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Thomas Dehaeze 2025-02-20 10:56:13 +01:00
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@ -148,6 +148,13 @@ One big advantage of doing the control in the cartesian plane, is that we don't
Maybe this should be done in A6 (simscape-nass).
Here it can be reminded when doing the control in the cartesian frame.
** TODO [#A] Missing =lead= filter for the simulations
[[*Robust Controller Design][Robust Controller Design]]
Missing lead in the simscape simulation.
Add it and recompute all the figures
** DONE [#A] Make detailed outline
CLOSED: [2025-01-30 Thu 11:34]
@ -459,12 +466,12 @@ CLOSED: [2024-11-12 Tue 16:03]
* Introduction :ignore:
The nano-hexapod's mounting and validation through dynamics measurements marks a crucial milestone in the development of the Nano Active Stabilization System (NASS).
To proceed with the full validation of the Nano Active Stabilization System (NASS), the nano-hexapod was mounted on top of the micro-station on ID31, as illustrated in figure ref:fig:test_id31_micro_station_nano_hexapod.
This section presents a comprehensive experimental evaluation of the complete system's performance on the ID31 beamline, focusing on its ability to maintain precise sample positioning under various experimental conditions.
Initially, the project planned to develop a long-stroke ($\approx 1 \, cm^3$) 5-DoF metrology system to measure the sample position relative to the granite base.
However, the complexity of this development prevented its completion before the experimental testing phase on ID31.
To validate the nano-hexapod and its associated control architecture, an alternative short-stroke ($> 100\,\mu m^3$) metrology system was developed, which is presented in Section ref:sec:test_id31_metrology.
To validate the nano-hexapod and its associated control architecture, an alternative short-stroke ($\approx 100\,\mu m^3$) metrology system was developed, which is presented in Section ref:sec:test_id31_metrology.
Then, several key aspects of the system validation are examined.
Section ref:sec:test_id31_open_loop_plant analyzes the identified dynamics of the nano-hexapod mounted on the micro-station under various experimental conditions, including different payload masses and rotational velocities.
@ -503,7 +510,7 @@ These include tomography scans at various speeds and with different payload mass
** Introduction :ignore:
The control of the nano-hexapod requires an external metrology system that measures the relative position of the nano-hexapod top platform with respect to the granite.
As a long-stroke ($\approx 1 \,cm^3$) metrology system was not yet developed, a stroke stroke ($> 100\,\mu m^3$) was used instead to validate the nano-hexapod control.
As a long-stroke ($\approx 1 \,cm^3$) metrology system was not yet developed, a stroke stroke ($\approx 100\,\mu m^3$) was used instead to validate the nano-hexapod control.
The first considered option was to use the "Spindle error analyzer" shown in Figure ref:fig:test_id31_lion.
This system comprises 5 capacitive sensors facing two reference spheres.
@ -572,7 +579,7 @@ Indeed, when the spheres are moving perpendicularly to the beam axis, the reflec
The proposed short-stroke metrology system is schematized in Figure ref:fig:test_id31_metrology_kinematics.
The point of interest is indicated by the blue frame $\{B\}$, which is located $H = 150\,mm$ above the nano-hexapod's top platform.
The spheres have a diameter $d = 25.4\,mm$, and the indicated dimensions are $l_1 = 60\,mm$ and $l_2 = 16.2\,mm$.
To compute the pose of the $\{B\}$ frame with respect to the granite (i.e. with respect to the fixed interferometer heads), the measured (small) displacements $[d_1,\ d_2,\ d_3,\ d_4,\ d_5]$ by the interferometers are first written as a function of the (small) linear and angular motion of the $\{B\}$ frame $[D_x,\ D_y,\ D_z,\ R_x,\ R_y]$ eqref:eq:test_id31_metrology_kinematics.
To compute the pose of $\{B\}$ with respect to the granite (i.e. with respect to the fixed interferometer heads), the measured (small) displacements $[d_1,\ d_2,\ d_3,\ d_4,\ d_5]$ by the interferometers are first written as a function of the (small) linear and angular motion of the $\{B\}$ frame $[D_x,\ D_y,\ D_z,\ R_x,\ R_y]$ eqref:eq:test_id31_metrology_kinematics.
\begin{equation}\label{eq:test_id31_metrology_kinematics}
d_1 = D_y - l_2 R_x, \quad d_2 = D_y + l_1 R_x, \quad d_3 = -D_x - l_2 R_y, \quad d_4 = -D_x + l_1 R_y, \quad d_5 = -D_z
@ -642,7 +649,7 @@ However, this first alignment should be sufficient to position the two sphere wi
<<ssec:test_id31_metrology_alignment>>
The short-stroke metrology system was placed on top of the main granite using granite blocs (Figure ref:fig:test_id31_short_stroke_metrology_overview).
Granite is used for its good vibration and thermal stability.
Granite is used for its good mechanical and thermal stability.
