Review from O.B.

Remove some parentheses
Corrected labels
2025-07-09 19:46:10 +02:00 · 2025-07-08 18:54:04 +02:00 · 2025-07-04 22:06:06 +02:00 · 2025-07-04 17:03:36 +02:00 · 2025-07-04 16:14:09 +02:00 · 2025-07-04 11:37:31 +02:00
19 changed files with 1377 additions and 1083 deletions
--- a/figs/chapter1_overview.pdf
+++ b/figs/chapter1_overview.pdf
--- a/figs/chapter1_overview.png
+++ b/figs/chapter1_overview.png
--- a/figs/detail_fem_apa95ml_mesh.pdf
+++ b/figs/detail_fem_apa95ml_mesh.pdf
--- a/figs/detail_fem_apa95ml_mesh.png
+++ b/figs/detail_fem_apa95ml_mesh.png
--- a/figs/inkscape/chapter1_overview.svg
+++ b/figs/inkscape/chapter1_overview.svg
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@@ -3037,14 +3037,14 @@
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-         style="font-size:3.52778px;stroke-width:0.264583"
-         x="43.176926"
-         y="113.7602">Nano-Hexapod</tspan></text><text
+         style="font-size:3.52778px;text-align:center;text-anchor:middle;stroke-width:0.264583"
+         x="54.679256"
+         y="113.7602">Active Platform</tspan></text><text
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--- a/figs/inkscape/detail_fem_apa95ml_mesh.svg
+++ b/figs/inkscape/detail_fem_apa95ml_mesh.svg
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--- a/figs/nass_soft_nano_hexapod_effect_Wz.pdf
+++ b/figs/nass_soft_nano_hexapod_effect_Wz.pdf
--- a/figs/nass_soft_nano_hexapod_effect_Wz.png
+++ b/figs/nass_soft_nano_hexapod_effect_Wz.png
--- a/figs/rotating_root_locus_iff_pure_int.pdf
+++ b/figs/rotating_root_locus_iff_pure_int.pdf
--- a/figs/rotating_root_locus_iff_pure_int.png
+++ b/figs/rotating_root_locus_iff_pure_int.png
--- a/figs/test_apa_frf_encoder.pdf
+++ b/figs/test_apa_frf_encoder.pdf
--- a/figs/test_apa_frf_encoder.png
+++ b/figs/test_apa_frf_encoder.png
--- a/figs/test_apa_frf_force.pdf
+++ b/figs/test_apa_frf_force.pdf
--- a/figs/test_apa_frf_force.png
+++ b/figs/test_apa_frf_force.png
--- a/phd-thesis.bib
+++ b/phd-thesis.bib
@@ -1954,6 +1954,8 @@
  number          = 10,
  pages           = {895--913},
  year            = 1976,
+  doi             = {10.1016/0020-7225(76)90102-6},
+  url             = {https://doi.org/10.1016/0020-7225(76)90102-6},
  publisher       = {Elsevier},
 }

@@ -1968,5 +1970,26 @@
  doi             = {10.1016/0045-7825(92)90112-W},
  url             =
                  {https://www.sciencedirect.com/science/article/pii/004578259290112W},
-  issn            = {0045-7825},
+}
+
+@article{macneal71_hybrid_method_compon_mode_synth,
+  author          = {MacNeal, Richard H},
+  title           = {A Hybrid Method of Component Mode Synthesis},
+  journal         = {Computers \& Structures},
+  volume          = 1,
+  number          = 4,
+  pages           = {581--601},
+  year            = 1971,
+  doi             = {10.1016/0045-7949(71)90031-9},
+  url             = {https://doi.org/10.1016/0045-7949(71)90031-9},
+  publisher       = {Elsevier},
+}
+
+@software{matlab_r2022a,
+  year            = {2022},
+  author          = {The MathWorks Inc.},
+  title           = {MATLAB R2022a},
+  publisher       = {The MathWorks Inc.},
+  address         = {Natick, Massachusetts, United States},
+  url             = {https://www.mathworks.com}
 }
--- a/phd-thesis.org
+++ b/phd-thesis.org
@@ -3489,7 +3489,7 @@ The position of each accelerometer with respect to the acrlong:com of the corres

 #+name: tab:modal_com_solid_bodies
 #+caption: Center of mass of considered solid bodies with respect to the acrlong:poi.
-#+attr_latex: :environment tabularx :width 0.5\linewidth :align Xccc
+#+attr_latex: :environment tabularx :width 0.6\linewidth :align Xccc
 #+attr_latex: :center t :booktabs t
 |                     | $X$             | $Y$              | $Z$                |
 |---------------------+-----------------+------------------+--------------------|
@@ -3757,6 +3757,10 @@ To do so, the effects of these disturbances were first measured experimentally a

 To validate the accuracy of the micro-station model, "real world" experiments are simulated and compared with measurements in Section\nbsp{}ref:sec:ustation_experiments.

