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\input{preamble.tex}
\input{preamble_extra.tex}
\bibliography{simscape-nano-hexapod.bib}
\author{Dehaeze Thomas}
\date{\today}
\title{Simscape Model - Nano Hexapod}
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 pdfauthor={Dehaeze Thomas},
 pdftitle={Simscape Model - Nano Hexapod},
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\usepackage{biblatex}

\begin{document}

\maketitle
\tableofcontents

\clearpage


Introduction:
\begin{itemize}
\item Choice of architecture to do 5DoF control (Section \ref{sec:nhexa_platform_review})
\item Stewart platform (Section \ref{sec:nhexa_stewart_platform})
Show what is an hexapod, how we can define its geometry, stiffness, etc\ldots{}
Some kinematics: stiffness matrix, mass matrix, etc\ldots{}
\item Need to model the active vibration platform: multi-body model (Section \ref{sec:nhexa_model})
Explain what we want to capture with this model
Key elements (plates, joints, struts): for now simplistic model (rigid body elements, perfect joints, \ldots{}), but in next section, FEM will be used
\item Control (Section \ref{sec:nhexa_control})
\end{itemize}

\chapter{Active Vibration Platforms}
\label{sec:nhexa_platform_review}
\textbf{Goals}:
\begin{itemize}
\item Explain why Stewart platform architecture is chosen
\item Explain what is a Stewart platform (quickly as it will be shown in details in the next section)
\item Quick review of active vibration platforms (5 or 6DoF)
\end{itemize}

Active vibration platform with 5DoF or 6DoF?
Synchrotron applications?


\begin{itemize}
\item Literature review? (\textbf{maybe more suited for chapter 2})
\begin{itemize}
\item \url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org}
\item Talk about flexible joint? Maybe not so much as it should be topic of second chapter.
Just say that we must of flexible joints that can be defined as 3 to 6DoF joints, and it will be optimize in chapter 2.
\end{itemize}
\item \cite{taghirad13_paral}
\item For some systems, just XYZ control (stack stages), example: holler
\item For other systems, Stewart platform (ID16a), piezo based
\item Examples of Stewart platforms for general vibration control, some with Piezo, other with Voice coil. IFF, \ldots{}
Show different geometry configuration
\item DCM: tripod?
\end{itemize}
\section{Active vibration control of sample stages}

\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A0-nass-introduction/nass-introduction.org}{Review of stages with online metrology for Synchrotrons}

\begin{itemize}
\item[{$\square$}] Talk about external metrology?
\item[{$\square$}] Talk about control architecture?
\item[{$\square$}] Comparison with the micro-station / NASS
\end{itemize}

\section{Serial and Parallel Manipulators}

\textbf{Goal}:
\begin{itemize}
\item Explain why a parallel manipulator is here preferred
\item Compact, 6DoF, higher control bandwidth, linear, simpler

\item Show some example of serial and parallel manipulators

\item A review of Stewart platform will be given in Chapter related to the detailed design of the Nano-Hexapod
\end{itemize}

\chapter{The Stewart platform}
\label{sec:nhexa_stewart_platform}
\begin{itemize}
\item Some history about Stewart platforms
\item What is so special and why it is so used in different fields: give examples
Explain advantages compared to serial architecture
\item Little review (very quick: two extreme sizes, piezo + voice coil)
Complete review of Stewart platforms will be made in Chapter 2
\item Presentation of tools used to analyze the properties of the Stewart platform => useful for design and control
\end{itemize}
\section{Mechanical Architecture}
\label{ssec:nhexa_stewart_platform_architecture}

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

Presentation of the typical architecture
\begin{itemize}
\item Explain the different frames, etc\ldots{}
\item explain key elements:
\begin{itemize}
\item two plates
\item joints
\item actuators
\end{itemize}
\end{itemize}

Make well defined notations.
\begin{itemize}
\item \{F\}, \{M\}
\item si, li, ai, bi, etc.

