Rename few figures to match the "prefix"

.latexmkrc

@@ -19,7 +19,7 @@
 # 3: dvi conversion, as specified by the $dvipdf variable (useless)
 # 4: lualatex, as specified by the $lualatex variable (best)
 # 5: xelatex, as specified by the $xelatex variable (second best)
-$pdf_mode = 1;
+$pdf_mode = 4;
 
 # Treat undefined references and citations as well as multiply defined references as
 # ERRORS instead of WARNINGS.
@@ -39,12 +39,12 @@ $pdf_mode = 1;
 $warnings_as_errors = 0;
 
 # Show used CPU time. Looks like: https://tex.stackexchange.com/a/312224/120853
-$show_time = 1;
+$show_time = 0;
 
 # Default is 5; we seem to need more owed to the complexity of the document.
 # Actual documents probably don't need this many since they won't use all features,
 # plus won't be compiling from cold each time.
-$max_repeat=7;
+$max_repeat=10;
 
 # --shell-escape option (execution of code outside of latex) is required for the
 #'svg' package.
@@ -65,7 +65,8 @@ $max_repeat=7;
 set_tex_cmds("--shell-escape -interaction=nonstopmode --synctex=1 %O %S");
 
 # Use default pdf viewer
-$pdf_previewer = 'zathura';
+$pdf_update_method = 1;
+$pdf_previewer = "zathura %O %S";
 
 # option 2 is same as 1 (run biber when necessary), but also deletes the
 # regeneratable bbl-file in a clenaup (`latexmk -c`). Do not use if original

nass-uniaxial-model.org

@@ -95,6 +95,9 @@
                                        org-ref-acronyms-before-parsing))
 #+END_SRC
 
+* Notes                                                             :noexport:
+Prefix is =uniaxial=
+
 * Introduction                                                        :ignore:
 
 In this report, a uniaxial model of the Nano Active Stabilization System (NASS) is developed and used to have a first idea of the challenges involved in this complex system.
@@ -291,14 +294,14 @@ Conclusion remarks are given in Section ref:sec:uniaxial_conclusion.
 ** Introduction                                                      :ignore:
 
 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.
+The measurement setup is shown in Figure ref:fig:uniaxial_ustation_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.
 
 From the measured frequency response functions (FRF), the model can be tuned to approximate the uniaxial dynamics of the micro-station.
 
-#+name: fig:micro_station_first_meas_dynamics
+#+name: fig:uniaxial_ustation_first_meas_dynamics
 #+caption: 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
 #+attr_latex: :width \linewidth
-[[file:figs/micro_station_first_meas_dynamics.jpg]]
+[[file:figs/uniaxial_ustation_first_meas_dynamics.jpg]]
 
 ** Matlab Init                                            :noexport:ignore:
 #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@@ -333,7 +336,7 @@ freqs = logspace(0, 3, 1000);
 
 ** Measured dynamics
 
-The measurement setup is schematically shown in Figure ref:fig:micro_station_meas_dynamics_schematic where:
+The measurement setup is schematically shown in Figure ref:fig:uniaxial_ustation_meas_dynamics_schematic where:
 - Two hammer hits are performed, one on the Granite (force $F_g$), and one on the micro-hexapod's top platform (force $F_h$)
 - The inertial motion of the granite $x_g$ and the micro-hexapod's top platform $x_h$ are measured using geophones.
 
@@ -342,7 +345,7 @@ From the forces applied by the instrumented hammer and the responses of the geop
 - from $F_g$ to $d_h$ (or from $F_h$ to $d_g$)
 - from $F_g$ to $d_g$
 
-#+begin_src latex :file micro_station_meas_dynamics_schematic.pdf :results file raw silent
+#+begin_src latex :file uniaxial_ustation_meas_dynamics_schematic.pdf :results file raw silent
 \begin{tikzpicture}
   % Parameters
   \def\blockw{6.0cm}
@@ -486,11 +489,11 @@ From the forces applied by the instrumented hammer and the responses of the geop
 #+name: fig:micro_station_uniaxial_model
 #+caption: Schematic of the Micro-Station measurement setup and uniaxial model.
 #+begin_figure
-#+attr_latex: :caption \subcaption{\label{fig:micro_station_meas_dynamics_schematic}Measurement setup - Schematic}
+#+attr_latex: :caption \subcaption{\label{fig:uniaxial_ustation_meas_dynamics_schematic}Measurement setup - Schematic}
 #+attr_latex: :options {0.69\textwidth}
 #+begin_subfigure
 #+attr_latex: :scale 1
-[[file:figs/micro_station_meas_dynamics_schematic.png]]
+[[file:figs/uniaxial_ustation_meas_dynamics_schematic.png]]
 #+end_subfigure
 #+attr_latex: :caption \subcaption{\label{fig:uniaxial_model_micro_station}Uniaxial model of the micro-station}
 #+attr_latex: :options {0.29\textwidth}
@@ -1139,11 +1142,11 @@ save('./mat/uniaxial_plants.mat', 'G_vc_light', 'G_md_light', 'G_pz_light', ...
 <<sec:uniaxial_disturbances>>
 ** Introduction                                                      :ignore:
 
