Add inkscape directory

figs/inkscape/convert_svg.sh

@@ -0,0 +1,18 @@
+#!/bin/bash
+
+# Directory containing SVG files
+INPUT_DIR="."
+
+# Loop through all SVG files in the directory
+for svg_file in "$INPUT_DIR"/*.svg; do
+    # Check if there are SVG files in the directory
+    if [ -f "$svg_file" ]; then
+        # Output PDF file name
+        pdf_file="../${svg_file%.svg}.pdf"
+        png_file="../${svg_file%.svg}"
+        
+        # Convert SVG to PDF using Inkscape
+        inkscape "$svg_file" --export-filename="$pdf_file" && \
+            pdftocairo -png -singlefile -cropbox "$pdf_file" "$png_file"
+    fi
+done

test-bench-apa.org

@@ -266,7 +266,7 @@ end
 data2orgtable(1e6*apa_d', {'APA 1', 'APA 2', 'APA 3', 'APA 4', 'APA 5', 'APA 6', 'APA 7'}, {'*Flatness* $[\mu m]$'}, ' %.1f ');
 #+end_src
 
-#+attr_latex: :options [b]{0.49\linewidth}
+#+attr_latex: :options [b]{0.48\linewidth}
 #+begin_minipage
 #+name: fig:test_apa_flatness_setup
 #+attr_latex: :width 0.7\linewidth :float nil
@@ -274,7 +274,7 @@ data2orgtable(1e6*apa_d', {'APA 1', 'APA 2', 'APA 3', 'APA 4', 'APA 5', 'APA 6',
 [[file:figs/test_apa_flatness_setup.png]]
 #+end_minipage
 \hfill
-#+attr_latex: :options [b]{0.49\linewidth}
+#+attr_latex: :options [b]{0.48\linewidth}
 #+begin_minipage
 #+name: tab:test_apa_flatness_meas
 #+attr_latex: :environment tabularx :width 0.6\linewidth :align Xc

test-bench-apa.tex

@@ -1,4 +1,4 @@
-% Created 2025-02-12 Wed 09:53
+% Created 2025-04-03 Thu 22:11
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
 
@@ -27,13 +27,6 @@
 \author{Dehaeze Thomas}
 \date{\today}
 \title{Test Bench - Amplified Piezoelectric Actuator}
-\hypersetup{
- pdfauthor={Dehaeze Thomas},
- pdftitle={Test Bench - Amplified Piezoelectric Actuator},
- pdfkeywords={},
- pdfsubject={},
- pdfcreator={Emacs 29.4 (Org mode 9.6)}, 
- pdflang={English}}
 \usepackage{biblatex}
 
 \begin{document}
@@ -42,7 +35,6 @@
 \tableofcontents
 
 \clearpage
-
 In this chapter, the goal is to ensure that the received APA300ML (shown in Figure \ref{fig:test_apa_received}) are complying with the requirements and that the dynamical models of the actuator accurately represent its dynamics.
 
 In section \ref{sec:test_apa_basic_meas}, the mechanical tolerances of the APA300ML interfaces are checked together with the electrical properties of the piezoelectric stacks and the achievable stroke.
@@ -64,16 +56,14 @@ This more complex model also captures well capture the axial dynamics of the APA
 \includegraphics[scale=1,width=0.7\linewidth]{figs/test_apa_received.jpg}
 \caption{\label{fig:test_apa_received}Picture of 5 out of the 7 received APA300ML}
 \end{figure}
-
-
 \chapter{First Basic Measurements}
 \label{sec:test_apa_basic_meas}
+
 Before measuring the dynamical characteristics of the APA300ML, simple measurements are performed.
 First, the tolerances (especially flatness) of the mechanical interfaces are checked in Section \ref{ssec:test_apa_geometrical_measurements}.
 Then, the capacitance of the piezoelectric stacks is measured in Section \ref{ssec:test_apa_electrical_measurements}.
 The achievable stroke of the APA300ML is measured using a displacement probe in Section \ref{ssec:test_apa_stroke_measurements}.
 Finally, in Section \ref{ssec:test_apa_spurious_resonances}, the flexible modes of the APA are measured and compared with a finite element model.
-
 \section{Geometrical Measurements}
 \label{ssec:test_apa_geometrical_measurements}
 