\item[{$\square$}] Make figure with defined frames, joints, etc\ldots{}
Maybe can use this figure as an example:
\begin{center}
\includesvg[scale=1]{/home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A0-nass-introduction/figs/introduction_stewart_du14}
\end{center}
\end{itemize}

\section{Kinematic Analysis}
\label{ssec:nhexa_stewart_platform_kinematics}
\paragraph{Inverse Kinematics}

\paragraph{Forward Kinematics}

\paragraph{Jacobian Matrix}

\begin{itemize}
\item Velocity Loop Closure
\item Static Forces
\end{itemize}

\paragraph{Singularities}

\begin{itemize}
\item Briefly mention singularities, and say that for small stroke, it is not an issue, the Jacobian matrix may be considered constant
\end{itemize}

\section{Static Analysis}
\label{ssec:nhexa_stewart_platform_static}

How stiffness varies with orientation of struts.
Same with stroke?
Or maybe in the detailed chapter?

\section{Dynamic Analysis}
\label{ssec:nhexa_stewart_platform_dynamics}

Very complex => multi-body model
For instance, compute the plant for massless struts and perfect joints (will be compared with Simscape model).
But say that if we want to model more complex cases, it becomes impractical (cite papers).

\section*{Conclusion}
All depends on the geometry.
Reasonable choice of geometry is made in chapter 1.
Optimization of the geometry will be made in chapter 2.

\chapter{Multi-Body Model}
\label{sec:nhexa_model}
\textbf{Goal}:
\begin{itemize}
\item Study the dynamics of Stewart platform
\item Instead of working with complex analytical models: a multi-body model is used.
Complex because has to model the inertia of the struts.
Cite papers that tries to model the stewart platform analytically
Advantage: it will be easily included in the model of the NASS

\item Mention the Toolbox (maybe make a DOI for that)

\item[{$\square$}] Have a table somewhere that summarizes the main characteristics of the nano-hexapod model
\begin{itemize}
\item location of joints
\item size / mass of platforms, etc\ldots{}
\end{itemize}
\end{itemize}
\section{Model Definition}
\label{ssec:nhexa_model_def}

\begin{itemize}
\item[{$\square$}] Make a schematic of the definition process (for instance knowing the ai, bi points + \{A\} and \{B\} allows to compute Jacobian, etc\ldots{})

\item What is important for the model:
\begin{itemize}
\item Inertia of plates and struts
\item Positions of joints / Orientation of struts
\item Definition of frames (for Jacobian, stiffness analysis, etc\ldots{})
\end{itemize}
\end{itemize}

Then, several things can be computed:
\begin{itemize}
\item Kinematics, stiffness, platform mobility, dynamics, etc\ldots{}
\end{itemize}


\begin{itemize}
\item Joints: can be 2dof to 6dof
\item Actuators: can be modelled as wanted
\end{itemize}

\section{Nano Hexapod}
\label{ssec:nhexa_model_nano_hexapod}

Start simple:
\begin{itemize}
\item Perfect joints, massless actuators
\end{itemize}

Joints: perfect 2dof/3dof (+ mass-less)
Actuators: APA + Encoder (mass-less)
\begin{itemize}
\item k = 1N/um
\item Force sensor
\end{itemize}

Definition of each part + Plant with defined inputs/outputs (force sensor, relative displacement sensor, etc\ldots{})

\section{Model Dynamics}
\label{ssec:nhexa_model_dynamics}

\begin{itemize}
\item If all is perfect (mass-less struts, perfect joints, etc\ldots{}), maybe compare analytical model with simscape model?
\item Say something about the model order
Model order is 12, and that we can compute modes from matrices M and K, compare with the Simscape model
\item Compare with analytical formulas (see number of states)
\end{itemize}

