to 36 (6 solid bodies with 6 DOF).
+
+From the reduced transfer function matrix, we can re-synthesize the response at the 69 measured degrees of freedom and we find that we have an exact match.
+
+This confirms the fact that the stages are indeed behaving as a *solid body* in the frequency band of interest.
+This thus means that a multi-body model can be used to represent the dynamics of the micro-station.
 
 * Identification of the Disturbances
 <<sec:identification_disturbances>>
 
 ** Introduction                                                      :ignore:
+In this section, we wish to list and identify all the disturbances affecting the system.
+
+Note that here we are not much interested by low frequency disturbances such as thermal effects and static guiding errors of each positioning stage.
+This is because the frequency content of these errors will be located in the controller bandwidth and thus will be easily compensated by the nano-hexapod.
+
+The problem are on the high frequency disturbances.
+In the following sections, we consider:
+- the ground motion
+- vibrations of each stage, due either to their control systems or their motion
+
+
 https://tdehaeze.github.io/meas-analysis/
-
 Open Loop Noise budget: https://tdehaeze.github.io/nass-simscape/disturbances.html
 
-
-Static Guiding errors:
-- measured at the PEL
-- low frequency errors, will thus be compensated
-
-The problem are on the high frequency disturbances
-
 ** Ground Motion
 <<sec:ground_motion>>
 
+The ground motion can easily be estimated using an inertial sensor with sufficient sensitivity.
 
+To verify that the inertial sensors are sensitive enough, a Huddle test has been performed (Figure [[fig:geophones]]).
+
+#+name: fig:geophones
+#+caption: Huddle Test Setup
+[[file:figs/geophones.jpg]]
+
+The measured Power Spectral Density of the ground motion at the ID31 floor is compared with other measurements performed at ID09 and at CERN.
+The low frequency differences between the ground motion at ID31 and ID09 is just due to the fact that for the later measurement, the low frequency sensitivity of the inertial sensor was not taken into account.
+
+#+name: fig:ground_motion_compare
+#+caption: Comparison of the PSD of the ground motion measured at different location
+[[file:figs/ground_motion_compare.png]]
 
 ** Stage Vibration - Effect of Control systems
 <<sec:stage_vibration_control>>
 
 Control system of each stage has been tested
-https://tdehaeze.github.io/meas-analysis/disturbance-control-system/index.html
-https://tdehaeze.github.io/meas-analysis/2018-10-15%20-%20Marc/index.html
+
+Each motor are turn off and then on.
+The goal is to see what noise is injected in the system due to the regulation loop of each stage.
+
+
+Complete reports on these measurements are accessible [[https://tdehaeze.github.io/meas-analysis/2018-10-15%20-%20Marc/index.html][here]] and [[https://tdehaeze.github.io/meas-analysis/disturbance-control-system/index.html][here]].
 
 25Hz vertical motion when the *Spindle* is turned on (even when not rotating).
 
