% Created 2024-05-30 Thu 15:40
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\input{preamble.tex}
\input{preamble_extra.tex}
\bibliography{nass-introduction.bib}
\author{Dehaeze Thomas}
\date{\today}
\title{Nano Active Stabilization System - Introduction}
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 pdfauthor={Dehaeze Thomas},
 pdftitle={Nano Active Stabilization System - Introduction},
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\usepackage{biblatex}

\begin{document}

\maketitle
\tableofcontents

\clearpage

\chapter{Context of this thesis}
\section{Synchrotron Radiation Facilities}
\paragraph{Accelerating electrons to produce intense X-ray}

\begin{itemize}
\item Explain what is a Synchrotron: light source
\item Say how many there are in the world (\textasciitilde{}50). The main ones are shown in Figure \ref{fig:introduction_synchrotrons}.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/introduction_synchrotrons.png}
\caption{\label{fig:introduction_synchrotrons}Major synchrotron radiation facilities in the world. 3rd generation Synchrotrons are shown in blue. Planned upgrades to 4th generation are shown in green, and 4th generation Synchrotrons in operation are shown in red.}
\end{figure}

\begin{itemize}
\item Electron part: LINAC, Booster, Storage Ring \ref{fig:introduction_esrf_schematic}
\item Synchrotron radiation: Insertion device / Bending magnet
\item Many beamlines (large diversity in terms of instrumentation and science)
\item Science that can be performed:
\begin{itemize}
\item structural biology, structure of materials, matter at extreme, \ldots{}
\end{itemize}
\end{itemize}

\paragraph{The European Synchrotron Radiation Facility}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_esrf_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_esrf_schematic} Schematic of the ESRF. The linear accelerator is shown in blue, the booster synchrotron in purple and the storage ring in green. There are over 40 beamlines, the ID31 beamline is highlighted in red}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_esrf_picture.jpg}
\end{center}
\subcaption{\label{fig:introduction_esrf_picture} European Synchrotron Radiation Facility}
\end{subfigure}
\caption{\label{fig:instroduction_esrf}Schematic (\subref{fig:introduction_esrf_schematic}) and picture (\subref{fig:introduction_esrf_picture}) of the European Synchrotron Radiation Facility}
\end{figure}

\paragraph{3rd and 4th generation Synchrotrons}

Brilliance: figure of merit for synchrotron

\begin{itemize}
\item 4th generation light sources \cite{raimondi21_commis_hybrid_multib_achrom_lattic}
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_moore_law_brillance.png}
\caption{\label{fig:introduction_moore_law_brillance}Evolution of the peak brilliance (expressed in \(\text{photons}/s/mm^2/mrad^2/0.1\%BW\)) of synchrotron radiation facilities. Note the vertical logarithmic scale.}
\end{figure}

\section{The ID31 ESRF Beamline}
\paragraph{Beamline Layout}

\begin{itemize}
\item General layout: source (insertion device), optical hutches (OH1, OH2), experimental hutch (EH)
\item Beamline layout (OH Figure \ref{fig:introduction_id31_oh}, EH \ref{fig:introduction_id31_cad})
All these optical instruments are used to ``shape'' the x-ray beam as wanted (monochromatic, wanted size, focused, etc\ldots{})
\item ID31 and Micro Station (Figure \ref{fig:introduction_id31_cad})
Check \url{https://www.esrf.fr/UsersAndScience/Experiments/StructMaterials/ID31}
\url{https://www.wayforlight.eu/beamline/23244}
\item X-ray beam + detectors + sample stage
\item Focusing optics
\item Optical schematic with: source, lens, sample and detector.
Explain that what is the most important is the relative position between the sample and the lens.
\item Explain the XYZ frame for all the thesis (ESRF convention: X: x-ray, Z gravity up)
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/introduction_id31_oh1.png}
\end{center}
\subcaption{\label{fig:introduction_id31_oh1}OH1}
\end{subfigure}

\bigskip
\begin{subfigure}{\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/introduction_id31_oh2.png}
\end{center}
\subcaption{\label{fig:introduction_id31_oh2}OH2}
\end{subfigure}
\caption{\label{fig:introduction_id31_oh}Schematic of the two ID31 optical hutches: OH1 (\subref{fig:introduction_id31_oh1}) and OH2 (\subref{fig:introduction_id31_oh2}). Distance from the source (the insertion device) is indicated in meters.}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.8\linewidth]{figs/introduction_id31_station_detector.png}
\caption{\label{fig:introduction_id31_cad}CAD view of the ID31 Experimal Hutch (EH). There are typically four main elements: the focusing optics in yellow, the sample stage in green, the sample itself in purple and the detector in blue. All these elements are fixed to the same granite.}
\end{figure}

\paragraph{Positioning End Station: The Micro-Station}

Micro-Station:
\begin{itemize}
\item DoF with strokes: Ty, Ry, Rz, Hexapod
\item Experiments: tomography, reflectivity, truncation rod, \ldots{}
Make a table to explain the different ``experiments''
\item Explain how it is used (positioning, scans), what it does. But not about the performances
\item Different sample environments
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_micro_station_dof.png}
\end{center}
\subcaption{\label{fig:introduction_micro_station_dof} CAD view}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_micro_station_picture.png}
\end{center}
\subcaption{\label{fig:introduction_micro_station_picture} Picture}
\end{subfigure}
\caption{\label{fig:introduction_micro_station}The micro-station. CAD view is shown in (\subref{fig:introduction_micro_station_dof}) with the associated degrees of freedom. A picture of the micro-station is shown in (\subref{fig:introduction_micro_station_picture}) during the assembly process.}
\end{figure}

