Add conclusion

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@@ -13642,8 +13642,146 @@ The system performed exceptionally well during vertical scans, though some limit
 
 With the implementation of an accurate online metrology system, the NASS will be ready for integration into the beamline environment, significantly enhancing the capabilities of high-precision X-ray experimentation on the ID31 beamline.
 
-* TODO Conclusion and Future Work
+* Conclusion and Future Work
 <<chap:conclusion>>
+#+LATEX: \begingroup
+#+LATEX: \def\clearpage{\par}
+** Summary of Findings
+#+LATEX: \endgroup
+
+The primary objective of this research was to enhance the positioning accuracy of the ID31 micro-station by approximately two orders of magnitude, enabling full exploitation of the new $4^{\text{th}}$ generation light source, without compromising the system's mobility or its capacity to handle payloads up to $50\,\text{kg}$.
+
+To meet this demanding objective, the concept of a Nano Active Stabilization System (NASS) was proposed and developed.
+This system comprises an active stabilization platform positioned between the existing micro-station and the sample.
+Integrated with an external online metrology system and an custom control architecture, the NASS was designed to actively measure and compensate for positioning errors originating from various sources, including micro-station imperfections, thermal drift, and vibrations.
+
+The conceptual design phase rigorously evaluated the feasibility of the NASS concept.
+Through progressive modeling, from simplified uniaxial representations to complex multi-body dynamic simulations, key design insights were obtained.
+It was determined that an active platform with moderate stiffness offered an optimal compromise, decoupling the system from micro-station dynamics while mitigating gyroscopic effects from continuous rotation.
+The multi-body modeling approach, informed by experimental modal analysis of the micro-station, was essential for capturing the system's complex dynamics.
+The Stewart platform architecture was selected for the active stage, and its viability was confirmed through closed-loop simulations employing a High-Authority Control / Low-Authority Control (HAC-LAC) strategy.
+This strategy incorporated a modified form of Integral Force Feedback (IFF), adapted to provide robust active damping despite the platform rotation and varying payloads.
+These simulations demonstrated the NASS concept could meet the nanometer-level stability requirements under realistic operating conditions.
+
+Following the conceptual validation, the detailed design phase focused on translating the NASS concept into an optimized, physically realizable system.
+Geometric optimization studies refined the Stewart platform configuration.
+A hybrid modeling technique combining Finite Element Analysis (FEA) with multi-body dynamics simulation was applied and experimentally validated.
+This approach enabled detailed optimization of components, such as amplified piezoelectric actuators and flexible joints, while efficiently simulating the complete system dynamics.
+Work was also undertaken on the optimization of the control strategy for the active platform.
+Instrumentation selection (sensors, actuators, control hardware) was guided by dynamic error budgeting to ensure component noise levels met the overall nanometer-level performance target.
+
+The final phase of the project was dedicated to the experimental validation of the developed NASS.
+Component tests confirmed the performance of the selected actuators and flexible joints, validated their respective models.
+Dynamic testing of the assembled nano-hexapod on an isolated test bench provided essential experimental data that correlated well with the predictions of the multi-body model.
+The final validation was performed on the ID31 beamline, utilizing a short-stroke metrology system to assess performance under realistic experimental conditions.
+These tests demonstrated that the NASS, operating with the implemented HAC-LAC control architecture, successfully achieved the target positioning stability – maintaining residual errors below $30\,\text{nm RMS}$ laterally, $15\,\text{nm RMS}$ vertically, and $250\,\text{nrad RMS}$ in tilt – during various experiments, including tomography scans with significant payloads.
+Crucially, the system's robustness to variations in payload mass and operational modes was confirmed.
+
+** Perspectives
+
+Although this research successfully validated the NASS concept, it concurrently highlighted specific areas where the system could be enhanced, alongside related topics that merit further investigation.
+
+***** Automatic tuning of a multi-body model from an experimental modal analysis
+
+The manual tuning process employed to match the multi-body model dynamics with experimental measurements was found to be laborious.
+Systems like the micro-station can be conceptually modeled as interconnected solid bodies, springs, and dampers, with component inertia readily obtainable from CAD models.
+An interesting perspective is the development of methods for the automatic tuning of the multi-body model's stiffness matrix (representing the interconnecting spring stiffnesses) directly from experimental modal analysis data.
+Such a capability would enable the rapid generation of accurate dynamic models for existing end-stations, which could subsequently be utilized for detailed system analysis and simulation studies.
