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@ -2000,7 +2000,7 @@ More recently, higher bandwidths (up to 100 Hz) have been demonstrated, particul
Figure ref:fig:introduction_active_stations showcases two end-stations incorporating online metrology and active feedback control.
The ID16A system at ESRF (Figure ref:fig:introduction_stages_villar) uses capacitive sensors and a piezoelectric hexapod to compensate for rotation stage errors and to perform accurate scans [[cite:&villar18_nanop_esrf_id16a_nano_imagin_beaml]].
Another example, shown in Figure ref:fig:introduction_stages_nazaretski, employs interferometers and piezoelectric stages to compensate for thermal drifts [[cite:&nazaretski15_pushin_limit;&nazaretski17_desig_perfor_x_ray_scann]].
A more comprehensive review of actively controlled end-stations is provided in Section [...].
A more comprehensive review of actively controlled end-stations is provided in Section ref:sec:nhexa_platform_review.
#+name: fig:introduction_active_stations
#+caption: Example of two end-stations with real-time position feedback based on an online metrology. (\subref{fig:introduction_stages_villar}) [[cite:&villar18_nanop_esrf_id16a_nano_imagin_beaml]]. (\subref{fig:introduction_stages_nazaretski}) [[cite:&nazaretski17_desig_perfor_x_ray_scann;&nazaretski15_pushin_limit]]
@ -2106,8 +2106,7 @@ A suitable candidate architecture for this platform is the Stewart platform (als
Stewart platforms are widely employed in positioning and vibration isolation applications due to their inherent stiffness and potential for high precision.
Various designs exist, differing in geometry, actuation technology, sensing methods, and control strategies, as exemplified in Figure ref:fig:introduction_stewart_platform_piezo.
A central challenge addressed in this thesis is the optimal mechatronic design of such an active platform tailored to the specific requirements of the NASS.
A more detailed review of Stewart platform and its main components will be given in Section [...].
# TODO - Review of Stewart platform ref:sec:detail_kinematics_stewart_review
A more detailed review of Stewart platform and its main components will be given in Section ref:sec:detail_kinematics_stewart_review.
#+name: fig:introduction_stewart_platform_piezo
#+caption: Example of Stewart platforms. (\subref{fig:introduction_stewart_du14}) [[cite:&du14_piezo_actuat_high_precis_flexib]] and (\subref{fig:introduction_stewart_hauge04}) [[cite:&hauge04_sensor_contr_space_based_six]]
@ -2161,132 +2160,93 @@ This thesis presents several original contributions aimed at addressing the chal
**** 6DoF vibration control of a rotating platform
While long stroke-short stroke architectures have been implemented for 1-DoF or 2-DoF systems, this work extends the concept to a fully coupled 6-DoF system operating on a continuously rotating base.
The active platform is designed not merely to correct rotational errors but to simultaneously compensate for errors originating from all underlying micro-station stages.
Traditional long-stroke/short-stroke architectures typically operate in one or two degrees of freedom.
This work extends the concept to six degrees of freedom, with the active platform designed not only to correct rotational errors but to simultaneously compensate for errors originating from all underlying micro-station stages.
The application of a continuously rotating Stewart platform for active vibration control and error compensation in this manner is believed to be novel in the reviewed literature.
**** Mechatronics design approach
A rigorous mechatronics design methodology was applied consistently throughout the NASS development lifecycle [[cite:&dehaeze18_sampl_stabil_for_tomog_exper;&dehaeze21_mechat_approac_devel_nano_activ_stabil_system]].
Although the mechatronics approach itself is not new, its comprehensive application here, from initial concept evaluation using simplified models to detailed design optimization and experimental validation informed by increasingly sophisticated models, is noteworthy.
Dynamical models were employed at every stage: for initial concept selection, detailed component optimization, understanding experimental observations, and optimizing control strategies.
Although the mechatronics approach itself is not new, its comprehensive application here, from initial concept evaluation using simplified models to detailed design optimization and experimental validation informed by increasingly sophisticated models, potentially offers useful insights to the existing literature.
This thesis documents this process chronologically, illustrating how models of varying complexity can be effectively utilized at different project phases and how design decisions were systematically based on quantitative model predictions and analyses.
While the resulting system is highly specific, the documented effectiveness of this integrated design approach may contribute to the broader adoption of mechatronics methodologies in the design of future synchrotron instrumentation.
While the resulting system is highly specific, the documented effectiveness of this design approach may contribute to the broader adoption of mechatronics methodologies in the design of future synchrotron instrumentation.
**** Multi-body simulations with reduced order flexible bodies obtained by FEA
A key enabling tool employed extensively in this work was a combined multi-body simulation and Finite Element Analysis technique, specifically utilizing Component Mode Synthesis (CMS) to represent flexible bodies within the multi-body framework [[cite:&brumund21_multib_simul_reduc_order_flexib_bodies_fea]].
A key tool employed extensively in this work was a combined multi-body simulation and Finite Element Analysis technique, specifically utilizing Component Mode Synthesis to represent flexible bodies within the multi-body framework [[cite:&brumund21_multib_simul_reduc_order_flexib_bodies_fea]].
This hybrid approach, while established, was experimentally validated in this work for components critical to the NASS, namely amplified piezoelectric actuators and flexible joints.
It proved invaluable for designing and optimizing components intended for integration into a larger, complex dynamic system.
This methodology, detailed in Section [...], is presented as a potentially useful tool for future mechatronic instrument development.
# TODO - Section ref:sec:detail_fem
This methodology, detailed in Section ref:sec:detail_fem, is presented as a potentially useful tool for future mechatronic instrument development.
**** Control Robustness by design
Addressing the critical challenge of robustness across varying experimental conditions (rotation speeds, payloads up to 50 kg) was approached through "robustness by design" rather than relying solely on complex robust control synthesis techniques (like $\mathcal{H}_\infty$ or $\mu\text{-synthesis}$).
The strategy involved selecting a system architecture (mechanics, sensors, actuators) inherently conducive to robust control.
