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Thomas Dehaeze 2025-02-04 15:13:10 +01:00
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test-bench-id31.org
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@ -1446,7 +1446,7 @@ exportFig('figs/test_id31_first_id_int_better_rz_align.pdf', 'width', 'wide', 'h
<<ssec:test_id31_open_loop_plant_mass>>
In order to see how the system dynamics changes with the payload, open-loop identification was performed for four payload conditions that are shown in Figure ref:fig:test_id31_picture_masses.
The obtained direct terms are compared with the model dynamics in Figure ref:fig:test_nhexa_comp_simscape_diag_masses.
The obtained direct terms are compared with the model dynamics in Figure ref:fig:test_id31_comp_simscape_diag_masses.
It is shown that the model dynamics well predicts the measured dynamics for all payload conditions.
Therefore the model can be used for model-based control is necessary.
@ -1775,7 +1775,7 @@ xticks([10, 20, 50, 100, 200, 500])
exportFig('figs/test_id31_comp_simscape_iff_diag_masses.pdf', 'width', 'half', 'height', 600);
#+end_src
#+name: fig:test_nhexa_comp_simscape_diag_masses
#+name: fig:test_id31_comp_simscape_diag_masses
#+caption: Comparison of the diagonal elements (i.e. "direct" terms) of the measured FRF matrix and the dynamics identified from the multi-body model. Both for the dynamics from $u$ to $\epsilon\mathcal{L}$ (\subref{fig:test_id31_comp_simscape_int_diag_masses}) and from $u$ to $V_s$ (\subref{fig:test_id31_comp_simscape_iff_diag_masses})
#+attr_latex: :options [htbp]
#+begin_figure

47
test-bench-id31.tex
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@ -1,4 +1,4 @@
% Created 2025-02-04 Tue 12:58
% Created 2025-02-04 Tue 15:13
% Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -123,7 +123,7 @@ 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, \qua
\begin{minipage}[b]{0.48\linewidth}
\begin{center}
\includegraphics[scale=1,width=\linewidth]{figs/test_id31_align_top_sphere_comparators.jpg}
\captionof{figure}{\label{fig:align_top_sphere_comparators}The top sphere is aligned with the rotation axis of the spindle using two probes.}
\captionof{figure}{\label{fig:test_id31_align_top_sphere_comparators}The top sphere is aligned with the rotation axis of the spindle using two probes.}
\end{center}
\end{minipage}
@ -147,7 +147,7 @@ The five equations \eqref{eq:test_id31_metrology_kinematics} can be written in a
\label{ssec:test_id31_metrology_sphere_rought_alignment}
The two reference spheres are aligned with the rotation axis of the spindle.
To do so, two measuring probes are used as shown in Figure \ref{fig:align_top_sphere_comparators}.
To do so, two measuring probes are used as shown in Figure \ref{fig:test_id31_align_top_sphere_comparators}.
To not damage the sensitive sphere surface, the probes are instead positioned on the cylinder on which the sphere is mounted.
First, the probes are fixed to the bottom (fixed) cylinder to align the first sphere with the spindle axis.
@ -160,13 +160,13 @@ However, this first alignment should permit to position the two sphere within th
\section{Tip-Tilt adjustment of the interferometers}
\label{ssec:test_id31_metrology_alignment}
The short-stroke metrology system is placed on top of the main granite using a gantry made of granite blocs (Figure \ref{fig:short_stroke_metrology_overview}).
The short-stroke metrology system is placed on top of the main granite using a gantry made of granite blocs (Figure \ref{fig:test_id31_short_stroke_metrology_overview}).
Granite is used to have good vibration and thermal stability.
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.8\linewidth]{figs/test_id31_short_stroke_metrology_overview.jpg}
\caption{\label{fig:short_stroke_metrology_overview}Granite gantry used to fix the short-stroke metrology system}
\caption{\label{fig:test_id31_short_stroke_metrology_overview}Granite gantry used to fix the short-stroke metrology system}
\end{figure}
The interferometer beams need to be position with respect to the two reference spheres as close as possible to the ideal case shown in Figure \ref{fig:test_id31_metrology_kinematics}.
@ -216,13 +216,12 @@ The remaining errors after alignment is in the order of \(\pm5\,\mu\text{rad}\)
\label{ssec:test_id31_metrology_acceptance}
Because the interferometers are pointing to spheres and not flat surfaces, the lateral acceptance is limited.
In order to estimate the metrology acceptance, the micro-hexapod is used to perform three accurate scans of \(\pm 1\,mm\), respectively along the the \(x\), \(y\) and \(z\) axes.