\paragraph{Scientific experiments performed on ID31}

\begin{itemize}
\item Few words about science made on ID31 and why nano-meter accuracy is required
\item Typical experiments (tomography, \ldots{}), various samples (up to 50kg), sample environments (high temp, cryo, etc..)
\begin{itemize}
\item Alignment of the sample, then
\item Reflectivity
\item Tomography
\item Diffraction tomography: most critical
\end{itemize}
\item Two example:
\begin{itemize}
\item Tomography: compute image as a function of the angle. To reconstruct 3D image, the position has to be known with good accuracy
\cite{schoeppler17_shapin_highl_regul_glass_archit}
\item Mapping: focused beam on the sample, 20nm step size, accuracy of the obtained image is directly linked to the beam size and the position accuracy/vibrations
\cite{sanchez-cano17_synch_x_ray_fluor_nanop}
\end{itemize}
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.65\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_tomography_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_tomography_schematic} Experimental setup}
\end{subfigure}
\begin{subfigure}{0.34\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_tomography_picture.png}
\end{center}
\subcaption{\label{fig:introduction_tomography_results} Obtained image \cite{schoeppler17_shapin_highl_regul_glass_archit}}
\end{subfigure}
\caption{\label{fig:introduction_tomography}Exemple of a tomography experiment. The sample is rotated and images are taken at several angles (\subref{fig:introduction_tomography_schematic}). Example of one 3D image obtained after tomography (\subref{fig:introduction_tomography_results}).}
\end{figure}


\begin{figure}[htbp]
\begin{subfigure}{0.65\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_scanning_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_scanning_schematic} Experimental setup}
\end{subfigure}
\begin{subfigure}{0.34\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_scanning_picture.png}
\end{center}
\subcaption{\label{fig:introduction_scanning_results} Obtained image \cite{sanchez-cano17_synch_x_ray_fluor_nanop}}
\end{subfigure}
\caption{\label{fig:introduction_scanning}Exemple of a scanning experiment. The sample is scanned in the Y-Z plane (\subref{fig:introduction_scanning_schematic}). Example of one 2D image obtained after scanning with a step size of 20nm (\subref{fig:introduction_scanning_results}).}
\end{figure}

\section{Need of Accurate Positioning End-Stations with High Dynamics}
\paragraph{A push towards brighter and smaller beams}

Improvement of both the light source and the instrumentation:
\begin{itemize}
\item EBS: smaller source + higher flux \ref{fig:introduction_beam_3rd_4th_gen}
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.69\textwidth}
\begin{center}
\includegraphics[scale=1,height=1.6cm]{figs/introduction_beam_3rd_gen.png}
\end{center}
\subcaption{\label{fig:introduction_beam_3rd_gen}$3^{rd}$ generation}
\end{subfigure}
\begin{subfigure}{0.29\textwidth}
\begin{center}
\includegraphics[scale=1,height=1.6cm]{figs/introduction_beam_4th_gen.png}
\end{center}
\subcaption{\label{fig:introduction_beam_4th_gen}$4^{th}$ generation}
\end{subfigure}
\caption{\label{fig:introduction_beam_3rd_4th_gen}View of the ESRF X-ray beam before the EBS upgrade (\subref{fig:introduction_beam_3rd_gen}) and after the EBS upgrade (\subref{fig:introduction_beam_4th_gen}). The brilliance is increased, whereas the horizontal size and emittance are reduced.}
\end{figure}

\begin{itemize}
\item ESRF Red Book (1987): very few beamline projects aiming even for 10 micron sized beams
Now optics exist for 10nm beams
\item Better focusing optic (add some links): beam size in the order of 10 to 20nm FWHM (reference) \ref{fig:introduction_moore_law_focus}
crossed silicon compound refractive lenses, KB mirrors [17], zone plates [18], or multilayer Laue lenses [19]
\cite{barrett16_reflec_optic_hard_x_ray}
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_moore_law_focus.png}
\caption{\label{fig:introduction_moore_law_focus}Evolution of the measured spot size for different hard x-ray focusing elements. CRL, KB, FZP, MLL}
\end{figure}

Higher flux density (+high energy of the ID31 beamline) => Radiation damage: needs to scan the sample quite fast with respect to the focused beam

\begin{itemize}
\item Allowed by better detectors: higher sampling rates and lower noise => possible to scan fast
\cite{hatsui15_x_ray_imagin_detec_synch_xfel_sourc}
\end{itemize}

\paragraph{New dynamical positioning needs}

``from traditional step by step scans to \emph{fly-scan}''

Fast scans + needs of high accuracy and stability => need mechatronics system with:
\begin{itemize}
\item accurate metrology
\item multi degree of freedom positioning systems
\item fast feedback loops
\end{itemize}

Shift from step by step scan to \emph{fly-scan} \cite{huang15_fly_scan_ptych}
\begin{itemize}
\item Much lower pixel size + large image => takes of lot of time if captured step by step.
Explain what is step by step scanning: move motors from point A to point B, stops, start detector acquisition, open shutter , close the shutter, move to point C, \ldots{}
\end{itemize}

\cite{xu23_high_nsls_ii}
\begin{quote}
In traditional step scan mode, each exposure position requires the system to stop prior to data acquisition, which may become a limiting factor when fast data collection is required.
Fly-scanning is chosen as a preferred solution that helps overcome such speed limitations [5, 6].
In fly-scan mode, the sample keeps moving and a triggering system generates trigger signals based on the position of the sample or the time elapsed.
The trigger signals are used to control detector exposure.
\end{quote}


\begin{figure}[htbp]
\begin{subfigure}{0.55\textwidth}
\begin{center}
\includegraphics[scale=1,height=6cm]{figs/introduction_scan_step.png}
\end{center}
\subcaption{\label{fig:introduction_scan_step} Step by step scan}
\end{subfigure}
\begin{subfigure}{0.44\textwidth}
\begin{center}
\includegraphics[scale=1,height=6cm]{figs/introduction_scan_fly.png}
\end{center}
\subcaption{\label{fig:introduction_scan_fly} Fly scan}
\end{subfigure}
\caption{\label{fig:introduction_scan_mode}Two acquisition modes. In step-by-step mode (\subref{fig:introduction_scan_step}), the motor moves at the wanted imaged position, the detector acquisition is started, the shutter is openned briefly to have the wanted exposition, the detector acquisition is stopped, and the motor can move to a new position. In \emph{fly-scan} mode (\subref{fig:introduction_scan_fly}), the shutter is openned during all the motion, and the detector is acquired only at the wanted positions, on the \emph{fly}.}
\end{figure}

