phd-thesis/phd-thesis.tex

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\newacronym{mimo}{MIMO}{Multiple-Inputs Multiple-Outputs}
\newacronym{siso}{SISO}{Single-Input Single-Output}
\newacronym{nass}{NASS}{Nano Active Stabilization System}
\newacronym{lti}{LTI}{Linear Time Invariant}
\newacronym{esrf}{ESRF}{European Synchrotron Radiation Facility}
\newglossaryentry{ka}{name=\ensuremath{k_a},description={{Actuator Stiffness in}}}
\newglossaryentry{phi}{name=\ensuremath{\phi},description={{A woody bush}}}
\input{config_extra.tex}
\addbibresource{ref.bib}
\addbibresource{phd-thesis.bib}
\author{Dehaeze Thomas}
\date{2024-04-12}
\title{Mechatronic approach for the design of a Nano Active Stabilization System}
\subtitle{PhD Thesis}
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    A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (PhD) in Engineering Science\\
    at\\
    \textsc{Liège Université}
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\newpage
\null
\thispagestyle{empty}
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\chapter*{Abstract}
\gls{phi}

\chapter*{Résumé}

\chapter*{Acknowledgments}

\dominitoc
\tableofcontents

\listoftables
\listoffigures

\chapter{Introduction}
\section{Context of this thesis / Background and Motivation}

\begin{itemize}
\item \gls{esrf} (Figure \ref{fig:esrf_picture})
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.7\linewidth]{figs/esrf_picture.jpg}
\caption{\label{fig:esrf_picture}European Synchrotron Radiation Facility}
\end{figure}

\begin{itemize}
\item ID31 and Micro Station (Figure \ref{fig:id31_microstation_picture})
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.49\linewidth]{figs/id31_microstation_picture.png}
\caption{\label{fig:id31_microstation_picture}Picture of the ID31 Micro-Station with annotations}
\end{figure}

Alternative: \texttt{id31\_microstation\_cad\_view.png} (CAD view)

\begin{itemize}
\item X-ray beam + detectors + sample stage (Figure \ref{fig:id31_beamline_schematic})
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/id31_beamline_schematic.png}
\caption{\label{fig:id31_beamline_schematic}ID31 Beamline Schematic. With light source, nano-focusing optics, sample stage and detector.}
\end{figure}

\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)
\item Where to explain the goal of each stage? (e.g. micro-hexapod: static positioning, Ty and Rz: scans, \ldots{})
\item Example of picture obtained (Figure \ref{fig:id31_tomography_result})
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.49\linewidth]{example-image-c.png}
\caption{\label{fig:id31_tomography_result}Image obtained on the ID31 beamline}
\end{figure}

\begin{itemize}
\item Explain wanted positioning accuracy and why micro-station cannot have this accuracy (backlash, play, thermal expansion, \ldots{})

\item Speak about the metrology concept, and why it is not included in this thesis
\end{itemize}

\section{Challenge definition}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/nass_concept_schematic.png}
\caption{\label{fig:nass_concept_schematic}Nass Concept. 1: micro-station, 2: nano-hexapod, 3: sample, 4: 5DoF metrology}
\end{figure}

\begin{itemize}
\item 6DoF vibration control platform on top of a complex positioning platform
\item \textbf{Goal}: Improve accuracy of 6DoF long stroke position platform
\item \textbf{Approach}: Mechatronic approach / model based / predictive
\item \textbf{Control}: Robust control approach / various payloads.
First hexapod with control bandwidth higher than the suspension modes that accepts various payloads?
\item Rotation aspect
\item Compactness? (more related to mechanical design)
\end{itemize}

\section{Literature Review}

\begin{figure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.8\linewidth]{example-image-a.png}
\end{center}
\subcaption{Stewart platform based on voice coil actuators}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.8\linewidth]{example-image-b.png}
\end{center}
\subcaption{Stewart platform based on piezoelectric actuators}
\end{subfigure}
\caption{\label{fig:stewart_platform_examples}Examples of Stewart Platforms}
\end{figure}

\begin{itemize}
\item Hexapods
\cite{li01_simul_fault_vibrat_isolat_point}
\cite{bishop02_devel_precis_point_contr_vibrat}
\cite{hanieh03_activ_stewar}
\cite{afzali-far16_vibrat_dynam_isotr_hexap_analy_studies}
\cite{naves20_desig}
\url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org}
\item Positioning stations
\item Mechatronic approach?
\cite{rankers98_machin}
\cite{monkhorst04_dynam_error_budget}
\cite{jabben07_mechat}
\end{itemize}