+The multi-body software used in this work is Simscape\nbsp{}[[cite:&matlab_r2022a]].
+This environment was chosen because it is fully integrated within Matlab/Simulink, which provides a comprehensive suite of tools for control analysis and synthesis.
+Moreover, the Speedgoat real-time target machine used in the experimental phase is programmed directly from Simulink, ensuring seamless transition from simulation to real-time implementation.
+
 *** Micro-Station Kinematics
 <<sec:ustation_kinematics>>
 **** Introduction                                                      :ignore:
@@ -7117,7 +7121,7 @@ Through this approach, system-level dynamic behavior under closed-loop control c

 Components exhibiting complex dynamical behavior are frequently found to be unsuitable for direct implementation within multi-body models.
 These components are traditionally analyzed using acrshort:fea software.
-However, a methodological bridge between these two analytical approaches has been established, whereby components whose dynamical properties have been determined through FEA can be integrated into multi-body models\nbsp{}[[cite:&hatch00_vibrat_matlab_ansys]].
+However, a methodological bridge between these two analytical approaches has been established, whereby components whose dynamical properties have been determined through FEA can be integrated into multi-body models\nbsp{}[[cite:&de76_dynam_flexib_bodies;&cardona92_super_formul_mechan_analy;&hatch00_vibrat_matlab_ansys]].
 This combined multibody-FEA modeling approach presents significant advantages, as it enables the accurate FE modeling to specific elements while maintaining the computational efficiency of multi-body analysis for the broader system\nbsp{}[[cite:&rankers98_machin]].

 The investigation of this hybrid modeling approach is structured in three sections.
@@ -7129,7 +7133,7 @@ Finally, the validity of this modeling approach is demonstrated through experime
 <<ssec:detail_fem_super_element_theory>>

 In this modeling approach, some components within the multi-body framework are represented as /reduced-order flexible bodies/, wherein their modal behavior is characterized through reduced mass and stiffness matrices derived from acrshort:fea models.
-These matrices are generated via modal reduction techniques, specifically through the application of component mode synthesis, thus establishing this design approach as a combined multibody-FEA methodology.
+These matrices are generated via modal reduction techniques, specifically through the application of component mode synthesis, thus establishing this design approach as a combined multibody-FEA methodology\nbsp{}[[cite:&macneal71_hybrid_method_compon_mode_synth]].

 Standard FEA implementations typically involve thousands or even hundreds of thousands of degrees of freedom, rendering direct integration into multi-body simulations computationally prohibitive.
 The objective of modal reduction is therefore to substantially decrease the number of degrees of freedom while preserving the essential dynamic characteristics of the component.
@@ -9193,8 +9197,8 @@ For these cases, the complementary filters analytical formula in Equation\nbsp{}

 \begin{subequations}\label{eq:detail_control_cf_2nd_order}
  \begin{align}
-    H_L(s) &= \frac{(1+\alpha) (\frac{s}{\omega_0})+1}{\left((\frac{s}{\omega_0})+1\right) \left((\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1\right)}\\
-    H_H(s) &= \frac{(\frac{s}{\omega_0})^2 \left((\frac{s}{\omega_0})+1+\alpha\right)}{\left((\frac{s}{\omega_0})+1\right) \left((\frac{s}{\omega_0})^2 + \alpha (\frac{s}{\omega_0}) + 1\right)}
+    H_L(s) &= \frac{(1+\alpha) (\frac{s}{\omega_0})+1}{\left(\frac{s}{\omega_0}+1\right) \left((\frac{s}{\omega_0})^2 + \alpha \frac{s}{\omega_0} + 1\right)}\\
+    H_H(s) &= \frac{(\frac{s}{\omega_0})^2 \left(\frac{s}{\omega_0}+1+\alpha\right)}{\left(\frac{s}{\omega_0}+1\right) \left((\frac{s}{\omega_0})^2 + \alpha \frac{s}{\omega_0} + 1\right)}
  \end{align}
 \end{subequations}