@@ -82,14 +72,14 @@ As shown in Figure \ref{fig:test_apa_flatness_setup}, the APA is fixed to a clam
 From the X-Y-Z coordinates of the measured eight points, the flatness is estimated by best fitting\footnote{The Matlab \texttt{fminsearch} command is used to fit the plane} a plane through all the points.
 The measured flatness values, summarized in Table \ref{tab:test_apa_flatness_meas}, are within the specifications.
 
-\begin{minipage}[b]{0.49\linewidth}
+\begin{minipage}[b]{0.48\linewidth}
 \begin{center}
 \includegraphics[scale=1,width=0.7\linewidth]{figs/test_apa_flatness_setup.png}
 \captionof{figure}{\label{fig:test_apa_flatness_setup}Measurement setup for flatness estimation}
 \end{center}
 \end{minipage}
 \hfill
-\begin{minipage}[b]{0.49\linewidth}
+\begin{minipage}[b]{0.48\linewidth}
 \begin{center}
 \begin{tabularx}{0.6\linewidth}{Xc}
 \toprule
@@ -108,7 +98,6 @@ APA 7 & 18.7\\
 
 \end{center}
 \end{minipage}
-
 \section{Electrical Measurements}
 \label{ssec:test_apa_electrical_measurements}
 
@@ -149,7 +138,6 @@ APA 7 & 4.85 & 9.85\\
 
 \end{center}
 \end{minipage}
-
 \section{Stroke and Hysteresis Measurement}
 \label{ssec:test_apa_stroke_measurements}
 
@@ -190,7 +178,6 @@ From now on, only the six remaining amplified piezoelectric actuators that behav
 \end{subfigure}
 \caption{\label{fig:test_apa_stroke}Generated voltage across the two piezoelectric stack actuators to estimate the stroke of the APA300ML (\subref{fig:test_apa_stroke_voltage}). Measured displacement as a function of applied voltage (\subref{fig:test_apa_stroke_hysteresis})}
 \end{figure}
-
 \section{Flexible Mode Measurement}
 \label{ssec:test_apa_spurious_resonances}
 
@@ -251,7 +238,6 @@ Another explanation is the shape difference between the manufactured APA300ML an
 \includegraphics[scale=1]{figs/test_apa_meas_freq_compare.png}
 \caption{\label{fig:test_apa_meas_freq_compare}Frequency response functions for the two tests using the instrumented hammer and the laser vibrometer. The Y-bending mode is measured at \(280\,\text{Hz}\) and the X-bending mode at \(412\,\text{Hz}\)}
 \end{figure}
-
 \chapter{Dynamical measurements}
 \label{sec:test_apa_dynamics}
 After the measurements on the APA were performed in Section \ref{sec:test_apa_basic_meas}, a new test bench was used to better characterize the dynamics of the APA300ML.
@@ -300,7 +286,6 @@ This is the typical behavior expected from a PZT stack actuator, where the hyste
 \includegraphics[scale=1]{figs/test_apa_meas_hysteresis.png}
 \caption{\label{fig:test_apa_meas_hysteresis}Displacement as a function of applied voltage for multiple excitation amplitudes}
 \end{figure}
-
 \section{Axial stiffness}
 \label{ssec:test_apa_stiffness}
 
@@ -362,7 +347,6 @@ To estimate this effect for the APA300ML, its stiffness is estimated using the `
 \end{itemize}
 