#+name: fig:test_id31_short_stroke_metrology_overview
#+caption: Granite gantry used to fix the short-stroke metrology system
@ -652,12 +659,12 @@ Granite is used for its good vibration and thermal stability.
The interferometer beams must be placed with respect to the two reference spheres as close as possible to the ideal case shown in Figure ref:fig:test_id31_metrology_kinematics.
Therefore, their positions and angles must be well adjusted with respect to the two spheres.
First, the vertical positions of the spheres is adjusted using the micro-hexapod to match the heights of the interferometers.
Then, the horizontal position of the gantry is adjusted such that the coupling efficiency (i.e. the intensity of the light reflected back in the fiber) of the top interferometer is maximized.
Then, the horizontal position of the gantry is adjusted such that the intensity of the light reflected back in the fiber of the top interferometer is maximized.
This is equivalent as to optimize the perpendicularity between the interferometer beam and the sphere surface (i.e. the concentricity between the top beam and the sphere center).
The lateral sensor heads (i.e. all except the top one) were each fixed to a custom tip-tilt adjustment mechanism.
This allows them to be individually oriented so that they all point to the spheres' center (i.e. perpendicular to the sphere surface).
This is achieved by maximizing the coupling efficiency of each interferometer.
This is achieved by maximizing the intensity of the reflected light of each interferometer.
After the alignment procedure, the top interferometer should coincide with the spindle axis, and the lateral interferometers should all be in the horizontal plane and intersect the centers of the spheres.
@ -1289,11 +1296,11 @@ exportFig('figs/test_id31_first_id_iff.pdf', 'width', 'half', 'height', 600);
One possible explanation of the increased coupling observed in Figure ref:fig:test_id31_first_id_int is the poor alignment between the external metrology axes (i.e. the interferometer supports) and the nano-hexapod axes.
To estimate this alignment, a decentralized low-bandwidth feedback controller based on the nano-hexapod encoders was implemented.
This allowed to perform two straight movements of the nano-hexapod along its $x$ and $y$ axes.
During these two movements, external metrology measurements were recorded and the results are shown in Figure ref:fig:test_id31_Rz_align_error_and_correct.
This allowed to perform two straight motions of the nano-hexapod along its $x$ and $y$ axes.
During these two motions, external metrology measurements were recorded and the results are shown in Figure ref:fig:test_id31_Rz_align_error_and_correct.
It was found that there was a misalignment of 2.7 degrees (rotation along the vertical axis) between the interferometer axes and nano-hexapod axes.
This was corrected by adding an offset to the spindle angle.
After alignment, the same movement was performed using the nano-hexapod while recording the signal of the external metrology.
After alignment, the same motion was performed using the nano-hexapod while recording the signal of the external metrology.
Results shown in Figure ref:fig:test_id31_Rz_align_correct are indeed indicating much better alignment.
#+begin_src matlab
@ -1452,7 +1459,7 @@ exportFig('figs/test_id31_first_id_int_better_rz_align.pdf', 'width', 'wide', 'h
To determine how the system dynamics changes with the payload, open-loop identification was performed for four payload conditions shown in Figure ref:fig:test_id31_picture_masses.
The obtained direct terms are compared with the model dynamics in Figure ref:fig:test_id31_comp_simscape_diag_masses.
It was found that the model well predicts the measured dynamics under all payload conditions.
Therefore, the model can be used for model-based control is necessary.
Therefore, the model can be used for model-based control if necessary.
It is interesting to note that the anti-resonances in the force sensor plant now appear as minimum-phase, as the model predicts (Figure ref:fig:test_id31_comp_simscape_iff_diag_masses).
@ -1980,8 +1987,6 @@ The spindle rotation had no visible effect on the measured dynamics, indicating
<<sec:test_id31_iff>>
** Introduction :ignore:
The HAC-LAC strategy, which was previously developed and validated using the multi-body model, was then experimentally implemented.
In this section, the low authority control part is first validated.
It consists of a decentralized Integral Force Feedback controller $\bm{K}_{\text{IFF}}$, with all the diagonal terms being equal eqref:eq:test_id31_Kiff.
@ -2062,7 +2067,7 @@ The decentralized Integral Force Feedback is implemented as shown in the block d
As the multi-body model is used to evaluate the stability of the IFF controller and to optimize the achievable damping, it is first checked whether this model accurately represents the system dynamics.
In the previous section (Figure ref:fig:test_id31_comp_simscape_iff_diag_masses), it was shown that the model well captures the dynamics from each actuator to its collocated force sensor, and that for all considered payloads.
Nevertheless, it is also important to well model the coupling in the system.
Nevertheless, it is also important to model accurately the coupling in the system.
To verify that, instead of comparing the 36 elements of the $6 \times 6$ frequency response matrix from $\bm{u}$ to $\bm{V_s}$, only 6 elements are compared in Figure ref:fig:test_id31_comp_simscape_Vs.
Similar results were obtained for all other 30 elements and for the different payload conditions.