Subject of this thesis: design of high performance positioning station with high dynamics and nanometer accuracy

\chapter{Challenge definition}
\section{Multi degrees of freedom, long stroke and highly accurate positioning end station}
\paragraph{Performance limitation of ``stacked-stages'' end-stations}

Typical positioning end station (Figure \ref{fig:introduction_translation_stage}):
\begin{itemize}
\item stacked stages
\item Ball-screw, linear guides, rotary motor
\end{itemize}

Explain the limitation of performances:
\begin{itemize}
\item Backlash, play, thermal expansion, guiding imperfections, \ldots{}
\item Give some numbers: straightness of the Ty stage for instance, change of \(0.1^oC\) with steel gives x nm of motion
\item Vibrations
\item Possibility to have linear/rotary encoders that correct the motion in the considered DoF, but does not change anything to the other 5DoF
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_translation_stage.png}
\caption{\label{fig:introduction_translation_stage}A classical translation stage composed of: a rotary motor and possibly reduction gears (in blue), a mechanism to transform the rotary motion to a translation (here a lead screw in green), a guiding mechanism (here linear rails and bearings in red). The mobile platform (in yellow) can then translate with respect to the fixed base.}
\end{figure}

Flexure based positioning stations may give better positioning requirements, but are limited to short stroke.
Advantages: no backlash, etc\ldots{}
But: limited to short stroke
Picture of schematic of one positioning station based on flexure

Explain example of Figure \ref{fig:introduction_flexure_stage}.

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_flexure_stage.png}
\caption{\label{fig:introduction_flexure_stage}A simple flexure stage}
\end{figure}

Combining, long stroke and accuracy in multi-DoF is challenging.

\paragraph{Positioning accuracy of the ID31 Micro-Station}

Presentation of the Micro-Station in details \ref{fig:introduction_micro_station}:
\begin{itemize}
\item Goal of each stage (e.g. micro-hexapod: static positioning, Ty and Rz: scans, \ldots{})
\item Stroke
\item Initial design objectives: as stiff as possible, smallest errors as possible
\end{itemize}

Explain that this micro-station can only have \textasciitilde{}10um / 10urad of accuracy due to physical limitation.

\paragraph{New positioning requirements}

\begin{itemize}
\item To benefits from nano-focusing optics, new source, etc\ldots{} new positioning requirements
\item Positioning requirements on ID31:
\begin{itemize}
\item Maybe make a table with the requirements and the associated performances of the micro-station
\item Make tables with the wanted motion, stroke, accuracy in different DoF, etc..
\end{itemize}
\item Sample masses
\end{itemize}

The goal in this thesis is to increase the positioning accuracy of the micro-station to fulfil the initial positioning requirements.

\textbf{Goal}: Improve accuracy of 6DoF long stroke position platform

\section{The Nano Active Stabilization System}
\paragraph{NASS Concept}

In order to address the new positioning requirements, the concept of\ldots{}

Briefly describe the NASS concept.
6DoF vibration control platform on top of a complex positioning platform that correct positioning errors based on an external metrology

It is composed of mainly four elements:
\begin{itemize}
\item The micro station
\item A 5 degrees of freedom metrology system
\item A 5 or 6 degrees of freedom stabilization platform
\item Control system and associated instrumentation
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_nass_concept_schematic.png}
\caption{\label{fig:introduction_nass_concept_schematic}The Nano Active Stabilization System concept}
\end{figure}

\paragraph{Online Metrology system}

The accuracy of the NASS will only depend on the accuracy of the metrology system.

Requirements:
\begin{itemize}
\item 5 DoF
\item long stroke
\item nano-meter accurate
\item high bandwidth
\end{itemize}

Concept:
\begin{itemize}
\item Fiber interferometers
\item Spherical reflector with flat bottom
\item Tracking system (tip-tilt mechanism) to keep the beam perpendicular to the mirror surface: Spherical mirror with center at the point of interest => No Abbe errors

\item XYZ positions from at least 3 interferometers pointing at the spherical surface
\item Rx/Ry angles from at least 3 interferometers pointing at the bottom flat surface
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_nass_metrology.png}
\caption{\label{fig:introduction_nass_metrology}2D representation of the NASS metrology system.}
\end{figure}

Complex mechatronics system on its own.
This metrology system is not further discussed in this thesis as it is still under active development.
In the following of this thesis, it is supposed that the metrology system is accurate, etc..

\paragraph{Active Stabilization Platform}

\begin{itemize}
\item 5 DoF
\item High dynamics
\item Nano-meter capable (no backlash)
\item Accept payloads up to 50kg
\end{itemize}

\paragraph{MIMO robust control strategies}

Explain the robustness need?
\begin{itemize}
\item 24 7/7 \ldots{}
\item That is why most of end-stations are based on well-proven design (stepper motors, linear guides, ball bearing, \ldots{})
\item Plant uncertainty: many different samples, use cases, rotating velocities, etc\ldots{}
\end{itemize}

Trade-off between robustness and performance in the design of feedback system.

