Présentation finie
This commit is contained in:
parent
ef4c00bfbb
commit
b53fb8106d
2 changed files with 59 additions and 141 deletions
Binary file not shown.
|
|
@ -354,7 +354,7 @@ minimum height=3em, minimum width=6em]
|
|||
\subsection{Analyse des frequences importantes au système}
|
||||
\begin{frame}
|
||||
\frametitle{Analyse des frequences importantes au système}
|
||||
Pour cette deuxième boucle du système, on commence par tracer le diagramme de Bode du système rail sans bille, pour mieux ananlyser les besoin du système.
|
||||
Pour cette deuxième boucle du système, nous commençons par tracer le diagramme de Bode du système bille sur rail.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
|
|
@ -363,30 +363,59 @@ minimum height=3em, minimum width=6em]
|
|||
\label{fig:bode_rail}
|
||||
\end{figure}
|
||||
\vspace{-1em}
|
||||
Le correcteur choisit est un correcteur avance de phase. POURQUOI !???!?
|
||||
Le correcteur choisit est un correcteur avance de phase.
|
||||
\end{frame}
|
||||
|
||||
|
||||
\begin{frame}
|
||||
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{\href{https://homepages.laas.fr/fgouaisb/donnees/M1ICM/slidesM1ICMp8.pdf}{https://homepages.laas.fr/fgouaisb/donnees/M1ICM/slidesM1ICMp8.pdf}} : $$G(p) = K_p \frac{1 + \alpha T p}{1 + T p}, avec \ \alpha \ > \ 1$$
|
||||
Le point critique où il faut ajouter de la marge de phase est quand la magnitude est à 0dB, c.à.d. à 1,4 rad/s. Donc on concoit le correcteur avance de phase pour cela. Le correcteur d'avance de phase a une fonction de transfert sur la forme canonique\footnote{\href{https://homepages.laas.fr/fgouaisb/donnees/M1ICM/slidesM1ICMp8.pdf}{https://homepages.laas.fr/fgouaisb/donnees/M1ICM/slidesM1ICMp8.pdf}} :
|
||||
|
||||
\begin{equation*}
|
||||
T_c(p) = K_p \frac{1 + \alpha T p}{1 + T p} \ , \ avec \ \alpha \ > \ 1
|
||||
\end{equation*}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\subsection{Calcul des paramètres du correcteur avance de phase}
|
||||
\begin{frame}
|
||||
\frametitle{Calcul des paramètres du correcteur avance de phase}
|
||||
Commençons par calculer la marge de phase désirée :
|
||||
\begin{equation*}
|
||||
\Theta_{Marge}=\Theta_{Desir\acute{e}e} - \Theta_{Systeme} = 125^\circ \Rightarrow \Theta_{Desir\acute{e}e} = 55^\circ
|
||||
\end{equation*}
|
||||
|
||||
Puis, calculons $\alpha$ :
|
||||
|
||||
\begin{equation*}
|
||||
\alpha = \frac {1 + \sin(\Theta)}{1 - \sin(\Theta)} = \frac {1 + \sin(55^\circ)}{1 - \sin(55^\circ)} \approx 10
|
||||
\end{equation*}
|
||||
|
||||
Enfin, calculons T :
|
||||
|
||||
\begin{equation*}
|
||||
T = \frac{1}{\omega_m*\sqrt{\alpha}} \Rightarrow T = \frac{1}{1.4*\sqrt 10} \approx 0,22
|
||||
\end{equation*}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\begin{frame}
|
||||
\includegraphics[scale=0.5]{./Illustrations/bodeCorrecteur.png}
|
||||
\end{frame}
|
||||
Ceci nous donne un correcteur avance de phase :
|
||||
|
||||
\begin{equation*}
|
||||
T_c(p) = \frac{1+2,2p}{1+0,22p}
|
||||
\end{equation*}
|
||||
|
||||
\begin{frame}
|
||||
$$a = \frac {1 + \sin(\Phi)}{1 - \sin(\phi)} = \frac {1 + \sin(55°)}{1 - \sin(55°)} \approx 10$$
|
||||
$$\omega_m = \frac{1}{T*\sqrt{a}} = \frac{1}{1.4*\sqrt 10} \approx 0,22$$
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[scale=0.5]{./Illustrations/bodeCorrecteur.png}
|
||||
\caption{Diagramme de Bode du correcteur avance de phase}
|
||||
\label{fig:bode_avance_phase}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\section{Vérification}
|
||||
\subsection{Expérimental}
|
||||
\subsection{Vérfication expérimentale}
|
||||
\begin{frame}
|
||||
\frametitle{Vérfication expérimentale}
|
||||
\vfill
|
||||
|
|
@ -398,146 +427,35 @@ minimum height=3em, minimum width=6em]
|
|||
\end{frame}
|
||||
|
||||
|
||||
\subsection{MATLAB - marge de phase}
|
||||
\subsection{Vérfication de la marge de phase}
|
||||
\begin{frame}
|
||||
\frametitle{Vérfication de la 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 :
|
||||
\begin{center}
|
||||
En utilisant la fonction de allmargin nous trouvons la marge de phase pour le système entier en boucle fermé.