This confirms that the multi-body model can be used to tune the IFF controller.
@ -3524,7 +3529,7 @@ Several scientific experiments were replicated, such as:
Unless explicitly stated, all closed-loop experiments were performed using the robust (i.e. conservative) high authority controller designed in Section ref:ssec:test_id31_iff_hac_controller.
For each experiment, the obtained performances are compared to the specifications for the most depending case in which nano-focusing optics are used to focus the beam down to $200\,nm\times 100\,nm$.
For each experiment, the obtained performances are compared to the specifications for the most demanding case in which nano-focusing optics are used to focus the beam down to $200\,nm\times 100\,nm$.
In this case, the goal is to keep the sample's point of interest in the beam, and therefore the $D_y$ and $D_z$ positioning errors should be less than $200\,nm$ and $100\,nm$ peak-to-peak, respectively.
The $R_y$ error should be less than $1.7\,\mu\text{rad}$ peak-to-peak.
In terms of RMS errors, this corresponds to $30\,nm$ in $D_y$, $15\,nm$ in $D_z$ and $250\,\text{nrad}$ in $R_y$ (a summary of the specifications is given in Table ref:tab:test_id31_experiments_specifications).
@ -3824,7 +3829,7 @@ data_tomo_m3_Wz6.Ry_rms_ol = rms(data_tomo_m3_Wz6.Ry_int(1:i_m3) - (y0 + R*sin(d
A tomography experiment was then performed with the highest rotational velocity of the Spindle: $180\,\text{deg/s}$[fn:test_id31_7].
The trajectory of the point of interest during the fast tomography scan is shown in Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp.
Although the experimental results closely mirror the simulation results (Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim), the actual performance was slightly lower than predicted.
Although the experimental results closely match the simulation results (Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim), the actual performance was slightly lower than predicted.
Nevertheless, even with this robust (i.e. conservative) HAC implementation, the system performance was already close to the specified requirements.
#+begin_src matlab
@ -3934,7 +3939,7 @@ data_tomo_m0_Wz180.Ry_rms_ol = rms(data_tomo_m0_Wz180.Ry_int(1:i_m0) - (y0 + R*s
**** Cumulative Amplitude Spectra
A comparative analysis was conducted using three tomography scans at $180,\text{deg/s}$ to evaluate the effectiveness of the HAC-LAC strategy in reducing positioning errors.
A comparative analysis was conducted using three tomography scans at $180\,\text{deg/s}$ to evaluate the effectiveness of the HAC-LAC strategy in reducing positioning errors.
The scans were performed under three conditions: open-loop, with decentralized IFF control, and with the complete HAC-LAC strategy.
For these specific measurements, an enhanced high authority controller was optimized for low payload masses to meet the performance requirements.
@ -4105,7 +4110,7 @@ exportFig('figs/test_id31_hac_cas_cl_ry.pdf', 'width', 'third', 'height', 'norma
<<ssec:test_id31_scans_reflectivity>>
X-ray reflectivity measurements involve scanning thin structures, particularly solid/liquid interfaces, through the beam by varying the $R_y$ angle.
In this experiment, a $R_y$ scan was executed at a rotational velocity of $100,\mu rad/s$, and the closed-loop positioning errors were monitored (Figure ref:fig:test_id31_reflectivity).
In this experiment, a $R_y$ scan was executed at a rotational velocity of $100\,\mu rad/s$, and the closed-loop positioning errors were monitored (Figure ref:fig:test_id31_reflectivity).
The results confirmed that the NASS successfully maintained the point of interest within the specified beam parameters throughout the scanning process.
#+begin_src matlab
@ -4338,7 +4343,7 @@ exportFig('figs/test_id31_dz_mim_1000nm_steps.pdf', 'width', 'third', 'height',
For these and subsequent experiments, the NASS performs "ramp scans" (constant velocity scans).
To eliminate tracking errors, the feedback controller incorporates two integrators, compensating for the plant's lack of integral action at low frequencies.
Initial testing at $10,\mu m/s$ demonstrated positioning errors well within specifications (indicated by dashed lines in Figure ref:fig:test_id31_dz_scan_10ums).
Initial testing at $10\,\mu m/s$ demonstrated positioning errors well within specifications (indicated by dashed lines in Figure ref:fig:test_id31_dz_scan_10ums).
#+begin_src matlab
%% Dirty layer scans - 10um/s
@ -4464,7 +4469,7 @@ exportFig('figs/test_id31_dz_scan_10ums_ry.pdf', 'width', 'third', 'height', 'no
#+end_subfigure
#+end_figure
A subsequent scan at $100,\mu m/s$ - the maximum velocity for high-precision $D_z$ scans[fn:test_id31_8] - maintains positioning errors within specifications during the constant velocity phase, with deviations occurring only during acceleration and deceleration phases (Figure ref:fig:test_id31_dz_scan_100ums).
