Add table with matlab files

nass-uniaxial-model.org

@@ -70,6 +70,19 @@ Once the system is well damped, a feedback position controller is applied, and t
 
 Conclusion remarks are given in Section ref:sec:conclusion.
 
+#+name: tab:section_matlab_code
+#+caption: Report sections and corresponding Matlab files
+#+attr_latex: :environment tabularx :width 0.6\linewidth :align lX
+#+attr_latex: :center t :booktabs t
+| *Sections*                                | *Matlab File*                       |
+|-------------------------------------------+-------------------------------------|
+| Section ref:sec:micro_station_model       | =uniaxial_1_micro_station_model.m=  |
+| Section ref:sec:nano_station_model        | =uniaxial_2_nano_hexapod_model.m=   |
+| Section ref:sec:uniaxial_disturbances     | =uniaxial_3_disturbances.m=         |
+| Section ref:sec:uniaxial_noise_budgeting  | =uniaxial_4_dynamic_noise_budget.m= |
+| Section ref:sec:uniaxial_active_damping   | =uniaxial_5_active_damping.m=       |
+| Section ref:sec:uniaxial_position_control | =uniaxial_6_hac_lac.m=              |
+
 #+begin_src latex :file uniaxial_overview_model_sections.pdf
 \begin{tikzpicture}
   % ====================
@@ -211,7 +224,6 @@ Conclusion remarks are given in Section ref:sec:conclusion.
 #+RESULTS:
 [[file:figs/uniaxial_overview_model_sections.png]]
 
-
 * Micro Station Model
 :PROPERTIES:
 :HEADER-ARGS:matlab+: :tangle matlab/uniaxial_1_micro_station_model.m

nass-uniaxial-model.tex

@@ -1,7 +1,25 @@
-% Created 2023-02-17 Fri 11:26
+% Created 2023-02-20 Mon 10:57
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, 10pt, DIV=12, parskip=full]{scrreprt}
-
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{grffile}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{textcomp}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\usepackage[most]{tcolorbox}
+\usepackage{bm}
+\usepackage{booktabs}
+\usepackage{tabularx}
+\usepackage{array}
+\usepackage{siunitx}
 \input{preamble.tex}
 \author{Dehaeze Thomas}
 \date{\today}
@@ -41,14 +59,31 @@ Once the system is well damped, a feedback position controller is applied, and t
 
 Conclusion remarks are given in Section \ref{sec:conclusion}.
 
+\begin{table}[htbp]
+\caption{\label{tab:section_matlab_code}Report sections and corresponding Matlab files}
+\centering
+\begin{tabularx}{0.5\linewidth}{lX}
+\toprule
+\textbf{Sections} & \textbf{Matlab File}\\
+\midrule
+Section \ref{sec:micro_station_model} & \texttt{uniaxial\_1\_micro\_station\_model.m}\\
+Section \ref{sec:nano_station_model} & \texttt{uniaxial\_2\_nano\_hexapod\_model.m}\\
+Section \ref{sec:uniaxial_disturbances} & \texttt{uniaxial\_3\_disturbances.m}\\
+Section \ref{sec:uniaxial_noise_budgeting} & \texttt{uniaxial\_4\_dynamic\_noise\_budget.m}\\
+Section \ref{sec:uniaxial_active_damping} & \texttt{uniaxial\_5\_active\_damping.m}\\
+Section \ref{sec:uniaxial_position_control} & \texttt{uniaxial\_6\_hac\_lac.m}\\
+\bottomrule
+\end{tabularx}
+\end{table}
+
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1]{figs/uniaxial_overview_model_sections.png}
 \caption{\label{fig:uniaxial_overview_model_sections}Uniaxial Micro-Station model in blue (Section \ref{sec:micro_station_model}), Nano-Hexapod and sample models in red (Section \ref{sec:nano_station_model}), Disturbances in yellow (Section \ref{sec:uniaxial_disturbances}), Active Damping in green (Section \ref{sec:uniaxial_active_damping}) and Position control in purple (Section \ref{sec:uniaxial_position_control})}
 \end{figure}
 