 The open-circuit stiffness is estimated at \(k_{\text{oc}} \approx 2.3\,N/\mu m\) while the closed-circuit stiffness \(k_{\text{sc}} \approx 1.7\,N/\mu m\).
-
 \section{Dynamics}
 \label{ssec:test_apa_meas_dynamics}
 
@@ -408,7 +392,6 @@ All the identified dynamics of the six APA300ML (both when looking at the encode
 \end{subfigure}
 \caption{\label{fig:test_apa_frf_dynamics}Measured frequency response function from generated voltage \(u\) to the encoder displacement \(d_e\) (\subref{fig:test_apa_frf_encoder}) and to the force sensor voltage \(V_s\) (\subref{fig:test_apa_frf_force}) for the six APA300ML}
 \end{figure}
-
 \section{Non Minimum Phase Zero?}
 \label{ssec:test_apa_non_minimum_phase}
 
@@ -437,8 +420,6 @@ However, this is not so important here because the zero is lightly damped (i.e.
 \end{subfigure}
 \caption{\label{fig:test_apa_non_minimum_phase}Measurement of the anti-resonance found in the transfer function from \(u\) to \(V_s\). The coherence (\subref{fig:test_apa_non_minimum_phase_coherence}) is quite good around the anti-resonance frequency. The phase (\subref{fig:test_apa_non_minimum_phase_zoom}) shoes a non-minimum phase behavior.}
 \end{figure}
-
-
 \section{Effect of the resistor on the IFF Plant}
 \label{ssec:test_apa_resistance_sensor_stack}
 
@@ -454,7 +435,6 @@ It is confirmed that the added resistor has the effect of adding a high-pass fil
 \includegraphics[scale=1]{figs/test_apa_effect_resistance.png}
 \caption{\label{fig:test_apa_effect_resistance}Transfer function from \(u\) to \(V_s\) with and without the resistor \(R\) in parallel with the piezoelectric stack used as the force sensor}
 \end{figure}
-
 \section{Integral Force Feedback}
 \label{ssec:test_apa_iff_locus}
 
@@ -513,10 +493,9 @@ The two obtained root loci are compared in Figure \ref{fig:test_apa_iff_root_loc
 \end{subfigure}
 \caption{\label{fig:test_apa_iff}Experimental results of applying Integral Force Feedback to the APA300ML. Obtained damped plant (\subref{fig:test_apa_identified_damped_plants}) and Root Locus (\subref{fig:test_apa_iff_root_locus}) corresponding to the implemented IFF controller \eqref{eq:test_apa_Kiff_formula}}
 \end{figure}
-
-
 \chapter{APA300ML - 2 degrees-of-freedom Model}
 \label{sec:test_apa_model_2dof}
+
 In this section, a multi-body model (Figure \ref{fig:test_apa_bench_model}) of the measurement bench is used to tune the two degrees-of-freedom model of the APA using the measured frequency response functions.
 
 This two degrees-of-freedom model is developed to accurately represent the APA300ML dynamics while having low complexity and a low number of associated states.
@@ -527,8 +506,7 @@ After the model is presented, the procedure for tuning the model is described, a
 \includegraphics[scale=1,width=0.8\linewidth]{figs/test_apa_bench_model.png}
 \caption{\label{fig:test_apa_bench_model}Screenshot of the multi-body model}
 \end{figure}
-
+\subsubsection{Two degrees-of-freedom APA Model}
-\paragraph{Two degrees-of-freedom APA Model}
 
 The model of the amplified piezoelectric actuator is shown in Figure \ref{fig:test_apa_2dof_model}.
 It can be decomposed into three components:
@@ -553,7 +531,6 @@ Such a simple model has some limitations:
 \includegraphics[scale=1]{figs/test_apa_2dof_model.png}
 \caption{\label{fig:test_apa_2dof_model}Schematic of the two degrees-of-freedom model of the APA300ML, adapted from \cite{souleille18_concep_activ_mount_space_applic}}
 \end{figure}
-
 9 parameters (\(m\), \(k_1\), \(c_1\), \(k_e\), \(c_e\), \(k_a\), \(c_a\), \(g_s\) and \(g_a\)) have to be tuned such that the dynamics of the model (Figure \ref{fig:test_apa_2dof_model_simscape}) well represents the identified dynamics in Section \ref{sec:test_apa_dynamics}.
 
