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figure en tikz

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Pierre-antoine Comby 2019-03-22 21:21:07 +01:00
parent 1e42bf08bd
commit bb45766921
3 changed files with 38 additions and 4 deletions
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424-Systeme_Non_Lineaires/Cours/5/1.png
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424-Systeme_Non_Lineaires/Cours/chap7.tex
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@ -11,11 +11,22 @@ Dans la suite du chapitre on étudiera le modèle suivant : Affine en la command
\section{Commande par bouclage linéarisant}
\begin{figure}[H]
\centering
\includegraphics[width=0.7\textwidth]{5/1.png}
\begin{tikzpicture}
\node[draw, minimum height=1cm] (C) at (0,0) {
\begin{tabular}{c}
Commande\\ Linéarisée
\end{tabular}};
\node[draw, minimum height=1cm] (S) at (5,0) {
\begin{tabular}{c}
Système\\ NL
\end{tabular}};
\draw[-latex] (-2,0) -- (C.west) node[near start,above]{$v$};
\draw[-latex] (C.east) -- (S.west) node[near start, above]{$u$};
\draw[-latex] (S.east) -- ++(2,0) node[above left]{$y$};
\draw[-latex] (S.south) |- ++(-2,-1) node[near start,right]{$x$} -| (C.south);
\end{tikzpicture}
\caption{Principe du bouclage linéarisant}
\end{figure}
% \img{0.5}{5/1} A rajouter !
Figure a rajouter
\subsection{Linéarisation entrées-sorties}
On se place dans le cas SISO: $u\in \R$ et $y\in\R$
@ -95,7 +106,29 @@ Qui nécessite le changement de base des variables d'états :
\begin{figure}[H]
\centering
\includegraphics[width=0.7\textwidth]{5/2.png}
\begin{tikzpicture}
\begin{scope}[at={(0,0)}]
\node[draw, minimum height=1cm] (C) at (0,0) {$\frac{v-a(z)}{b(z)}$};
\node[draw, minimum height=1cm] (S) at (3.5,0) {$\dot{x}=f(x)+g(x)u$};
\node[draw, minimum height=1cm] (N) at (7,0) {$z=\Phi(x)$};
\draw[-latex] (-2,0) -- (C.west) node[near start,above]{$v$};
\draw[-latex] (C.east) -- (S.west) node[near start, above]{$u$};
\draw[-latex] (S.east) -- (N.west);
\draw[-latex] (N.east) -- ++(1,0) node[above left]{$y$};
\draw[-latex] (N.south) |- ++(-2,-1) node[near start,right]{$x$} -| (C.south);
\end{scope}
\node at (3,-2.5){\Large$\Updownarrow$};
\begin{scope}[shift={(0,-4)}]
\node[draw, minimum height=1cm] (I1) at (0,0) {$\int$};
\node[draw, minimum height=1cm] (I2) at (2,0) {$\int$};
\node[draw, minimum height=1cm] (I3) at (5,0) {$\int$};
\draw[-latex] (-2,0) -- (I1.west) node[near start, above]{$v$};
\draw[-latex] (I1.east) -- (I2.west) node[near start, above]{$z_n$};
\draw[-latex] (I2.east) -- ++(1,0) node[midway,above]{$z_{n-1}$};
\draw[-latex,dashed] (I2.east)++(1,0) -- (I3.west) node[near end, above]{$z_{2}$};
\draw[-latex] (I3.east) -- ++(2,0) node[near end, above]{$z_1=y$};
\end{scope}
\end{tikzpicture}
\caption{Forme normale}
\end{figure}
@ -123,6 +156,7 @@ Ainsi on défini la dynamique des zéros. Le système commandé est en régime s
\dot{v}=0 y=0 ..
\]
La dynamique des zéro est celle $\dot{\eta} =q(\eta,0,v)$. Puisque la commande est linéaire on aussi prendre $v=0$
\end{rem}
\subsection{Dynamique des zéros}
\begin{defin}
C'est la dynamique interne pour une sortie identiquement nulle.