Re-read section about the dynamical measurements

index.org

@@ -386,15 +386,16 @@ 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 controller.
+As explained before, it is very important to have a good estimation of the micro-station dynamics as it will be used:
+- to tune the developed multi-body model of the micro-station with which the simulations will be performed
+- for the design of the nano-hexapod as it will be coupled with the micro-station
+- for the design of 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.
 
 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.
 
 
 The general procedure to identify the dynamics of the micro-station is shown in Figure [[fig:vibration_analysis_procedure]].
-
 The steps are:
 1. extract a Response Model (Frequency Response Functions) from measurements
 2. convert the Response Model into a Modal Model (Natural Frequencies and Mode Shapes)
@@ -405,24 +406,25 @@ The steps are:
 [[file:figs/vibration_analysis_procedure.png]]
 
 The extraction of the Spatial Model (3rd step) was not performed as it requires a lot of time and was not judge necessary.
+Instead, the model will be tuned using both the modal model and the response model.
 
-** Setup
+** Experimental Setup
 <<sec:id_setup>>
 
 To measure the dynamics of such complicated system, it as been chosen to perform a 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).
+Thus, to fully describe the dynamics of the station, we (only) need to measure 6 degrees of freedom for each positioning stage (that is 36 degrees of freedom for the 6 considered 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*
+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
 
-The measurement thus consists of:
-- Exciting the structure at the same location with the Hammer (Figure [[fig:hammer_z]])
-- Move the accelerometers to measure all the DOF of the structure.
+The measurement consists of:
+- Exciting the structure at the same location with the instrumented hammer (Figure [[fig:hammer_z]])
+- Fix the accelerometers on each of the stages to measure all the DOF of the structure.
   The position of the accelerometers are:
   - 4 on the first granite
   - 4 on the second granite
@@ -433,7 +435,7 @@ The measurement thus consists of:
 
 In total, 69 degrees of freedom are measured (23 tri axis accelerometers) which is more that what was required.
 
-We chose to have some redundancy in the measurement to be able to verify that the solid-body assumption is correct for each of the stage.
+It was chosen to have some redundancy in the measurement to be able to verify the correctness of the solid-body assumption.
 
 #+name: fig:hammer_z
 #+caption: Example of one hammer impact
@@ -446,9 +448,10 @@ We chose to have some redundancy in the measurement to be able to verify that th
 ** 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.
+From the measurements are extracted 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]].
+Modal shapes and natural frequencies are then computed.
+Example of the obtained micro-station's mode shapes are shown in Figures [[fig:mode1]] and [[fig:mode6]].
 
 #+name: fig:mode1
 #+caption: First mode that shows a suspension mode, probably due to bad leveling of one Airloc
@@ -465,9 +468,9 @@ From the reduced transfer function matrix, we can re-synthesize the response at
 
 #+begin_important
 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.
-#+end_important
 
+This thus means that *a multi-body model can be used to correctly represent the dynamics of the micro-station*.
+#+end_important
 
 Many Frequency Response Functions (FRF) are obtained from the measurements.
 Examples of FRF are shown in Figure [[fig:frf_all_bodies_one_direction]].
@@ -479,7 +482,8 @@ These FRF will be used to compare the dynamics of the multi-body model with the
 
 ** Conclusion
 #+begin_important
-  The modal analysis of the micro-station confirmed the fact that a multi-body model should be able to correctly represents the micro-station dynamics.
+  The dynamical measurements made on the micro-station confirmed the fact that a multi-body model is a good option to correctly represents the micro-station dynamics.
+
   In Section [[sec:multi_body_model]], the obtained Frequency Response Functions will be used to compare the model dynamics with the micro-station dynamics.
 #+end_important