An example is the deliberate use of collocated actuator/sensor pairs, enabling the potential application of passivity-based control principles to guarantee stability.
Informed architectural choices were made by systematically evaluating different sensor combination strategies (e.g., HAC/LAC, sensor fusion, two-sensor control) and comparing various MIMO decoupling approaches.
This comparative analysis of control architectures, presented in Section [...], was identified as somewhat lacking in existing literature.
The requirement for robust operation across diverse conditions—including payloads up to 50kg, complex underlying dynamics from the micro-station, and varied operational modes like different rotation speeds—presented a critical design challenge.
This challenge was met by embedding robustness directly into the active platform's design, rather than depending solely on complex post-design control synthesis techniques such as $\mathcal{H}_\infty\text{-synthesis}$ and $\mu\text{-synthesis}$.
Key elements of this strategy included the model-based evaluation of active stage designs to identify architectures inherently easier to control, the incorporation of collocated actuator/sensor pairs to leverage passivity-based guaranteed stability, and the comparison of architecture to combine several sensors such as sensor fusion and High Authority Control / Low Authority Control (HAC-LAC).
Furthermore, decoupling strategies for parallel manipulators were compared (Section ref:sec:detail_control_decoupling), addressing a topic identified as having limited treatment in the literature.
Consequently, the specified performance targets were met utilizing controllers which, facilitated by this design approach, proved to be robust, readily tunable, and easily maintained.
**** Active Damping of rotating mechanical systems using Integral Force Feedback
During conceptual design, it was found that the guaranteed stability properties of the established active damping technique known as Integral Force Feedback (IFF) are compromised when applied to rotating platforms like the NASS.
During conceptual design, it was found that the guaranteed stability property of the established active damping technique known as Integral Force Feedback (IFF) is compromised when applied to rotating platforms like the NASS.
To address this instability issue, two modifications to the classical IFF control scheme were proposed and analyzed.
The first involves a minor adjustment to the control law itself, while the second incorporates physical springs in parallel with the force sensors.
Stability conditions and optimal parameter tuning guidelines were derived for both modified schemes.
This is further discussed in Section [...] and was the subject of publications [[cite:&dehaeze20_activ_dampin_rotat_platf_integ_force_feedb;&dehaeze21_activ_dampin_rotat_platf_using]].
# TODO - Section ref:sec:rotating
This is further discussed in Section ref:sec:rotating and was the subject of publications [[cite:&dehaeze20_activ_dampin_rotat_platf_integ_force_feedb;&dehaeze21_activ_dampin_rotat_platf_using]].
**** Design of complementary filters using $\mathcal{H}_\infty$ Synthesis
For implementing sensor fusion, where signals from multiple sensors are combined, complementary filters are often employed.
A novel method for designing these filters using $\mathcal{H}_\infty$ synthesis techniques was developed [[cite:&dehaeze19_compl_filter_shapin_using_synth]].
This method allows explicit shaping of the filter norms, providing guarantees on the performance of the sensor fusion process.
This design strategy, discussed further in Section [...], has subsequently found application in optimizing sensor fusion for gravitational wave detectors [[cite:&tsang22_optim_sensor_fusion_method_activ]].
The integration of such filters into feedback control architectures can also lead to advantageous control structures, as proposed in [[cite:&verma20_virtual_sensor_fusion_high_precis_contr]] and further studied in Section [...].
# TODO - Section ref:sec:detail_control_cf
This synthesis technique, discussed further in Section ref:sec:detail_control_sensor, has subsequently found application in optimizing sensor fusion for gravitational wave detectors [[cite:&tsang22_optim_sensor_fusion_method_activ]].
The integration of such filters into feedback control architectures can also lead to advantageous control structures, as proposed in [[cite:&verma20_virtual_sensor_fusion_high_precis_contr]] and further studied in Section ref:sec:detail_control_cf.
**** Experimental validation of the Nano Active Stabilization System
The conclusion of this work involved the experimental implementation and validation of the complete NASS on the ID31 beamline.
Experimental results demonstrate that the system successfully improves the effective positioning accuracy of the micro-station from its native ~10 µm level down to the target ~100 nm range during representative scientific experiments.
Crucially, robustness to variations in sample mass (up to 39 kg tested) and diverse experimental conditions (e.g., tomography scans) was verified.
The NASS thus provides a versatile end-station solution, uniquely combining high payload capacity with nanometer-level accuracy and stability, enabling optimal utilization of the advanced capabilities of the ESRF-EBS beam and associated detectors.
Experimental results, presented in Section ref:sec:test_id31, demonstrate that the system successfully improves the effective positioning accuracy of the micro-station from its native $\approx 10\,\mu m$ level down to the target $\approx 100\,nm$ range during representative scientific experiments.
Crucially, robustness to variations in sample mass and diverse experimental conditions was verified.
The NASS thus provides a versatile end-station solution, uniquely combining high payload capacity with nanometer-level accuracy, enabling optimal utilization of the advanced capabilities of the ESRF-EBS beam and associated detectors.
To the author's knowledge, this represents the first demonstration of such a 5-DoF active stabilization platform being used to enhance the accuracy of a complex positioning system to this level.
# TODO - Section ref:sec:test_id31
* Thesis Outline - Mechatronics Design Approach
**** Introduction :ignore:
This thesis is structured chronologically, mirroring the phases of the mechatronics development approach employed for the NASS project.
It is divided into three chapters, each corresponding to a distinct phase of this methodology: Conceptual Design, Detailed Design, and Experimental Validation.
A brief overview of each chapter's content, is provided below.
While the chapters follow this logical progression, care has been taken to structure each chapter such that its constitutive sections may also be consulted independently based on the reader's specific interests.
**** Conceptual design development
- Talk about dynamic error budgeting
- Talk about used model
The goal of this first chapter is to find a concept:
- that will provide the wanted performances with high level of confidence
- As such system is costly, a mechatronics design approach is used [[cite:&monkhorst04_dynam_error_budget]] to be able to design the system "right the first time":
- When the system is finally build, its performance level should satisfy the specifications.
- No significant changes are allowed in the post design phase.
- Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.
To do so:
- Dynamical models are used, with included disturbances, feedback architecture, etc..
These models can be used to perform simulations, evaluate performances
- General idea is to start with very simple models, that can easily be understood (mass-spring-damper uniaxial model)
- Increase the model complexity if important physical phenomenon are to be modelled (cf the rotating model)
- Only when better understanding of the physical effects in play, and only if required, go for higher model complexity (here multi-body model)
To better understand the performance limitations, for different models, /dynamic error budgeting/ [[cite:&monkhorst04_dynam_error_budget;&okyay16_mechat_desig_dynam_contr_metrol]] are performed.
It consists of:
- Disturbance and noise signals are modeled by their spectral content, i.e. by their power spectral density (PSD)
- The effect of each error sources on the final error, while the feedback control is active, can be easily estimated
- Therefore, the effect that have the greatest impact on the achievable performance can be easily spotted and improved
- Different concepts can be compared
- This tool is therefore key in better understanding the main limitations, and guide the determination of the best concept, early in the project.
This chapter concludes with accurate time domain simulations of a tomography experiment, validating the developed concept.
The conceptual design phase, detailed in Chapter ref:chap:concept, followed a methodical progression from simplified uniaxial models to more complex multi-body representations.
Initial uniaxial analysis (Section ref:sec:uniaxial) provided fundamental insights, particularly regarding the influence of active platform stiffness on performance.
The introduction of rotation in a 3-DoF model (Section ref:sec:rotating) allowed investigation of gyroscopic effects, revealing challenges for softer platform designs.
Experimental modal analysis of the existing micro-station (Section ref:sec:modal) confirmed its complex dynamics but supported a rigid-body assumption for the different stages, justifying the development of a detailed multi-body model.
This model, tuned against experimental data and incorporating measured disturbances, was validated through simulation (Section ref:sec:ustation).
The Stewart platform architecture was selected for the active stage, and its kinematics, dynamics, and control were analyzed (Section ref:sec:nhexa).
The chapter culminates in Section ref:sec:nass with closed-loop simulations of the integrated NASS concept under realistic conditions, validating its feasibility and providing confidence for proceeding to the detailed design phase.
Dynamic error budgeting [[cite:&monkhorst04_dynam_error_budget;&okyay16_mechat_desig_dynam_contr_metrol]] was employed throughout this phase to identify performance limitations and guide concept selection.
**** Detailed design
- In the second chapter, the chosen concept can be design in more details.
- First, the architecture and geometry of the active platform is optimized.
- Then, key components of the active platform, such as the flexible joints and the actuators, are optimized using the combined multi-body / FEA design approach.
- This allowed to optimize the components using very accurate models (thanks to FEA), while still being able to integrate these components in the complete multi-body model of the NASS for time domain simulations.
- Different aspects of the control of the NASS, such as the optimal use of multiple sensors integrated in the active platform, the best adapted decoupling strategy and the design of the robust controller, are then discussed.
- The requirements for all the associated instrumentation (digital to analog converters, analog to digital converters, voltage amplifiers, relative motion sensors) are chosen based on dynamic error budgeting.
Using such approach, it was made sure that none of these instrumentation will limit the overall performance of the system.
- This chapter concludes with a presentation of the final design of the active platform.
Chapter ref:chap:detail focuses on translating the validated NASS concept into an optimized, implementable design.
Building upon the conceptual model which used idealized components, this phase addresses the detailed specification and optimization of each subsystem.
It starts with the determination of the optimal nano-hexapod geometry (Section ref:sec:detail_kinematics), analyzing the influence of geometric parameters on mobility, stiffness, and dynamics, leading to specific requirements for actuator stroke and joint mobility.
A hybrid multi-body/FEA modeling methodology is introduced and experimentally validated (Section ref:sec:detail_fem), then applied to optimize the actuators (Section ref:sec:detail_fem_actuator) and flexible joints (Section ref:sec:detail_fem_joint) while maintaining system-level simulation capability.
Control strategy refinement (Section ref:sec:detail_control) involves optimal integration of multiple sensors in the control architecture, evaluating decoupling strategies, and discussing controller optimization for decoupled systems.
Instrumentation selection (Section ref:sec:detail_instrumentation) is guided by dynamic error budgeting to establish noise specifications, followed by experimental characterization.
The chapter concludes (Section ref:sec:detail_design) by presenting the final, optimized nano-hexapod design, ready for procurement and assembly.
**** Experimental validation
After converging to a detailed design that give acceptable performance based on the models, the different parts were ordered and the experimental phase began.
Instead of directly assembling the active platform and testing it on the ID31 micro-station, a systematic approach was followed to characterize individual components.
- Therefore, actuators and flexible joints were individual characterized.
This allowed to update the model of these components, and obtained a more accurate model of the active platform
Systematic validation/refinement of models with experimental measurements
- Actuators and flexible joints were combined to form the active "struts" of the active platform.
These struts are also characterized
- Once the active platform were assembled, its dynamical model were found to over a very good match with the measured dynamics.
- This chapter conclude with the experimental tests on the ID31 micro-station of the complete NASS.
- Various scientific experiments are performed, such as tomography, and with various payload masses, to access the performances of the final system.
Chapter ref:chap:test details the experimental validation process, proceeding systematically from component-level characterization to full system evaluation on the beamline.
Actuators of the active platform were characterized, models validated, and active damping (IFF) tested (Section ref:sec:test_apa).
Flexible joints were tested on a dedicated bench to verify stiffness and stroke specifications (Section ref:sec:test_joints).
Assembled struts (actuators + joints) were then characterized to ensure consistency and validate multi-body models (Section ref:sec:test_struts).
The complete nano-hexapod assembly was tested on an isolated table, allowing accurate dynamic identification and model validation under various payload conditions (Section ref:sec:test_nhexa).
Finally, the integrated NASS was validated on the ID31 beamline using a purpose-built short-stroke metrology system (Section ref:sec:test_id31).
The implemented control architecture was tested under realistic experimental scenarios, including tomography with heavy payloads, confirming the system's performance and robustness.
