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Addressed "TODOs" in the document

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Thomas Dehaeze 2025-04-23 10:59:03 +02:00
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@ -393,12 +393,10 @@ While this enhanced beam quality presents unprecedented scientific opportunities
:PROPERTIES:
:UNNUMBERED: t
:END:
# TODO - Make a short introduction to the beamline goal
Each beamline begins with a "white" beam generated by the insertion device.
This beam carries substantial power, typically exceeding kilowatts, and is generally unsuitable for direct application to samples.
Instead, the beam passes through a series of optical elements—including absorbers, mirrors, slits, and monochromators—that filter and shape the X-rays to the desired specifications.
The goal of the beamline is therefore to filter and shape the X-rays to the desired specifications using a series of optical elements such as absorbers, mirrors, slits, and monochromators.
These components are housed in multiple Optical Hutches, as depicted in Figure\nbsp{}ref:fig:introduction_id31_oh.
#+name: fig:introduction_id31_oh
@ -1927,7 +1925,6 @@ The transfer functions from $F$ to $L$ (i.e., control of the relative motion of
When the relative displacement of the active platform $L$ is controlled (dynamics shown in Figure\nbsp{}ref:fig:uniaxial_effect_support_compliance_dynamics), having a stiff active platform (i.e., with a suspension mode at higher frequency than the mode of the support) makes the dynamics less affected by the limited support compliance (Figure\nbsp{}ref:fig:uniaxial_effect_support_compliance_dynamics_stiff).
This is why it is very common to have stiff piezoelectric stages fixed at the very top of positioning stages.
In such a case, the control of the piezoelectric stage using its integrated metrology (typically capacitive sensors) is quite simple as the plant is not much affected by the dynamics of the support on which it is fixed.
# TODO - Add references of such stations with piezo stages on top, for instance [[cite:&schropp20_ptynam]]
If a soft active platform is used, the support dynamics appears in the dynamics between $F$ and $L$ (see Figure\nbsp{}ref:fig:uniaxial_effect_support_compliance_dynamics_soft) which will impact the control robustness and performance.
@ -4125,8 +4122,7 @@ The inertia of the solid bodies and the stiffness properties of the guiding mech
The obtained dynamics is then compared with the modal analysis performed on the micro-station (Section\nbsp{}ref:ssec:ustation_model_comp_dynamics).
# TODO - Add reference to uniaxial model
As the dynamics of the active platform is impacted by the micro-station compliance, the most important dynamical characteristic that should be well modeled is the overall compliance of the micro-station.
As the dynamics of the active platform is impacted by the micro-station compliance (see Section ref:sec:uniaxial_support_compliance), the most important dynamical characteristic that should be well modeled is the overall compliance of the micro-station.
To do so, the 6-DoF compliance of the micro-station is measured and then compared with the 6-DoF compliance extracted from the multi-body model (Section\nbsp{}ref:ssec:ustation_model_compliance).
**** Multi-Body Model
@ -4910,8 +4906,6 @@ Although various numerical methods exist for solving this problem, they can be c
For the active platform application, where displacements are typically small, an approximate solution based on linearization around the operating point provides a practical alternative.
This approximation, which is developed in subsequent sections through the Jacobian matrix analysis, is particularly useful for real-time control applications.
# TODO - Add references
**** The Jacobian Matrix
<<ssec:nhexa_stewart_platform_jacobian>>
***** Introduction :ignore:
@ -6165,8 +6159,7 @@ Third, the optimization of controllers for decoupled plants is discussed, introd
Section\nbsp{}ref:sec:detail_instrumentation focuses on instrumentation selection using a dynamic error budgeting approach to establish maximum acceptable noise specifications for each component.
The selected instrumentation is then experimentally characterized to verify compliance with these specifications, ensuring that the combined effect of all noise sources remains within acceptable limits.
# TODO - Refine this part when the corresponding section is fully written
The chapter concludes with a concise presentation of the obtained optimized active platform design, called the "nano-hexapod", in Section\nbsp{}ref:sec:detail_design, summarizing how the various optimizations contribute to a system that balances the competing requirements of precision positioning, vibration isolation, and practical implementation constraints.
The chapter concludes with a concise presentation of the obtained optimized active platform design, called the "nano-hexapod" (Section\nbsp{}ref:sec:detail_design).