In order to estimate the metrology acceptance, the micro-hexapod is used to perform three accurate scans of \(\pm 1\,mm\), respectively along the \(x\), \(y\) and \(z\) axes.
During these scans, the 5 interferometers are recorded individually, and the ranges in which each interferometer has enough coupling efficiency to be able to measure the displacement are estimated.
Results are summarized in Table \ref{tab:test_id31_metrology_acceptance}.
The obtained lateral acceptance for pure displacements in any direction is estimated to be around \(+/-0.5\,mm\), which is enough for the current application as it is well above the micro-station errors to be actively corrected by the NASS.
\begin{table}[htbp]
\caption{\label{tab:test_id31_metrology_acceptance}Estimated measurement range for each interferometer, and for three different directions.}
\centering
\begin{tabularx}{0.45\linewidth}{Xccc}
\toprule
@ -235,6 +234,8 @@ The obtained lateral acceptance for pure displacements in any direction is estim
\(d_5\) (z) & \(1.33\, mm\) & \(1.06\,mm\) & \(>2\,mm\)\\
\bottomrule
\end{tabularx}
\caption{\label{tab:test_id31_metrology_acceptance}Estimated measurement range for each interferometer, and for three different directions.}
\end{table}
@ -372,7 +373,7 @@ The flexible modes of the top platform can be passively damped while the modes o
\label{ssec:test_id31_open_loop_plant_mass}
In order to see how the system dynamics changes with the payload, open-loop identification was performed for four payload conditions that are shown in Figure \ref{fig:test_id31_picture_masses}.
The obtained direct terms are compared with the model dynamics in Figure \ref{fig:test_nhexa_comp_simscape_diag_masses}.
The obtained direct terms are compared with the model dynamics in Figure \ref{fig:test_id31_comp_simscape_diag_masses}.
It is shown that the model dynamics well predicts the measured dynamics for all payload conditions.
Therefore the model can be used for model-based control is necessary.
@ -411,7 +412,7 @@ It is interesting to note that the anti-resonances in the force sensor plant are
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/test_id31_comp_simscape_int_diag_masses.png}
\end{center}
\subcaption{\label{fig:test_id31_comp_simscape_int_diag_masses}from $u$ to $e\mathcal{L}$}
\subcaption{\label{fig:test_id31_comp_simscape_int_diag_masses}from $u$ to $\epsilon\mathcal{L}$}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
@ -419,7 +420,7 @@ It is interesting to note that the anti-resonances in the force sensor plant are
\end{center}
\subcaption{\label{fig:test_id31_comp_simscape_iff_diag_masses}from $u$ to $V_s$}
\end{subfigure}
\caption{\label{fig:test_nhexa_comp_simscape_diag_masses}Comparison of the diagonal elements (i.e. ``direct'' terms) of the measured FRF matrix and the dynamics identified from the multi-body model. Both for the dynamics from \(u\) to \(e\mathcal{L}\) (\subref{fig:test_id31_comp_simscape_int_diag_masses}) and from \(u\) to \(V_s\) (\subref{fig:test_id31_comp_simscape_iff_diag_masses})}
\caption{\label{fig:test_id31_comp_simscape_diag_masses}Comparison of the diagonal elements (i.e. ``direct'' terms) of the measured FRF matrix and the dynamics identified from the multi-body model. Both for the dynamics from \(u\) to \(\epsilon\mathcal{L}\) (\subref{fig:test_id31_comp_simscape_int_diag_masses}) and from \(u\) to \(V_s\) (\subref{fig:test_id31_comp_simscape_iff_diag_masses})}
\end{figure}
\section{Effect of Spindle Rotation}
@ -427,7 +428,7 @@ It is interesting to note that the anti-resonances in the force sensor plant are
To verify that all the kinematics in Figure \ref{fig:test_id31_block_schematic_plant} are correct and to check whether the system dynamics is affected by Spindle rotation of not, three identification experiments were performed: no spindle rotation, spindle rotation at \(36\,\text{deg}/s\) and at \(180\,\text{deg}/s\).
The comparison of the obtained dynamics from command signal \(u\) to estimated strut error \(e\mathcal{L}\) is done in Figure \ref{fig:test_id31_effect_rotation}.
The comparison of the obtained dynamics from command signal \(u\) to estimated strut error \(\epsilon\mathcal{L}\) is done in Figure \ref{fig:test_id31_effect_rotation}.