+
+***** Better addressing plant uncertainty coming from a change of payload
+
+For most high-performance mechatronic systems like lithography machines or atomic force microscopes, payloads inertia are often known and fixed, allowing controllers to be precisely optimized.
+However, synchrotron end-stations frequently handle samples with widely varying masses and inertias – ID31 being an extreme example, but many require nanometer positioning for samples from very light masses up to 5kg.
+
+The conventional strategy involves implementing controllers with relatively small bandwidth to accommodate various payloads.
+When controllers are optimized for a specific payload, changing payloads may destabilize the feedback loops that needs to be re-tuned.
+
+In this thesis, the HAC-IFF robust control approach was employed to maintain stability despite payload variations, though this resulted in relatively modest bandwidth.
+Therefore, a key objective for future work is to enhance the management of payload-induced plant uncertainty, aiming for improved performance without sacrificing robustness.
+Potential strategies to be explored include adaptive control (involving automatic plant identification and controller tuning after a change of payload) and robust control techniques such as $\mu\text{-synthesis}$ (allowing the controller to be synthesized while explicitly considering a specified range of payload masses).
+
+***** Control based on Complementary Filters
+
+The control architecture based on complementary filters (detailed in Section ref:sec:detail_control_cf) has been successfully implemented in several instruments at the ESRF.
+This approach has proven straightforward to implement and offers the valuable capability of modifying closed-loop behavior in real time, which proves advantageous for many applications.
+For instance, the controller can be optimized according to the scan type: constant velocity scans benefit from a $+2$ slope for the sensitivity transfer function, while ptychography may be better served by a $+1$ slope with slightly higher bandwidth to minimize point-to-point transition times.
+
+Nevertheless, a more rigorous analysis of this control architecture and its comparison with similar approaches documented in the literature is necessary to fully understand its capabilities and limitations.
+
+***** Sensor Fusion
+
+While the HAC-LAC approach demonstrated a simple and comprehensive methodology for controlling the NASS, sensor fusion represents an interesting alternative that is worth investigating.
+While the synthesis method developed for complementary filters facilitates their design (Section ref:sec:detail_control_sensor), their application specifically for sensor fusion within the NASS context was not examined in detail.
+
+One potential approach involves fusing external metrology (utilized at low frequencies) with force sensors (employed at high frequencies).
+This configuration could enhance robustness through the collocation of force sensors with actuators.
+The integration of encoder feedback into the control architecture could also be explored.
+
+***** Development of multi-DoF metrology systems
+
+Although experimental validation using the short-stroke metrology prototype was achieved, the NASS remains unsuitable for beamline applications due to the lack of a long stroke metrology system.
+Efforts were initiated during this project to develop such a metrology system, though these were not presented herein as the focus was directed toward the active platform, instrumentation, and controllers.
+The development process revealed that the metrology system constitutes a complex mechatronic system, which could benefit significantly from the design approach employed throughout this thesis.
+This challenge is particularly complex when continuous rotation is combined with long stroke movements.
+Yet, the development of such metrology systems is considered critical for future end-stations, especially for future tomography end stations where nano-meter accuracy is desired across larger strokes.
+
+Promising approaches have been presented in the literature.
+A ball lens retroreflector is used in [[cite:&schropp20_ptynam]], providing a $\approx 1\,\text{mm}^3$ measuring volume, but does not fully accommodate complete rotation.
+In [[cite:&geraldes23_sapot_carnaub_sirius_lnls]], an interesting metrology approach is presented, utilizing interferometers for long stroke/non-rotated movements and capacitive sensors for short stroke/rotated positioning.
+
+***** Alternative Architecture for the NASS
+
+The original micro-station design was driven by optimizing positioning accuracy, utilizing dedicated actuators for different DoFs (leading to simple kinematics and a stacked configuration), and maximizing stiffness.
+This design philosophy ensured that the micro-station would remain functional for micro-focusing applications even if the NASS project did not meet expectations.
+
+Analyzing the NASS as an complete system reveals that the positioning accuracy is primarily determined by the metrology system and the feedback control.
+Consequently, the underlying micro-station's own positioning accuracy has minimal influence on the final performances (it does however impact the required mobility of the active platform).
+Nevertheless, it remains crucial that the micro-station itself does not generate detrimental high-frequency vibrations, particularly during movements, as evidenced by issues previously encountered with stepper motors.