\section{Predictive Design}

\begin{itemize}
\item The performances of the system will depend on many factors:
\begin{itemize}
\item sensors
\item actuators
\item mechanical design
\item achievable bandwidth
\end{itemize}
\item Need to evaluate the different concepts, and predict the performances to guide the design
\item The goal is to design, built and test this system such that it work as expected the first time.
Very costly system, so must be correct.
\item Challenge:
\begin{itemize}
\item proper design methodology
\item accurate models
\end{itemize}
\end{itemize}

\section{Control Challenge}

High bandwidth, 6 DoF system for vibration control, fixed on top of a complex multi DoF positioning station, robust, \ldots{}

\begin{itemize}
\item Many different configurations (tomography, Ty scans, slow fast, \ldots{})
\item Complex MIMO system. Dynamics of the system could be coupled to the complex dynamics of the micro station
\item Rotation aspect, gyroscopic effects, actuators are rotating with respect to the sensors
\item Robustness to payload change: very critical.
Say that high performance systems (lithography machines, etc\ldots{}) works with calibrated payloads.
Being robust to change of payload inertia means large stability margins and therefore less performance.
\end{itemize}

\chapter{Literature Review}
\section{Nano Positioning End-Stations}
\paragraph{End-Station with Stacked Stages}

Stacked stages:
\begin{itemize}
\item errors are combined
\end{itemize}

To have acceptable performances / stability:
\begin{itemize}
\item limited number of stages
\item high performances stages (air bearing etc\ldots{})
\end{itemize}

Examples:
\begin{itemize}
\item ID01 \cite{leake19_nanod_beaml_id01}
\item ID11 \cite{wright20_new_oppor_at_mater_scien}
\item ID13 \cite{riekel10_progr_micro_nano_diffr_at}
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_endstation_id16b.png}
\end{center}
\subcaption{\label{fig:introduction_endstation_id16b}ID16b}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_endstation_id11.png}
\end{center}
\subcaption{\label{fig:introduction_endstation_id11}ID11}
\end{subfigure}
\caption{\label{fig:introduction_passive_stations}Example of two nano end-stations without online metrology: (\subref{fig:introduction_endstation_id16b}) \cite{martinez-criado16_id16b} and (\subref{fig:introduction_endstation_id11}) \cite{wright20_new_oppor_at_mater_scien}}
\end{figure}

Explain limitations => Thermal drifts, run-out errors of spindles (improved by using air bearing), straightness of translation stages, \ldots{}

\paragraph{Online Metrology and Active Control of Positioning Errors}

The idea of having an external metrology to correct for errors is not new.

Several strategies:
\begin{itemize}
\item only used for measurements (post processing)
\item for calibration
\item for triggering detectors
\item for real time positioning control (Figure \ref{fig:introduction_active_stations})
\end{itemize}

Sensors:
\begin{itemize}
\item Capacitive: \cite{schroer17_ptynam,villar18_nanop_esrf_id16a_nano_imagin_beaml,schropp20_ptynam}
\item Fiber Interferometers Interferometers:
\begin{itemize}
\item Attocube FPS3010 Fabry-Pérot interferometers: \cite{nazaretski15_pushin_limit,stankevic17_inter_charac_rotat_stages_x_ray_nanot,engblom18_nanop_resul,nazaretski22_new_kirkp_baez_based_scann}
\item Attocube IDS3010 Fabry-Pérot interferometers: \cite{holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage,kelly22_delta_robot_long_travel_nano}
\item PicoScale SmarAct Michelson interferometers: \cite{schroer17_ptynam,schropp20_ptynam,xu23_high_nsls_ii,geraldes23_sapot_carnaub_sirius_lnls}
\end{itemize}
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stages_wang.png}
\end{center}
\subcaption{\label{fig:introduction_stages_wang} Wang}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stages_schroer.png}
\end{center}
\subcaption{\label{fig:introduction_stages_schroer} Schroer}
\end{subfigure}
\caption{\label{fig:introduction_metrology_stations}Two examples of end-station with integrated online metrology. (\subref{fig:introduction_stages_wang}) \cite{wang12_autom_marker_full_field_hard} and (\subref{fig:introduction_stages_schroer}) \cite{schroer17_ptynam}}
\end{figure}

For some applications (especially when using a nano-beam), the position has not only to be measured, but to be controlled.

\textbf{Actuators}:
\begin{itemize}
\item Piezoelectric: \cite{nazaretski15_pushin_limit,holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage,villar18_nanop_esrf_id16a_nano_imagin_beaml,nazaretski22_new_kirkp_baez_based_scann}
\item 3-phase linear motor: \cite{stankevic17_inter_charac_rotat_stages_x_ray_nanot,engblom18_nanop_resul}
\item Voice Coil: \cite{kelly22_delta_robot_long_travel_nano,geraldes23_sapot_carnaub_sirius_lnls}
\end{itemize}


Bandwidth: rarely specificity.
Usually slow, so that only drifts are compensated.
Only recently, high bandwidth (100Hz) have been reported with the use of voice coil actuators \cite{kelly22_delta_robot_long_travel_nano,geraldes23_sapot_carnaub_sirius_lnls}.

Full rotation for tomography:
\begin{itemize}
\item Spindle above XYZ stage: \cite{stankevic17_inter_charac_rotat_stages_x_ray_nanot,holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage,villar18_nanop_esrf_id16a_nano_imagin_beaml,engblom18_nanop_resul,nazaretski22_new_kirkp_baez_based_scann,xu23_high_nsls_ii}
\item Spindle bellow XYZ stage: \cite{wang12_autom_marker_full_field_hard,schroer17_ptynam,schropp20_ptynam,geraldes23_sapot_carnaub_sirius_lnls}
\end{itemize}
Only for mapping: \cite{nazaretski15_pushin_limit,kelly22_delta_robot_long_travel_nano}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_stages_villar.png}
\end{center}
\subcaption{\label{fig:introduction_stages_villar} ID16a}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stages_nazaretski.png}
\end{center}
\subcaption{\label{fig:introduction_stages_nazaretski} 1 and 2 are stage to position the focusing optics. 3 is the sample location, 4 the sample stage and 5 the interferometers}
\end{subfigure}
\caption{\label{fig:introduction_active_stations}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}}
\end{figure}

Payload capabilities:
\begin{itemize}
\item All are only supported calibrated, micron scale samples
\item Higher sample masses to up to 500g have been reported in \cite{nazaretski22_new_kirkp_baez_based_scann,kelly22_delta_robot_long_travel_nano}
\end{itemize}

100 times heavier payload capabilities than previous stations with similar performances.

