diff --git a/latex/Questions/Q13.tex b/latex/Questions/Q13.tex index 3379f1f..6f325a2 100644 --- a/latex/Questions/Q13.tex +++ 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} diff --git a/latex/Questions/Q17.log b/latex/Questions/Q17.log index 80b4dac..c151b70 100644 --- a/latex/Questions/Q17.log +++ b/latex/Questions/Q17.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 19:29 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 19:39 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -339,30 +339,9 @@ Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] - -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.21 p - _{\text{des}} = -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - -Missing character: There is no p in font nullfont! -! Missing $ inserted. - - $ -l.21 p_ - {\text{des}} = -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - ! Undefined control sequence. -l.21 p_{\text - {des}} = +l.6 $p_{\text + {des}} =$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct @@ -370,31 +349,128 @@ spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. +Overfull \hbox (27.81807pt too wide) in paragraph at lines 6--7 + \OML/cmm/m/it/10 p[] \/cmr/m/n/10 =$ + [] + + ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.22 \begin{bmatrix} - +l.8 \begin{bmatrix} + Your command was ignored. Type I to replace it with another command, or to continue without it. +! Misplaced alignment tab character &. +l.9 -85 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. -! LaTeX Error: \begin{document} ended by \end{bmatrix}. +! Misplaced alignment tab character &. +l.10 -8+69i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.11 -8-69i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 -28+17i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.13 -28-17i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.14 -16 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.15 -4+3i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.16 -4-3i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 7 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.32 \end{bmatrix} +l.18 \end{bmatrix} ^{T} Your command was ignored. 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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] +\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} - \caption{$T_s = 0{,}01\,\mathrm{s}$.} + \includegraphics[scale=0.3]{Illustrations/Q40100} + \caption{$T_s = 0.01\,\mathrm{s}$.} \end{subfigure} - - \vspace{0.3cm} - - \begin{subfigure}{0.48\textwidth} + \begin{subfigure}{0.48\textwidth} \centering - \includegraphics[width=\textwidth]{Illustrations/Q40200} - \caption{$T_s = 0{,}02\,\mathrm{s}$.} + \includegraphics[scale=0.3]{Illustrations/Q40200} + \caption{$T_s = 0.02\,\mathrm{s}$.} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} \centering - \includegraphics[width=\textwidth]{Illustrations/Q40400} - \caption{$T_s = 0{,}04\,\mathrm{s}$.} + \includegraphics[scale=0.3]{Illustrations/Q40400} + \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. + diff --git a/latex/main.aux b/latex/main.aux index dcadd29..1b1507b 100644 --- a/latex/main.aux +++ b/latex/main.aux @@ -15,10 +15,11 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Dynamique avec EDP}{1}{subsection.1.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Discrétisation par éléments finis}{1}{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.}}{3}{figure.caption.1}\protected@file@percent } -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Response du système en boucle ouverte.}}{3}{figure.caption.2}\protected@file@percent } +\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}} +\newlabel{fig:q9_eigenvalues}{{1}{3}{Comparaison des valeurs propres du système en temps continu et en temps discret}{figure.caption.1}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Response du système en boucle ouverte.}}{4}{figure.caption.2}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {2}Retour de sortie}{4}{section.2}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Suivi de la consigne $w_c(t)$ par la position $w(L,t)$.}}{4}{figure.caption.3}\protected@file@percent } -\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}} \newlabel{fig:Q8_1}{{3}{4}{Suivi de la consigne $w_c(t)$ par la position $w(L,t)$}{figure.caption.3}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Retour de sortie par ZOH}{4}{subsection.2.1}\protected@file@percent } \newlabel{fig:q9_eigenvalues}{{\caption@xref {fig:q9_eigenvalues}{ on input line 30}}{5}{Retour de sortie par ZOH}{figure.caption.4}{}} diff --git a/latex/main.log b/latex/main.log index 5250fb3..b9ee2ab 100644 --- a/latex/main.log +++ b/latex/main.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 19:33 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 19:57 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1067,7 +1067,11 @@ LaTeX Font Info: Trying to load font information for T1+phv on input line 50 (/usr/share/texlive/texmf-dist/tex/latex/psnfss/t1phv.fd File: t1phv.fd 2020/03/25 scalable font definitions for T1/phv. -) (./main.aux) +) (./main.aux + +LaTeX Warning: Label `fig:q9_eigenvalues' multiply defined. + +) \openout1 = `main.aux'. 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