-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).
+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:uniaxial_ustation_meas_disturbances).
 
 The geophone on the floor is used to measured the floor motion $x_f$ while the geophone on the micro-hexapod is used to measure vibrations introduced by scanning of the $T_y$ stage and $R_z$ stage.
 
-#+begin_src latex :file micro_station_meas_disturbances.pdf
+#+begin_src latex :file uniaxial_ustation_meas_disturbances.pdf
 \begin{tikzpicture}
   % Parameters
   \def\blockw{6.0cm}
@@ -1279,15 +1282,15 @@ The geophone on the floor is used to measured the floor motion $x_f$ while the g
 \end{tikzpicture}
 #+end_src
 
-#+name: fig:micro_station_meas_disturbances
+#+name: fig:uniaxial_ustation_meas_disturbances
 #+caption: Disturbance measurement setup - Schematic
 #+RESULTS:
-[[file:figs/micro_station_meas_disturbances.png]]
+[[file:figs/uniaxial_ustation_meas_disturbances.png]]
 
-#+name: fig:micro_station_dynamical_id_setup
+#+name: fig:uniaxial_ustation_dynamical_id_setup
 #+caption: Two geophones are used to measure the micro-station vibrations induced by the scanning of the $T_y$ and $R_z$ stages
 #+attr_latex: :width 0.6\linewidth
-[[file:figs/micro_station_dynamical_id_setup.jpg]]
+[[file:figs/uniaxial_ustation_dynamical_id_setup.jpg]]
 
 ** Matlab Init                                              :noexport:ignore:
 #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@@ -1375,7 +1378,7 @@ with:
 psd_xf = psd_V.*abs(squeeze(freqresp(G_geo, f, 'Hz'))).^2; % [m^2/Hz]
 #+end_src
 
-The amplitude spectral density $\Gamma_{x_f}$ of the measured displacement $x_f$ is shown in Figure ref:fig:asd_floor_motion_id31.
+The amplitude spectral density $\Gamma_{x_f}$ of the measured displacement $x_f$ is shown in Figure ref:fig:uniaxial_asd_floor_motion_id31.
 
 #+begin_src matlab :exports none :results none
 %% Amplitude Spectral Density of the measured Floor motion on ID31
@@ -1390,13 +1393,13 @@ legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/asd_floor_motion_id31.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/uniaxial_asd_floor_motion_id31.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:asd_floor_motion_id31
+#+name: fig:uniaxial_asd_floor_motion_id31
 #+caption: Amplitude Spectral Density of the measured Floor motion on ID31
 #+RESULTS:
-[[file:figs/asd_floor_motion_id31.png]]
+[[file:figs/uniaxial_asd_floor_motion_id31.png]]
 
 ** Stage Vibration
 During Spindle rotation (here at 6rpm), the granite velocity and micro-hexapod's top platform velocity are measured with the geophones.
@@ -1420,7 +1423,7 @@ win = hanning(ceil(2*Fs)); % Hanning window
 [psd_off, ~] = pwelch(spindle_off.vh-spindle_off.vg, win, [], [], Fs); % [(m/s)^2/Hz]
 #+end_src
 
-It is then integrated to obtain the Amplitude Spectral Density of the relative motion which is compared with a non-rotating case (Figure ref:fig:asd_vibration_spindle_rotation).
+It is then integrated to obtain the Amplitude Spectral Density of the relative motion which is compared with a non-rotating case (Figure ref:fig:uniaxial_asd_vibration_spindle_rotation).
 It is shown that the spindle rotation induces vibrations in a wide frequency spectrum.
 