A subsequent scan at $100\,\mu m/s$ - the maximum velocity for high-precision $D_z$ scans[fn:test_id31_8] - maintains positioning errors within specifications during the constant velocity phase, with deviations occurring only during acceleration and deceleration phases (Figure ref:fig:test_id31_dz_scan_100ums).
Since detectors typically operate only during the constant velocity phase, these transient deviations do not compromise the measurement quality.
However, performance during acceleration phases could be enhanced through the implementation of feedforward control.
@ -4570,7 +4575,7 @@ The scanning range is constrained $\pm 100\,\mu m$ due to the limited acceptance
**** Slow scan
Initial testing utilized a scanning velocity of $10,\mu m/s$, which is typical for these experiments.
Initial testing utilized a scanning velocity of $10\,\mu m/s$, which is typical for these experiments.
Figure ref:fig:test_id31_dy_10ums compares the positioning errors between open-loop (without NASS) and closed-loop operation.
In the scanning direction, open-loop measurements reveal periodic errors (Figure ref:fig:test_id31_dy_10ums_dy) attributable to the $T_y$ stage's stepper motor.
These micro-stepping errors, which are inherent to stepper motor operation, occur 200 times per motor rotation with approximately $1\,\text{mrad}$ angular error amplitude.
@ -4822,8 +4827,8 @@ data_ty_cl_100ums.Ry_rms = rms(detrend(data_ty_cl_100ums.e_ry(i_ty_cl_100ums), 0
** Diffraction Tomography
<<ssec:test_id31_scans_diffraction_tomo>>
In diffraction tomography experiments, the micro-station executes combined motions: continuous rotation around the $R_z$ axis while performing lateral scans along $D_y$.
For this validation, the spindle maintained a constant rotational velocity of $6\,\text{deg/s}$ while the nano-hexapod executed the lateral scanning motion.
In diffraction tomography experiments, the micro-station performs combined motions: continuous rotation around the $R_z$ axis while performing lateral scans along $D_y$.
For this validation, the spindle maintained a constant rotational velocity of $6\,\text{deg/s}$ while the nano-hexapod performs the lateral scanning motion.
To avoid high-frequency vibrations typically induced by the stepper motor, the $T_y$ stage was not utilized, which constrained the scanning range to approximately $\pm 100\,\mu m/s$.
The system performance was evaluated at three lateral scanning velocities: $0.1\,mm/s$, $0.5\,mm/s$, and $1\,mm/s$. Figure ref:fig:test_id31_diffraction_tomo_setpoint presents both the $D_y$ position setpoints and the corresponding measured $D_y$ positions for all tested velocities.
@ -4883,7 +4888,7 @@ exportFig('figs/test_id31_diffraction_tomo_setpoint.pdf', 'width', 'wide', 'heig
The positioning errors measured along $D_y$, $D_z$, and $R_y$ directions are displayed in Figure ref:fig:test_id31_diffraction_tomo.
The system maintained positioning errors within specifications for both $D_z$ and $R_y$ (Figures ref:fig:test_id31_diffraction_tomo_dz and ref:fig:test_id31_diffraction_tomo_ry).
However, the lateral positioning errors exceeded specifications during the acceleration and deceleration phases (Figure ref:fig:test_id31_diffraction_tomo_dy).
These large errors occurred only during $\approx 20\,ms$ intervals; thus, the issue could be addressed by implementing a corresponding delay in detector integration.
These large errors occurred only during $\approx 20\,ms$ intervals; thus, a delay of $20\,ms$ could be implemented in the detector the avoid integrating the beam when these large errors are occurring.
Alternatively, a feedforward controller could improve the lateral positioning accuracy during these transient phases.
#+begin_src matlab :exports none :results none
@ -5125,7 +5130,7 @@ The careful alignment of the fibered interferometers targeting the two reference
The implementation of the control architecture validated the theoretical framework developed earlier in this project.
The decentralized Integral Force Feedback (IFF) controller successfully provided robust damping of suspension modes across all payload conditions (0-39 kg), reducing peak amplitudes by approximately a factor of 10.
The High Authority Controller (HAC) effectively managed low-frequency disturbances, although its performance showed some dependency on payload mass, particularly for lateral motion control.
The High Authority Controller (HAC) effectively rejects low-frequency disturbances, although its performance showed some dependency on payload mass, particularly for lateral motion control.
The experimental validation covered a wide range of scientific scenarios.
The system demonstrated remarkable performance under most conditions, meeting the stringent positioning requirements (30 nm RMS in $D_y$, 15 nm RMS in $D_z$, and 250 nrad RMS in $R_y$) for the majority of test cases.