Both direct terms (Figure \ref{fig:test_id31_effect_rotation_direct}) and coupling terms (Figure \ref{fig:test_id31_effect_rotation_coupling}) are unaffected by the rotation.
The same can be observed for the dynamics from the command signal to the encoders and to the force sensors.
This confirms that the rotation has no significant effect on the plant dynamics.
@ -446,7 +447,7 @@ This also indicates that the metrology kinematics is correct and is working in r
\end{center}
\subcaption{\label{fig:test_id31_effect_rotation_coupling}Coupling terms}
\end{subfigure}
\caption{\label{fig:test_id31_effect_rotation}Effect of the spindle rotation on the plant dynamics from \(u\) to \(e\mathcal{L}\). Three rotational velocities are tested (\(0\,\text{deg}/s\), \(36\,\text{deg}/s\) and \(180\,\text{deg}/s\)). Both direct terms (\subref{fig:test_id31_effect_rotation_direct}) and coupling terms (\subref{fig:test_id31_effect_rotation_coupling}) are displayed.}
\caption{\label{fig:test_id31_effect_rotation}Effect of the spindle rotation on the plant dynamics from \(u\) to \(\epsilon\mathcal{L}\). Three rotational velocities are tested (\(0\,\text{deg}/s\), \(36\,\text{deg}/s\) and \(180\,\text{deg}/s\)). Both direct terms (\subref{fig:test_id31_effect_rotation_direct}) and coupling terms (\subref{fig:test_id31_effect_rotation_coupling}) are displayed.}
\end{figure}
\section*{Conclusion}
@ -775,7 +776,6 @@ In terms of RMS errors, this corresponds to \(30\,nm\) in \(D_y\), \(15\,nm\) in
Results obtained for all the experiments are summarized and compared to the specifications in Section \ref{ssec:test_id31_scans_conclusion}.
\begin{table}[htbp]
\caption{\label{tab:test_id31_experiments_specifications}Specifications for the Nano-Active-Stabilization-System}
\centering
\begin{tabularx}{0.45\linewidth}{Xccc}
\toprule
@ -785,10 +785,12 @@ peak 2 peak & 200nm & 100nm & \(1.7\,\mu\text{rad}\)\\
RMS & 30nm & 15nm & \(250\,\text{nrad}\)\\
\bottomrule
\end{tabularx}
\caption{\label{tab:test_id31_experiments_specifications}Specifications for the Nano-Active-Stabilization-System}
\end{table}
\section{Tomography Scans}
\label{ssec:test_id31_scans_tomography}
\paragraph{Slow Tomography scans}
\subsubsection{Slow Tomography scans}
First, tomography scans are performed with a rotational velocity of \(6\,\text{deg/s}\) for all considered payload masses (shown in Figure \ref{fig:test_id31_picture_masses}).
Each experimental sequence consisted of two complete spindle rotations: an initial open-loop rotation followed by a closed-loop rotation.
@ -825,7 +827,7 @@ These experimental findings align with the predictions from the tomography simul
\caption{\label{fig:test_id31_tomo_Wz36_results}Measured errors in the \(Y-Z\) plane during tomography experiments at \(6\,\text{deg/s}\) for all considered payloads. In the open-loop case, the effect of eccentricity is removed from the data.}
\end{figure}
\paragraph{Fast Tomography scans}
\subsubsection{Fast Tomography scans}
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 this fast tomography scan is shown in Figure \ref{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp}.
@ -848,7 +850,7 @@ Nevertheless, even with this robust (conservative) HAC implementation, the syste
\caption{\label{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp}Experimental results of a tomography experiment at 180 deg/s without payload. Position error of the sample is shown in the XY (\subref{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp_xy}) and YZ (\subref{fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp_yz}) planes.}
\end{figure}
\paragraph{Cumulative Amplitude Spectra}
\subsubsection{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.
The scans were performed under three conditions: open-loop, with decentralized IFF control, and with the complete HAC-LAC strategy.
@ -915,7 +917,7 @@ The results confirm that the NASS successfully maintains the point of interest w
\label{ssec:test_id31_scans_dz}
In some cases, samples are composed of several atomic ``layers'' that are first aligned in the horizontal plane through \(R_x\) and \(R_y\) positioning, followed by vertical scanning with precise \(D_z\) motion.
These vertical scans can be executed either continuously or in a step-by-step manner.
\paragraph{Step by Step \(D_z\) motion}
\subsubsection{Step by Step \(D_z\) motion}
The vertical step motion is performed exclusively with the nano-hexapod.