With the detailed design completed and components procured, the project advances to the experimental validation phase, which will be addressed in the subsequent chapter.
** Optimal Active Platform Geometry
@ -6209,13 +6202,11 @@ Since then, the Stewart platform (sometimes referred to as the Stewart-Gough pla
#+end_subfigure
#+end_figure
# TODO - Section\nbsp{}ref:sec:nhexa_stewart_platform
As explained in the conceptual phase, Stewart platforms comprise the following key elements: two plates connected by six struts, with each strut composed of a joint at each end, an actuator, and one or several sensors.
As explained in Section\nbsp{}ref:sec:nhexa_stewart_platform, Stewart platforms comprise the following key elements: two plates connected by six struts, with each strut composed of a joint at each end, an actuator, and one or several sensors.
# TODO -\nbsp{}ref:sec:detail_fem_joint
The specific geometry (i.e., position of joints and orientation of the struts) can be selected based on the application requirements, resulting in numerous designs throughout the literature.
This discussion focuses primarily on Stewart platforms designed for nano-positioning and vibration control, which necessitates the use of flexible joints.
The implementation of these flexible joints, will be discussed when designing the active platform flexible joints.
The implementation of these flexible joints, will be discussed when designing the active platform flexible joints in Section\nbsp{}ref:sec:detail_fem_joint.
Long stroke Stewart platforms are not addressed here as their design presents different challenges, such as singularity-free workspace and complex kinematics\nbsp{}[[cite:&merlet06_paral_robot]].
In terms of actuation, mainly two types are used: voice coil actuators and piezoelectric actuators.
@ -6310,8 +6301,7 @@ The influence of strut orientation and joint positioning on Stewart platform pro
<<sec:detail_kinematics_geometry>>
**** Introduction :ignore:
# TODO - Section\nbsp{}ref:sec:nhexa_stewart_platform (page\nbsp{}pageref:sec:nhexa_stewart_platform),
As was demonstrated during the conceptual phase, the geometry of the Stewart platform impacts the stiffness and compliance characteristics, the mobility (or workspace), the force authority, and the dynamics of the manipulator.
As was demonstrated in Section\nbsp{}ref:sec:nhexa_stewart_platform, the geometry of the Stewart platform impacts the stiffness and compliance characteristics, the mobility (or workspace), the force authority, and the dynamics of the manipulator.
It is therefore essential to understand how the geometry impacts these properties, and to develop methodologies for optimizing the geometry for specific applications.
A useful analytical tool for this study is the Jacobian matrix, which depends on $\bm{b}_i$ (joints' position with respect to the top platform) and $\hat{\bm{s}}_i$ (struts' orientation).
@ -6896,8 +6886,7 @@ When the cube size $H_c$ is smaller than twice the height of the CoM $H_{CoM}$ e
H_c < 2 H_{CoM}
\end{equation}
# TODO - Add link to Figure\nbsp{}ref:fig:nhexa_stewart_piezo_furutani (page\nbsp{}pageref:fig:nhexa_stewart_piezo_furutani)
This configuration is similar to that described in\nbsp{}[[cite:&furutani04_nanom_cuttin_machin_using_stewar]], although they do not explicitly identify it as a cubic configuration.
This configuration is similar to that described in\nbsp{}[[cite:&furutani04_nanom_cuttin_machin_using_stewar]] (Figure\nbsp{}ref:fig:nhexa_stewart_piezo_furutani, page\nbsp{}pageref:fig:nhexa_stewart_piezo_furutani), although they do not explicitly identify it as a cubic configuration.
Adjacent struts are parallel to each other, differing from the typical architecture where parallel struts are positioned opposite to each other.
This approach yields a compact architecture, but the small cube size may result in insufficient rotational stiffness.
@ -7082,8 +7071,7 @@ The positioning angles, as shown in Figure\nbsp{}ref:fig:detail_kinematics_nano_
The resulting geometry is illustrated in Figure\nbsp{}ref:fig:detail_kinematics_nano_hexapod.
While minor refinements may occur during detailed mechanical design to address manufacturing and assembly considerations, the fundamental geometry will remain consistent with this configuration.