-
 \chapter{Micro Station Model}
+\label{sec:org4e07986}
 \label{sec:micro_station_model}
 In this section, a uni-axial model of the micro-station is tuned in order to match measurements made on the micro-station
 The measurement setup is shown in Figure \ref{fig:micro_station_first_meas_dynamics} where several geophones are fixed to the micro-station and an instrumented hammer is used to inject forces on different stages of the micro-station.
@@ -61,6 +96,7 @@ From the measured frequency response functions (FRF), the model can be tuned to
 \caption{\label{fig:micro_station_first_meas_dynamics}Experimental Setup for the first dynamical measurements on the Micro-Station. Geophones are fixed to the micro-station, and the granite as well as the micro-hexapod's top platform are impact with an instrumented hammer}
 \end{figure}
 \section{Measured dynamics}
+\label{sec:org525a6c0}
 
 The measurement setup is schematically shown in Figure \ref{fig:micro_station_meas_dynamics_schematic} where:
 \begin{itemize}
@@ -95,6 +131,7 @@ load('meas_microstation_frf.mat');
 \end{figure}
 
 \section{Uniaxial Model}
+\label{sec:orge223677}
 The uni-axial model of the micro-station is shown in Figure \ref{fig:uniaxial_comp_frf_meas_model}, with:
 \begin{itemize}
 \item Disturbances:
@@ -137,6 +174,7 @@ cg = 2*0.08*sqrt(kg*mg); % [N/(m/s)]
 \end{minted}
 
 \section{Comparison of the model and measurements}
+\label{sec:orgfa10aaa}
 The comparison between the measurements and the model is done in Figure \ref{fig:uniaxial_comp_frf_meas_model}.
 
 As the model is simplistic, the goal is not to match exactly the measurement but to have a first approximation.
@@ -149,6 +187,7 @@ More accurate models will be used later on.
 \end{figure}
 
 \chapter{Nano-Hexapod Model}
+\label{sec:org5ef4103}
 \label{sec:nano_station_model}
 A model of the nano-hexapod and sample is now added on top of the uni-axial model of the micro-station (Figure \ref{fig:uniaxial_model_micro_station-nass}).
 
@@ -170,6 +209,7 @@ The effect of having resonances between the sample's point of interest and the n
 \caption{\label{fig:uniaxial_model_micro_station-nass}Uni-axial model of the micro-station with added nano-hexapod (represented in blue) and sample (represented in green)}
 \end{figure}
 \section{Nano-Hexapod Parameters}
+\label{sec:orge14d0af}
 The parameters for the nano-hexapod and sample are:
 \begin{itemize}
 \item \(m_s\) the sample mass that can vary from 1kg up to 50kg
@@ -190,6 +230,7 @@ ms = 10; % [kg]
 \end{minted}
 
 \section{Obtained Dynamics}
+\label{sec:orgddb8cf5}
 The sensitivity to disturbances (i.e. \(x_f\), \(f_t\) and \(f_s\)) are shown in Figure \ref{fig:uniaxial_sensitivity_dist_first_params}.
 The \emph{plant} (i.e. the transfer function from actuator force \(f\) to measured displacement \(d\)) is shown in Figure \ref{fig:uniaxial_plant_first_params}.
 
@@ -207,6 +248,7 @@ For further analysis, 9 configurations are considered: three nano-hexapod stiffn
 \caption{\label{fig:uniaxial_plant_first_params}Bode Plot of the transfer function from actuator forces to measured displacement by the metrology}
 \end{figure}
 \chapter{Disturbance Identification}
+\label{sec:org2036233}
 \label{sec:uniaxial_disturbances}
 In order to measure disturbances, two geophones are used, on located on the floor and on on the micro-hexapod's top platform (see Figure \ref{fig:micro_station_meas_disturbances}).
 
@@ -224,6 +266,7 @@ The geophone on the floor is used to measured the floor motion \(x_f\) while the
 \caption{\label{fig:micro_station_dynamical_id_setup}Two geophones are used to measure the micro-station vibrations induced by the scanning of the \(T_y\) and \(R_z\) stages}
 \end{figure}
 \section{Ground Motion}
+\label{sec:org931b2ea}
 The geophone fixed to the floor to measure the floor motion.
 
 \begin{minted}[]{matlab}
@@ -284,6 +327,7 @@ The amplitude spectral density \(\Gamma_{x_f}\) of the measured displacement \(x
 \end{figure}
 
 \section{Stage Vibration}
+\label{sec:orga7b3779}
 During Spindle rotation (here at 6rpm), the granite velocity and micro-hexapod's top platform velocity are measured with the geophones.
 