-
 ** Stage Vibration - Effect of Motion
 <<sec:stage_vibration_motion>>
 
-We consider:
-- The rotation of the Spindle
-- The translation of the Translation Stage
+We consider here the vibrations induced by the scans of the translation stage and rotation of the spindle.
+
+Details reports are accessible [[https://tdehaeze.github.io/meas-analysis/disturbance-ty/index.html][here]] for the translation stage and [[https://tdehaeze.github.io/meas-analysis/disturbance-sr-rz/index.html][here]] for the spindle/slip-ring.
+
+*** Spindle and Slip-Ring
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+The setup for the measurement of vibrations induced by rotation of the Spindle and Slip-ring is shown in Figure [[fig:rz_meas_errors]].
+
+#+name: fig:rz_meas_errors
+#+caption: Measurement of the sample's vertical motion when rotating at 6rpm
+[[file:figs/rz_meas_errors.gif]]
+
+A geophone is fixed at the location of the sample and we measure the motion:
+- without rotation
+- when rotating at 6rpm using the slip-ring motor
+- when rotating at 6rpm using the spindle motor synchronized with the slip-ring motor
+
+The obtained Power Spectral Density of the sample's absolute velocity are shown in Figure [[fig:sr_sp_psd_sample_compare]].
+
+We can see that when using the Slip-ring motor to rotate the sample, only a little increase of the motion is observed above 100Hz.
+
+However, when rotating with the Spindle (normal functioning mode):
+- a very sharp peak at 23Hz is observed. Its cause has not been identified yet
+- a general large increase in motion above 30Hz
+
+#+name: fig:sr_sp_psd_sample_compare
+#+caption: Comparison of the ASD of the measured voltage from the Geophone at the sample location
+[[file:figs/sr_sp_psd_sample_compare.png]]
+
+#+begin_important
+  Some investigation should be performed on the Spindle to determine where does this 23Hz motion comes from.
+#+end_important
+
+*** Translation Stage
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
+
+The same setup is used (a geophone is located at the sample's location and another on the granite).
+
+We impose a 1Hz triangle motion with an amplitude of $\pm 2.5mm$ on the translation stage (Figure [[fig:figure_name]]), and we measure the absolute velocity of both the sample and the granite.
+
+#+name: fig:figure_name
+#+caption: Y position of the translation stage measured by the encoders
+[[file:figs/ty_position_time.png]]
+
+
+The time domain absolute vertical velocity of the sample and granite are shown in Figure [[fig:ty_z_time]].
+It is shown that quite large motion of the granite is induced by the translation stage scans.
+This could be a problem if this is shown to excite the metrology frame of the nano-focusing lens position stage.
+
+#+name: fig:ty_z_time
+#+caption: Vertical velocity of the sample and marble when scanning with the translation stage
+[[file:figs/ty_z_time.png]]
+
+The Amplitude Spectral Densities of the measured absolute velocities are shown in Figure [[fig:asd_z_direction]].
+We can see many peaks starting from 1Hz showing the large spectral content probably due to the triangular reference of the translation stage.
+
+#+name: fig:asd_z_direction
+#+caption: Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz
+[[file:figs/asd_z_direction.png]]
+
+#+begin_important
+  A smoother motion for the translation stage (such as a sinus motion) could probably help reducing much of the vibrations produced.
+#+end_important
 
 ** Sum of all disturbances
+We can now compare the effect of all the disturbance sources on the position error (relative motion of the sample with respect to the granite).
+
+The Power Spectral Density of the motion error due to the ground motion, translation stage scans and spindle rotation are shown in Figure [[fig:dist_effect_relative_motion]].
+
+We can see that the ground motion is quite small compare to the translation stage and spindle induced motions.
 
 #+name: fig:dist_effect_relative_motion
 #+caption: Amplitude Spectral Density fo the motion error due to disturbances
 [[file:figs/dist_effect_relative_motion.png]]
 
+The Cumulative Amplitude Spectrum is shown in Figure [[fig:dist_effect_relative_motion_cas]].
+It is shown that the motion induced by translation stage scans and spindle rotation are in the micro-meter range.
 
 #+name: fig:dist_effect_relative_motion_cas
 #+caption: Cumulative Amplitude Spectrum of the motion error due to disturbances
 [[file:figs/dist_effect_relative_motion_cas.png]]
 
+We can also estimate the required bandwidth by seeing that $10\ nm [rms]$ motion is induced by the perturbations above 100Hz.
 
-Expected required bandwidth
+This means that if the controller compensate all the motion errors below 100Hz (ideal case), 10nm [rms] of motion will still remain.
 
-** Better measurement of the effect of disturbances
-Here, the measurement were made with inertial sensors.
-However, we are interested in the relative motion of the sample with respect to the granite and not the absolute motion.
+From that, we can conclude that we will probably need a control bandwidth to around 100Hz.
 
+** Better estimation of the disturbances
+All the disturbance measurements were made with inertial sensors, and to obtain the relative motion sample/granite, two inertial sensors were used and the signals were subtracted.
 
-The best measurement of the disturbances would be to have the metrology already functioning.
+This is not perfect as using only one geophone on the sample and one on the granite do not permit to separate the translations and the rotations.
 
+An alternative could be to position a reference object at the sample location and to use the X-ray to measure its motion.
 
-We could perform a measurement using the X-ray.
-
-Detector Requirement:
+The detector requirement would be:
 - Sample frequency above $400Hz$
-- Resolution of $\approx 20nm$
+- Resolution of $\approx 100nm$ (to be discussed)
 
 ** Conclusion
+Main disturbance sources have been identified.
+These disturbances will then be included in the multi-body model.
+
+
+Other disturbance sources were not estimated such as cable forces and acoustic disturbances.
+If heavy/stiff cables are to be fixed to the sample, this should be quantified and included in the model.
+
+
+Having better estimation of the disturbances would allows to more precisely estimate the attainable performances.
+This should however not change the conclusion of this study nor significantly change the nano-hexapod design.
 
 * Multi Body Model
 <<sec:multi_body_model>>