* Bibliography :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]

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% Created 2025-04-17 Thu 21:14
% Created 2025-04-18 Fri 10:35
% Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -321,7 +321,7 @@ More recently, higher bandwidths (up to 100 Hz) have been demonstrated, particul
Figure \ref{fig:introduction_active_stations} showcases two end-stations incorporating online metrology and active feedback control.
The ID16A system at ESRF (Figure \ref{fig:introduction_stages_villar}) uses capacitive sensors and a piezoelectric hexapod to compensate for rotation stage errors and to perform accurate scans \cite{villar18_nanop_esrf_id16a_nano_imagin_beaml}.
Another example, shown in Figure \ref{fig:introduction_stages_nazaretski}, employs interferometers and piezoelectric stages to compensate for thermal drifts \cite{nazaretski15_pushin_limit,nazaretski17_desig_perfor_x_ray_scann}.
A more comprehensive review of actively controlled end-stations is provided in Section [\ldots{}].
A more comprehensive review of actively controlled end-stations is provided in Section \ref{sec:nhexa_platform_review}.
\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
@ -369,24 +369,23 @@ This approach allows combining extended travel with high precision and good dyna
\end{figure}
\chapter{Challenge definition}
The advent of fourth-generation light sources, coupled with advancements in focusing optics and detector technology, imposes stringent new requirements on sample positioning systems.
For the ID31 beamline, the smallest anticipated beam size is approximately 200 nm (horizontal, Dy) by 100 nm (vertical, Dz).
To effectively utilize such beams, the positioning system must maintain the sample's point of interest within the beam profile throughout the experiment.
This translates to required peak-to-peak positioning stability better than 200 nm in Dy and 100 nm in Dz, corresponding to RMS values of approximately 30 nm and 15 nm, respectively.
Furthermore, tilt errors (Ry) must be controlled to below approximately 1.7 µrad peak-to-peak (250 nrad RMS).
Crucially, these specifications must be met even when considering high-frequency vibrations, owing to the use of high-frame-rate detectors.
These demanding stability requirements must be achieved within the specific context of the ID31 beamline, which necessitates building upon the existing micro-station infrastructure, accommodating a wide range of experimental configurations requiring high mobility, and handling substantial payloads up to 50 kg.
With ID31's anticipated minimum beam dimensions of approximately \(200\,\text{nm}\times 100\,\text{nm}\), the primary experimental objective is maintaining the sample's point of interest within this beam.
This necessitates peak-to-peak positioning errors below \(200\,\text{nm}\) in \(D_y\) and \(200\,\text{nm}\) in \(D_z\), corresponding to RMS errors of \(30\,\text{nm}\) and \(15\,\text{nm}\), respectively.
Additionally, the \(R_y\) tilt angle error must remain below \(0.1\,\text{mdeg}\) (\(250\,\text{nrad RMS}\)).
Given the high frame rates of modern detectors, these specified positioning errors must be maintained even when considering high-frequency vibrations.
These demanding stability requirements must be achieved within the specific context of the ID31 beamline, which necessitates the integration with the existing micro-station, accommodating a wide range of experimental configurations requiring high mobility, and handling substantial payloads up to 50 kg.
The existing micro-station, despite being composed of high-performance stages, exhibits positioning accuracy limited to approximately \(10\,\mu m\) and \(10\,\mu\text{rad}\) due to inherent factors such as backlash, mechanical play, thermal expansion, imperfect guiding, and vibrations.
The existing micro-station, despite being composed of high-quality stages, exhibits positioning accuracy limited to approximately \(10\,\mu m\) and \(10\,\mu\text{rad}\) due to inherent factors such as backlash, mechanical play, thermal expansion, imperfect guiding, and vibrations.
While individual stage encoders can correct motion along their primary axis, they do not compensate for parasitic motions in other degrees of freedom.
The primary objective of this project is therefore defined as enhancing the positioning accuracy and stability of the ID31 micro-station by roughly two orders of magnitude, to fully leverage the capabilities offered by the ESRF-EBS source and modern detectors, without compromising its existing mobility and payload capacity.
\subsubsection{The Nano Active Stabilization System Concept}
To address these challenges, the concept of a Nano Active Stabilization System (NASS) is proposed.
As schematically illustrated in Figure \ref{fig:introduction_nass_concept_schematic}, the NASS comprises four principal components integrated with the existing micro-station (yellow): a 5-DoF online metrology system (red), a 5- or 6-DoF active stabilization platform (blue), and the associated control system and instrumentation (purple).
As schematically illustrated in Figure \ref{fig:introduction_nass_concept_schematic}, the NASS comprises four principal components integrated with the existing micro-station (yellow): a 5-DoF online metrology system (red), an active stabilization platform (blue), and the associated control system and instrumentation (purple).
This system essentially functions as a high-performance, multi-axis vibration isolation and error correction platform situated between the micro-station and the sample.
It actively compensates for positioning errors measured by the external metrology system.
The overarching goal is to improve the effective positioning accuracy from the micro-station's native \(\approx 10\,\mu m\) level down to below \(100\,\text{nm}\), while preserving the full mobility and 50 kg payload capability of the underlying stages.
\begin{figure}[htbp]
\centering
@ -396,7 +395,7 @@ The overarching goal is to improve the effective positioning accuracy from the m
\subsubsection{Online Metrology system}
The performance of the NASS is fundamentally reliant on the accuracy and bandwidth of its online metrology system, as the active control is based directly on these measurements.
This metrology system must fulfill several criteria: measure the sample position in 5 DoF (excluding rotation about the vertical Z-axis); ideally, measure position relative to the X-ray focusing optics; possess a measurement range compatible with the micro-station's extensive mobility and continuous spindle rotation; achieve accuracy commensurate with the sub-100 nm positioning target; and offer high bandwidth for real-time control.
