MàJ Rapport LaTex

Ajouter sur la section Bille sur Rail + commencer une section sur la validation du système

latex/Illustrations/bodeRail1.svg

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+  ></g
+></svg
+>

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.