\section{Outline of thesis / Thesis Summary / Thesis Contributions}

\textbf{Mechatronic Design Approach} / \textbf{Model Based Design}:
\begin{itemize}
\item \cite{monkhorst04_dynam_error_budget} high costs of the design process: the designed system must be \textbf{first time right}.
When the system is finally build, its performance level should satisfy the specifications.
No significant changes are allowed in the post design phase.
Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.
\end{itemize}

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

\textbf{Goals}:
\begin{itemize}
\item Design \gls{nass} such that it is easy to control (and maintain).
Have good performances by design and not by complex control strategies.
\end{itemize}


\textbf{Models}:
\begin{itemize}
\item Uniaxial Model:
\begin{itemize}
\item Effect of limited support compliance
\item Effect of change of payload
\end{itemize}
\item Rotating Model
\begin{itemize}
\item Gyroscopic effects
\end{itemize}
\item Multi Body Model
\item Finite Element Models
\end{itemize}

\chapter{Conceptual Design Development}
\minitoc
\paragraph{Abstract}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/chapter1_overview.png}
\caption{\label{fig:chapter1_overview}Figure caption}
\end{figure}

\section{Uni-axial Model}

\begin{itemize}
\item Explain what we want to capture with this model
\item Schematic of the uniaxial model (with X-ray)
\item Identification of disturbances (ground motion, stage vibrations)
\item Optimal nano-hexapod stiffness/actuator: Voice coil VS Piezo (conclusion?)
\item Control architecture (IFF, DVF, \ldots{})?
\item Conclusion
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/mass_spring_damper_nass.png}
\caption{\label{fig:mass_spring_damper_nass}3-DoF uniaxial mass-spring-damper model of the NASS}
\end{figure}

\subsection{Micro Station Model}
\subsection{Nano Hexapod Model}
\subsection{Disturbance Identification}
\subsection{Open Loop Dynamic Noise Budgeting}

\begin{itemize}
\item List all disturbances with their spectral densities
\item Show how they have been measured
\item Say that repeatable errors can be calibrated (show measurement of Hans-Peter?)
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.4\linewidth]{measurement_microstation_vibration_picture.jpg}
\caption{\label{fig:measurement_microstation_vibration_picture}Setup used to measure the micro-station vibrations during operation}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.49\linewidth]{example-image-b.png}
\caption{\label{fig:asd_ground_motion_ustation_dist}Amplitude Spectral density of the measured disturbance sources}
\end{figure}

\subsection{Active Damping}

Conclusion: IFF is better for this application

\paragraph{Integral Force Feedback}

\begin{itemize}
\item Mass spring damper model
\item Root Locus
\item Sensitivity to disturbances
\end{itemize}

\paragraph{Direct Velocity Feedback}

\begin{itemize}
\item Mass spring damper model
\item Root Locus
\item Sensitivity to disturbances
\end{itemize}


\subsection{Position Feedback Controller}
\subsection{Effect of support compliance}

\begin{itemize}
\item \textbf{goal}: make the nano-hexapod independent of the support compliance
\item Simple 2DoF model
\item Generalized to any support compliance
\item \textbf{conclusion}: frequency of nano-hexapod resonances should be lower than first suspension mode of the support
\end{itemize}

\subsection{Effect of payload dynamics}

\begin{itemize}
\item \textbf{goal}: be robust to a change of payload
\item Simple 2DoF model
\item Generalized to any payload dynamics
\end{itemize}

\subsection{Conclusion}

\section{Effect of rotation}

Papers:
\begin{itemize}
\item \cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb}
\item \cite{dehaeze21_activ_dampin_rotat_platf_using}
\end{itemize}