 #+begin_src matlab :exports none :results none
@@ -1437,13 +1440,13 @@ xlim([1, 500]); ylim([1e-12, 1e-7])
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/asd_vibration_spindle_rotation.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/uniaxial_asd_vibration_spindle_rotation.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:asd_vibration_spindle_rotation
+#+name: fig:uniaxial_asd_vibration_spindle_rotation
 #+caption: Amplitude Spectral Density of the relative motion measured between the granite and the micro-hexapod's top platform during Spindle rotating
 #+RESULTS:
-[[file:figs/asd_vibration_spindle_rotation.png]]
+[[file:figs/uniaxial_asd_vibration_spindle_rotation.png]]
 
 In order to compute the equivalent disturbance force $f_t$ that induces such motion, the transfer function from $f_t$ to the relative motion of the hexapod's top platform and the granite is extracted from the model.
 #+begin_src matlab :exports none
@@ -1477,7 +1480,7 @@ with:
 psd_ft = (psd_vft./(2*pi*f).^2)./abs(squeeze(freqresp(G('Dh', 'ft') - G('Dg', 'ft'), f, 'Hz'))).^2;
 #+end_src
 
-The obtained amplitude spectral density of the disturbance force $f_t$ is shown in Figure ref:fig:asd_disturbance_force.
+The obtained amplitude spectral density of the disturbance force $f_t$ is shown in Figure ref:fig:uniaxial_asd_disturbance_force.
 #+begin_src matlab :exports none :results none
 %% Estimated disturbance force ft from measurement and uniaxial model
 figure;
@@ -1491,13 +1494,13 @@ legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 #+end_src
 
 #+begin_src matlab :tangle no :exports results :results file replace
-exportFig('figs/asd_disturbance_force.pdf', 'width', 'wide', 'height', 'normal');
+exportFig('figs/uniaxial_asd_disturbance_force.pdf', 'width', 'wide', 'height', 'normal');
 #+end_src
 
-#+name: fig:asd_disturbance_force
+#+name: fig:uniaxial_asd_disturbance_force
 #+caption: Estimated disturbance force ft from measurement and uniaxial model
 #+RESULTS:
-[[file:figs/asd_disturbance_force.png]]
+[[file:figs/uniaxial_asd_disturbance_force.png]]
 
 The vibrations induced by the $T_y$ stage are not considered here because:
 - the induced vibrations have less amplitude than the vibrations induced by the $R_z$ stage

nass-uniaxial-model.tex

@@ -1,4 +1,4 @@
-% Created 2023-07-03 Mon 17:24
+% Created 2024-03-21 Thu 18:24
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
 
@@ -12,7 +12,7 @@
  pdftitle={Nano Active Stabilization System - Uniaxial Model},
  pdfkeywords={},
  pdfsubject={},
- pdfcreator={Emacs 28.2 (Org mode 9.5.2)}, 
+ pdfcreator={Emacs 29.2 (Org mode 9.7)}, 
  pdflang={English}}
 \usepackage{biblatex}
 
@@ -22,7 +22,6 @@
 \tableofcontents
 
 \clearpage
-
 In this report, a uniaxial model of the Nano Active Stabilization System (NASS) is developed and used to have a first idea of the challenges involved in this complex system.
 Note that in this document, only the vertical direction is considered (which is the most stiff), but other directions were considered as well and yields similar conclusions.
 The model is schematically shown in Figure \ref{fig:uniaxial_overview_model_sections} where the colors are representing the studied parts in different sections.
@@ -42,10 +41,10 @@ Once the system is well damped, a feedback position controller is applied, and t
 
 Two key effects that may limit that positioning performances are then considered: the limited micro-station compliance (Section \ref{sec:uniaxial_support_compliance}) and the presence of dynamics between the nano-hexapod and the sample's point of interest (Section \ref{sec:uniaxial_payload_dynamics}).
 
-Conclusion remarks are given in Section \ref{sec:conclusion}.
+Conclusion remarks are given in Section \ref{sec:uniaxial_conclusion}.
 
 \begin{table}[htbp]
-\caption{\label{tab:section_matlab_code}Report sections and corresponding Matlab files}
+\caption{\label{tab:uniaxial_section_matlab_code}Report sections and corresponding Matlab files}
 \centering
 \begin{tabularx}{0.6\linewidth}{lX}
 \toprule
@@ -68,22 +67,21 @@ Section \ref{sec:uniaxial_payload_dynamics} & \texttt{uniaxial\_8\_payload\_dyna
 \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 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}), Position control in purple (Section \ref{sec:uniaxial_position_control}) and Sample dynamics in cyan (Section \ref{sec:uniaxial_payload_dynamics})}
 \end{figure}
-
 \chapter{Micro Station Model}
 \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.
+The measurement setup is shown in Figure \ref{fig:uniaxial_ustation_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.
 