\begin{table}[htbp]
\caption{\label{tab:introduction_active_stations}End-Stations with integrated feedback loops based on online metrology. Stages used for static positioning are ommited for readability. Stages used for feedback are indicated in bold font.}
\centering
\scriptsize
\begin{tabularx}{0.95\linewidth}{cccccc}
\toprule
\textbf{Architecture} & \textbf{Metrology} & \textbf{Stroke} & \textbf{Bandwidth} & \textbf{Institute} & \textbf{References}\\
\midrule
Mirror / Sample & 3 Interferometers &  &  & APS & \cite{nazaretski15_pushin_limit}\\
\textbf{XYZ piezo motors} & \(D_xD_yD_z\) & \(D_xD_yD_z: 3\,\text{mm}\) &  &  & Figure \ref{fig:introduction_stages_nazaretski}\\
\midrule
Metrology Ring / Sample & 12 Capacitive & light & 10 Hz & ESRF & \cite{villar18_nanop_esrf_id16a_nano_imagin_beaml}\\
Spindle & \(D_xD_yD_zR_xR_y\) & \(R_z: 180\,\text{deg}\) &  & (ID16a) & Figure \ref{fig:introduction_stages_villar}\\
\textbf{Piezo Hexapod} &  & \(D_xD_yD_z: 50\,\mu m\) &  &  & \\
 &  & \(R_x R_y: 500\,\mu \text{rad}\) &  &  & \\
\midrule
Spherical Reference / Sample & 5 Interferometers & light &  & PSI & \cite{holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage}\\
Spindle & \(D_yD_zR_x\) & \(R_z: 365\,\text{deg}\) &  & (OMNY) & \\
\textbf{Piezo Tripod} &  & \(D_xD_yD_z: 400\,\mu m\) &  &  & \\
\midrule
Cylindrical Reference / Sample & 5 Interferometers & light &  & Soleil & \cite{stankevic17_inter_charac_rotat_stages_x_ray_nanot,engblom18_nanop_resul}\\
Spindle & \(D_xD_yD_zR_xR_y\) & \(R_z: 360\,\text{deg}\) &  &  & \\
\textbf{Stacked XYZ linear motors} &  & \(D_xD_yD_z: 400\,\mu m\) &  &  & \\
\midrule
Metrology Ring / Sample & 3 Interferometers & up to 500g &  & NSLS & \cite{nazaretski22_new_kirkp_baez_based_scann}\\
Spindle & \(D_xD_yD_z\) & \(R_z: 360\,\text{deg}\) &  & (SRX) & \\
\textbf{XYZ piezo} &  & \(D_xD_yD_z: 100\,\mu m\) &  &  & \\
\midrule
Mirrors / Sample & 3 Interferometers & up to 350g & 100 Hz & Diamond & \cite{kelly22_delta_robot_long_travel_nano}\\
\textbf{Parallel XYZ voice coil} & \(D_xD_yD_z\) & \(D_xD_yD_z: 3\,\text{mm}\) &  & (I14) & \\
\midrule
Retroreflectors / Samples & 3 Interferometers & light & 100 Hz & LNLS & \cite{geraldes23_sapot_carnaub_sirius_lnls}\\
\textbf{Parallel XYZ voice coil} & \(D_xD_yD_z\) & \(D_yD_z: 3\,\text{mm}\) &  & (Carnauba) & \\
Spindle &  & \(R_z: \pm 110\,\text{deg}\) &  &  & \\
\midrule
Sample & 6 Interferometers & \textbf{up to 50kg} &  & ESRF & \cite{dehaeze18_sampl_stabil_for_tomog_exper,dehaeze21_mechat_approac_devel_nano_activ_stabil_system}\\
\textbf{Hexapod} & \(D_xD_yD_zR_xR_y\) &  &  & (ID31) & \\
Spindle &  & \(R_z : 360\,\text{deg}\) &  &  & \\
Ry &  & \(R_y : \pm 3\,\text{deg}\) &  &  & \\
Ty &  & \(D_y : \pm 5\,\text{mm}\) &  &  & \\
\bottomrule
\end{tabularx}
\end{table}


\paragraph{Long Stroke - Short Stroke architecture}

Speak about two stage control?
\begin{itemize}
\item Long stroke + short stroke
\item Usually applied to 1dof, 3dof (show some examples: disk drive, wafer scanner)
\item Any application in 6DoF? Maybe new!
\item In the table, say which ones are long stroke / short stroke. Some new stages are just long stroke (voice coil)
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_two_stage_schematic.png}
\caption{\label{fig:introduction_two_stage_schematic}Typical Long Stroke - Short Stroke architecture. The long stroke stage is \ldots{}}
\end{figure}

\begin{figure}[htbp]
\begin{subfigure}{0.59\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_two_stage_control_example.png}
\end{center}
\subcaption{\label{fig:introduction_two_stage_control_example} Two stage control with classical stage and voice coil}
\end{subfigure}
\begin{subfigure}{0.39\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_two_stage_control_h_bridge.png}
\end{center}
\subcaption{\label{fig:introduction_two_stage_control_h_bridge} H-bridge. $y_1$, $y_2$ and $x$ are 3-phase linear motors. Short stroke actuators are voice coils.}
\end{subfigure}
\caption{\label{fig:introduction_two_stage_example}(\subref{fig:introduction_two_stage_control_example}) \cite{shinno11_newly_devel_long_range_posit}, (\subref{fig:introduction_two_stage_control_h_bridge}) \cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}}
\end{figure}

\section{Multi-DoF dynamical positioning stations}
\paragraph{Serial and Parallel Kinematics}

Example of several dynamical stations:
\begin{itemize}
\item XYZ piezo stages
\item Delta robot? Octoglide?
\item Stewart platform
\end{itemize}

Serial vs parallel kinematics (table?)