Testing was conducted across step sizes ranging from \(10,nm\) to \(1,\mu m\), with results presented in Figure \ref{fig:test_id31_dz_mim_steps}. The system successfully resolves 10nm steps when detectors integrate over a 50ms period (illustrated by the red curve in Figure \ref{fig:test_id31_dz_mim_10nm_steps}), which is compatible with many experimental requirements.
@ -946,7 +948,7 @@ This settling duration typically decreases for smaller step sizes.
\caption{\label{fig:test_id31_dz_mim_steps}Vertical steps performed with the nano-hexapod. 10nm steps are shown in (\subref{fig:test_id31_dz_mim_10nm_steps}) with the low pass filtered data corresponding to an integration time of \(50\,ms\). 100nm steps are shown in (\subref{fig:test_id31_dz_mim_100nm_steps}). The response time to reach a peak to peak error of \(\pm 20\,nm\) is \(\approx 70\,ms\) as shown in (\subref{fig:test_id31_dz_mim_1000nm_steps}) for a \(1\,\mu m\) step.}
\end{figure}
\paragraph{Continuous \(D_z\) motion: Dirty Layer Scans}
\subsubsection{Continuous \(D_z\) motion: Dirty Layer Scans}
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.
@ -1007,7 +1009,7 @@ Lateral scans are executed using the \(T_y\) stage.
The stepper motor controller\footnote{The ``IcePAP'' \cite{janvier13_icepap} which is developed at the ESRF.} generates a setpoint that is transmitted to the Speedgoat.
Within the Speedgoat, the system computes the positioning error by comparing the measured \(D_y\) sample position against the received setpoint, and the Nano-Hexapod compensates for positioning errors introduced during \(T_y\) stage scanning.
The scanning range is constrained \(\pm 100\,\mu m\) due to the limited acceptance of the metrology system.
\paragraph{Slow scan}
\subsubsection{Slow scan}
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.
@ -1040,7 +1042,7 @@ Under closed-loop control, positioning errors remain within specifications acros
\caption{\label{fig:test_id31_dy_10ums}Open-Loop (in blue) and Closed-loop (i.e. using the NASS, in red) during a \(10\,\mu m/s\) scan with the \(T_y\) stage. Errors in \(D_y\) is shown in (\subref{fig:test_id31_dy_10ums_dy}).}
\end{figure}
\paragraph{Fast Scan}
\subsubsection{Fast Scan}
System performance was evaluated at an increased scanning velocity of \(100\,\mu m/s\), with results presented in Figure \ref{fig:test_id31_dy_100ums}.
At this velocity, the micro-stepping errors generate \(10\,\text{Hz}\) vibrations, which are further amplified by micro-station resonances.
@ -1132,11 +1134,10 @@ For lateral scanning, the system performed well at moderate speeds (\(10\,\mu m/
The most challenging test case - diffraction tomography combining rotation and lateral scanning - demonstrated the system's ability to maintain vertical and angular stability while highlighting some limitations in lateral positioning during rapid accelerations.
These limitations could potentially be addressed through feedforward control or alternative detector triggering strategies.
Overall, the experimental results validate the effectiveness of the developed control architecture and demonstrate that the NASS meets most design specifications across a wide range of operating conditions (summarized in Table \ref{tab:id31_experiments_results_summary}).
Overall, the experimental results validate the effectiveness of the developed control architecture and demonstrate that the NASS meets most design specifications across a wide range of operating conditions (summarized in Table \ref{tab:test_id31_experiments_results_summary}).
The identified limitations, primarily related to high-speed lateral scanning and heavy payload handling, provide clear directions for future improvements.
\begin{table}[htbp]
\caption{\label{tab:id31_experiments_results_summary}Summary of the experimental results performed with the NASS on ID31. Open-loop errors are indicated at the left of the arrows. Closed-loop errors that are out of specifications are indicated by bold number.}
\centering
\begin{tabularx}{\linewidth}{Xccc}
\toprule
@ -1165,6 +1166,8 @@ Diffraction tomography (\(6\,\text{deg/s}\), \(1\,mm/s\)) & \(\bm{53}\) & \(10\)
\textbf{Specifications} & \(30\) & \(15\) & \(250\)\\
\bottomrule
\end{tabularx}
\caption{\label{tab:test_id31_experiments_results_summary}Summary of the experimental results performed with the NASS on ID31. Open-loop errors are indicated at the left of the arrows. Closed-loop errors that are out of specifications are indicated by bold number.}
\end{table}
\chapter*{Conclusion}