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[scale = 0.5]{./Illustrations/allmarginBode.png}
|
||||
\end{center}
|
||||
|
||||
%%\includesvg{./Illustrations/StepRespnseRail}
|
||||
\caption{Diagramme de Bode du système entier}
|
||||
\label{fig:bode_allmargin}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\section{Conclusion}
|
||||
\begin{frame}
|
||||
\frametitle{Conclusion}
|
||||
La boucle est bouclée et la balle est en equilibre.
|
||||
La boucle est bouclée et la balle est en équilibre.
|
||||
\end{frame}
|
||||
|
||||
|
||||
%\section{Introduction}
|
||||
%
|
||||
%\begin{frame}{Introduction}
|
||||
%
|
||||
%\begin{itemize}
|
||||
% \item But: Balancer une bille sur un rail.
|
||||
% \item Identification du système
|
||||
% \item Loi de commande
|
||||
%\end{itemize}
|
||||
%
|
||||
%\end{frame}
|
||||
%
|
||||
%\subsection{The chemistry packages}
|
||||
%\begin{frame}{The chemistry packages}
|
||||
%
|
||||
%We focus on two \LaTeX{} chemistry packages:
|
||||
%\begin{block}{The \texttt{chemfig} package}
|
||||
%This package provides the command which draws molecules. Created by Christian Tellechea, a detailed user guide can be found here:\\[0.4cm]
|
||||
%\small{\url{https://mirror.ox.ac.uk/sites/ctan.org/macros/generic/chemfig/chemfig-en.pdf}}
|
||||
%\end{block}
|
||||
%\begin{block}{The \texttt{mhchem} package}
|
||||
%The \texttt{mhchem} package provides simple commands for typesetting chemical molecular formulae and equations. Created by Martin Hensel, a detailed user guide can be found here:\\[0.4cm]
|
||||
%\small{\url{https://anorien.csc.warwick.ac.uk/mirrors/CTAN/macros/latex/contrib/mhchem/mhchem.pdf}}
|
||||
%\end{block}
|
||||
%% The LaTeX wikibook is also a good source of info, e.g.
|
||||
%% http://en.wikibooks.org/wiki/LaTeX/Chemical_Graphics
|
||||
%
|
||||
%\end{frame}
|
||||
%
|
||||
%\section{Using chemistry packages with \LaTeX{}}
|
||||
%
|
||||
%\subsection{Chemical equations with \texttt{mhchem}}
|
||||
%
|
||||
%\begin{frame}[fragile]
|
||||
%\frametitle{Chemical equations with \texttt{mhchem}}
|
||||
%
|
||||
%\begin{itemize}
|
||||
%\item The \texttt{mhchem} package lets you write chemical equations in \LaTeX{} with the minimum of effort.
