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\input{preamble.tex}
\input{preamble_extra.tex}
\bibliography{simscape-nass.bib}
\author{Dehaeze Thomas}
\date{\today}
\title{Simscape Model - Nano Active Stabilization System}
\hypersetup{
 pdfauthor={Dehaeze Thomas},
 pdftitle={Simscape Model - Nano Active Stabilization System},
 pdfkeywords={},
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 pdfcreator={Emacs 29.4 (Org mode 9.6)}, 
 pdflang={English}}
\usepackage{biblatex}

\begin{document}

\maketitle
\tableofcontents

\clearpage

From last sections:
\begin{itemize}
\item Uniaxial: No stiff nano-hexapod (should also demonstrate that here)
\item Rotating: No soft nano-hexapod, Decentralized IFF can be used robustly by adding parallel stiffness
\end{itemize}

In this section:
\begin{itemize}
\item Take the model of the nano-hexapod with stiffness 1um/N
\item Apply decentralized IFF
\item Apply HAC-LAC
\item Check robustness to payload change
\item Simulation of experiments
\end{itemize}

\chapter{Control Kinematics}
\label{sec:nass_kinematics}
\begin{itemize}
\item Explained during the last section: HAC-IFF
Decentralized IFF
Centralized HAC, control in the frame of the struts
\item To compute the positioning errors in the frame of the struts
\begin{itemize}
\item Compute the wanted pose of the sample with respect to the granite using the micro-station kinematics (Section \ref{ssec:nass_ustation_kinematics})
\item Measure the sample pose with respect to the granite using the external metrology and internal metrology for Rz (Section \ref{ssec:nass_sample_pose_error})
\item Compute the sample pose error and map these errors in the frame of the struts (Section \ref{ssec:nass_error_struts})
\end{itemize}
\item The complete control architecture is shown in Section \ref{ssec:nass_control_architecture}

\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning\_error.org}{positioning\_error}: Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)

\item[{$\square$}] Schematic with micro-station + nass + metrology + control system => explain what is inside the control system
\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/nass_concept_schematic.png}
\caption{\label{fig:nass_concept_schematic}Figure caption}
\end{figure}
\section{Micro Station Kinematics}
\label{ssec:nass_ustation_kinematics}

\begin{itemize}
\item from \ref{ssec:ustation_kinematics}, computation of the wanted sample pose from the setpoint of each stage.
\end{itemize}

wanted pose = Tdy * Try * Trz * Tu


\section{Computation of the sample's pose error}
\label{ssec:nass_sample_pose_error}

From metrology (here supposed to be perfect 6-DoF), compute the sample's pose error.
Has to invert the homogeneous transformation.

In reality, 5DoF metrology => have to estimate the Rz using spindle encoder + nano-hexapod internal metrology (micro-hexapod does not perform Rz rotation).

\section{Position error in the frame of the struts}
\label{ssec:nass_error_struts}

Explain how to compute the errors in the frame of the struts (rotating):
\begin{itemize}
\item Errors in the granite frame
\item Errors in the frame of the nano-hexapod
\item Errors in the frame of the struts => used for control
\end{itemize}

\section{Control Architecture}
\label{ssec:nass_control_architecture}

\begin{itemize}
\item Say that there are many control strategies.
It will be the topic of chapter 2.3.
Here, we start with something simple: control in the frame of the struts
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/nass_control_architecture.png}
\caption{\label{fig:nass_control_architecture}The physical systems are shown in blue, the control kinematics in red, the decentralized Integral Force Feedback in yellow and the centralized High Authority Controller in green.}
\end{figure}

\chapter{Decentralized Active Damping}
\label{sec:nass_active_damping}
\begin{itemize}
\item How to apply/optimize IFF on an hexapod?
\item Robustness to payload mass
\item Root Locus
\item Damping optimization
\item \textbf{Parallel stiffness?}
\end{itemize}

Explain which samples are tested:
\begin{itemize}
\item 1kg, 25kg, 50kg
\item cylindrical, 200mm height?

