Changement de la matrice B

latex/Questions/Q13.tex

@@ -4,7 +4,7 @@ Avec le même periode d'echantillonnage comme dans la section precedente: $T_e=0
 
 \begin{figure}[H]
     \centering
-    \includegraphics[scale=0.3]{Illustrations/NouveauxImages/Q13} 
+    \includegraphics[scale=0.5]{Illustrations/NouveauxImages/Q13} 
     \caption{Pôles du système avec temps d'echantillonnage: $T_e = 0.0356$}
     \label{fig:q13}
 \end{figure}

latex/Questions/Q17.log

@@ -1,4 +1,4 @@
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latex/Questions/Q17.tex

@@ -18,18 +18,20 @@ $p_{\text{des}} =$
 \end{bmatrix}^{T}
 \end{equation}
 
-\begin{equation}
+%\begin{equation}
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+
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latex/Questions/Q3.tex

@@ -46,15 +46,17 @@ B=
 \end{bmatrix}
 =
 \begin{bmatrix}
-0\\
+0 &
-0\\
+0 &
-0\\
+0 &
-0\\
+0 &
-4\\
+4 &
--16\\
+-16 &
--60\\
+-60 &
 -120
-\end{bmatrix}
+\end{bmatrix}^{T}
+\end{equation}
+\begin{equation}
 \qquad
 C=
 \begin{bmatrix}

latex/Questions/Q4.tex

@@ -1,40 +1,35 @@
 \textbf{Question 4}
 
-La Figure 1a correspond aux valeurs propres en temps continu, tandis que les figures \textit{1b, 1c et 1d} montrent les valeurs propres discrètes obtenues avec les méthodes de Tustin et ZOH pour différents temps d'échantillonnage.
+Voici le lieu des racines du système en continu et en temps discret. $T_s = {0.01 ; 0.02 ; 0.04}$ avec le cercle unitaire. Comme tous nos pôles sont à $|z|=1$, nous ne pouvons pas conclure sur la stabilité ni l'instabilité. En temps continu nous avons instabilité, à cause des pôles: $Re\{\lambda\}>0$
 
-\begin{figure}[h]
+\begin{figure}[H]
 \centering
-
     \begin{subfigure}{0.48\textwidth}
         \centering
-        \includegraphics[width=\textwidth]{Illustrations/Q4eigenValTEMPSCONT}
+    \includegraphics[scale=0.3]{Illustrations/Q4eigenValTEMPSCONT}
         \caption{Valeurs propres en temps continu.}
     \end{subfigure}
     \hfill
     \begin{subfigure}{0.48\textwidth}
         \centering
-        \includegraphics[width=\textwidth]{Illustrations/Q40100}
+        \includegraphics[scale=0.3]{Illustrations/Q40100}
-        \caption{$T_s = 0{,}01\,\mathrm{s}$.}
+        \caption{$T_s = 0.01\,\mathrm{s}$.}
     \end{subfigure}
-
-    \vspace{0.3cm}
-
       \begin{subfigure}{0.48\textwidth}
         \centering
-        \includegraphics[width=\textwidth]{Illustrations/Q40200}
+    \includegraphics[scale=0.3]{Illustrations/Q40200}
-        \caption{$T_s = 0{,}02\,\mathrm{s}$.}
+        \caption{$T_s = 0.02\,\mathrm{s}$.}
     \end{subfigure}
     \hfill
     \begin{subfigure}{0.48\textwidth}
         \centering
-        \includegraphics[width=\textwidth]{Illustrations/Q40400}
+        \includegraphics[scale=0.3]{Illustrations/Q40400}
-        \caption{$T_s = 0{,}04\,\mathrm{s}$.}
+        \caption{$T_s = 0.04\,\mathrm{s}$.}
     \end{subfigure}
-
     \caption{Comparaison des valeurs propres du système en temps continu et en temps discret.}
+    \label{fig:q9_eigenvalues}
 \end{figure}
 
-En temps continu, le système présente deux pôles à partie réelle positive, ce qui montre son instabilité. 
+
-Après discrétisation, les pôles obtenus avec les méthodes de Tustin et ZOH se trouvent sur ou proches du cercle unité. Comme tous nos pôles sont à $|z|=1$, nous ne pouvons pas conclure sur la stabilité ni l'instabilité.
 
 

latex/main.aux

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