From cf9dad7f62fc919af0e3e3f2b71ce4409de8c20e Mon Sep 17 00:00:00 2001 From: Gabriela Date: Sun, 3 May 2026 01:32:20 +0200 Subject: [PATCH] mise a jour Q-7-8 --- latex/Illustrations/Q8.png | Bin 0 -> 18510 bytes latex/Questions/{Q6 => Q6.tex} | 0 latex/Questions/Q7.tex | 28 ++++++++++++++++++ latex/Questions/Q8.tex | 9 ++++++ latex/Questions/Q9.tex | 36 +++++++++++++++++++++++ latex/contents.tex | 4 ++- latex/main.aux | 4 ++- latex/main.fdb_latexmk | 34 ++++++++++++--------- latex/main.fls | 40 ++++++++++++++++++++++--- latex/main.log | 52 +++++++++++++++++++++------------ latex/main.pdf | Bin 335166 -> 361515 bytes latex/main.synctex.gz | Bin 30640 -> 35333 bytes 12 files changed, 169 insertions(+), 38 deletions(-) create mode 100644 latex/Illustrations/Q8.png rename latex/Questions/{Q6 => Q6.tex} (100%) create mode 100644 latex/Questions/Q7.tex create mode 100644 latex/Questions/Q8.tex create mode 100644 latex/Questions/Q9.tex diff --git a/latex/Illustrations/Q8.png 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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 @@ Une introduction %%Q2 \input{Questions/Q2} %%%% ->>>>>>> 10ca19c (mise a jour du rapport) %%Q3 \input{Questions/Q3} @@ -25,7 +24,10 @@ Une introduction \newpage \input{Questions/Q5} %% +\input{Questions/Q7} +\input{Questions/Q8} +\input{Questions/Q9} % \section{Une autre section} diff --git a/latex/main.aux b/latex/main.aux index 86eced7..7cd4c29 100644 --- a/latex/main.aux +++ b/latex/main.aux @@ -17,7 +17,9 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Discrétisation par éléments finis}{2}{subsection.1.2}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Comparaison des valeurs propres du système en temps continu et en temps discret.}}{4}{figure.caption.2}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Response du système en boucle ouverte.}}{4}{figure.caption.3}\protected@file@percent } +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Suivi de la 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