\subsection{System Description and Analysis}

\begin{itemize}
\item x-y-Rz model
\item explain why this is representing the NASS
\item Equation of motion
\item Centrifugal forces, Coriolis
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/2dof_rotating_system.png}
\caption{\label{fig:2dof_rotating_system}Mass spring damper model of an X-Y stage on top of a rotating stage}
\end{figure}

\subsection{Integral Force Feedback}

\begin{itemize}
\item Control diagram
\item Root Locus: unstable with pure IFF
\end{itemize}

\subsection{IFF with an High Pass Filter}

\subsection{IFF with a stiffness in parallel with the force sensor}

\subsection{Relative Damping Control}

\subsection{Comparison of Active Damping Techniques}

\subsection{Rotating Nano-Hexapod}

\subsection{Nano Active Stabilization System with rotation}

\subsection{Conclusion}

\begin{itemize}
\item problem with voice coil actuator
\item Two solutions: add parallel stiffness, or change controller
\item Conclusion: minimum stiffness is required
\item APA is a nice architecture for parallel stiffness + integrated force sensor (have to speak about IFF before that)
\end{itemize}

\section{Micro Station - Modal Analysis}
Conclusion:
\begin{itemize}
\item complex dynamics: need multi-body model of the micro-station to represent the limited compliance\ldots{}
\end{itemize}

\subsection{Measurement Setup}

\subsection{Frequency Analysis}

\subsection{Modal Analysis}

\section{Micro Station - Multi Body Model}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.7\linewidth]{figs/simscape_first_model_screenshot.jpg}
\caption{\label{fig:simscape_first_model_screenshot}3D view of the multi-body model of the micro-station}
\end{figure}

\subsection{Kinematics}

\url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/kinematics.org}

\begin{itemize}
\item Small overview of each stage and associated stiffnesses / inertia
\item schematic that shows to considered DoF
\item import from CAD
\end{itemize}

\subsection{Modal Analysis and Dynamic Modeling}
\begin{itemize}
\item Picture of the experimental setup
\item Location of accelerometers
\item Show obtained modes
\item Validation of rigid body assumption
\item Explain how this helps tuning the multi-body model
\end{itemize}

\subsection{Disturbances and Positioning errors}

\subsection{Validation of the Model}

\begin{itemize}
\item Most important metric: support compliance
\item Compare model and measurement
\end{itemize}

\section{Nano Hexapod - Multi Body Model}

\begin{itemize}
\item What we want to capture with this model
\item Explain what is a multi body model (rigid body, springs, etc\ldots{})
\item Key elements (plates, joints, struts): for now simplistic model (rigid body elements, perfect joints, \ldots{}), but in next section, FEM will be used
\item Matlab/Simulink developed toolbox for the study of Stewart platforms
\end{itemize}

\subsection{Stewart Platform Architecture}

\begin{figure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.8\linewidth]{stewart_architecture_example.png}
\end{center}
\subcaption{Initial position}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.8\linewidth]{stewart_architecture_example_pose.png}
\end{center}
\subcaption{After some motion}
\end{subfigure}
\caption{\label{fig:stewart_platform_architecture}Stewart Platform Architecture}
\end{figure}

Configurable Simscape Model: \url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org}
\begin{itemize}
\item Explain the different frames, etc\ldots{}

\item Little review
\item explain key elements:
\begin{itemize}
\item two plates
\item joints
\item actuators
\end{itemize}
\item explain advantages compared to serial architecture
\end{itemize}

\subsection{Kinematics}

\begin{itemize}
\item Well define elements, frames, \ldots{}
\item Derivation of jacobian matrices: for forces and for displacement
\item Explain this is true for small displacements (show how small)
\end{itemize}

\subsection{Model of an Amplified Piezoelectric Actuator}

\begin{itemize}
\item APA test bench
\item Piezoelectric effects
\item mass spring damper representation (2dof)
\item Compare the model and the experiment
\item Here, just a basic 2DoF model of the APA is used
\end{itemize}

\subsection{Dynamics of the Nano-Hexapod}

\begin{itemize}
\item Effect of joints stiffnesses

\item[{$\square$}] The APA model should maybe not be used here, same for the nice top and bottom plates. Here the detailed design is not yet performed
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/simscape_nano_hexapod.png}
\caption{\label{fig:simscape_nano_hexapod}3D view of the multi-body model of the Nano-Hexapod (simplified)}
\end{figure}