\section*{Conclusion}
\begin{itemize}
\item Validation of multi-body model in a simple case
\item Possible to increase the model complexity when required
\begin{itemize}
\item If considered 6dof joint stiffness, model order increases
\item Can have an effect on IFF performances: \cite{preumont07_six_axis_singl_stage_activ}
\item Conclusion: during the conceptual design, we consider a perfect, but will be taken into account later
\item Optimization of the Flexible joint will be performed in Chapter 2.2
\end{itemize}
\item MIMO system: how to control? => next section
\end{itemize}

\chapter{Control of Stewart Platforms}
\label{sec:nhexa_control}
MIMO control: much more complex than SISO control because of interaction.
Possible to ignore interaction when good decoupling is achieved.
Important to have tools to study interaction
Different ways to try to decouple a MIMO plant.

Reference book: \cite{skogestad07_multiv_feedb_contr}
\section{Centralized and Decentralized Control}
\label{ssec:nhexa_control_centralized_decentralized}

\begin{itemize}
\item Explain what is centralized and decentralized:
\begin{itemize}
\item linked to the sensor position relative to the actuators
\item linked to the fact that sensors and actuators pairs are ``independent'' or each other (related to the control architecture, not because there is no coupling)
\end{itemize}
\item When can decentralized control be used and when centralized control is necessary?
Study of interaction: RGA
\end{itemize}

\section{Choice of the control space}
\label{ssec:nhexa_control_space}

\begin{itemize}
\item[{$\square$}] \url{file:///home/thomas/Cloud/research/matlab/decoupling-strategies/svd-control.org}

\item Jacobian matrices, CoK, CoM, control in the frame of the struts, SVD, Modal, \ldots{}
\item Combined CoM and CoK => Discussion of cubic architecture ? (quick, as it is going to be in detailed in chapter 2)
\item Explain also the link with the setpoint: it is interesting to have the controller in the frame of the performance variables
Also speak about disturbances? (and how disturbances can be mixed to different outputs due to control and interaction)
\item Table that summarizes the trade-off for each strategy
\item Say that in this study, we will do the control in the frame of the struts for simplicity (even though control in the cartesian frame was also tested)
\end{itemize}

\section{Active Damping with Decentralized IFF}
\label{ssec:nhexa_control_iff}

Guaranteed stability: \cite{preumont08_trans_zeros_struc_contr_with}
\begin{itemize}
\item[{$\square$}] I think there is another paper about that
\end{itemize}

For decentralized control: ``MIMO root locus'' can be used to estimate the damping / optimal gain
Poles and converging towards \emph{transmission zeros}

How to optimize the added damping to all modes?
\begin{itemize}
\item[{$\square$}] Add some papers citations
\end{itemize}

Compute:
\begin{itemize}
\item[{$\square$}] Plant dynamics
\item[{$\square$}] Root Locus
\end{itemize}

\section{MIMO High-Authority Control - Low-Authority Control}
\label{ssec:nhexa_control_hac_lac}

Compute:
\begin{itemize}
\item[{$\square$}] compare open-loop and damped plant (outputs are the encoders)
\item[{$\square$}] Implement decentralized control?
\item[{$\square$}] Check stability:
\begin{itemize}
\item Characteristic Loci: Eigenvalues of \(G(j\omega)\) plotted in the complex plane
\item Generalized Nyquist Criterion: If \(G(s)\) has \(p_0\) unstable poles, then the closed-loop system with return ratio \(kG(s)\) is stable if and only if the characteristic loci of \(kG(s)\), taken together, encircle the point \(-1\), \(p_0\) times anti-clockwise, assuming there are no hidden modes
\end{itemize}
\item[{$\square$}] Show some performance metric? For instance compliance?
\end{itemize}

\section*{Conclusion}


\chapter*{Conclusion}
\label{sec:nhexa_conclusion}

\begin{itemize}
\item Configurable Stewart platform model
\item Will be included in the multi-body model of the micro-station => nass multi body model
\item Control: complex problem, try to use simplest architecture
\end{itemize}

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