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_serial_kinematics.png}
\end{center}
\subcaption{\label{fig:introduction_serial_kinematics} Serial Kinematics}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_parallel_kinematics.png}
\end{center}
\subcaption{\label{fig:introduction_parallel_kinematics} Parallel Kinematics}
\end{subfigure}
\caption{\label{fig:introduction_kinematics}Two positioning platforms with \(D_x/D_y/R_z\) degrees of freedom. One is using serial kinematics (\subref{fig:introduction_serial_kinematics}), while the other uses parallel kinematics (\subref{fig:introduction_parallel_kinematics})}
\end{figure}

\paragraph{Stewart platforms}

\begin{itemize}
\item[{$\square$}] Explain the normal stewart platform architecture
\item[{$\square$}] Make a table that compares the different stewart platforms for vibration control.
Geometry (cubic), Actuator (soft, stiff), Sensor, Flexible joints, etc.
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.8]{figs/introduction_stewart_architecture.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_architecture} Stewart Platform Architecture}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.8]{figs/introduction_stewart_pose.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_pose} Change of mobile platform pose}
\end{subfigure}
\caption{\label{fig:introduction_stewart_platform}The Stewart Platform. Architecutre is shown in (\subref{fig:introduction_stewart_architecture}). Change of pose induce by change of strut length is shown in (\subref{fig:introduction_stewart_pose})}
\end{figure}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_stewart_du14.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_du14}PZT based, for positioning purposes}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_stewart_hauge04.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_hauge04}Voice coil based, Cubic architecture, for vibration isolation}
\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}

\section{Mechatronics approach}
\paragraph{Predicting performances using models}

\cite{monkhorst04_dynam_error_budget}
Can use several models:
\begin{description}
\item[{Lumped mass-spring-damper models}] usually uniaxial, easily put into equations, 1dof per considered mass
\cite{rankers98_machin}
\item[{Multi-Body Models}] usually 6dof per considered solid body, some may be constrained using joints
\item[{Finite element models}] Can include FEM into multi-body models: Sub structuring (\cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea})
\end{description}

\begin{figure}[htbp]
\begin{subfigure}{0.3\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_model_lumped.png}
\end{center}
\subcaption{\label{fig:introduction_model_lumped} Mass-Spring-Damper model}
\end{subfigure}
\begin{subfigure}{0.39\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/introduction_model_multibody.png}
\end{center}
\subcaption{\label{fig:introduction_model_multibody} Multi-Body model}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/introduction_model_fem.jpg}
\end{center}
\subcaption{\label{fig:introduction_model_fem} Finite Element Model}
\end{subfigure}
\caption{\label{fig:introduction_models}Types of models used when using a mechatronics approach. (\subref{fig:introduction_model_lumped}) (\subref{fig:introduction_model_multibody}) (\subref{fig:introduction_model_fem})}
\end{figure}

\paragraph{Closed-Loop Simulations}

\cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}

Once a model of the system is obtained: develop controller based on linearized model.

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_closed_loop.png}
\caption{\label{fig:introduction_closed_loop}Block diagram of a typical feedback control architecture}
\end{figure}

Say what can limit the performances for a complex mechatronics systems as this one:
\begin{itemize}
\item Disturbances affecting the plant output \(d_y\)
\item Measurement noise \(n\)
\item DAC / amplifier noise (actuator) \(d_u\)
\item Feedback system / bandwidth
\item \(r\), \(y_m\)
\end{itemize}

Simulations can help evaluate the behavior of the system.

\paragraph{Dynamic Error Budgeting}

\cite{monkhorst04_dynam_error_budget}
\cite{jabben07_mechat}

\cite{okyay16_mechat_desig_dynam_contr_metrol}
\begin{itemize}
\item ``the disturbance signals are modeled with their power spectral density (PSD), assuming that they are stationary stochastic processes which are not correlated with each other''
\item Effects of \(d_u\), \(d_y\) and \(n\) on \(y\) can be estimated from their PSD and the closed-loop transfer functions
This gives a first idea of the limiting factor as a function of frequency.
In order to determine whether each disturbance/noise impact the performances, cumulative power spectrum can be used: this gives the RMS value
Then, this help to know the different actions to improve the performances: reduce sensor noise or driver electrical noise, work on reducing disturbances like damping resonances, increase feedback bandwidth, \ldots{})
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/introduction_psd.png}
\end{center}
\subcaption{\label{fig:introduction_psd} Power Spectral Density - Open Loop}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/introduction_cps.png}
\end{center}
\subcaption{\label{fig:introduction_cps} Cumulative Power Spectrum - Open Loop}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/introduction_cps_cl.png}
\end{center}
\subcaption{\label{fig:introduction_cps_cl} Cumulative Power Spectrum - Comparison}
\end{subfigure}
\caption{\label{fig:introduction_deb}Tools used for the dynamic error budgeting. First the Power Spectral Density can be compared (\subref{fig:introduction_psd}). The cumulative power spectrum is shown in (\subref{fig:introduction_cps}). To compare the effectivness of different strategies, the cumulative power spectrum can be compared (\subref{fig:introduction_cps_cl})}
\end{figure}

\section{Stewart platforms: Control architecture}
Different control goals:
\begin{itemize}
\item Vibration Isolation \ref{fig:introduction_stewart_isolation}
\item Position \ref{fig:introduction_stewart_positioning}
\end{itemize}

Depending on the goal, different sensors and different architectures.

For the NASS, both objectives.

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stewart_isolation.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_isolation} Vibration Isolation}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stewart_positioning.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_positioning} Positioning}
\end{subfigure}
\caption{\label{fig:introduction_stewart_control_goal}Example of two control goals. In (\subref{fig:introduction_stewart_isolation}), the Stewart platform is used to isolate the payload from a vibration environment. In (\subref{fig:introduction_stewart_positioning}), the Stewart platform is used to position the payload along a defined trajectory.}
\end{figure}


\paragraph{Active Damping and Vibration Control}

Two main active vibration isolation strategies \cite{collette11_review_activ_vibrat_isolat_strat}:
\begin{itemize}
\item IFF using collocated force sensors / load cell \cite{chesne16_enhan_dampin_flexib_struc_using_force_feedb}
\item Skyhook damping using inertial sensors (accelerometers, geophones), usually in the frame of the struts
\end{itemize}

Usually, ``decentralized'', in the frame of the struts (Figure \ref{fig:introduction_control_decentralized}).
Optimization based on one ``strut'', and then applied to all the struts simultaneously to obtained a 6-DoF active damping / vibration control system.