This metrology system must fulfill several criteria: measure the sample position in 5 DoF (excluding rotation about the vertical Z-axis); possess a measurement range compatible with the micro-station's extensive mobility and continuous spindle rotation; achieve an accuracy compatible with the sub-100 nm positioning target; and offer high bandwidth for real-time control.
\begin{figure}[htbp]
\centering
@ -404,25 +403,25 @@ This metrology system must fulfill several criteria: measure the sample position
\caption{\label{fig:introduction_nass_metrology}2D representation of the NASS metrology system.}
\end{figure}
An initial concept, depicted in Figure \ref{fig:introduction_nass_metrology}, involves a spherical reflector with a flat bottom surface fixed beneath the sample.
The sphere's center is intended to coincide with the X-ray focus.
Fiber interferometers are directed at both the spherical and flat surfaces.
A tracking system is needed to maintain interferometer alignment, eliminating Abbe errors by measuring directly relative to the point of interest.
Translational positions (XYZ) are derived from measurements on the spherical surface, while tilt angles (Rx/Ry) are determined from measurements on the flat bottom surface.
A proposed concept (illustrated in Figure \ref{fig:introduction_nass_metrology}) features a spherical reflector with a flat bottom attached below the sample, with its center aligned to the X-ray focus.
Fiber interferometers target both surfaces.
A tracking system maintains perpendicularity between the interferometer beams and the mirror, such that Abbe errors are eliminated.
Interferometers pointing at the spherical surface provides translation measurement, while the ones pointing at the flat bottom surface yield tilt angles.
The development of this complex metrology system constitutes a significant mechatronic project in itself and is currently ongoing; it is not further detailed within this thesis.
For the work presented herein, the metrology system is assumed to provide accurate, high-bandwidth 5-DoF position measurements.
\subsubsection{Active Stabilization Platform}
\subsubsection{Active Stabilization Platform Design}
The active stabilization platform, positioned between the micro-station top plate and the sample, must satisfy several demanding requirements.
It needs to provide active motion compensation in 5 DoF (Dx, Dy, Dz, Rx, Ry).
It needs to provide active motion compensation in 5 degrees of freedom (\(D_x\), \(D_y\), \(D_z\), \(R_x\) and \(R_y\)).
It must possess excellent dynamic properties to enable high-bandwidth control capable of suppressing vibrations and tracking desired trajectories with nanometer-level precision.
Consequently, it must be free from backlash and play, and its active components (e.g., actuators) should introduce minimal vibrations.
Critically, it must reliably support and actuate payloads up to 50 kg.
Critically, it must accommodate payloads up to 50 kg.
A suitable candidate architecture for this platform is the Stewart platform (or hexapod), a parallel kinematic mechanism capable of 6-DoF motion.
A suitable candidate architecture for this platform is the Stewart platform (also known as ``hexapod''), a parallel kinematic mechanism capable of 6-DoF motion.
Stewart platforms are widely employed in positioning and vibration isolation applications due to their inherent stiffness and potential for high precision.
Various designs exist, differing in geometry, actuation technology, sensing methods, and control strategies, as exemplified in Figure \ref{fig:introduction_stewart_platform_piezo}.
A central challenge addressed in this thesis is the optimal mechatronic design of such an active platform tailored to the specific requirements of the NASS.
A more detailed review of Stewart platform and its main components will be given in Section \ref{sec:detail_kinematics_stewart_review}.
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
@ -439,156 +438,109 @@ A central challenge addressed in this thesis is the optimal mechatronic design o
\end{subfigure}
\caption{\label{fig:introduction_stewart_platform_piezo}Example of Stewart platforms. (\subref{fig:introduction_stewart_du14}) \cite{du14_piezo_actuat_high_precis_flexib} and (\subref{fig:introduction_stewart_hauge04}) \cite{hauge04_sensor_contr_space_based_six}}
\end{figure}
\subsubsection{MIMO robust control strategies}
\subsubsection{Robust Control}
The NASS inherently involves multi-input, multi-output (MIMO) feedback control.
The control system must process position measurements from the online metrology system and reference positions derived from the desired micro-station movements, commanding the active platform in real time to stabilize the sample and compensate for all error sources, including stage imperfections, thermal drifts, and vibrations.
Ensuring the stability and robustness of these feedback loops is paramount, especially within the demanding operational context of a synchrotron beamline, which requires reliable 24/7 operation with minimal intervention.
This contrasts with many traditional synchrotron instruments built using proven, passively stable components like stepper motors and conventional bearings.
The control system must compute the position measurements from the online metrology system and computes the reference positions derived from each micro-station desired movement.
It then commands the active platform in real time to stabilize the sample and compensate for all error sources, including stage imperfections, thermal drifts, and vibrations.
Ensuring the stability and robustness of these feedback loops is crucial, especially within the demanding operational context of a synchrotron beamline, which requires reliable 24/7 operation with minimal intervention.
Several factors complicate the design of robust feedback control for the NASS.
The system must perform reliably across diverse experimental conditions, including different scan types (tomography, linear scans) and velocities (slow drifts to fast fly-scans).
The continuous rotation of the spindle introduces gyroscopic coupling effects and means actuators rotate relative to stationary sensors, altering the system dynamics.
Perhaps the most significant challenge is the wide variation in payload mass, from potentially 1 kg up to 50 kg.
High-performance positioning controllers often assume a fixed, well-characterized payload, as seen in applications like lithography or atomic force microscopy (AFM).
First, the system must operate under across diverse experimental conditions, including different scan types (tomography, linear scans) and payloads' inertia.
The continuous rotation of the spindle introduces gyroscopic effects that can affect the system dynamics.
As actuators of the active platforms rotate relative to stationary sensors, the control kinematics to map the errors in the frame of the active platform is complex.
But perhaps the most significant challenge is the wide variation in payload mass (1 kg up to 50 kg) that the system must accommodate.
Designing for robustness against large payload variations typically necessitates larger stability margins, which can compromise achievable performance.
Furthermore, unlike many systems where the active stage and sample are significantly lighter than the underlying coarse stages, the NASS payload mass can be substantially greater than the mass of the micro-station's top stages.
This leads to strong dynamic coupling between the active platform and the micro-station structure, resulting in a more complex MIMO system with significant cross-talk between axes.