@@ -13252,11 +13256,11 @@ This design choice, while beneficial for system simplicity, introduces inherent

 A diagonal controller was designed to be robust against changes in payload mass, which means that every damped plant shown in Figure\nbsp{}ref:fig:test_id31_comp_all_undamped_damped_plants must be considered during the controller design.
 For this controller design, a crossover frequency of $5\,\text{Hz}$ was chosen to limit the multivariable effects, as explain in Section\nbsp{}ref:sec:test_id31_hac_interaction_analysis.
-One integrator is added to increase the low-frequency gain, a lead is added around $5\,\text{Hz}$ to increase the stability margins and a first-order low-pass filter with a cut-off frequency of $30\,\text{Hz}$ is added to improve the robustness to dynamical uncertainty at high-frequency.
+One integrator is added to increase the low-frequency gain and a first-order low-pass filter with a cut-off frequency of $30\,\text{Hz}$ is added to improve the robustness to dynamical uncertainty at high-frequency.
 The controller transfer function is shown in\nbsp{}eqref:eq:test_id31_robust_hac.

 \begin{equation}\label{eq:test_id31_robust_hac}
-K_{\text{HAC}}(s) = g_0 \cdot \underbrace{\frac{\omega_c}{s}}_{\text{int}} \cdot \underbrace{\frac{1}{\sqrt{\alpha}}\frac{1 + \frac{s}{\omega_c/\sqrt{\alpha}}}{1 + \frac{s}{\omega_c\sqrt{\alpha}}}}_{\text{lead}} \cdot \underbrace{\frac{1}{1 + \frac{s}{\omega_0}}}_{\text{LPF}}, \quad \left( \omega_c = 2\pi5\,\text{rad/s},\ \alpha = 2,\ \omega_0 = 2\pi30\,\text{rad/s} \right)
+K_{\text{HAC}}(s) = g_0 \cdot \underbrace{\frac{\omega_c}{s}}_{\text{int}} \cdot \underbrace{\frac{1}{1 + \frac{s}{\omega_0}}}_{\text{LPF}}, \quad \left( \omega_c = 2\pi5\,\text{rad/s},\ \omega_0 = 2\pi30\,\text{rad/s} \right)
 \end{equation}

 The obtained "decentralized" loop-gains (i.e. the diagonal element of the controller times the diagonal terms of the plant) are shown in Figure\nbsp{}ref:fig:test_id31_hac_loop_gain.
@@ -13332,7 +13336,7 @@ The multi-body model was first validated by comparing it with the measured frequ
 This validation confirmed that the model can be reliably used to tune the feedback controller and evaluate its performance.

 An interaction analysis using the RGA-number was then performed, which revealed that higher payload masses lead to increased coupling when implementing control in the strut reference frame.
-Based on this analysis, a diagonal controller with a crossover frequency of $5\,\text{Hz}$ was designed, incorporating an integrator, a lead compensator, and a first-order low-pass filter.
+Based on this analysis, a diagonal controller with a crossover frequency of $5\,\text{Hz}$ was designed, incorporating an integrator and a first-order low-pass filter.

 Finally, tomography experiments were simulated to validate the acrshort:haclac architecture.
 The closed-loop system remained stable under all tested payload conditions (0 to $39\,\text{kg}$).
@@ -13915,34 +13919,54 @@ With the implementation of an accurate online metrology system, the NASS will be
 ** 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 $50\,\text{kg}$.
+The primary objective of this research was to enhance the positioning accuracy of the ID31 micro-station by approximately two orders of magnitude, to enable 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.
+Integrated with an external online metrology system and a 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.
+
+A rigorous and comprehensive mechatronic design methodology was consistently applied throughout the NASS development lifecycle.
+While the mechatronic approach itself is established, its thorough application in this thesis, from initial concept evaluation using simplified models to detailed design optimization and experimental validation informed by increasingly sophisticated models, offers useful insights into the existing literature.
+This documented process illustrates how models of varying complexity can be effectively used at different project phases, and how design decisions were systematically based on quantitative model predictions and analyses.