\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control\_active\_damping.org}{control\_active\_damping}
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org}{active damping for stewart platforms}
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org}{Vibration Control and Active Damping}
\end{itemize}
\section{IFF Plant}

\begin{itemize}
\item[{$\square$}] Show how it changes with the payload mass (1, 25, 50)
\item[{$\square$}] Effect of rotation (no rotation - 60rpm)
\item[{$\square$}] Added parallel stiffness
\end{itemize}

Coupling

Effect of rotation

Effect of payload mass

\section{Controller Design}

Low pass filter needs to be added (because now: DC gain)

\begin{equation}\label{eq:nass_kiff}
    \bm{K}_{\text{IFF}}(s) = g \cdot \begin{bmatrix}
        K_{\text{IFF}}(s) & & 0 \\
        & \ddots & \\
        0 & & K_{\text{IFF}}(s)
    \end{bmatrix}, \quad K_{\text{IFF}}(s) = \frac{1}{s}
\end{equation}

Loop Gain:
Root Locus => Stability

\begin{itemize}
\item Use Integral controller (with parallel stiffness)
\item Show Root Locus (show that without parallel stiffness => unstable?)
\item Choose optimal gain.
Here in MIMO, cannot have optimal damping for all modes. (there is a paper that tries to optimize that)
\item[{$\square$}] Show robustness to change of payload (loci?) / Change of rotating velocity ?
\item Reference to paper showing stability in MIMO for decentralized IFF
\end{itemize}


\section{Sensitivity to disturbances}

Disturbances:
\begin{itemize}
\item floor motion
\item Spindle X and Z
\item Direct forces?

\item Compute sensitivity to disturbances with and without IFF (and compare without the NASS)

\item Maybe noise budgeting, but may be complex in MIMO\ldots{} ?
\end{itemize}

\chapter{Centralized Active Vibration Control}
\label{sec:nass_hac}
\begin{itemize}
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty\_experiment.org}{uncertainty\_experiment}: Effect of experimental conditions on the plant (payload mass, Ry position, Rz position, Rz velocity, etc\ldots{})
\item Effect of micro-station compliance
\item Effect of IFF
\item Effect of payload mass
\item Decoupled plant
\item Controller design
\end{itemize}

From control kinematics:
\begin{itemize}
\item Talk about issue of not estimating Rz from external metrology? (maybe could be nice to discuss that during the experiments!)
\item Show what happens is Rz is not estimated (for instance supposed equaled to zero => increased coupling)
\end{itemize}
\section{HAC Plant}

\begin{itemize}
\item[{$\square$}] Compute transfer function from \(\bm{f}\) to \(\bm{\epsilon\mathcal{L}}\) (with IFF applied) for all masses
\item[{$\square$}] Show effect of rotation
\item[{$\square$}] Show effect of payload mass
\item[{$\square$}] Compare with undamped plants
\end{itemize}

Effect of rotation:

Effect of IFF:

Effect of payload mass

Advantage of using IFF:
\section{Controller design}

\begin{itemize}
\item[{$\square$}] Show design HAC with formulas and parameters
\item[{$\square$}] Show robustness with Loci for all masses
\end{itemize}

\begin{equation}\label{eq:nass_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)
\end{equation}

``Decentralized'' Loop Gain:
Characteristic Loci for three masses:
\section{Sensitivity to disturbances}

\begin{itemize}
\item Compute transfer functions from spindle vertical error to sample vertical error with HAC-IFF
Compare without the NASS, and with just IFF
\item Same for horizontal
\end{itemize}

\section{Tomography experiment}

\begin{itemize}
\item With HAC-IFF, perform tomography experiment, and compare with open-loop

\item Take into account disturbances, metrology sensor noise. Maybe say here that we don't take in account other noise sources as they will be optimized latter (detail design phase)
\item Tomography + lateral scans (same as what was done in open loop \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A4-simscape-micro-station/simscape-micro-station.org}{here})
\item Validation of concept
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/nass_tomography_hac_iff_m1.png}
\end{center}
\subcaption{\label{fig:nass_tomography_hac_iff_m1} $m = 1\,kg$}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/nass_tomography_hac_iff_m25.png}
\end{center}
\subcaption{\label{fig:nass_tomography_hac_iff_m25} $m = 25\,kg$}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/nass_tomography_hac_iff_m50.png}
\end{center}
\subcaption{\label{fig:nass_tomography_hac_iff_m50} $m = 50\,kg$}
\end{subfigure}
\caption{\label{fig:nass_tomography_hac_iff}Simulation of tomography experiments}
\end{figure}

\chapter{Conclusion}
\label{sec:nass_conclusion}


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