Consequently, high-performance positioning stages often work with well-characterized payload, as seen in systems like wafer-scanners or atomic force microscopes.
Furthermore, unlike many systems where the active stage and sample are significantly lighter than the underlying coarse stages, the NASS payload mass can be substantially greater than the mass of the micro-station's top stage.
This leads to strong dynamic coupling between the active platform and the micro-station structure, resulting in a more complex multi-inputs multi-outputs (MIMO) system with significant cross-talk between axes.
These variations in operating conditions and payload translate into significant uncertainty or changes in the plant dynamics that the controller must handle.
Therefore, the feedback controller must be designed to be robust against this plant uncertainty while still delivering the required nanometer-level performance.
\subsubsection{Predictive Design / Mechatronics approach}
The overall performance of the NASS will be determined by the interplay of numerous factors, including sensor accuracy and noise, actuator force and bandwidth, mechanical design stiffness and resonances, and the achievable control bandwidth.
To navigate this complexity and ensure the final system meets its stringent specifications, a predictive design methodology, specifically a mechatronics approach, is essential.
The goal is to rigorously evaluate different concepts, predict performance limitations, and guide the design process towards an optimal solution that functions correctly upon first assembly, given the significant cost and complexity involved.
Key challenges within this approach include developing appropriate design methodologies, creating accurate simulation models capable of comparing different concepts quantitatively, and converging on a final design that demonstrably achieves the target performance levels.
The overall performance achieved by the NASS is determined by numerous factors, such as external disturbances, the noise characteristics of the instrumentation, the dynamics resulting from the chosen mechanical architecture, and the achievable bandwidth dictated by the control architecture.
Ensuring the final system met its stringent specifications requires the implementation of a predictive design methodology, also known as a mechatronics design approach.
The goal is to rigorously evaluate different concepts, predict performance limitations, and guide the design process.
Key challenges within this approach include developing appropriate design methodologies, creating accurate models capable of comparing different concepts quantitatively, and converging on a final design that achieves the target performance levels.
\chapter{Original Contributions}
This thesis presents several original contributions aimed at addressing the challenges inherent in the design, control, and implementation of the Nano Active Stabilization System, primarily within the fields of Control Theory, Mechatronics Design, and Experimental Validation.
\subsubsection{6DoF vibration control of a rotating platform}
While long stroke-short stroke architectures have been implemented for 1-DoF or 2-DoF systems, this work extends the concept to a fully coupled 6-DoF system operating on a continuously rotating base.
The active platform is designed not merely to correct rotational errors but to simultaneously compensate for errors originating from all underlying micro-station stages.
Traditional long-stroke/short-stroke architectures typically operate in one or two degrees of freedom.
This work extends the concept to six degrees of freedom, with the active platform designed not only to correct rotational errors but to simultaneously compensate for errors originating from all underlying micro-station stages.
The application of a continuously rotating Stewart platform for active vibration control and error compensation in this manner is believed to be novel in the reviewed literature.
\subsubsection{Mechatronics design approach}
A rigorous mechatronics design methodology was applied consistently throughout the NASS development lifecycle \cite{dehaeze18_sampl_stabil_for_tomog_exper,dehaeze21_mechat_approac_devel_nano_activ_stabil_system}.
Although the mechatronics approach itself is not new, its comprehensive application here, from initial concept evaluation using simplified models to detailed design optimization and experimental validation informed by increasingly sophisticated models, is noteworthy.
Dynamical models were employed at every stage: for initial concept selection, detailed component optimization, understanding experimental observations, and optimizing control strategies.
Although the mechatronics approach itself is not new, its comprehensive application here, from initial concept evaluation using simplified models to detailed design optimization and experimental validation informed by increasingly sophisticated models, potentially offers useful insights to the existing literature.
This thesis documents this process chronologically, illustrating how models of varying complexity can be effectively utilized at different project phases and how design decisions were systematically based on quantitative model predictions and analyses.
While the resulting system is highly specific, the documented effectiveness of this integrated design approach may contribute to the broader adoption of mechatronics methodologies in the design of future synchrotron instrumentation.
While the resulting system is highly specific, the documented effectiveness of this design approach may contribute to the broader adoption of mechatronics methodologies in the design of future synchrotron instrumentation.
\subsubsection{Multi-body simulations with reduced order flexible bodies obtained by FEA}
A key enabling tool employed extensively in this work was a combined multi-body simulation and Finite Element Analysis technique, specifically utilizing Component Mode Synthesis (CMS) to represent flexible bodies within the multi-body framework \cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}.
A key tool employed extensively in this work was a combined multi-body simulation and Finite Element Analysis technique, specifically utilizing Component Mode Synthesis to represent flexible bodies within the multi-body framework \cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}.
This hybrid approach, while established, was experimentally validated in this work for components critical to the NASS, namely amplified piezoelectric actuators and flexible joints.
It proved invaluable for designing and optimizing components intended for integration into a larger, complex dynamic system.
This methodology, detailed in Section [\ldots{}], is presented as a potentially useful tool for future mechatronic instrument development.
This methodology, detailed in Section \ref{sec:detail_fem}, is presented as a potentially useful tool for future mechatronic instrument development.
\subsubsection{Control Robustness by design}
Addressing the critical challenge of robustness across varying experimental conditions (rotation speeds, payloads up to 50 kg) was approached through ``robustness by design'' rather than relying solely on complex robust control synthesis techniques (like \(\mathcal{H}_\infty\) or \(\mu\text{-synthesis}\)).
The strategy involved selecting a system architecture (mechanics, sensors, actuators) inherently conducive to robust control.
An example is the deliberate use of collocated actuator/sensor pairs, enabling the potential application of passivity-based control principles to guarantee stability.
Informed architectural choices were made by systematically evaluating different sensor combination strategies (e.g., HAC/LAC, sensor fusion, two-sensor control) and comparing various MIMO decoupling approaches.
This comparative analysis of control architectures, presented in Section [\ldots{}], was identified as somewhat lacking in existing literature.
