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\textbf{Question 13} -nous avons testé plusieurs périodes d'échantillonnage entre $0{,}1\,\mathrm{s}$ et $5\,\mathrm{s}$. +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] diff --git a/latex/Questions/Q14.tex b/latex/Questions/Q14.tex index e69de29..3dc8359 100644 --- a/latex/Questions/Q14.tex +++ b/latex/Questions/Q14.tex @@ -0,0 +1,11 @@ +\textbf{Question 14} + +D'après la Figure~\ref{fig:q14_reponses}, les petites périodes d'échantillonnage permettent de mieux approcher la réponse temporelle continue, comme le montre la Figure~\ref{fig:Q15}. +On choisit donc $T_s = 0{,}01\,\mathrm{s}$, car cette valeur conserve un comportement proche de la réponse continue. + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{Illustrations/im2} % Remplacez par votre image + \caption{Réponses temporelles du système pour différentes périodes d'échantillonnage.} + \label{fig:q14_reponses} +\end{figure} \ No newline at end of file diff --git a/latex/Questions/Q15.tex b/latex/Questions/Q15.tex new file mode 100644 index 0000000..a13f61e --- /dev/null +++ b/latex/Questions/Q15.tex @@ -0,0 +1,4 @@ +\textbf{Question 15} + +:o + diff --git a/latex/Questions/Q16.tex b/latex/Questions/Q16.tex new file mode 100644 index 0000000..0a6f821 --- /dev/null +++ b/latex/Questions/Q16.tex @@ -0,0 +1,12 @@ +\textbf{Question 16} + + +La Figure~\ref{fig:q16_perturbation} montre que le système ne corrige pas l'erreur due à la perturbation. +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{Illustrations/im3} % Remplacez par votre image + \caption{Simulation du système avec une perturbation.} + \label{fig:q16_perturbation} +\end{figure} + +Pour résoudre ce problème, il faudra ajouter une action intégrale. \ No newline at end of file diff --git a/latex/Questions/Q17.tex b/latex/Questions/Q17.tex new file mode 100644 index 0000000..1486807 --- /dev/null +++ b/latex/Questions/Q17.tex @@ -0,0 +1,25 @@ +\textbf{Question 17} + +À partir des huit pôles obtenus avec la commande par retour d'état de la Question 11, on ajoute un pôle supplémentaire associé à l'action intégrale. + +\begin{equation} +p_i = -4{,}3805 +\end{equation} + +Ainsi, les pôles désirés du système augmenté sont : + +\begin{equation} +p_{\text{dés}} = +\begin{bmatrix} +-84{,}6647\\ +-7{,}5585+68{,}7669i\\ +-7{,}5585-68{,}7669i\\ +-27{,}9691+17{,}2408i\\ +-27{,}9691-17{,}2408i\\ +-15{,}9108\\ +-4{,}3805+2{,}6626i\\ +-4{,}3805-2{,}6626i\\ +-4{,}3805 +\end{bmatrix}. +\end{equation} + diff --git a/latex/Questions/Q18.tex b/latex/Questions/Q18.tex new file mode 100644 index 0000000..0d4f986 --- /dev/null +++ b/latex/Questions/Q18.tex @@ -0,0 +1,17 @@ +\textbf{Question 18} + +En utilisant la fonction \texttt{place} sous MATLAB, nous avons calculé les gains $K_1$ et $K_i$ : + +\begin{equation} +K_1 = +\begin{bmatrix} +-3{,}1081 & -18{,}9367 & -0{,}1707 & 2{,}1192 & 19{,}4677 & -2{,}3049 & 2{,}3377 & -1{,}7524 +\end{bmatrix} +\end{equation} + +\begin{equation} +K_i = +\begin{bmatrix} +26{,}2831 +\end{bmatrix}. +\end{equation} diff --git a/latex/Questions/Q19.tex b/latex/Questions/Q19.tex new file mode 100644 index 0000000..7f66f0a --- /dev/null +++ b/latex/Questions/Q19.tex @@ -0,0 +1,11 @@ +\textbf{Question 19} + +La Figure~\ref{fig:q19_integrale} montre qu'avec l'action intégrale, la perturbation est rejetée et l'erreur en régime permanent est annulée. + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{Illustrations/Q17} % Remplacez par votre image + \caption{Simulation du système avec correction par action intégrale.