 From the measured frequency response functions (FRF), the model can be tuned to approximate the uniaxial dynamics of the micro-station.
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1,width=\linewidth]{figs/micro_station_first_meas_dynamics.jpg}
+\includegraphics[scale=1,width=\linewidth]{figs/uniaxial_ustation_first_meas_dynamics.jpg}
-\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}
+\caption{\label{fig:uniaxial_ustation_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}
 
-The measurement setup is schematically shown in Figure \ref{fig:micro_station_meas_dynamics_schematic} where:
+The measurement setup is schematically shown in Figure \ref{fig:uniaxial_ustation_meas_dynamics_schematic} where:
 \begin{itemize}
 \item Two hammer hits are performed, one on the Granite (force \(F_g\)), and one on the micro-hexapod's top platform (force \(F_h\))
 \item The inertial motion of the granite \(x_g\) and the micro-hexapod's top platform \(x_h\) are measured using geophones.
@@ -99,9 +97,9 @@ From the forces applied by the instrumented hammer and the responses of the geop
 \begin{figure}
 \begin{subfigure}{0.69\textwidth}
 \begin{center}
-\includegraphics[scale=1,scale=1]{figs/micro_station_meas_dynamics_schematic.png}
+\includegraphics[scale=1,scale=1]{figs/uniaxial_ustation_meas_dynamics_schematic.png}
 \end{center}
-\subcaption{\label{fig:micro_station_meas_dynamics_schematic}Measurement setup - Schematic}
+\subcaption{\label{fig:uniaxial_ustation_meas_dynamics_schematic}Measurement setup - Schematic}
 \end{subfigure}
 \begin{subfigure}{0.29\textwidth}
 \begin{center}
@@ -113,7 +111,6 @@ From the forces applied by the instrumented hammer and the responses of the geop
 \end{figure}
 
 Due to the bad coherence at low frequency, the frequency response functions will only be shown between 20 and 200Hz (solid lines in Figure \ref{fig:uniaxial_comp_frf_meas_model}).
-
 \section{Uniaxial Model}
 The uni-axial model of the micro-station is shown in Figure \ref{fig:uniaxial_model_micro_station}, with:
 \begin{itemize}
@@ -142,7 +139,6 @@ More accurate models will be used later on.
 \includegraphics[scale=1]{figs/uniaxial_comp_frf_meas_model.png}
 \caption{\label{fig:uniaxial_comp_frf_meas_model}Comparison of the measured FRF and identified ones from the uni-axial model}
 \end{figure}
-
 \chapter{Nano-Hexapod Model}
 \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}).
@@ -173,7 +169,6 @@ The parameters for the nano-hexapod and sample are:
 \end{itemize}
 
 As a first example, let's choose a nano-hexapod stiffness of \(10\,N/\mu m\) and a sample mass of 10kg.
-
 \section{Obtained Dynamic Response}
 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}.
@@ -195,20 +190,20 @@ For further analysis, 9 configurations are considered: three nano-hexapod stiffn
 \end{figure}
 \chapter{Disturbance Identification}
 \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}).
+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:uniaxial_ustation_meas_disturbances}).
 
 The geophone on the floor is used to measured the floor motion \(x_f\) while the geophone on the micro-hexapod is used to measure vibrations introduced by scanning of the \(T_y\) stage and \(R_z\) stage.
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/micro_station_meas_disturbances.png}
+\includegraphics[scale=1]{figs/uniaxial_ustation_meas_disturbances.png}
-\caption{\label{fig:micro_station_meas_disturbances}Disturbance measurement setup - Schematic}
+\caption{\label{fig:uniaxial_ustation_meas_disturbances}Disturbance measurement setup - Schematic}
 \end{figure}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1,width=0.6\linewidth]{figs/micro_station_dynamical_id_setup.jpg}
+\includegraphics[scale=1,width=0.6\linewidth]{figs/uniaxial_ustation_dynamical_id_setup.jpg}
-\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}
+\caption{\label{fig:uniaxial_ustation_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}
 The geophone fixed to the floor to measure the floor motion.
@@ -227,25 +222,24 @@ with:
 \item \(\omega\) is here to integrate and have the displacement instead of the velocity
 \end{itemize}
 
-The amplitude spectral density \(\Gamma_{x_f}\) of the measured displacement \(x_f\) is shown in Figure \ref{fig:asd_floor_motion_id31}.
+The amplitude spectral density \(\Gamma_{x_f}\) of the measured displacement \(x_f\) is shown in Figure \ref{fig:uniaxial_asd_floor_motion_id31}.
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/asd_floor_motion_id31.png}
+\includegraphics[scale=1]{figs/uniaxial_asd_floor_motion_id31.png}
-\caption{\label{fig:asd_floor_motion_id31}Amplitude Spectral Density of the measured Floor motion on ID31}
+\caption{\label{fig:uniaxial_asd_floor_motion_id31}Amplitude Spectral Density of the measured Floor motion on ID31}
 \end{figure}
-
 \section{Stage Vibration}
 During Spindle rotation (here at 6rpm), the granite velocity and micro-hexapod's top platform velocity are measured with the geophones.
 
