mise a jour Q-11-12-13

latex/Questions/Q10.tex

@@ -0,0 +1,7 @@
+
+\textbf{Question 10}
+
+Nous avons obtenu une valeur maximale de $0{,}5\,\mathrm{s}$ pour la période d'échantillonnage.
+
+Manque l'image!!!!!!!!!!!
+

latex/Questions/Q11.tex

@@ -0,0 +1,10 @@
+\textbf{Question 11}
+
+Avec la fonction \texttt{lqr} de MATLAB, le gain de retour d'état obtenu est :
+
+\begin{equation}
+K =
+\begin{bmatrix}
+0{,}97 & -14{,}62 & 0{,}66 & 1{,}32 & 19{,}32 & 0{,}39 & 2{,}40 & -2{,}11
+\end{bmatrix}
+\end{equation}

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}

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}
+

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.
+

latex/contents.tex

@@ -2,14 +2,12 @@
 Une introduction
 
 \newpage
-\section{Dynamique du système avec équations différentielles partielles}
+\section{Modélisation du système}
-\subsection{Espace d'état}
 
 %%%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]

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+\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
+\newlabel{fig:q9_eigenvalues}{{4}{6}{Comparaison des valeurs propres du système en boucle fermée}{figure.caption.5}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Retour d'état}{6}{section.3}\protected@file@percent }
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