\section{Control Architecture - Concept Validation}

Discussion of:
\begin{itemize}
\item Transformation matrices / control architecture (computation of the position error in the frame of the nano-hexapod)
\item Control of parallel architectures
\item Control in the frame of struts or cartesian?
\item Effect of rotation on IFF? => APA
\item HAC-LAC
\item New noise budgeting?
\end{itemize}

\subsection{Control Kinematics}

\begin{itemize}
\item Explain how the position error can be expressed in the frame of the nano-hexapod
\item block diagram
\item Explain how to go from external metrology to the frame of the nano-hexapod
\end{itemize}

\subsection{High Authority Control - Low Authority Control (HAC-LAC)}

\begin{itemize}
\item general idea
\item case for parallel manipulator: decentralized LAC + centralized HAC
\end{itemize}

\subsection{Decoupling Strategies for parallel manipulators}
\href{file:///home/thomas/Cloud/research/matlab/decoupling-strategies/svd-control.org}{study}

\begin{itemize}
\item Jacobian matrices, CoK, CoM, \ldots{}
\item Discussion of cubic architecture
\item SVD, Modal, \ldots{}
\end{itemize}

\subsection{Decentralized Integral Force Feedback (LAC)}

\begin{itemize}
\item Root Locus
\item Damping optimization
\end{itemize}

\subsection{Decoupled Dynamics}

\begin{itemize}
\item Centralized HAC
\item Control in the frame of the struts
\item Effect of IFF
\end{itemize}

\subsection{Centralized Position Controller (HAC)}

\begin{itemize}
\item Decoupled plant
\item Controller design
\end{itemize}

\section{Conceptual Design - Conclusion}

\chapter{Detailed Design}
\minitoc
\paragraph{Abstract}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/chapter2_overview.png}
\caption{\label{fig:chapter2_overview}Figure caption}
\end{figure}

\section{Nano-Hexapod Kinematics - Optimal Geometry?}
\begin{itemize}
\item[{$\square$}] Maybe this can be just merged with the last section in this chapter?
\end{itemize}

\subsection{Optimal strut orientation}


\subsection{Cubic Architecture: a Special Case?}

\url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org}

\section{Nano-Hexapod Dynamics - Including Flexible elements in the Multi-body model}
\begin{itemize}
\item[{$\square$}] Should this be an appendix?
\end{itemize}
Reduced order flexible bodies \cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}
\begin{itemize}
\item Used with APA, Flexible joints, Plates
\end{itemize}

\subsection{Reduced order flexible bodies}

\begin{itemize}
\item Quick explanation of the theory
\item Implementation with Ansys (or Comsol) and Simscape
\end{itemize}

\subsection{Numerical Validation}

\begin{itemize}
\item Numerical Validation Ansys VS Simscape (APA)
\item Figure with 0 and 1kg mass
\end{itemize}

\subsection{Experimental Validation}

\begin{itemize}
\item Test bench
\item Obtained transfer functions and comparison with Simscape model with reduced order flexible body
\end{itemize}

\section{Actuator Choice}

\begin{itemize}
\item From previous study: APA seems a nice choice
\item First tests with the APA95ML: validation of a basic model (maybe already presented)
\item Optimal stiffness?
\item Talk about piezoelectric actuator? bandwidth? noise?
\item Specifications: stiffness, stroke, \ldots{} => choice of the APA
\item FEM of the APA
\item Validation with flexible APA in the simscape model
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.49\linewidth]{example-image-a.png}
\caption{\label{fig:apa_schmeatic}Schematical representation of an Amplified Piezoelectric Actuator}
\end{figure}

\subsection{Model}

Piezoelectric equations

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.49\linewidth]{example-image-a.png}
\caption{\label{fig:apa_schmeatic_2dof}Schematical representation of a 2DoF model of an Amplified Piezoelectric Actuator}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.49\linewidth]{example-image-b.png}
\caption{\label{fig:apa_schmeatic_fem}Schematical representation of a FEM of an Amplified Piezoelectric Actuator}
\end{figure}

\begin{itemize}
\item FEM
\item Simscape model
\item (2 DoF, FEM, \ldots{})
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/root_locus_iff_rot_stiffness.png}
\caption{\label{fig:root_locus_iff_rot_stiffness}Limitation of the attainable damping due to the APA design}
\end{figure}