 The Power Spectral Density of the relative velocity between the hexapod and the granite is computed.
-It is then integrated to obtain the Amplitude Spectral Density of the relative motion which is compared with a non-rotating case (Figure \ref{fig:asd_vibration_spindle_rotation}).
+It is then integrated to obtain the Amplitude Spectral Density of the relative motion which is compared with a non-rotating case (Figure \ref{fig:uniaxial_asd_vibration_spindle_rotation}).
 It is shown that the spindle rotation induces vibrations in a wide frequency spectrum.
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/asd_vibration_spindle_rotation.png}
+\includegraphics[scale=1]{figs/uniaxial_asd_vibration_spindle_rotation.png}
-\caption{\label{fig:asd_vibration_spindle_rotation}Amplitude Spectral Density of the relative motion measured between the granite and the micro-hexapod's top platform during Spindle rotating}
+\caption{\label{fig:uniaxial_asd_vibration_spindle_rotation}Amplitude Spectral Density of the relative motion measured between the granite and the micro-hexapod's top platform during Spindle rotating}
 \end{figure}
 
 In order to compute the equivalent disturbance force \(f_t\) that induces such motion, the transfer function from \(f_t\) to the relative motion of the hexapod's top platform and the granite is extracted from the model.
@@ -259,11 +253,11 @@ with:
 \item \(G_{\text{model}}\) the transfer function (extracted from the uniaxial model) from \(f_t\) to the relative motion between the micro-hexapod's top platform and the granite
 \end{itemize}
 
-The obtained amplitude spectral density of the disturbance force \(f_t\) is shown in Figure \ref{fig:asd_disturbance_force}.
+The obtained amplitude spectral density of the disturbance force \(f_t\) is shown in Figure \ref{fig:uniaxial_asd_disturbance_force}.
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1]{figs/asd_disturbance_force.png}
+\includegraphics[scale=1]{figs/uniaxial_asd_disturbance_force.png}
-\caption{\label{fig:asd_disturbance_force}Estimated disturbance force ft from measurement and uniaxial model}
+\caption{\label{fig:uniaxial_asd_disturbance_force}Estimated disturbance force ft from measurement and uniaxial model}
 \end{figure}
 
 The vibrations induced by the \(T_y\) stage are not considered here because:
@@ -271,7 +265,6 @@ The vibrations induced by the \(T_y\) stage are not considered here because:
 \item the induced vibrations have less amplitude than the vibrations induced by the \(R_z\) stage
 \item it can be scanned at lower velocities if the induced vibrations are an issue
 \end{itemize}
-
 \chapter{Open-Loop Dynamic Noise Budgeting}
 \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}.
@@ -301,7 +294,6 @@ From Figure \ref{fig:uniaxial_sensitivity_disturbances_nano_hexapod_stiffnesses}
 \includegraphics[scale=1]{figs/uniaxial_sensitivity_disturbances_nano_hexapod_stiffnesses.png}
 \caption{\label{fig:uniaxial_sensitivity_disturbances_nano_hexapod_stiffnesses}Sensitivity to disturbances for three different nano-hexpod stiffnesses}
 \end{figure}
-
 \section{Open-Loop Dynamic Noise Budgeting}
 Now, the power spectral density of the disturbances is taken into account to estimate the residual motion \(d\) in each case.
 
@@ -323,7 +315,6 @@ The conclusion is that the sample's mass has little effect on the cumulative amp
 \includegraphics[scale=1]{figs/uniaxial_cas_d_disturbances_payload_masses.png}
 \caption{\label{fig:uniaxial_cas_d_disturbances_payload_masses}Cumulative Amplitude Spectrum of the relative motion d due to all disturbances, for two sample masses}
 \end{figure}
-
 \section{Conclusion}
 
 \begin{important}
@@ -338,7 +329,6 @@ This can be explained by the fact that for frequencies larger than the suspensio
 