 The conceptual design phase rigorously evaluated the feasibility of the NASS concept.
+A key original contribution of this work lies in the extension of active vibration control from traditional one or two degrees of freedom to a six degrees of freedom for a continuously rotating platform.
 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.
+It was determined that an active platform with moderate stiffness offered an optimal compromise, with good decoupling from the micro-station dynamics while mitigating gyroscopic effects induced by the spindle 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 acrfull:haclac strategy.
-This strategy used 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.
+The Stewart platform architecture was selected for the active stage, and its viability was confirmed through closed-loop simulations employing a acrfull:haclac strategy, demonstrating the NASS concept could meet the nanometer-level stability requirements under realistic operating conditions.
+
+An original contribution was made in the area of active damping for rotating mechanical systems using acrfull:iff.
+It was found that the guaranteed stability property of the established acrshort:iff technique is compromised when applied to rotating platforms like the NASS.
+To address this, two specific modifications to the classical IFF control scheme were proposed and analyzed: one involving a minor adjustment to the control law itself, and the second incorporating physical springs in parallel with the force sensors.
+Stability conditions and optimal parameter tuning guidelines were derived for both modified schemes.

 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 acrfull:fea with multi-body dynamics simulation was applied and experimentally validated.
-This approach enabled detailed optimization of components, such as acrfull:apa and flexible joints, while efficiently simulating the complete system dynamics.
-By dedicating one stack of the acrshort:apa specifically to force sensing, excellent collocation with the actuator stacks was achieved, which is critical for implementing robust decentralized IFF.
-Work was also undertaken on the optimization of the control strategy for the active platform.
+Furthermore, a hybrid modeling technique combining acrfull:fea with multi-body dynamics simulation was applied and experimentally validated.
+This approach enabled detailed optimization of components, such as the acrfull:apa and the flexible joint, while efficiently simulating the complete system dynamics.
+
+Robustness was embedded directly into the active platform's design, rather than solely relying on complex post-design control synthesis techniques.
+This involved model-based evaluation of active stage designs to identify architectures inherently easier to control and the incorporation of collocated actuator/sensor pairs to leverage passivity-based guaranteed stability.
+Additionally, decoupling strategies for parallel manipulators were compared, addressing a topic identified as having limited treatment in the literature.
+This design approach facilitated the use of robust, readily tunable, and easily maintained controllers that met the specified performance targets.
+
+For implementing sensor fusion, a novel method for designing complementary filters using $\mathcal{H}_{\infty}\text{-synthesis}$ techniques was developed.
+This method allows explicit shaping of the filter norms, providing guarantees on the performance of the sensor fusion process.
+
 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.
+Component tests confirmed the performance of the selected actuators and flexible joints, and allowed for the refinement of 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, using a short-stroke metrology system to assess performance under realistic experimental conditions.
-These tests demonstrated that the NASS, operating with the implemented acrshort:haclac 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.
+
+The work culminated in the experimental validation of the complete NASS on the ID31 beamline.
+Experimental results demonstrated that the NASS, operating with the implemented acrshort:haclac 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 sample mass and diverse experimental conditions was verified.
+
+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, uniquely combining high mobility, high payload capacity with nanometer-level accuracy.
+
+The NASS enables the optimal use of the advanced capabilities of the ESRF-EBS beam, thereby opening new scientific opportunities on the ID31 beamline.

 ** Perspectives

--- a/phd-thesis.pdf
+++ b/phd-thesis.pdf
--- a/phd-thesis.tex
+++ b/phd-thesis.tex
Author	SHA1	Message	Date
Thomas Dehaeze	6930beb9bb	Review from O.B.	2025-07-09 19:46:10 +02:00
Thomas Dehaeze	2e3115bf49	Remove some parentheses	2025-07-08 18:54:04 +02:00
Thomas Dehaeze	61a74a1730	Corrected labels	2025-07-04 22:06:06 +02:00
Thomas Dehaeze	7b2f38625b	Enlarge table	2025-07-04 17:03:36 +02:00
Thomas Dehaeze	503c99a599	Add omega_0 in the figures	2025-07-04 16:14:09 +02:00
Thomas Dehaeze	50cc4dfade	Nano-Hexapod => Active Platform	2025-07-04 11:37:31 +02:00
Thomas Dehaeze	ca778a7824	Recompute 2 figures	2025-07-03 10:23:19 +02:00
Thomas Dehaeze	2c431f46d8	Remove the "lead" in the HAC	2025-07-03 10:22:56 +02:00