 \begin{minted}[]{matlab}
@@ -339,9 +383,11 @@ The vibrations induced by the \(T_y\) stage are not considered here as:
 \end{itemize}
 
 \chapter{Open-Loop Dynamic Noise Budgeting}
+\label{sec:org11bfa6e}
 \label{sec:uniaxial_noise_budgeting}
 Now that we have a model of the NASS and an estimation of the power spectral density of the disturbances, it is possible to perform an \emph{open-loop dynamic noise budgeting}.
 \section{Sensitivity to disturbances}
+\label{sec:org469c500}
 From the Uni-axial model, the transfer function from the disturbances (\(f_s\), \(x_f\) and \(f_t\)) to the displacement \(d\) are computed.
 
 This is done for \textbf{two extreme sample masses} \(m_s = 1\,\text{kg}\) and \(m_s = 50\,\text{kg}\) and \textbf{three nano-hexapod stiffnesses}:
@@ -369,6 +415,7 @@ From Figure \ref{fig:uniaxial_sensitivity_disturbances_nano_hexapod_stiffnesses}
 \end{figure}
 
 \section{Open-Loop Dynamic Noise Budgeting}
+\label{sec:org99b18ec}
 Now, the power spectral density of the disturbances is taken into account to estimate the residual motion \(d\) in each case.
 
 The Cumulative Amplitude Spectrum of the relative motion \(d\) due to both the floor motion \(x_f\) and the stage vibrations \(f_t\) are shown in Figure \ref{fig:uniaxial_cas_d_disturbances_stiffnesses} for the three nano-hexapod stiffnesses.
@@ -391,6 +438,7 @@ The conclusion is that the sample's mass has little effect on the cumulative amp
 \end{figure}
 
 \section{Conclusion}
+\label{sec:org6160aae}
 \begin{important}
 The conclusion is that in order to have a closed-loop residual vibration \(d \approx 20\,nm\text{ rms}\), if a simple feedback controller is used, the required closed-loop bandwidth would be:
 \begin{itemize}
@@ -405,6 +453,7 @@ This gives a first advantage to having a soft nano-hexapod.
 \end{important}
 
 \chapter{Active Damping}
+\label{sec:orgc25f9e5}
 \label{sec:uniaxial_active_damping}
 In this section, three active damping are applied on the nano-hexapod (see Figure \ref{fig:uniaxial_active_damping_strategies}): Integral Force Feedback (IFF), Relative Damping Control (RDC) and Direct Velocity Feedback (DVF).
 
@@ -421,6 +470,7 @@ These active damping techniques are compared in terms of:
 \caption{\label{fig:uniaxial_active_damping_strategies}Three active damping strategies: Integral Force Feedback (IFF) using a force sensor, Relative Damping Control (RDC) using a relative displacement sensor, and Direct Velocity Feedback (DVF) using a geophone}
 \end{figure}
 \section{Active Damping Strategies}
+\label{sec:org224d0f3}
 
 The Integral Force Feedback strategy consists of using a force sensor in series with the actuator (see Figure \ref{fig:uniaxial_active_damping_iff_equiv}, left).
 
@@ -470,6 +520,7 @@ This is usually refers to as ``\emph{sky hook damper}''.
 \end{figure}
 
 \section{Plant Dynamics for Active Damping}
+\label{sec:orga11bdaf}
 The plant dynamics for all three active damping techniques are shown in Figure \ref{fig:uniaxial_plant_active_damping_techniques}.
 All have \textbf{alternating poles and zeros} meaning that the phase is bounded to \(\pm 90\,\text{deg}\) which makes the controller very robust.
 
@@ -485,6 +536,7 @@ Therefore, it is expected that the micro-station dynamics might impact the achie
 \end{figure}
 
 \section{Achievable Damping - Root Locus}
+\label{sec:org682230b}
 The Root Locus are computed for the three nano-hexapod stiffnesses and for the three active damping techniques.
 They are shown in Figure \ref{fig:uniaxial_root_locus_damping_techniques}.
 
@@ -506,6 +558,7 @@ This can be explained by the fact that above the suspension mode of the soft nan
 \end{figure}
 
 \section{Change of sensitivity to disturbances}
+\label{sec:org240dd20}
 The sensitivity to disturbances (direct forces \(f_s\), stage vibrations \(f_t\) and floor motion \(x_f\)) for all three active damping techniques are compared in Figure \ref{fig:uniaxial_sensitivity_dist_active_damping}.
 The comparison is done with the nano-hexapod having a stiffness \(k_n = 1\,N/\mu m\).
 