 This gives a first advantage to having a soft nano-hexapod.
 \end{important}
-
 \chapter{Active Damping}
 \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) \cite{preumont91_activ}, Relative Damping Control (RDC) \cite[Chapter 7.2]{preumont18_vibrat_contr_activ_struc_fourt_edition} and Direct Velocity Feedback (DVF) \cite{karnopp74_vibrat_contr_using_semi_activ_force_gener,serrand00_multic_feedb_contr_isolat_base_excit_vibrat,preumont02_force_feedb_versus_accel_feedb}.
@@ -374,8 +364,6 @@ The mechanical equivalent of this strategy is to add a dashpot in series with th
 \includegraphics[scale=1]{figs/uniaxial_active_damping_iff_equiv.png}
 \caption{\label{fig:uniaxial_active_damping_iff_equiv}Integral Force Feedback is equivalent as to add a damper in series with the stiffness (the initial damping is here neglected for simplicity)}
 \end{figure}
-
-
 \paragraph{Relative Damping Control (RDC)}
 For the Relative Damping Control strategy, a relative motion sensor that measures the motion of the actuator is used (see Figure \ref{fig:uniaxial_active_damping_rdc_equiv}, left).
 
@@ -391,7 +379,6 @@ The mechanical equivalent is to add a dashpot in parallel with the actuator with
 \includegraphics[scale=1]{figs/uniaxial_active_damping_rdc_equiv.png}
 \caption{\label{fig:uniaxial_active_damping_rdc_equiv}Relative Damping Control is equivalent as adding a damper in parallel with the actuator/relative motion sensor}
 \end{figure}
-
 \paragraph{Direct Velocity Feedback (DVF)}
 Finally, the Direct Velocity Feedback strategy consists of using an inertial sensor (usually a geophone), that measured the ``absolute'' velocity of the body fixed on top of the actuator (se Figure \ref{fig:uniaxial_active_damping_dvf_equiv}, left).
 
@@ -408,7 +395,6 @@ This is usually refers to as ``\emph{sky hook damper}''.
 \includegraphics[scale=1]{figs/uniaxial_active_damping_dvf_equiv.png}
 \caption{\label{fig:uniaxial_active_damping_dvf_equiv}Direct velocity Feedback using an inertial sensor is equivalent to a ``sky hook damper''}
 \end{figure}
-
 \section{Plant Dynamics for Active Damping}
 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 do not vary by more than \(\pm 90\,\text{deg}\) which makes the design of a robust controller very easy.
@@ -424,7 +410,6 @@ Therefore, it is expected that the micro-station dynamics might impact the achie
 \includegraphics[scale=1]{figs/uniaxial_plant_active_damping_techniques.png}
 \caption{\label{fig:uniaxial_plant_active_damping_techniques}Plant dynamics for the three active damping techniques (IFF: right, RDC: middle, DVF: left), for three nano-hexapod stiffnesses (\(k_n = 0.01\,N/\mu m\) in blue, \(k_n = 1\,N/\mu m\) in red and \(k_n = 100\,N/\mu m\) in yellow) and three sample's masses (\(m_s = 1\,kg\): solid curves, \(m_s = 25\,kg\): dot-dashed curves, and \(m_s = 50\,kg\): dashed curves).}
 \end{figure}
-
 \section{Achievable Damping - Root Locus}
 \label{ssec:uniaxial_active_damping_achievable_damping}
 The Root Locus are computed for the three nano-hexapod stiffnesses and for the three active damping techniques.
@@ -452,7 +437,6 @@ The micro-station and the nano-hexapod masses are connected through a large damp
 \includegraphics[scale=1]{figs/uniaxial_root_locus_damping_techniques_micro_station_mode.png}
 \caption{\label{fig:uniaxial_root_locus_damping_techniques_micro_station_mode}Root Locus for the three damping techniques applied with the soft nano-hexapod. It is shown that the RDC active damping technique has some authority on one mode of the micro-station. This mode corresponds to the suspension mode of the micro-hexapod.}
 \end{figure}
-
 \section{Change of sensitivity to disturbances}
 \label{ssec:uniaxial_active_damping_sensitivity_disturbances}
 