@ -6561,10 +6566,10 @@ function [nano_hexapod] = initializeNanoHexapod(args)
args.actuator_ce (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*100
args.actuator_ca (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*50
args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m]
% For Flexible Frame
% For Flexible Frame
args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m]
args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m]
% Misalignment
% Misalignment
args.actuator_d_align (6,3) double {mustBeNumeric} = zeros(6,3) % [m]
args.actuator_xi (1,1) double {mustBeNumeric} = 0.01 % Damping Ratio

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test-bench-id31.tex
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@ -1,4 +1,4 @@
% Created 2025-02-05 Wed 11:20
% Created 2025-02-20 Thu 10:55
% Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -29,12 +29,12 @@
\clearpage
The nano-hexapod's mounting and validation through dynamics measurements marks a crucial milestone in the development of the Nano Active Stabilization System (NASS).
To proceed with the full validation of the Nano Active Stabilization System (NASS), the nano-hexapod was mounted on top of the micro-station on ID31, as illustrated in figure \ref{fig:test_id31_micro_station_nano_hexapod}.
This section presents a comprehensive experimental evaluation of the complete system's performance on the ID31 beamline, focusing on its ability to maintain precise sample positioning under various experimental conditions.
Initially, the project planned to develop a long-stroke (\(\approx 1 \, cm^3\)) 5-DoF metrology system to measure the sample position relative to the granite base.
However, the complexity of this development prevented its completion before the experimental testing phase on ID31.
To validate the nano-hexapod and its associated control architecture, an alternative short-stroke (\(> 100\,\mu m^3\)) metrology system was developed, which is presented in Section \ref{sec:test_id31_metrology}.
To validate the nano-hexapod and its associated control architecture, an alternative short-stroke (\(\approx 100\,\mu m^3\)) metrology system was developed, which is presented in Section \ref{sec:test_id31_metrology}.
Then, several key aspects of the system validation are examined.
Section \ref{sec:test_id31_open_loop_plant} analyzes the identified dynamics of the nano-hexapod mounted on the micro-station under various experimental conditions, including different payload masses and rotational velocities.
@ -66,7 +66,7 @@ These include tomography scans at various speeds and with different payload mass
\chapter{Short Stroke Metrology System}
\label{sec:test_id31_metrology}
The control of the nano-hexapod requires an external metrology system that measures the relative position of the nano-hexapod top platform with respect to the granite.
As a long-stroke (\(\approx 1 \,cm^3\)) metrology system was not yet developed, a stroke stroke (\(> 100\,\mu m^3\)) was used instead to validate the nano-hexapod control.
As a long-stroke (\(\approx 1 \,cm^3\)) metrology system was not yet developed, a stroke stroke (\(\approx 100\,\mu m^3\)) was used instead to validate the nano-hexapod control.
The first considered option was to use the ``Spindle error analyzer'' shown in Figure \ref{fig:test_id31_lion}.
This system comprises 5 capacitive sensors facing two reference spheres.
@ -107,7 +107,7 @@ Indeed, when the spheres are moving perpendicularly to the beam axis, the reflec
The proposed short-stroke metrology system is schematized in Figure \ref{fig:test_id31_metrology_kinematics}.
The point of interest is indicated by the blue frame \(\{B\}\), which is located \(H = 150\,mm\) above the nano-hexapod's top platform.
The spheres have a diameter \(d = 25.4\,mm\), and the indicated dimensions are \(l_1 = 60\,mm\) and \(l_2 = 16.2\,mm\).
To compute the pose of the \(\{B\}\) frame with respect to the granite (i.e. with respect to the fixed interferometer heads), the measured (small) displacements \([d_1,\ d_2,\ d_3,\ d_4,\ d_5]\) by the interferometers are first written as a function of the (small) linear and angular motion of the \(\{B\}\) frame \([D_x,\ D_y,\ D_z,\ R_x,\ R_y]\) \eqref{eq:test_id31_metrology_kinematics}.
To compute the pose of \(\{B\}\) with respect to the granite (i.e. with respect to the fixed interferometer heads), the measured (small) displacements \([d_1,\ d_2,\ d_3,\ d_4,\ d_5]\) by the interferometers are first written as a function of the (small) linear and angular motion of the \(\{B\}\) frame \([D_x,\ D_y,\ D_z,\ R_x,\ R_y]\) \eqref{eq:test_id31_metrology_kinematics}.
\begin{equation}\label{eq:test_id31_metrology_kinematics}
d_1 = D_y - l_2 R_x, \quad d_2 = D_y + l_1 R_x, \quad d_3 = -D_x - l_2 R_y, \quad d_4 = -D_x + l_1 R_y, \quad d_5 = -D_z
@ -161,7 +161,7 @@ However, this first alignment should be sufficient to position the two sphere wi
\label{ssec:test_id31_metrology_alignment}
The short-stroke metrology system was placed on top of the main granite using granite blocs (Figure \ref{fig:test_id31_short_stroke_metrology_overview}).
Granite is used for its good vibration and thermal stability.
Granite is used for its good mechanical and thermal stability.
\begin{figure}[htbp]
\centering
@ -172,12 +172,12 @@ Granite is used for its good vibration and thermal stability.
The interferometer beams must be placed with respect to the two reference spheres as close as possible to the ideal case shown in Figure \ref{fig:test_id31_metrology_kinematics}.