The requirement for robust operation across diverse conditions—including payloads up to 50kg, complex underlying dynamics from the micro-station, and varied operational modes like different rotation speeds—presented a critical design challenge.
This challenge was met by embedding robustness directly into the active platform's design, rather than depending solely on complex post-design control synthesis techniques such as \(\mathcal{H}_\infty\text{-synthesis}\) and \(\mu\text{-synthesis}\).
Key elements of this strategy included the model-based evaluation of active stage designs to identify architectures inherently easier to control, the incorporation of collocated actuator/sensor pairs to leverage passivity-based guaranteed stability, and the comparison of architecture to combine several sensors such as sensor fusion and High Authority Control / Low Authority Control (HAC-LAC).
Furthermore, decoupling strategies for parallel manipulators were compared (Section \ref{sec:detail_control_decoupling}), addressing a topic identified as having limited treatment in the literature.
Consequently, the specified performance targets were met utilizing controllers which, facilitated by this design approach, proved to be robust, readily tunable, and easily maintained.
\subsubsection{Active Damping of rotating mechanical systems using Integral Force Feedback}
During conceptual design, it was found that the guaranteed stability properties of the established active damping technique known as Integral Force Feedback (IFF) are compromised when applied to rotating platforms like the NASS.
During conceptual design, it was found that the guaranteed stability property of the established active damping technique known as Integral Force Feedback (IFF) is compromised when applied to rotating platforms like the NASS.
To address this instability issue, two modifications to the classical IFF control scheme were proposed and analyzed.
The first involves a minor adjustment to the control law itself, while the second incorporates physical springs in parallel with the force sensors.
Stability conditions and optimal parameter tuning guidelines were derived for both modified schemes.
This is further discussed in Section [\ldots{}] and was the subject of publications \cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb,dehaeze21_activ_dampin_rotat_platf_using}.
This is further discussed in Section \ref{sec:rotating} and was the subject of publications \cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb,dehaeze21_activ_dampin_rotat_platf_using}.
\subsubsection{Design of complementary filters using \(\mathcal{H}_\infty\) Synthesis}
For implementing sensor fusion, where signals from multiple sensors are combined, complementary filters are often employed.
A novel method for designing these filters using \(\mathcal{H}_\infty\) synthesis techniques was developed \cite{dehaeze19_compl_filter_shapin_using_synth}.
This method allows explicit shaping of the filter norms, providing guarantees on the performance of the sensor fusion process.
This design strategy, discussed further in Section [\ldots{}], has subsequently found application in optimizing sensor fusion for gravitational wave detectors \cite{tsang22_optim_sensor_fusion_method_activ}.
The integration of such filters into feedback control architectures can also lead to advantageous control structures, as proposed in \cite{verma20_virtual_sensor_fusion_high_precis_contr} and further studied in Section [\ldots{}].
This synthesis technique, discussed further in Section \ref{sec:detail_control_sensor}, has subsequently found application in optimizing sensor fusion for gravitational wave detectors \cite{tsang22_optim_sensor_fusion_method_activ}.
The integration of such filters into feedback control architectures can also lead to advantageous control structures, as proposed in \cite{verma20_virtual_sensor_fusion_high_precis_contr} and further studied in Section \ref{sec:detail_control_cf}.
\subsubsection{Experimental validation of the Nano Active Stabilization System}
The conclusion of this work involved the experimental implementation and validation of the complete NASS on the ID31 beamline.
Experimental results demonstrate that the system successfully improves the effective positioning accuracy of the micro-station from its native \textasciitilde{}10 µm level down to the target \textasciitilde{}100 nm range during representative scientific experiments.
Crucially, robustness to variations in sample mass (up to 39 kg tested) and diverse experimental conditions (e.g., tomography scans) was verified.
The NASS thus provides a versatile end-station solution, uniquely combining high payload capacity with nanometer-level accuracy and stability, enabling optimal utilization of the advanced capabilities of the ESRF-EBS beam and associated detectors.
Experimental results, presented in Section \ref{sec:test_id31}, demonstrate that the system successfully improves the effective positioning accuracy of the micro-station from its native \(\approx 10\,\mu m\) level down to the target \(\approx 100\,nm\) range during representative scientific experiments.
Crucially, robustness to variations in sample mass and diverse experimental conditions was verified.
The NASS thus provides a versatile end-station solution, uniquely combining high payload capacity with nanometer-level accuracy, enabling optimal utilization of the advanced capabilities of the ESRF-EBS beam and associated detectors.
To the author's knowledge, this represents the first demonstration of such a 5-DoF active stabilization platform being used to enhance the accuracy of a complex positioning system to this level.
\chapter{Thesis Outline - Mechatronics Design Approach}
This thesis is structured chronologically, mirroring the phases of the mechatronics development approach employed for the NASS project.
It is divided into three chapters, each corresponding to a distinct phase of this methodology: Conceptual Design, Detailed Design, and Experimental Validation.
A brief overview of each chapter's content, is provided below.
While the chapters follow this logical progression, care has been taken to structure each chapter such that its constitutive sections may also be consulted independently based on the reader's specific interests.
\subsubsection{Conceptual design development}
\begin{itemize}
\item Talk about dynamic error budgeting
\item Talk about used model
\end{itemize}
The goal of this first chapter is to find a concept:
\begin{itemize}
\item that will provide the wanted performances with high level of confidence
\item As such system is costly, a mechatronics design approach is used \cite{monkhorst04_dynam_error_budget} to be able to design the system ``right the first time'':
\begin{itemize}
\item When the system is finally build, its performance level should satisfy the specifications.
\item No significant changes are allowed in the post design phase.
\item Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.
\end{itemize}
\end{itemize}
To do so:
\begin{itemize}
\item Dynamical models are used, with included disturbances, feedback architecture, etc..
These models can be used to perform simulations, evaluate performances
\item General idea is to start with very simple models, that can easily be understood (mass-spring-damper uniaxial model)
\item Increase the model complexity if important physical phenomenon are to be modelled (cf the rotating model)
\item Only when better understanding of the physical effects in play, and only if required, go for higher model complexity (here multi-body model)
\end{itemize}
To better understand the performance limitations, for different models, \emph{dynamic error budgeting} \cite{monkhorst04_dynam_error_budget,okyay16_mechat_desig_dynam_contr_metrol} are performed.
