diff --git a/latex/Illustrations/Q8.png b/latex/Illustrations/Q8.png new file mode 100644 index 0000000..da92aa1 Binary files /dev/null and b/latex/Illustrations/Q8.png differ diff --git a/latex/Questions/Q6 b/latex/Questions/Q6.tex similarity index 100% rename from latex/Questions/Q6 rename to latex/Questions/Q6.tex diff --git a/latex/Questions/Q7.tex b/latex/Questions/Q7.tex new file mode 100644 index 0000000..14a4f73 --- /dev/null +++ b/latex/Questions/Q7.tex @@ -0,0 +1,28 @@ +\textbf{Question 7} + +Nous avons utilisé une boucle \texttt{for} sous MATLAB afin de tester les valeurs de $k$ entre 0 e 100. + + +Le gain $H$ est ensuite calculé à partir d'un système en boucle fermée de la forme : + +\begin{equation} +\dot{x}(t) = (A-BK)x(t) + BHr(t), +\qquad +y(t)=Cx(t), +\end{equation} + +on impose que, en régime permanent, la sortie suive la consigne. On utilise donc : + +\begin{equation} +H = -\frac{1}{C(A-BK)^{-1}B}. +\end{equation} + +Ainsi, les valeurs retenues pour la commande en boucle fermée sont : + +\begin{equation} +\boxed{ +k = 1{,}85, +\qquad +H = -3. +} +\end{equation} \ No newline at end of file diff --git a/latex/Questions/Q8.tex b/latex/Questions/Q8.tex new file mode 100644 index 0000000..f9f04a5 --- /dev/null +++ b/latex/Questions/Q8.tex @@ -0,0 +1,9 @@ +\textbf{Question 8} + +La figure montre que $w(L,t)$ suit la consigne $w_c(t)$ et converge vers 1, avec une erreur nulle en régime permanent. + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{Illustrations/Q8} % Remplacez par votre image + \caption{Suivi de la consigne $wc(t)$ par la position $w(L,t)$.} +\end{figure} \ No newline at end of file diff --git a/latex/Questions/Q9.tex b/latex/Questions/Q9.tex new file mode 100644 index 0000000..b94b128 --- /dev/null +++ b/latex/Questions/Q9.tex @@ -0,0 +1,36 @@ +\newpage +\textbf{Question 9} + +REWRITE + +\begin{figure}[h] + \centering + + \begin{subfigure}{0.48\textwidth} + \centering + %%\includegraphics[width=\textwidth]{Illustrations/Q9Poles} + \caption{Valeurs propres en temps continu.} + \end{subfigure} + \hfill + \begin{subfigure}{0.48\textwidth} + \centering + %%\includegraphics[width=\textwidth]{Illustrations/Q9001} + \caption{$T_s = 0{,}01\,\mathrm{s}$.} + \end{subfigure} + + \vspace{0.3cm} + + \begin{subfigure}{0.48\textwidth} + \centering + %%\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_} + \caption{$T_s = 0{,}04\,\mathrm{s}$.} + \end{subfigure} + + \caption{Comparaison des valeurs propres du système en boucle fermée.} +\end{figure} diff --git a/latex/contents.tex b/latex/contents.tex index cd4017b..cabcb5e 100644 --- a/latex/contents.tex +++ b/latex/contents.tex @@ -13,7 +13,6 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