Therefore, their positions and angles must be well adjusted with respect to the two spheres.
First, the vertical positions of the spheres is adjusted using the micro-hexapod to match the heights of the interferometers.
Then, the horizontal position of the gantry is adjusted such that the coupling efficiency (i.e. the intensity of the light reflected back in the fiber) of the top interferometer is maximized.
Then, the horizontal position of the gantry is adjusted such that the intensity of the light reflected back in the fiber of the top interferometer is maximized.
This is equivalent as to optimize the perpendicularity between the interferometer beam and the sphere surface (i.e. the concentricity between the top beam and the sphere center).
The lateral sensor heads (i.e. all except the top one) were each fixed to a custom tip-tilt adjustment mechanism.
This allows them to be individually oriented so that they all point to the spheres' center (i.e. perpendicular to the sphere surface).
This is achieved by maximizing the coupling efficiency of each interferometer.
This is achieved by maximizing the intensity of the reflected light of each interferometer.
After the alignment procedure, the top interferometer should coincide with the spindle axis, and the lateral interferometers should all be in the horizontal plane and intersect the centers of the spheres.
@ -333,11 +333,11 @@ This issue was later solved.
One possible explanation of the increased coupling observed in Figure \ref{fig:test_id31_first_id_int} is the poor alignment between the external metrology axes (i.e. the interferometer supports) and the nano-hexapod axes.
To estimate this alignment, a decentralized low-bandwidth feedback controller based on the nano-hexapod encoders was implemented.
This allowed to perform two straight movements of the nano-hexapod along its \(x\) and \(y\) axes.
During these two movements, external metrology measurements were recorded and the results are shown in Figure \ref{fig:test_id31_Rz_align_error_and_correct}.
This allowed to perform two straight motions of the nano-hexapod along its \(x\) and \(y\) axes.
During these two motions, external metrology measurements were recorded and the results are shown in Figure \ref{fig:test_id31_Rz_align_error_and_correct}.
It was found that there was a misalignment of 2.7 degrees (rotation along the vertical axis) between the interferometer axes and nano-hexapod axes.
This was corrected by adding an offset to the spindle angle.
After alignment, the same movement was performed using the nano-hexapod while recording the signal of the external metrology.
After alignment, the same motion was performed using the nano-hexapod while recording the signal of the external metrology.
Results shown in Figure \ref{fig:test_id31_Rz_align_correct} are indeed indicating much better alignment.
\begin{figure}[htbp]
@ -374,7 +374,7 @@ The flexible modes of the top platform can be passively damped, whereas the mode
To determine how the system dynamics changes with the payload, open-loop identification was performed for four payload conditions shown in Figure \ref{fig:test_id31_picture_masses}.
The obtained direct terms are compared with the model dynamics in Figure \ref{fig:test_id31_comp_simscape_diag_masses}.
It was found that the model well predicts the measured dynamics under all payload conditions.
Therefore, the model can be used for model-based control is necessary.
Therefore, the model can be used for model-based control if necessary.
It is interesting to note that the anti-resonances in the force sensor plant now appear as minimum-phase, as the model predicts (Figure \ref{fig:test_id31_comp_simscape_iff_diag_masses}).
@ -456,8 +456,6 @@ The spindle rotation had no visible effect on the measured dynamics, indicating
\chapter{Decentralized Integral Force Feedback}
\label{sec:test_id31_iff}
The HAC-LAC strategy, which was previously developed and validated using the multi-body model, was then experimentally implemented.
In this section, the low authority control part is first validated.
It consists of a decentralized Integral Force Feedback controller \(\bm{K}_{\text{IFF}}\), with all the diagonal terms being equal \eqref{eq:test_id31_Kiff}.
@ -482,7 +480,7 @@ The decentralized Integral Force Feedback is implemented as shown in the block d
As the multi-body model is used to evaluate the stability of the IFF controller and to optimize the achievable damping, it is first checked whether this model accurately represents the system dynamics.
In the previous section (Figure \ref{fig:test_id31_comp_simscape_iff_diag_masses}), it was shown that the model well captures the dynamics from each actuator to its collocated force sensor, and that for all considered payloads.
Nevertheless, it is also important to well model the coupling in the system.
Nevertheless, it is also important to model accurately the coupling in the system.
To verify that, instead of comparing the 36 elements of the \(6 \times 6\) frequency response matrix from \(\bm{u}\) to \(\bm{V_s}\), only 6 elements are compared in Figure \ref{fig:test_id31_comp_simscape_Vs}.
Similar results were obtained for all other 30 elements and for the different payload conditions.
This confirms that the multi-body model can be used to tune the IFF controller.
@ -766,7 +764,7 @@ Several scientific experiments were replicated, such as:
Unless explicitly stated, all closed-loop experiments were performed using the robust (i.e. conservative) high authority controller designed in Section \ref{ssec:test_id31_iff_hac_controller}.