 \begin{figure}[htbp]
@@ -609,7 +586,6 @@ The obtained parameters of the model shown in Figure \ref{fig:test_apa_2dof_mode
 \caption{\label{tab:test_apa_2dof_parameters}Summary of the obtained parameters for the 2 DoF APA300ML model}
 
 \end{table}
-
 The dynamics of the two degrees-of-freedom model of the APA300ML are extracted using optimized parameters (listed in Table \ref{tab:test_apa_2dof_parameters}) from the multi-body model.
 This is compared with the experimental data in Figure \ref{fig:test_apa_2dof_comp_frf}.
 A good match can be observed between the model and the experimental data, both for the encoder (Figure \ref{fig:test_apa_2dof_comp_frf_enc}) and for the force sensor (Figure \ref{fig:test_apa_2dof_comp_frf_force}).
@@ -630,9 +606,9 @@ This indicates that this model represents well the axial dynamics of the APA300M
 \end{subfigure}
 \caption{\label{fig:test_apa_2dof_comp_frf}Comparison of the measured frequency response functions and the identified dynamics from the 2DoF model of the APA300ML. Both for the dynamics from \(u\) to \(d_e\) (\subref{fig:test_apa_2dof_comp_frf_enc}) (\subref{fig:test_apa_2dof_comp_frf_force}) and from \(u\) to \(V_s\) (\subref{fig:test_apa_2dof_comp_frf_force})}
 \end{figure}
-
 \chapter{APA300ML - Super Element}
 \label{sec:test_apa_model_flexible}
+
 In this section, a \emph{super element} of the APA300ML is computed using a finite element software\footnote{Ansys\textsuperscript{\textregistered} was used}.
 It is then imported into multi-body (in the form of a stiffness matrix and a mass matrix) and included in the same model that was used in \ref{sec:test_apa_model_2dof}.
 This procedure is illustrated in Figure \ref{fig:test_apa_super_element_simscape}.
@@ -648,50 +624,12 @@ Finally, two \emph{remote points} (\texttt{4} and \texttt{5}) are located across
 \includegraphics[scale=1,width=1.0\linewidth]{figs/test_apa_super_element_simscape.png}
 \caption{\label{fig:test_apa_super_element_simscape}Finite Element Model of the APA300ML with ``remotes points'' on the left. Simscape model with included ``Reduced Order Flexible Solid'' on the right.}
 \end{figure}
-
+\subsubsection{Identification of the Actuator and Sensor constants}
-\paragraph{Identification of the Actuator and Sensor constants}
 