This geometry serves as the foundation for estimating required actuator stroke (Section\nbsp{}ref:ssec:detail_kinematics_nano_hexapod_actuator_stroke), determining flexible joint stroke requirements (Section\nbsp{}ref:ssec:detail_kinematics_nano_hexapod_joint_stroke), performing noise budgeting for instrumentation selection, and developing control strategies.
# TODO - Add link to sections
This geometry serves as the foundation for estimating the required actuator stroke (Section\nbsp{}ref:ssec:detail_kinematics_nano_hexapod_actuator_stroke), flexible joint stroke (Section\nbsp{}ref:ssec:detail_kinematics_nano_hexapod_joint_stroke) and to perform noise budgeting for instrumentation selection (Section\nbsp{}ref:sec:detail_instrumentation).
Implementing a cubic architecture as proposed in Section\nbsp{}ref:ssec:detail_kinematics_cubic_design was considered.
However, positioning the cube's center $150\,\text{mm}$ above the top platform would have resulted in platform dimensions exceeding the maximum available size.
@ -13525,8 +13513,7 @@ For this specific measurement, an enhanced high authority controller (discussed
Figure\nbsp{}ref:fig:test_id31_hac_cas_cl presents the cumulative amplitude spectra of the position errors for all three cases.
The results reveal two distinct control contributions: the decentralized IFF effectively attenuates vibrations near the nano-hexapod suspension modes (an achievement not possible with HAC alone), while the high authority controller suppresses low-frequency vibrations primarily arising from Spindle guiding errors.
Notably, the spectral patterns in Figure\nbsp{}ref:fig:test_id31_hac_cas_cl closely resemble the cumulative amplitude spectra computed in the project's early stages.
# TODO - Add link to initial noise budget?
Notably, the spectral patterns in Figure\nbsp{}ref:fig:test_id31_hac_cas_cl closely resemble the cumulative amplitude spectra computed in the project's early stages (Figure\nbsp{}ref:fig:uniaxial_cas_hac_lac_mid in page\nbps{}pageref:fig:uniaxial_cas_hac_lac_mid).
This experiment also illustrates that when needed, performance can be enhanced by designing controllers for specific experimental conditions rather than relying solely on robust controllers that can accommodate all payload ranges.
@ -13812,8 +13799,7 @@ Alternatively, a feedforward controller could improve the lateral positioning ac
**** Feedback Control using Complementary Filters
<<ssec:test_id31_cf_control>>
# TODO - Add link to section
A control architecture based on complementary filters to shape the closed-loop transfer functions was proposed during the detail design phase.
A control architecture based on complementary filters to shape the closed-loop transfer functions was proposed during the detail design phase (Section\nbsp{}ref:sec:detail_control_cf).
Experimental validation of this architecture using the NASS is presented herein.
Given that performance requirements are specified in the Cartesian frame, decoupling of the plant within this frame was achieved using Jacobian matrices.
@ -13825,11 +13811,9 @@ A schematic of the proposed control architecture is illustrated in Figure\nbsp{}
#+caption: Control architecture in the Cartesian frame. Only the controller corresponding to the $D_z$ direction is shown. $H_L$ and $H_H$ are complementary filters.
[[file:figs/test_id31_cf_control.png]]
# TODO - Add link to 2DoF model
Implementation of this control architecture necessitates a plant model, which must subsequently be inverted.
This plant model was derived from the multi-body model incorporating the previously detailed 2-DoF acrshort:apa model, such that the model order stays relatively low.
Proposed analytical formulas for complementary filters having $40\,\text{dB/dec}$ were used during this experimental validation.
# TODO - Add link to the analytical formulas
This plant model was derived from the multi-body model incorporating the previously detailed 2-DoF acrshort:apa (Section\nbsp{}ref:sec:test_apa_model_2dof) model and 4-DoF flexible joints, such that the model order stays relatively low.
Analytical formulas for complementary filters having $40\,\text{dB/dec}$ slopes, proposed in Section\nbsp{}ref:ssec:detail_control_cf_analytical_complementary_filters, were used during this experimental validation.
An initial experimental validation was conducted under no-payload conditions, with control applied solely to the $D_y$, $D_z$, and $R_y$ directions.
Increased control bandwidth was achieved for the $D_z$ and $R_y$ directions through appropriate tuning of the parameter $\omega_0$.