If narrow band disturbances: Adaptive feedforward control.


\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_damping_iff.png}
\end{center}
\subcaption{\label{fig:introduction_damping_iff} Integral Force Feedback}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_damping_skyhook.png}
\end{center}
\subcaption{\label{fig:introduction_damping_skyhook} "Sky-hook" Damping}
\end{subfigure}
\caption{\label{fig:introduction_damping}Uniaxial vibration isolation strategies. Integral force feedback (\subref{fig:introduction_damping_iff}) and ``sky-hook'' damping (\subref{fig:introduction_damping_skyhook}).}
\end{figure}


\begin{figure}[htbp]
\begin{subfigure}{0.54\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_control_decentralized_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_control_decentralized_schematic} Decentralized Control applied on Stewart platform}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_control_decentralized_diagram.png}
\end{center}
\subcaption{\label{fig:introduction_control_decentralized_diagram} Equivalent block diagram}
\end{subfigure}
\caption{\label{fig:introduction_control_decentralized}Decentralized control. Example of decentralized force feedback (\subref{fig:introduction_control_decentralized_schematic}), only three struts are shown for simplicity. Equivalent block diagram (\subref{fig:introduction_control_decentralized_diagram}), the controller is then diagonal.}
\end{figure}

\paragraph{Position and Pointing Control}

Control based on position sensors.
Wanted position is generally expressed in the cartesian frame.

Sensors can be:
\begin{itemize}
\item In the frame of the struts (LVDT, Encoder, Strain gauges): usually decentralized control (Figure \ref{fig:introduction_control_decentralized_diagram})
\item External sensors: centralized
\end{itemize}

When using external sensors, a decoupling strategy is usually employed (Figure \ref{fig:introduction_control_decoupling}):
\begin{itemize}
\item Jacobian matrices: frame of the struts or cartesian frame
\item Modal control
\item Singular Value Decomposition
\item Multivariable control: LQG, H-Infinity (Figure \ref{fig:introduction_control_mimo})
\end{itemize}

From \cite{thayer02_six_axis_vibrat_isolat_system}:
\begin{quote}
Experimental closed-loop control results using the hexapod have shown that controllers designed using a decentralized single-strut design work well when compared to full multivariable methodologies.
\end{quote}


\begin{figure}[htbp]
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_control_mimo.png}
\end{center}
\subcaption{\label{fig:introduction_control_mimo} Multivariable Control}
\end{subfigure}
\begin{subfigure}{0.66\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_control_decoupling.png}
\end{center}
\subcaption{\label{fig:introduction_control_decoupling} Decoupling Control}
\end{subfigure}
\caption{\label{fig:introduction_control_mimo_vs_decoupling}Two strategies to control a multi-inputs-multi-outputs system. Use of a multivariable controller (\subref{fig:introduction_control_mimo}), or first decouple the plant with matrices, and then designing several single-input-single-output controllers (\subref{fig:introduction_control_decoupling})}
\end{figure}

\begin{itemize}
\item Explain the Jacobian matrix
\end{itemize}

When decoupling using the Jacobian matrix, the control can be performed in the frame of the struts (Figure \ref{fig:introduction_control_centralized_struts}) or in the cartesian frame (Figure \ref{fig:introduction_control_centralized_cartesian}).

\begin{figure}[htbp]
\begin{subfigure}{0.95\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_control_centralized_struts.png}
\end{center}
\subcaption{\label{fig:introduction_control_centralized_struts} Control in the frame of the struts}
\end{subfigure}

\bigskip
\begin{subfigure}{0.95\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_control_centralized_cartesian.png}
\end{center}
\subcaption{\label{fig:introduction_control_centralized_cartesian} Control in the cartesian frame}
\end{subfigure}
\caption{\label{fig:introduction_control_centralized}Two centralized control strategies. Express the position error in the frame of the struts and design one controller for each strut (\subref{fig:introduction_control_centralized_struts}). Design one controller for each direction, and then map the forces and torques to each struts (\subref{fig:introduction_control_centralized_cartesian}).}
\end{figure}

\paragraph{Use of Multiple Sensors}

Often, both vibration control and position control is wanted.
In that case, the use of multiple sensors can lead to improved performances.

Sensors:
\begin{itemize}
\item collocated force (load cell) sensors
\item collocated accelerometer
\item displacement (eddy current)
\end{itemize}

Several strategies can be employed:
\begin{itemize}
\item HAC-LAC \cite{geng95_intel_contr_system_multip_degree,wang16_inves_activ_vibrat_isolat_stewar,li01_simul_vibrat_isolat_point_contr,pu11_six_degree_of_freed_activ,xie17_model_contr_hybrid_passiv_activ}
\item Sensor Fusion \cite{tjepkema12_activ_ph,tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip,hauge04_sensor_contr_space_based_six}
\item Two Sensor control: \cite{hauge04_sensor_contr_space_based_six,tjepkema12_activ_ph}
\end{itemize}

Comparison between ``two sensor control'' and ``sensor fusion'' is given in \cite{beijen14_two_sensor_contr_activ_vibrat}.