@@ -473,7 +457,6 @@ Conclusions from Figure \ref{fig:uniaxial_sensitivity_dist_active_damping} are:
 \includegraphics[scale=1]{figs/uniaxial_sensitivity_dist_active_damping.png}
 \caption{\label{fig:uniaxial_sensitivity_dist_active_damping}Change of sensitivity to disturbance with all three active damping strategies}
 \end{figure}
-
 \section{Noise Budgeting after Active Damping}
 \label{ssec:uniaxial_active_damping_noise_budget}
 Cumulative Amplitude Spectrum of the distance \(d\) with all three active damping techniques are compared in Figure \ref{fig:uniaxial_cas_active_damping}.
@@ -486,7 +469,6 @@ Compared to the open-loop case, the active damping helps to lower the vibrations
 \includegraphics[scale=1]{figs/uniaxial_cas_active_damping.png}
 \caption{\label{fig:uniaxial_cas_active_damping}Comparison of the cumulative amplitude spectrum (CAS) of the distance \(d\) for all three active damping techniques (OL in black, IFF in blue, RDC in red and DVF in yellow).}
 \end{figure}
-
 \section{Obtained Closed Loop Response}
 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.
@@ -503,7 +485,6 @@ The damped plants are shown in Figure \ref{fig:uniaxial_damped_plant_change_samp
 \includegraphics[scale=1]{figs/uniaxial_damped_plant_change_sample_mass.png}
 \caption{\label{fig:uniaxial_damped_plant_change_sample_mass}Damped plant \(d/f\) - Robustness to change of sample's mass for all three active damping techniques. Grey curves are the open-loop (i.e. undamped) plants.}
 \end{figure}
-
 \section{Robustness to change of payload's mass}
 \label{ssec:uniaxial_active_damping_robustness}
 
@@ -517,7 +498,6 @@ We can see that having heavier samples yields larger damping for IFF and smaller
 \includegraphics[scale=1]{figs/uniaxial_active_damping_robustness_mass_root_locus.png}
 \caption{\label{fig:uniaxial_active_damping_robustness_mass_root_locus}Active Damping Robustness to change of sample's mass - Root Locus for all three damping techniques with 3 different sample's masses}
 \end{figure}
-
 \section{Conclusion}
 
 \begin{important}
@@ -549,7 +529,6 @@ Conclusions for Active Damping:
 \bottomrule
 \end{tabularx}
 \end{table}
-
 \chapter{Position Feedback Controller}
 \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}.
@@ -595,7 +574,6 @@ Such effect will be explained in Section \ref{sec:uniaxial_support_compliance}.
 \includegraphics[scale=1]{figs/uniaxial_hac_iff_damped_plants_masses.png}
 \caption{\label{fig:uniaxial_hac_iff_damped_plants_masses}Obtained damped plant using Integral Force Feedback for three sample's masses}
 \end{figure}
-
 \section{Position Feedback Controller}
 \label{ssec:uniaxial_position_control_design}
 
@@ -677,7 +655,6 @@ The goal is just to have a first estimation of the attainable performance.
 \includegraphics[scale=1]{figs/uniaxial_loop_gain_hac.png}
 \caption{\label{fig:uniaxial_loop_gain_hac}Loop Gain - High Authority Controller for all three nano-hexapod stiffnesses (soft one in blue, moderately stiff in red and very stiff in yellow) and all sample masses (corresponding to the three curves of each color)}
 \end{figure}
-
 \section{Closed-Loop Noise Budgeting}
 \label{ssec:uniaxial_position_control_cl_noise_budget}
 
@@ -700,7 +677,6 @@ Obtained root mean square values of the distance \(d\) are better for the soft n
 \includegraphics[scale=1]{figs/uniaxial_cas_hac_lac.png}
 \caption{\label{fig:uniaxial_cas_hac_lac}Cumulative Amplitude Spectrum for all three nano-hexapod stiffnesses - Comparison of OL, IFF and HAC-LAC cases}
 \end{figure}
-
 \section{Conclusion}
 \begin{important}
 Based on the open-loop noise budgeting made in Section \ref{sec:uniaxial_noise_budgeting}, the closed-loop bandwidth required to obtain acceptable vibration levels was estimated.
@@ -710,7 +686,6 @@ In this section, feedback controllers were design in such a way that the require
 The attainable vibration control performances were estimated for the three nano-hexapod stiffnesses and were found to be close to the required values.
 A slight advantage can be given to the soft nano-hexapod as it requires less feedback bandwidth while giving better stability results.
 \end{important}
-
 \chapter{Effect of limited micro-station compliance}
 \label{sec:uniaxial_support_compliance}
 In this section, the impact of the compliance of the support (i.e. the micro-station) on the dynamics of the plant to control will be studied.
@@ -754,7 +729,6 @@ When neglecting the support compliance, large feedback bandwidth can be achieve
 \includegraphics[scale=1]{figs/uniaxial_effect_support_compliance_neglected.png}
 \caption{\label{fig:uniaxial_effect_support_compliance_neglected}Obtained transfer functions from \(F\) to \(L^{\prime}\) when neglecing support compliance}
 \end{figure}
-
 \section{Effect of support compliance on \(L/F\)}
 