@@ -525,6 +578,7 @@ Conclusions from Figure \ref{fig:uniaxial_sensitivity_dist_active_damping} are:
 \end{figure}
 
 \section{Noise Budgeting after Active Damping}
+\label{sec:org59aa5fa}
 Cumulative Amplitude Spectrum of the distance \(d\) with all three active damping techniques are compared in Figure \ref{fig:uniaxial_cas_active_damping}.
 All three active damping methods are giving similar results (except the RDC which is a little bit worse for the stiff nano-hexapod).
 
@@ -537,6 +591,7 @@ Compare to the open-loop case, the active damping helps to lower the vibrations
 \end{figure}
 
 \section{Obtained Damped Plant}
+\label{sec:org534205b}
 The transfer functions from the plant input \(f\) to the relative displacement \(d\) while the active damping is implemented are shown in Figure \ref{fig:uniaxial_damped_plant_three_active_damping_techniques}.
 All three active damping techniques yield similar damped plants.
 
@@ -554,6 +609,7 @@ The damped plants are shown in Figure \ref{fig:uniaxial_damped_plant_change_samp
 \end{figure}
 
 \section{Robustness to change of payload's mass}
+\label{sec:org1194b7f}
 The Root Locus for the three damping techniques are shown in Figure \ref{fig:uniaxial_active_damping_robustness_mass_root_locus} for three sample's mass (1kg, 25kg and 50kg).
 The closed-loop poles are shown by the squares for a specific gain.
 
@@ -566,6 +622,7 @@ We can see that having heavier samples yields larger damping for IFF and smaller
 \end{figure}
 
 \section{Conclusion}
+\label{sec:orgd9c89ae}
 
 \begin{important}
 Conclusions for Active Damping:
@@ -598,6 +655,7 @@ Conclusions for Active Damping:
 \end{table}
 
 \chapter{Position Feedback Controller}
+\label{sec:orgb8f8fbb}
 \label{sec:uniaxial_position_control}
 The High Authority Control - Low Authority Control (HAC-LAC) architecture is shown in Figure \ref{fig:uniaxial_hac_lac_architecture}.
 It corresponds to a \emph{two step} control strategy:
@@ -625,6 +683,7 @@ Combined with the uniaxial model, it is shown in Figure \ref{fig:uniaxial_hac_la
 \caption{\label{fig:uniaxial_hac_lac}High Authority Control - Low Authority Control (HAC-LAC)}
 \end{figure}
 \section{Damped Plant Dynamics}
+\label{sec:orge78415e}
 As was shown in Section \ref{sec:uniaxial_active_damping}, all three proposed active damping techniques yield similar damping plants.
 Therefore, \emph{Integral Force Feedback} will be used in this section to study the HAC-LAC performances.
 
@@ -637,6 +696,7 @@ The obtained damped plants for the three nano-hexapod stiffnesses are shown in F
 \end{figure}
 
 \section{Position Feedback Controller}
+\label{sec:orgbfebc9e}
 The objective now is to design a position feedback controller for each of the three nano-hexapods that are robust to the change of sample's mass.
 
 The required feedback bandwidth was approximately determined un Section \ref{sec:uniaxial_noise_budgeting}:
@@ -683,6 +743,7 @@ The goal is just to have a first estimation of the attainable performances.
 \end{figure}
 
 \section{Closed-Loop Noise Budgeting}
+\label{sec:org6f05561}
 The high authority position feedback controllers are then implemented and the closed-loop sensitivity to disturbances are computed.
 These are compared with the open-loop and damped plants cases in Figure \ref{fig:uniaxial_sensitivity_dist_hac_lac} for just one configuration (moderately stiff nano-hexapod with 25kg sample's mass).
 As expected, the sensitivity to disturbances is decreased in the controller bandwidth and slightly increase outside this bandwidth.
@@ -704,6 +765,7 @@ Obtained root mean square values of the distance \(d\) are better for the soft n
 \end{figure}
 
 \chapter{Conclusion}
+\label{sec:org1cd0a09}
 \label{sec:conclusion}
 
 In this study, a uniaxial model of the nano-active-stabilization-system has been tuned both from dynamical measurements (Section \ref{sec:micro_station_model}) and from disturbances measurements (Section \ref{sec:uniaxial_disturbances}).