\subsection{Experimental System Identification}

\begin{itemize}
\item Experimental validation (granite test bench)
\item Electrical parameters
\item Required instrumentation to read force sensor?
\item Add resistor to include high pass filtering: no risk of saturating the ADC
\item Estimation of piezoelectric parameters
\end{itemize}

\subsection{Validation with Simscape model}

\begin{itemize}
\item Tuned Simscape model
\item IFF results: OK
\end{itemize}

\section{Design of Nano-Hexapod Flexible Joints}

\begin{itemize}
\item Perfect flexible joint
\item Imperfection of the flexible joint: Model
\item Study of the effect of limited stiffness in constrain directions and non-null stiffness in other directions
\item Obtained Specification
\item Design optimisation (FEM)
\item Implementation of flexible elements in the Simscape model: close to simplified model
\end{itemize}

\subsection{Effect of flexible joint characteristics on obtained dynamics}

\begin{itemize}
\item Based on Simscape model
\item Effect of axial stiffness, bending stiffness, \ldots{}
\item Obtained specifications (trade-off)
\end{itemize}


\subsection{Flexible joint geometry optimization}

\begin{itemize}
\item Chosen geometry
\item Show different existing geometry for flexible joints used on hexapods
\item Optimisation with Ansys
\item Validation with Simscape model
\end{itemize}

\subsection{Experimental identification}

\begin{itemize}
\item Experimental validation, characterisation (\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/test-bench-flexible-joints-adv/bending.org}{study})
\item Visual inspection
\item Test bench
\item Obtained results
\end{itemize}

\section{Choice of Instrumentation}

\begin{itemize}
\item Discussion of the choice of other elements:
\begin{itemize}
\item Encoder
\item DAC
\item ADC (reading of the force sensors)
\item real time controller
\item Voltage amplifiers
\end{itemize}
\item Give some requirements + chosen elements + measurements / validation
\end{itemize}

\subsection{DAC and ADC}

\begin{itemize}
\item Force sensor
\end{itemize}

\subsection{Voltage amplifier (\href{https://research.tdehaeze.xyz/test-bench-pd200/}{link})}

\begin{itemize}
\item Test Bench: capacitive load, ADC, DAC, Instrumentation amplifier
\item Noise measurement
\item Transfer function measurement
\end{itemize}

\subsection{Encoder (\href{https://research.tdehaeze.xyz/test-bench-vionic/}{link})}
\begin{itemize}
\item Noise measurement
\end{itemize}

\section{Obtained Design}
\begin{itemize}
\item Explain again the different specifications in terms of space, payload, etc..
\item CAD view of the nano-hexapod
\item Chosen geometry, materials, ease of mounting, cabling, \ldots{}
\item Validation on Simscape with accurate model?
\end{itemize}

\section{Detailed Design - Conclusion}
\chapter{Experimental Validation}
\minitoc
\paragraph{Abstract}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/chapter3_overview.png}
\caption{\label{fig:chapter3_overview}Figure caption}
\end{figure}

Schematic representation of the experimental validation process.
\begin{itemize}
\item APA
\item Strut
\item Nano-hexapod on suspended table
\item Nano-hexapod with Spindle
\end{itemize}

\section{Amplified Piezoelectric Actuator}

\section{Flexible Joints}

\section{Struts}

\section{Nano-Hexapod}

\section{Rotating Nano-Hexapod}

\section{ID31 Micro Station}

\section{Experimental Validation - Conclusion}
\chapter{Conclusion and Future Work}

\section{Alternative Architecture}
\url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/alternative-micro-station-architecture.org}

\appendix

\chapter{Mathematical Tools for Mechatronics}
\section{Feedback Control}


\section{Dynamical Noise Budgeting}
\subsection{Power Spectral Density}

\subsection{Cumulative Amplitude Spectrum}

\chapter{Stewart Platform - Kinematics}
\printbibliography[heading=bibintoc,title={Bibliography}]

\chapter*{List of Publications}
\begin{refsection}[ref.bib]
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\end{refsection}

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