|
||||
%\item The example below shows how the standard representation of a reaction (on the left) is created from the simple code on the right:
|
||||
%\end{itemize}
|
||||
%
|
||||
%\begin{center}
|
||||
%\ce{CO2 + C -> 2CO} is created with \verb|\ce{CO2 + C -> 2CO}|
|
||||
%\end{center}
|
||||
%
|
||||
%\begin{itemize}
|
||||
%\item More complicated reactions are still easy to write:
|
||||
%\end{itemize}
|
||||
%
|
||||
%\begin{center}
|
||||
%\ce{SO4^2- + Ba^2+ -> BaSO4 v}\\[0.1cm]
|
||||
%is created with\\[0.1cm]
|
||||
%\verb|\ce{SO4^2- + Ba^2+ -> BaSO4 v}|
|
||||
%\end{center}
|
||||
%
|
||||
%\end{frame}
|
||||
%
|
||||
%\subsection{Getting started with some \texttt{chemfig} coffee}
|
||||
%
|
||||
%\begin{frame}[fragile]
|
||||
%\frametitle{Getting started with some \texttt{chemfig} coffee}
|
||||
%
|
||||
%It's easy to use the \texttt{chemfig} package for drawing complex molecules:
|
||||
%
|
||||
%\vskip 0.5cm
|
||||
%
|
||||
%\begin{center}\small\setchemfig{atom sep=2.0em}
|
||||
%\schemestart
|
||||
%\chemfig{*6((=O)-N(-CH_3)-*5(-N=-N(-CH_3)-=)--(=O)-N(-H_3C)-)}
|
||||
%\schemestop
|
||||
%\end{center}
|
||||
%
|
||||
%This is the caffeine molecule, represented clearly and neatly, and built from a single line of text: \small{\verb|\chemfig{*6((=O)-N(-CH_3)-*5(-N=-N(-CH_3)-=)--(=O)-N(-H_3C)-)}|}\\[0.3cm]
|
||||
%
|
||||
%If that looks quite daunting, we can learn from simpler molecules\dots{}how about a single water molecule?
|
||||
%
|
||||
%\end{frame}
|
||||
%
|
||||
%\subsection{Experiments with water and rings}
|
||||
%
|
||||
%\begin{frame}[fragile]
|
||||
%\frametitle{Experiments with water and rings}
|
||||
%
|
||||
%To see how the \texttt{chemfig} package creates the drawings from your code, let us look at the simple water molecule:
|
||||
%
|
||||
%\vskip 0.3cm
|
||||
%\begin{center}
|
||||
%\chemfig{H_2O} is created with \verb|\chemfig{H_2O}|
|
||||
%\end{center}
|
||||
%
|
||||
%The simple \LaTeX{} code on the right is automatically converted into the molecular formula for water on the left.
|
||||
%\vskip 0.3cm
|
||||
%Rings are similarly easy to code - consider the examples below:
|
||||
%
|
||||
%\vskip 0.3cm
|
||||
%
|
||||
%\chemfig[atom style={scale=0.5}]{A*5(-B-C-D-E-)} =
|
||||
%\verb|\chemfig{A*5(-B-C-D-E-)}|
|
||||
%
|
||||
%\vskip 0.3cm
|
||||
%
|
||||
%\chemfig[atom style={scale=0.5}]{*6(=-=-=-)} = \verb|\chemfig{*6(=-=-=-)}|
|
||||
%
|
||||
%
|
||||
%\end{frame}
|
||||
%
|
||||
%\section{Where to go next\dots{}}
|
||||
%
|
||||
%\begin{frame}{Where to go next\dots{}}
|
||||
%
|
||||
%\begin{itemize}
|
||||
%\item This short example was designed to introduce you to using Overleaf for scientific presentations.
|
||||
%\item This is made possible by the many great packages that have been developed for \LaTeX{}, including the two we focused on here (plus the \texttt{Beamer} package used for the overall presentation style).
|
||||
%\item For more help on using \LaTeX{}, see the links on the Overleaf help page: \url{www.overleaf.com/help} or check out our free introductory webinars: \url{www.overleaf.com/events/webinars}.
|
||||
%\end{itemize}
|
||||
%
|
||||
%\begin{center}
|
||||
%Follow @overleaf on Twitter for all the latest news and updates.\\[0.3cm]
|
||||
%Happy \LaTeX ing!
|
||||
%\end{center}
|
||||
%
|
||||
%\end{frame}
|
||||
\begin{frame}
|
||||
\frametitle{Fin}
|
||||
\vfill
|
||||
\centering
|
||||
\begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title}
|
||||
\usebeamerfont{title}\Huge\textbf{Merci!}
|
||||
\end{beamercolorbox}
|
||||
\vfill
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
|
|
|||
Loading…
Reference in a new issue