 Once the APA300ML \emph{super element} is included in the multi-body model, the transfer function from \(F_a\) to \(d_L\) and \(d_e\) can be extracted.
 The gains \(g_a\) and \(g_s\) are then tuned such that the gains of the transfer functions match the identified ones.
 By doing so, \(g_s = 4.9\,V/\mu m\) and \(g_a = 23.2\,N/V\) are obtained.
-
+\subsubsection{Comparison of the obtained dynamics}
-To ensure that the sensitivities \(g_a\) and \(g_s\) are physically valid, it is possible to estimate them from the physical properties of the piezoelectric stack material.
-
-From \cite[p. 123]{fleming14_desig_model_contr_nanop_system}, the relation between relative displacement \(d_L\) of the sensor stack and generated voltage \(V_s\) is given by \eqref{eq:test_apa_piezo_strain_to_voltage} and from \cite{fleming10_integ_strain_force_feedb_high} the relation between the force \(F_a\) and the applied voltage \(V_a\) is given by \eqref{eq:test_apa_piezo_voltage_to_force}.
-
-\begin{subequations}
-\begin{align}
-  V_s &= \underbrace{\frac{d_{33}}{\epsilon^T s^D n}}_{g_s} d_L \label{eq:test_apa_piezo_strain_to_voltage} \\
-  F_a &= \underbrace{d_{33} n k_a}_{g_a} \cdot V_a, \quad k_a = \frac{c^{E} A}{L} \label{eq:test_apa_piezo_voltage_to_force}
-\end{align}
-\end{subequations}
-
-Unfortunately, the manufacturer of the stack was not willing to share the piezoelectric material properties of the stack used in the APA300ML.
-However, based on the available properties of the APA300ML stacks in the data-sheet, the soft Lead Zirconate Titanate ``THP5H'' from Thorlabs seemed to match quite well the observed properties.
-The properties of this ``THP5H'' material used to compute \(g_a\) and \(g_s\) are listed in Table \ref{tab:test_apa_piezo_properties}.
-
-From these parameters, \(g_s = 5.1\,V/\mu m\) and \(g_a = 26\,N/V\) were obtained, which are close to the constants identified using the experimentally identified transfer functions.
-
-\begin{table}[htbp]
-\centering
-\begin{tabularx}{1\linewidth}{ccX}
-\toprule
-\textbf{Parameter} & \textbf{Value} & \textbf{Description}\\
-\midrule
-\(d_{33}\) & \(680 \cdot 10^{-12}\,m/V\) & Piezoelectric constant\\
-\(\epsilon^{T}\) & \(4.0 \cdot 10^{-8}\,F/m\) & Permittivity under constant stress\\
-\(s^{D}\) & \(21 \cdot 10^{-12}\,m^2/N\) & Elastic compliance understand constant electric displacement\\
-\(c^{E}\) & \(48 \cdot 10^{9}\,N/m^2\) & Young's modulus of elasticity\\
-\(L\) & \(20\,mm\) per stack & Length of the stack\\
-\(A\) & \(10^{-4}\,m^2\) & Area of the piezoelectric stack\\
-\(n\) & \(160\) per stack & Number of layers in the piezoelectric stack\\
-\bottomrule
-\end{tabularx}
-\caption{\label{tab:test_apa_piezo_properties}Piezoelectric properties used for the estimation of the sensor and actuators sensitivities}
-
-\end{table}
-
-\paragraph{Comparison of the obtained dynamics}
 
 The obtained dynamics using the \emph{super element} with the tuned ``sensor sensitivity'' and ``actuator sensitivity'' are compared with the experimentally identified frequency response functions in Figure \ref{fig:test_apa_super_element_comp_frf}.
 A good match between the model and the experimental results was observed.
@@ -714,7 +652,6 @@ Using this simple test bench, it can be concluded that the \emph{super element}
 \end{subfigure}
 \caption{\label{fig:test_apa_super_element_comp_frf}Comparison of the measured frequency response functions and the identified dynamics from the finite element model of the APA300ML. Both for the dynamics from \(u\) to \(d_e\) (\subref{fig:test_apa_super_element_comp_frf_enc}) and from \(u\) to \(V_s\) (\subref{fig:test_apa_super_element_comp_frf_force})}
 \end{figure}
-
 \chapter{Conclusion}
 \label{sec:test_apa_conclusion}
 
@@ -737,8 +674,6 @@ Here, the \emph{super element} represents the dynamics of the APA300ML in all di
 However, only the axial dynamics could be compared with the experimental results, yielding a good match.
 The benefit of employing this model over the two degrees-of-freedom model is not immediately apparent due to its increased complexity and the larger number of model states involved.
 Nonetheless, the \emph{super element} model's value will become clear in subsequent sections, when its capacity to accurately model the APA300ML's flexibility across various directions will be important.
-
 \printbibliography[heading=bibintoc,title={Bibliography}]
-
 \printglossaries
 \end{document}