+
+Designing a future end-station with the understanding that a functional NASS will ensure final positioning accuracy could allow for a significantly simplified long-stroke stage architecture, perhaps chosen primarily to facilitate the integration of the online metrology.
+One possible configuration, illustrated in Figure ref:fig:conclusion_nass_architecture, would comprise a long-stroke Stewart platform providing the required mobility without generating high-frequency vibrations; a spindle that need not deliver exceptional performance but should be stiff and avoid inducing high-frequency vibrations (an air-bearing spindle might not be essential); and a short-stroke Stewart platform for correcting errors from the long-stroke stage and spindle.
+
+#+name: fig:conclusion_nass_architecture
+#+caption: Proposed alternative configuration for an end-station including the Nano Active Stabilization System
+#+attr_latex: :options [h!tbp]
+[[file:figs/conclusion_nass_architecture.png]]
+
+With this architecture, the online metrology could be divided into two systems, as proposed by [[cite:&geraldes23_sapot_carnaub_sirius_lnls]]: a long-stroke metrology system potentially using interferometers, and a short-stroke metrology system using capacitive sensors, as successfully demonstrated by [[cite:&villar18_nanop_esrf_id16a_nano_imagin_beaml]].
+
+***** Development of long stroke high performance stage
+
+As an alternative to the short-stroke/long-stroke architecture, the development of a high-performance long-stroke stage seems worth investigating.
+Stages based on voice coils, offering nano-positioning capabilities with $3\,mm$ stroke, have recently been reported in the literature [[cite:&schropp20_ptynam;&kelly22_delta_robot_long_travel_nano]].
+
+Magnetic levitation also emerges as a particularly interesting technology to be explored, especially for microscopy  [[cite:&fahmy22_magnet_xy_theta_x;&heyman23_levcub]] and tomography [[cite:&dyck15_magnet_levit_six_degree_freed_rotar_table;&fahmy22_magnet_xy_theta_x]] end-stations.
+Two notable designs illustrating these capabilities are shown in Figure ref:fig:conclusion_maglev.
+Specifically, a compact 6DoF stage known as LevCube, providing a mobility of approximately $1\,\text{cm}^3$, is depicted in Figure ref:fig:conclusion_maglev_heyman23, while a 6DoF stage featuring infinite rotation, is shown in Figure ref:fig:conclusion_maglev_dyck15.
+However, implementations of such magnetic levitation stages on synchrotron beamlines have yet to be documented in the literature.
+
+#+name: fig:conclusion_maglev
+#+caption: Example of magnetic levitation stages. LevCube allowing for 6DoF control of the position with $\approx 1\,\text{cm}^3$ mobility (\subref{fig:conclusion_maglev_heyman23}). Magnetic levitation stage with infinite $R_z$ rotation mobility (\subref{fig:conclusion_maglev_dyck15})
+#+attr_latex: :options [htbp]
+#+begin_figure
+#+attr_latex: :caption \subcaption{\label{fig:conclusion_maglev_heyman23}LevCube with $\approx 1\,\text{cm}^3$ mobility \cite{heyman23_levcub}}
+#+attr_latex: :options {0.49\textwidth}
+#+begin_subfigure
+#+attr_latex: :width 0.9\linewidth
+[[file:figs/conclusion_maglev_heyman23.jpg]]
+#+end_subfigure
+#+attr_latex: :caption \subcaption{\label{fig:conclusion_maglev_dyck15}Stage with infinite $R_z$ rotation \cite{dyck15_magnet_levit_six_degree_freed_rotar_table}}
+#+attr_latex: :options {0.49\textwidth}
+#+begin_subfigure
+#+attr_latex: :width 0.9\linewidth
+[[file:figs/conclusion_maglev_dyck15.jpg]]
+#+end_subfigure
+#+end_figure
+
+***** Extending the design methodology to complete beamlines
+
+The application of dynamic error budgeting and the mechatronic design approach to an entire beamline represents an interesting direction for future work.
+During the early design phases of a beamline, performance metrics are typically expressed as integrated values (usually RMS values) rather than as functions of frequency.
+However, the frequency content of these performance metrics (such as beam stability, energy stability, and sample stability) is crucial, as factors like detector integration time can filter out high-frequency components.
+Therefore, adopting a design approach utilizing dynamic error budgets, cascading from overall beamline requirements down to individual component specifications, is considered a potentially valuable direction for future investigation.
 
 * Bibliography                                                        :ignore:
 #+latex: \printbibliography[heading=bibintoc,title={Bibliography}]