From 4aeab8daa661531778e8a8fc128077eef1735d4b Mon Sep 17 00:00:00 2001 From: Gabriela Date: Sun, 3 May 2026 21:31:02 +0200 Subject: [PATCH] mise a jour Q-11-12-13 --- latex/Illustrations/Q12.png | Bin 0 -> 19248 bytes latex/Illustrations/Q9001.png | Bin 0 -> 24271 bytes latex/Illustrations/Q9002.png | Bin 0 -> 24408 bytes latex/Illustrations/Q9004.png | Bin 0 -> 24519 bytes latex/Illustrations/Q9continu.png | Bin 0 -> 14131 bytes latex/Questions/Q10.tex | 7 ++ latex/Questions/Q11.tex | 10 +++ latex/Questions/Q12.tex | 7 ++ latex/Questions/Q13.tex | 12 +++ latex/Questions/Q14.tex | 0 latex/Questions/Q9.tex | 20 ++--- latex/contents.tex | 20 +++-- latex/main.aux | 14 +++- latex/main.fdb_latexmk | 49 +++++++++---- latex/main.fls | 83 +++++++++++++++++++-- latex/main.log | 118 +++++++++++++++++++++--------- latex/main.maf | 2 + latex/main.out | 7 +- latex/main.pdf | Bin 361515 -> 501964 bytes latex/main.stc2 | 2 - latex/main.stc4 | 4 +- latex/main.synctex.gz | Bin 35333 -> 39322 bytes 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& 0{,}39 & 2{,}40 & -2{,}11 +\end{bmatrix} +\end{equation} \ No newline at end of file diff --git a/latex/Questions/Q12.tex b/latex/Questions/Q12.tex new file mode 100644 index 0000000..b899e87 --- /dev/null +++ b/latex/Questions/Q12.tex @@ -0,0 +1,7 @@ +\textbf{Question 12} + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{Illustrations/Q12} % Remplacez par votre image + \caption{Simulation numérique du système continu en boucle fermée.} +\end{figure} \ No newline at end of file diff --git a/latex/Questions/Q13.tex b/latex/Questions/Q13.tex new file mode 100644 index 0000000..f00f2f7 --- /dev/null +++ b/latex/Questions/Q13.tex @@ -0,0 +1,12 @@ +\textbf{Question 13} + +nous avons testé plusieurs périodes d'échantillonnage entre $0{,}1\,\mathrm{s}$ et $5\,\mathrm{s}$. +Les valeurs propres discrètes restent à l'intérieur du cercle unité, comme le montre la Figure~\ref{fig:q13}. + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{Illustrations/im1} % Remplacez par votre image + \caption{Valeurs propres pour différentes périodes d'échantillonnage.} + \label{fig:q13} +\end{figure} + diff --git a/latex/Questions/Q14.tex b/latex/Questions/Q14.tex new file mode 100644 index 0000000..e69de29 diff --git a/latex/Questions/Q9.tex b/latex/Questions/Q9.tex index b94b128..f5e7a8a 100644 --- a/latex/Questions/Q9.tex +++ b/latex/Questions/Q9.tex @@ -1,20 +1,19 @@ -\newpage -\textbf{Question 9} -REWRITE +\textbf{Question 9} +La Figure~\ref{fig:q9_eigenvalues} compare les valeurs propres du système en boucle fermée en temps continu avec celles obtenues après discrétisation par ZOH, pour les trois périodes d'échantillonnage proposées. + \begin{figure}[h] \centering - \begin{subfigure}{0.48\textwidth} \centering - %%\includegraphics[width=\textwidth]{Illustrations/Q9Poles} + \includegraphics[width=\textwidth]{Illustrations/Q9continu} \caption{Valeurs propres en temps continu.} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} \centering - %%\includegraphics[width=\textwidth]{Illustrations/Q9001} + \includegraphics[width=\textwidth]{Illustrations/Q9001} \caption{$T_s = 0{,}01\,\mathrm{s}$.} \end{subfigure} @@ -22,15 +21,18 @@ REWRITE \begin{subfigure}{0.48\textwidth} \centering - %%\includegraphics[width=\textwidth]{Illustrations/Q9002_} + \includegraphics[width=\textwidth]{Illustrations/Q9002} \caption{$T_s = 0{,}02\,\mathrm{s}$.} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} \centering - %%\includegraphics[width=\textwidth]{Illustrations/Q9004_} + \includegraphics[width=\textwidth]{Illustrations/Q9004} \caption{$T_s = 0{,}04\,\mathrm{s}$.} \end{subfigure} - \caption{Comparaison des valeurs propres du système en boucle fermée.} + \label{fig:q9_eigenvalues} \end{figure} + +Les pôles discrets restent à l'intérieur du cercle unité pour les trois valeurs de $T_s$, ce qui montre que le système discret reste stable. + diff --git a/latex/contents.tex b/latex/contents.tex index cabcb5e..729ad31 100644 --- a/latex/contents.tex +++ b/latex/contents.tex @@ -2,14 +2,12 @@ Une introduction \newpage -\section{Dynamique du système avec équations différentielles partielles} -\subsection{Espace d'état} +\section{Modélisation du système} %%%Q1 \input{Questions/Q1} %%% -\subsection{Discrétisation par éléments finis} %%Q2 \input{Questions/Q2} %%%% @@ -21,15 +19,27 @@ Une introduction \input{Questions/Q4} %% %%%Q5 -\newpage \input{Questions/Q5} +%%Q6 + + +\section{Retour de sortie} %% \input{Questions/Q7} \input{Questions/Q8} +%%newpage pour les imgs q9 +\newpage \input{Questions/Q9} +\input{Questions/Q10} -% \section{Une autre section} +\section{Retour d'état} +\input{Questions/Q11} +\input{Questions/Q12} + +\subsection{Retour d'état par ZOH} +\input{Questions/Q13} +\input{Questions/Q14} % \begin{table}[h] diff --git a/latex/main.aux b/latex/main.aux index 7cd4c29..51374fc 100644 --- a/latex/main.aux +++ b/latex/main.aux @@ 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