For each experiment, the obtained performances are compared to the specifications for the most depending case in which nano-focusing optics are used to focus the beam down to \(200\,nm\times 100\,nm\).
For each experiment, the obtained performances are compared to the specifications for the most demanding case in which nano-focusing optics are used to focus the beam down to \(200\,nm\times 100\,nm\).
In this case, the goal is to keep the sample's point of interest in the beam, and therefore the \(D_y\) and \(D_z\) positioning errors should be less than \(200\,nm\) and \(100\,nm\) peak-to-peak, respectively.
The \(R_y\) error should be less than \(1.7\,\mu\text{rad}\) peak-to-peak.
In terms of RMS errors, this corresponds to \(30\,nm\) in \(D_y\), \(15\,nm\) in \(D_z\) and \(250\,\text{nrad}\) in \(R_y\) (a summary of the specifications is given in Table \ref{tab:test_id31_experiments_specifications}).
@ -828,7 +826,7 @@ These experimental findings are consistent with the predictions from the tomogra
A tomography experiment was then performed with the highest rotational velocity of the Spindle: \(180\,\text{deg/s}\)\footnote{The highest rotational velocity of \(360\,\text{deg/s}\) could not be tested due to an issue in the Spindle's controller.}.
The trajectory of the point of interest during the fast tomography scan is shown in Figure \ref{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp}.
Although the experimental results closely mirror the simulation results (Figure \ref{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim}), the actual performance was slightly lower than predicted.
Although the experimental results closely match the simulation results (Figure \ref{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim}), the actual performance was slightly lower than predicted.
Nevertheless, even with this robust (i.e. conservative) HAC implementation, the system performance was already close to the specified requirements.
\begin{figure}[htbp]
@ -849,7 +847,7 @@ Nevertheless, even with this robust (i.e. conservative) HAC implementation, the
\paragraph{Cumulative Amplitude Spectra}
A comparative analysis was conducted using three tomography scans at \(180,\text{deg/s}\) to evaluate the effectiveness of the HAC-LAC strategy in reducing positioning errors.
A comparative analysis was conducted using three tomography scans at \(180\,\text{deg/s}\) to evaluate the effectiveness of the HAC-LAC strategy in reducing positioning errors.
The scans were performed under three conditions: open-loop, with decentralized IFF control, and with the complete HAC-LAC strategy.
For these specific measurements, an enhanced high authority controller was optimized for low payload masses to meet the performance requirements.
@ -885,7 +883,7 @@ This experiment also illustrates that when needed, performance can be enhanced b
\label{ssec:test_id31_scans_reflectivity}
X-ray reflectivity measurements involve scanning thin structures, particularly solid/liquid interfaces, through the beam by varying the \(R_y\) angle.
In this experiment, a \(R_y\) scan was executed at a rotational velocity of \(100,\mu rad/s\), and the closed-loop positioning errors were monitored (Figure \ref{fig:test_id31_reflectivity}).
In this experiment, a \(R_y\) scan was executed at a rotational velocity of \(100\,\mu rad/s\), and the closed-loop positioning errors were monitored (Figure \ref{fig:test_id31_reflectivity}).
The results confirmed that the NASS successfully maintained the point of interest within the specified beam parameters throughout the scanning process.
\begin{figure}[htbp]
@ -952,7 +950,7 @@ The settling duration typically decreases for smaller step sizes.
For these and subsequent experiments, the NASS performs ``ramp scans'' (constant velocity scans).
To eliminate tracking errors, the feedback controller incorporates two integrators, compensating for the plant's lack of integral action at low frequencies.
Initial testing at \(10,\mu m/s\) demonstrated positioning errors well within specifications (indicated by dashed lines in Figure \ref{fig:test_id31_dz_scan_10ums}).
Initial testing at \(10\,\mu m/s\) demonstrated positioning errors well within specifications (indicated by dashed lines in Figure \ref{fig:test_id31_dz_scan_10ums}).
\begin{figure}[htbp]
\begin{subfigure}{0.33\textwidth}
@ -976,7 +974,7 @@ Initial testing at \(10,\mu m/s\) demonstrated positioning errors well within sp
\caption{\label{fig:test_id31_dz_scan_10ums}\(D_z\) scan at a velocity of \(10\,\mu m/s\). \(D_z\) setpoint, measured position and error are shown in (\subref{fig:test_id31_dz_scan_10ums_dz}). Errors in \(D_y\) and \(R_y\) are respectively shown in (\subref{fig:test_id31_dz_scan_10ums_dy}) and (\subref{fig:test_id31_dz_scan_10ums_ry})}
\end{figure}
A subsequent scan at \(100,\mu m/s\) - the maximum velocity for high-precision \(D_z\) scans\footnote{Such scan could corresponding to a 1ms integration time (which is typically the smallest integration time) and 100nm ``resolution'' (equal to the vertical beam size).} - maintains positioning errors within specifications during the constant velocity phase, with deviations occurring only during acceleration and deceleration phases (Figure \ref{fig:test_id31_dz_scan_100ums}).
