From 43ef264421c1d8bd039bfd4f0c6d9ccdac80ae5f Mon Sep 17 00:00:00 2001 From: Oskar Date: Mon, 13 Apr 2026 23:13:38 +0200 Subject: [PATCH] =?UTF-8?q?M=C3=A0J=20Rapport=20LaTex?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Ajouter sur la section Bille sur Rail + commencer une section sur la validation du système --- latex/Illustrations/bodeRail1.svg | 306 ++++++++++++++++++++++++++++++ latex/compteRendu.pdf | Bin 158065 -> 327049 bytes latex/contents.tex | 40 ++-- 3 files changed, 334 insertions(+), 12 deletions(-) create mode 100755 latex/Illustrations/bodeRail1.svg diff --git a/latex/Illustrations/bodeRail1.svg b/latex/Illustrations/bodeRail1.svg new file mode 100755 index 0000000..a939d43 --- /dev/null +++ b/latex/Illustrations/bodeRail1.svg @@ -0,0 +1,306 @@ + + + diff --git a/latex/compteRendu.pdf b/latex/compteRendu.pdf index 1c4c77cd5d5ed50ac4097f9a24baffc8bfa38ac8..fa4c954c1b343a9baaeafadc534f51f19cf9dbdc 100644 GIT binary patch delta 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zpeS~1L`1u3t(&DC+82lxP{dg%LVtNac%y=}uRNEpg2aiu&`HmWS;89-j+WveyKf%| zuc(d@{ThL#D@efI;j|$swIOnd$aBqTJ~79(efKHZ(il(6SZ&&|F$z zvZP}b#|C49fM2;s7ya{n5MXfuLPlXyU$AzDsg+S$$rMlBe++!b_RWxEPgb*Id@m0< zl%C7>oFD)e0^|}Ff|I9T>r`IIJ{qn?ZqHxYSY@d#q3TrNVWn!fXDD{syt7|H9C_($ z>QP%8fzMX3jpI*v7)gwi9_kRt?9NR2SUuDCVrSwYgXiU42`7)VQwlw)Xk%{P?yP-` zZ8Zbn-qWZLeV2_9hKppX>QS|{*ia$ldUqD2aAb|NQjYe KaH!}&N&W-j*B)2^ diff --git a/latex/contents.tex b/latex/contents.tex index a4a33af..671be19 100644 --- a/latex/contents.tex +++ b/latex/contents.tex @@ -14,7 +14,9 @@ Nous avons remarqué que l'identification du système se fait en bouclé fermé. \subsection{Mise en oeuvre de N4SID} On a utilisé la fonction n4sid() que pouvons retrouver sur matlab. Nous avons fait une experiènce temporel, frequentiel et avec Loewner. -Voici le comportement des differents modèles obtenu: \{Sett inn bilde av n4sid\} +Voici le comportement des differents modèles obtenu: \hfill +\includesvg{./Illustrations/multisine1} \\ +\includesvg{./Illustrations/multisine2} Après avoir comparé les differents modèles avec le vrai système, Cela nous avait mené à résumer le systeme du rail à la fonction de transfert suivante : @@ -22,7 +24,7 @@ $$G(p) = \frac{NUM}{DEN}$$ \subsection{Fonction transfert du système: Rail} -Après avoir trouvé un modèle qui nous va, nous avons ensuite retrouvé la vraie fonction transferte du rail. Avec la relation qui suit: +Après avoir trouvé un modèle qui nous va, nous avons ensuite retrouvé la vraie fonction de transfert du rail. Avec la relation qui suit: \\ @@ -127,7 +129,7 @@ node[midway, below=10pt] {$H_C(s)$}; %\draw [->] \end{tikzpicture} -Après avoir conçu le système avec n4sid(), nous avons retrouvé la fonction transferte: +Après avoir conçu le système avec n4sid(), nous avons retrouvé la fonction de transfert : \begin{equation} G(s)=\frac{H(s)}{1+H(s)} @@ -137,22 +139,36 @@ Après avoir conçu le système avec n4sid(), nous avons retrouvé la fonction t G_{BF}(s)=\frac{P*G(s)}{1+P*G(s)} \end{equation} +Finalement, on essaie des différents valeurs de P pour observer le temps de réponse dans la boucle fermée. Nous tracons les différents valeurs dans un seul schèma pour voir l'impact d'un échelon sur le système. +\includesvg{./Illustrations/StepRespnseRail} \section{Loi de commande du bille sur rail} Pour cette deuxième boucle du système, on commence avec la boucle déjà existante. On trace le diagramme de Bode pour cet système pour mieux ananlyser les besoin du système. Cet diagramme est comme suit : -\newpage -\includesvg{./Illustrations/bodeRail} \\ -Pour qu'on puisse augmenter les marges de phase, on utilise un correcteur d'avance de phase. -Le correcteur d'avance de phase a une fonction de transfert sur la forme canonique : $$G(p) = \frac{1 + \alpha T p}{1 + T p}, avec \ \alpha \ > \ 1$$ +%\newpage +\hfill + + +\includesvg{./Illustrations/bodeRail1} \\ +Nous verrons que le point critique où il faut ajouter de la phase est à 1,4 rad/s. Donc on concoit le correcteur pour cela. Pour qu'on puisse augmenter les marges de phase, on utilise un correcteur d'avance de phase. +Le correcteur d'avance de phase a une fonction de transfert sur la forme canonique\footnote{https://homepages.laas.fr/fgouaisb/donnees/M1ICM/slidesM1ICMp8.pdf} : $$G(p) = K_p \frac{1 + \alpha T p}{1 + T p}, avec \ \alpha \ > \ 1$$ + \includesvg{./Illustrations/bodeCorrecteur} \\ +$$a = \frac {1 + \sin(\Phi)}{1 - \sin(\phi)} = \frac {1 + \sin(55°)}{1 - \sin(55°)} \approx 10$$ +$$\omega_m = \frac{1}{T*\sqrt{a}} = \frac{1}{1.4*\sqrt 10} \approx 0,22$$ -\section{Another section} -\subsection{Une sous section} -\subsubsection{Une sous sous section} -Un mot compliqué\footnote{Une note de bas de page} +\newpage +\section{Vérification} +\subsection{Expérimental} +\begin{center} +{\Huge ** Démonstration **} +\end{center} +\subsection{MATLAB - marge de phase} +En utilisant la fonction de allmargin nous trouvons le marge de phase pour le système entier en boucle fermé. Traçons le diagramme de Bode du système pour analyser le systeme même sans négliger la fonction de transfert du moteur : \hfill + +\includesvg{./Illustrations/StepRespnseRail} \newpage \psection{Conclusion} -Une conclusion +La boucle est bouclée et la balle est en equilibre.