It consists of:
\begin{itemize}
\item Disturbance and noise signals are modeled by their spectral content, i.e. by their power spectral density (PSD)
\item The effect of each error sources on the final error, while the feedback control is active, can be easily estimated
\item Therefore, the effect that have the greatest impact on the achievable performance can be easily spotted and improved
\item Different concepts can be compared
\item This tool is therefore key in better understanding the main limitations, and guide the determination of the best concept, early in the project.
\end{itemize}
This chapter concludes with accurate time domain simulations of a tomography experiment, validating the developed concept.
The conceptual design phase, detailed in Chapter \ref{chap:concept}, followed a methodical progression from simplified uniaxial models to more complex multi-body representations.
Initial uniaxial analysis (Section \ref{sec:uniaxial}) provided fundamental insights, particularly regarding the influence of active platform stiffness on performance.
The introduction of rotation in a 3-DoF model (Section \ref{sec:rotating}) allowed investigation of gyroscopic effects, revealing challenges for softer platform designs.
Experimental modal analysis of the existing micro-station (Section \ref{sec:modal}) confirmed its complex dynamics but supported a rigid-body assumption for the different stages, justifying the development of a detailed multi-body model.
This model, tuned against experimental data and incorporating measured disturbances, was validated through simulation (Section \ref{sec:ustation}).
The Stewart platform architecture was selected for the active stage, and its kinematics, dynamics, and control were analyzed (Section \ref{sec:nhexa}).
The chapter culminates in Section \ref{sec:nass} with closed-loop simulations of the integrated NASS concept under realistic conditions, validating its feasibility and providing confidence for proceeding to the detailed design phase.
Dynamic error budgeting \cite{monkhorst04_dynam_error_budget,okyay16_mechat_desig_dynam_contr_metrol} was employed throughout this phase to identify performance limitations and guide concept selection.
\subsubsection{Detailed design}
\begin{itemize}
\item In the second chapter, the chosen concept can be design in more details.
\item First, the architecture and geometry of the active platform is optimized.
\item Then, key components of the active platform, such as the flexible joints and the actuators, are optimized using the combined multi-body / FEA design approach.
\item This allowed to optimize the components using very accurate models (thanks to FEA), while still being able to integrate these components in the complete multi-body model of the NASS for time domain simulations.
\item Different aspects of the control of the NASS, such as the optimal use of multiple sensors integrated in the active platform, the best adapted decoupling strategy and the design of the robust controller, are then discussed.
\item The requirements for all the associated instrumentation (digital to analog converters, analog to digital converters, voltage amplifiers, relative motion sensors) are chosen based on dynamic error budgeting.
Using such approach, it was made sure that none of these instrumentation will limit the overall performance of the system.
\item This chapter concludes with a presentation of the final design of the active platform.
\end{itemize}
Chapter \ref{chap:detail} focuses on translating the validated NASS concept into an optimized, implementable design.
Building upon the conceptual model which used idealized components, this phase addresses the detailed specification and optimization of each subsystem.
It starts with the determination of the optimal nano-hexapod geometry (Section \ref{sec:detail_kinematics}), analyzing the influence of geometric parameters on mobility, stiffness, and dynamics, leading to specific requirements for actuator stroke and joint mobility.
A hybrid multi-body/FEA modeling methodology is introduced and experimentally validated (Section \ref{sec:detail_fem}), then applied to optimize the actuators (Section \ref{sec:detail_fem_actuator}) and flexible joints (Section \ref{sec:detail_fem_joint}) while maintaining system-level simulation capability.
Control strategy refinement (Section \ref{sec:detail_control}) involves optimal integration of multiple sensors in the control architecture, evaluating decoupling strategies, and discussing controller optimization for decoupled systems.
Instrumentation selection (Section \ref{sec:detail_instrumentation}) is guided by dynamic error budgeting to establish noise specifications, followed by experimental characterization.
The chapter concludes (Section \ref{sec:detail_design}) by presenting the final, optimized nano-hexapod design, ready for procurement and assembly.
\subsubsection{Experimental validation}
After converging to a detailed design that give acceptable performance based on the models, the different parts were ordered and the experimental phase began.
Instead of directly assembling the active platform and testing it on the ID31 micro-station, a systematic approach was followed to characterize individual components.
\begin{itemize}
\item Therefore, actuators and flexible joints were individual characterized.
This allowed to update the model of these components, and obtained a more accurate model of the active platform
Systematic validation/refinement of models with experimental measurements
\item Actuators and flexible joints were combined to form the active ``struts'' of the active platform.
These struts are also characterized
\item Once the active platform were assembled, its dynamical model were found to over a very good match with the measured dynamics.
\item This chapter conclude with the experimental tests on the ID31 micro-station of the complete NASS.
\item Various scientific experiments are performed, such as tomography, and with various payload masses, to access the performances of the final system.
\end{itemize}
Chapter \ref{chap:test} details the experimental validation process, proceeding systematically from component-level characterization to full system evaluation on the beamline.
Actuators of the active platform were characterized, models validated, and active damping (IFF) tested (Section \ref{sec:test_apa}).
Flexible joints were tested on a dedicated bench to verify stiffness and stroke specifications (Section \ref{sec:test_joints}).
Assembled struts (actuators + joints) were then characterized to ensure consistency and validate multi-body models (Section \ref{sec:test_struts}).
The complete nano-hexapod assembly was tested on an isolated table, allowing accurate dynamic identification and model validation under various payload conditions (Section \ref{sec:test_nhexa}).
Finally, the integrated NASS was validated on the ID31 beamline using a purpose-built short-stroke metrology system (Section \ref{sec:test_id31}).
The implemented control architecture was tested under realistic experimental scenarios, including tomography with heavy payloads, confirming the system's performance and robustness.
\printbibliography[heading=bibintoc,title={Bibliography}]
\end{document}