 Let's now add some support compliance and use the model shown in Figure \ref{fig:uniaxial_support_compliance_test_system}.
@@ -773,7 +747,6 @@ If a soft nano-hexapod is used, the support dynamics appears in the dynamics bet
 \includegraphics[scale=1]{figs/uniaxial_effect_support_compliance_dynamics.png}
 \caption{\label{fig:uniaxial_effect_support_compliance_dynamics}Effect of the support compliance on the transfer functions from \(F\) to \(L\)}
 \end{figure}
-
 \section{Effect of support compliance on \(d/F\)}
 
 When the motion to be controlled is the relative displacement \(d\) between the granite and the nano-hexapod's top platform, the effect of the support compliance on the plant dynamics is opposite than what was previously observed.
@@ -785,7 +758,6 @@ On the contrary, if a ``stiff'' nano-hexapod is used, the support dynamics appea
 \includegraphics[scale=1]{figs/uniaxial_effect_support_compliance_dynamics_d.png}
 \caption{\label{fig:uniaxial_effect_support_compliance_dynamics_d}Effect of the support compliance on the transfer functions from \(F\) to \(d\)}
 \end{figure}
-
 \section{Conclusion}
 \begin{important}
 In order to study the impact of the support compliance on the plant dynamics, simple models shown in Figure \ref{fig:uniaxial_support_compliance_models} were used.
@@ -809,9 +781,9 @@ Note that observations made in this section are also affected by the ratio betwe
 \bottomrule
 \end{tabularx}
 \end{table}
-
 \chapter{Effect of Payload Dynamics}
 \label{sec:uniaxial_payload_dynamics}
+
 Up to this section, the sample was modelled as a mass rigidly fixed to the nano-hexapod (as shown in Figure \ref{fig:uniaxial_paylaod_dynamics_rigid_schematic}).
 However, such sample may present internal dynamics and its fixation to the nano-hexapod may have limited stiffness.
 
@@ -832,7 +804,6 @@ To study the effect of the sample dynamics, models shown in Figure \ref{fig:unia
 \end{subfigure}
 \caption{\label{fig:uniaxial_payload_dynamics_models}Models used to study the effect of payload dynamics}
 \end{figure}
-
 \section{Impact on the plant dynamics}
 \label{ssec:uniaxial_payload_dynamics_effect_dynamics}
 
@@ -877,7 +848,6 @@ The general conclusion is that the stiffer the nano-hexapod, the less it is impa
 
 This is why high-bandwidth soft positioning stages are usually restricted to constant and calibrated payloads (CD-player, lithography machines, isolation system for gravitational wave detectors, \ldots{}), while stiff positioning systems can more easily accept various payloads.
 \end{important}
-
 \section{Impact on the positioning stability}
 \label{ssec:uniaxial_payload_dynamics_effect_stability}
 
@@ -920,7 +890,6 @@ What happens is that above \(\omega_s\), even though the motion \(d\) can be con
 \end{subfigure}
 \caption{\label{fig:uniaxial_sample_flexibility_noise_budget}Cumulative Amplitude Spectrum of the distances \(d\) and \(y\). The effect of the sample's flexibility does not affects much \(d\) but is detrimental to the stability of \(y\). A sample mass \(m_s = 1\,\text{kg}\) is used for the simulations.}
 \end{figure}
-
 \section{Conclusion}
 \begin{important}
 Payload dynamics is usually a major concern when designing a positioning system.
@@ -934,9 +903,8 @@ Having some flexibility between the measurement point and the point of interest
 
 It will be therefore important to take special care when designing sampling environments, especially is a soft nano-hexapod is used.
 \end{important}
-
 \chapter{Conclusion}
-\label{sec:conclusion}
+\label{sec:uniaxial_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}).
 
@@ -948,6 +916,5 @@ These controllers were shown to be robust to the change of sample's masses, and
 It has been found that having a soft nano-hexapod makes the plant dynamics easier to control (because decoupled from the micro-station dynamics, see Section \ref{sec:uniaxial_support_compliance}) and requires less position feedback bandwidth to fulfill the requirements.
 The moderately stiff nano-hexapod (\(k_n = 1\,N/\mu m\)) is requiring a bit more position feedback bandwidth, but it still seems to give acceptable results.
 However, the stiff nano-hexapod is the most complex to control and gives the worst positioning performance.
-
 \printbibliography[heading=bibintoc,title={Bibliography}]
 \end{document}

preamble.tex

@@ -25,8 +25,6 @@
 
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