} + \label{fig:q19_integrale} +\end{figure} + diff --git a/latex/Questions/Q20.tex b/latex/Questions/Q20.tex new file mode 100644 index 0000000..e69de29 diff --git a/latex/Questions/Q3.tex b/latex/Questions/Q3.tex index c41b539..703e6de 100644 --- a/latex/Questions/Q3.tex +++ b/latex/Questions/Q3.tex @@ -19,7 +19,7 @@ En multipliant les deux premières équations par $E^{-1}$, on obtient : \end{aligned} \end{equation} -En multipliant les deux premières équations par $E^{-1}$, on obtient comme valeurs de $A$, $B$ et $C$ : +Et, on obtient comme valeurs de $A$, $B$ et $C$ : \begin{equation} A = diff --git a/latex/Questions/Q6.tex b/latex/Questions/Q6.tex index e69de29..5790287 100644 --- a/latex/Questions/Q6.tex +++ b/latex/Questions/Q6.tex @@ -0,0 +1,4 @@ +\textbf{Question 6} + +:o + diff --git a/latex/Questions/Q9.tex b/latex/Questions/Q9.tex index f5e7a8a..d55442a 100644 --- a/latex/Questions/Q9.tex +++ b/latex/Questions/Q9.tex @@ -1,5 +1,6 @@ \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. diff --git a/latex/README.md b/latex/README.md index d22fdec..5ce894e 100644 --- a/latex/README.md +++ b/latex/README.md @@ -9,3 +9,13 @@ Tous les éléments présent dans le `/template` ne sont pas à modifier. Afin d'arranger les éléments souhaités dans la page, il faut commenter ou décommenter les sections correspondantes dans `main.tex`. Il suffit ensuite de remplir le `contents.tex` (le corp) ainsi que les fichiers `contents/*` qui permettent de segmenter les différentes sections de préambule et de fin de document. +------------- + +##DZLL: + +- Il manque les question 6, 15, 20 et l'image de la question 10. + +- Dans la question 10, il manque un parenteses que change le valeur obtenu: + fmax=max(abs(real(meilleurs_poles)))/(2*pi) + +- J'ai au un problem de indentation suer les question 19, 12, 8 \ No newline at end of file diff --git a/latex/contents.tex b/latex/contents.tex index 729ad31..1014c5d 100644 --- a/latex/contents.tex +++ b/latex/contents.tex @@ -1,38 +1,32 @@ -\psection{Introduction} -Une introduction +%\psection{Introduction} +%Une introduction \newpage +%%%%%%%%%%%%%% \section{Modélisation du système} - -%%%Q1 +\subsection{Dynamique avec EDP} \input{Questions/Q1} -%%% - -%%Q2 +\subsection{Discrétisation par éléments finis} \input{Questions/Q2} -%%%% - -%%Q3 \input{Questions/Q3} -%% -%%Q4 \input{Questions/Q4} -%% -%%%Q5 \input{Questions/Q5} -%%Q6 +\input{Questions/Q6} +%%%%%%%%%%%%%% \section{Retour de sortie} -%% \input{Questions/Q7} \input{Questions/Q8} +\subsection{Retour de sortie par ZOH} %%newpage pour les imgs q9 \newpage \input{Questions/Q9} \input{Questions/Q10} + +%%%%%%%%%%%%%% \section{Retour d'état} \input{Questions/Q11} \input{Questions/Q12} @@ -41,24 +35,13 @@ Une introduction \input{Questions/Q13} \input{Questions/Q14} +%%%%%%%%%%%%%% +\section{Rejet de perturbation} +\input{Questions/Q15} +\input{Questions/Q16} -% \begin{table}[h] -% \centering -% \caption{Ceci est un exemple de tableau.} -% \begin{tabular}{|c|c|c|} -% \hline -% Colonne 1 & Colonne 2 & Colonne 3 \\ \hline -% Donnée 1 & Donnée 2 & Donnée 3 \\ \hline -% Donnée 4 & Donnée 5 & Donnée 6 \\ \hline -% \end{tabular} -% \label{tab:example} -% \end{table} - -% \section{Another section} -% \subsection{Une sous section} -% \subsubsection{Une sous sous section} -% Un mot compliqué\footnote{Une note 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