A subsequent scan at \(100\,\mu m/s\) - the maximum velocity for high-precision \(D_z\) scans\footnote{Such scan could corresponding to a 1ms integration time (which is typically the smallest integration time) and 100nm ``resolution'' (equal to the vertical beam size).} - maintains positioning errors within specifications during the constant velocity phase, with deviations occurring only during acceleration and deceleration phases (Figure \ref{fig:test_id31_dz_scan_100ums}).
Since detectors typically operate only during the constant velocity phase, these transient deviations do not compromise the measurement quality.
However, performance during acceleration phases could be enhanced through the implementation of feedforward control.
@ -1010,7 +1008,7 @@ Within the Speedgoat, the system computes the positioning error by comparing the
The scanning range is constrained \(\pm 100\,\mu m\) due to the limited acceptance of the metrology system.
\paragraph{Slow scan}
Initial testing utilized a scanning velocity of \(10,\mu m/s\), which is typical for these experiments.
Initial testing utilized a scanning velocity of \(10\,\mu m/s\), which is typical for these experiments.
Figure \ref{fig:test_id31_dy_10ums} compares the positioning errors between open-loop (without NASS) and closed-loop operation.
In the scanning direction, open-loop measurements reveal periodic errors (Figure \ref{fig:test_id31_dy_10ums_dy}) attributable to the \(T_y\) stage's stepper motor.
These micro-stepping errors, which are inherent to stepper motor operation, occur 200 times per motor rotation with approximately \(1\,\text{mrad}\) angular error amplitude.
@ -1078,8 +1076,8 @@ For applications requiring small \(D_y\) scans, the nano-hexapod can be used exc
\section{Diffraction Tomography}
\label{ssec:test_id31_scans_diffraction_tomo}
In diffraction tomography experiments, the micro-station executes combined motions: continuous rotation around the \(R_z\) axis while performing lateral scans along \(D_y\).
For this validation, the spindle maintained a constant rotational velocity of \(6\,\text{deg/s}\) while the nano-hexapod executed the lateral scanning motion.
In diffraction tomography experiments, the micro-station performs combined motions: continuous rotation around the \(R_z\) axis while performing lateral scans along \(D_y\).
For this validation, the spindle maintained a constant rotational velocity of \(6\,\text{deg/s}\) while the nano-hexapod performs the lateral scanning motion.
To avoid high-frequency vibrations typically induced by the stepper motor, the \(T_y\) stage was not utilized, which constrained the scanning range to approximately \(\pm 100\,\mu m/s\).
The system performance was evaluated at three lateral scanning velocities: \(0.1\,mm/s\), \(0.5\,mm/s\), and \(1\,mm/s\). Figure \ref{fig:test_id31_diffraction_tomo_setpoint} presents both the \(D_y\) position setpoints and the corresponding measured \(D_y\) positions for all tested velocities.
@ -1092,7 +1090,7 @@ The system performance was evaluated at three lateral scanning velocities: \(0.1
The positioning errors measured along \(D_y\), \(D_z\), and \(R_y\) directions are displayed in Figure \ref{fig:test_id31_diffraction_tomo}.
The system maintained positioning errors within specifications for both \(D_z\) and \(R_y\) (Figures \ref{fig:test_id31_diffraction_tomo_dz} and \ref{fig:test_id31_diffraction_tomo_ry}).
However, the lateral positioning errors exceeded specifications during the acceleration and deceleration phases (Figure \ref{fig:test_id31_diffraction_tomo_dy}).
These large errors occurred only during \(\approx 20\,ms\) intervals; thus, the issue could be addressed by implementing a corresponding delay in detector integration.
These large errors occurred only during \(\approx 20\,ms\) intervals; thus, a delay of \(20\,ms\) could be implemented in the detector the avoid integrating the beam when these large errors are occurring.
Alternatively, a feedforward controller could improve the lateral positioning accuracy during these transient phases.
\begin{figure}[htbp]
@ -1180,7 +1178,7 @@ The careful alignment of the fibered interferometers targeting the two reference
The implementation of the control architecture validated the theoretical framework developed earlier in this project.
The decentralized Integral Force Feedback (IFF) controller successfully provided robust damping of suspension modes across all payload conditions (0-39 kg), reducing peak amplitudes by approximately a factor of 10.
The High Authority Controller (HAC) effectively managed low-frequency disturbances, although its performance showed some dependency on payload mass, particularly for lateral motion control.
The High Authority Controller (HAC) effectively rejects low-frequency disturbances, although its performance showed some dependency on payload mass, particularly for lateral motion control.
The experimental validation covered a wide range of scientific scenarios.
The system demonstrated remarkable performance under most conditions, meeting the stringent positioning requirements (30 nm RMS in \(D_y\), 15 nm RMS in \(D_z\), and 250 nrad RMS in \(R_y\)) for the majority of test cases.