\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_architecture_hac_lac.png}
\end{center}
\subcaption{\label{fig:introduction_architecture_hac_lac} HAC-LAC}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_architecture_two_sensor_control.png}
\end{center}
\subcaption{\label{fig:introduction_architecture_two_sensor_control} Two Sensor Control}
\end{subfigure}

\bigskip
\begin{subfigure}{0.95\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_architecture_sensor_fusion.png}
\end{center}
\subcaption{\label{fig:introduction_architecture_sensor_fusion} Sensor Fusion}
\end{subfigure}
\caption{\label{fig:introduction_control_multiple_sensors}Different control strategies when using multiple sensors. High Authority Control / Low Authority Control (\subref{fig:introduction_architecture_hac_lac}). Sensor Fusion (\subref{fig:introduction_architecture_sensor_fusion}). Two-Sensor Control (\subref{fig:introduction_architecture_two_sensor_control})}
\end{figure}

\chapter{Original Contributions}
This thesis proposes several contributions in the fields of Control, Mechatronics Design and Experimental validation.

\paragraph{Active Damping of rotating mechanical systems using Integral Force Feedback}

\cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb,dehaeze21_activ_dampin_rotat_platf_using}
\begin{quote}
This paper investigates the use of Integral Force Feedback (IFF) for the active damping of rotating mechanical systems.
Guaranteed stability, typical benefit of IFF, is lost as soon as the system is rotating due to gyroscopic effects.
To overcome this issue, two modifications of the classical IFF control scheme are proposed.
The first consists of slightly modifying the control law while the second consists of adding springs in parallel with the force sensors.
Conditions for stability and optimal parameters are derived.
The results reveal that, despite their different implementations, both modified IFF control scheme have almost identical damping authority on the suspension modes.
\end{quote}

\paragraph{Design of complementary filters using \(\mathcal{H}_\infty\) Synthesis and sensor fusion}

\cite{dehaeze19_compl_filter_shapin_using_synth}
\cite{verma20_virtual_sensor_fusion_high_precis_contr}
\cite{tsang22_optim_sensor_fusion_method_activ}

\begin{itemize}
\item Several uses (link to some papers).
\item For the NASS, they could be use to further improve the robustness of the system.
\end{itemize}

\paragraph{Multi-body simulations with reduced order flexible bodies obtained by FEA}

\cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}

Combined multi-body / FEA techniques and experimental validation on a Stewart platform containing amplified piezoelectric actuators
Super-element of amplified piezoelectric actuator / combined multibody-FEA technique, experimental validation on an amplified piezoelectric actuator and further validated on a complete stewart platform

\begin{quote}
We considered sub-components in the multi-body model as \emph{reduced order flexible bodies} representing the component’s modal behaviour with reduced mass and stiffness matrices obtained from finite element analysis (FEA) models.
These matrices were created from FEA models via modal reduction techniques, more specifically the \emph{component mode synthesis} (CMS).
This makes this design approach a combined multibody-FEA technique.
We validated the technique with a test bench that confirmed the good modelling capabilities using reduced order flexible body models obtained from FEA for an amplified piezoelectric actuator (APA).
\end{quote}

\paragraph{Robustness by design}

\begin{itemize}
\item Design of a Stewart platform and associated control architecture that is robust to large plant uncertainties due to large variety of payload and experimental conditions.
\item Instead of relying on complex controller synthesis (such as \(\mathcal{H}_\infty\) synthesis or \(\mu\text{-synthesis}\)) to guarantee the robustness and performance.
\item The approach here is to choose an adequate architecture (mechanics, sensors, actuators) such that controllers are robust by nature.
\item Example: collocated actuator/sensor pair => controller can easily be made robust
\item This is done by using models and using HAC-LAC architecture
\end{itemize}

\paragraph{Mechatronics design}

Conduct a rigorous mechatronics design approach for a nano active stabilization system
\cite{dehaeze18_sampl_stabil_for_tomog_exper,dehaeze21_mechat_approac_devel_nano_activ_stabil_system}

Approach from start to finish:
\begin{itemize}
\item From first concepts using basic models, to concept validation
\item Detailed design phase
\item Experimental phase
\end{itemize}

Complete design with clear choices based on models.
Such approach, while not new, is here applied
This can be used for the design of future end-stations.

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach.png}
\caption{\label{fig:introduction_nass_mechatronics_approach}Overview of the mechatronic approach used for the Nano-Active-Stabilization-System}
\end{figure}

\paragraph{6DoF vibration control of a rotating platform}

Vibration control in 5DoF of a rotating stage
To the author's knowledge, the use of a continuously rotating stewart platform for vibration control has not been proved in the literature.

\paragraph{Experimental validation of the Nano Active Stabilization System}

Demonstration of the improvement of the the positioning accuracy of a complex multi DoF (the micro-station) by several orders of magnitude (Section \ldots{}) using \ldots{}

\chapter{Thesis Outline - Mechatronics Design Approach}
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/introduction_overview_chapters.png}
\caption{\label{fig:introduction_overview_chapters}Overview of the sections}
\end{figure}

This thesis
\begin{itemize}
\item has a structure that follows the mechatronics design approach
\end{itemize}

Is structured in three chapters that corresponds to the three mains parts of the proposed mechatronics approach.

A brief overview of these three chapters is given bellow.

\paragraph{Conceptual design development}

\begin{itemize}
\item Start with simple models for witch trade offs can be easily understood (uniaxial)
\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)
\item The system concept and main characteristics should be extracted from the different models and validated with closed-loop simulations with the most accurate model
\item Once the concept is validated, the chosen concept can be design in mode details
\end{itemize}

\paragraph{Detailed design}

\begin{itemize}
\item During this detailed design phase, models are refined from the obtained CAD and using FEM
\item The models are used to assists the design and to optimize each element based on dynamical analysis and closed-loop simulations
\item The requirements for all the associated instrumentation can be determined from a dynamical noise budgeting
\item After converging to a detailed design that give acceptable performance based on the models, the different parts can be ordered and the experimental phase begins
\end{itemize}

\paragraph{Experimental validation}

\begin{itemize}
\item It is advised that the important characteristics of the different elements are evaluated individually
Systematic validation/refinement of models with experimental measurements
\item The obtained characteristics can be used to refine the models
\item Then, an accurate model of the system is obtained which can be used during experimental tests (for control synthesis for instance)
\end{itemize}


\printbibliography[heading=bibintoc,title={Bibliography}]
\end{document}
