74 lines
1.3 KiB
TeX
74 lines
1.3 KiB
TeX
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\documentclass[main.tex]{subfiles}
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\begin{document}
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\section{Intro}
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\section{Modèle de commande}
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\section{Couplage réseau}
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\[
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\deriv[(i)]{t} = -[L]^{-1}[R](i) - [L]^{-1}\left\{(v)-p\Omega \deriv[(\Phi_0)]{t}\right\}
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\]
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On a donc égalité des amplitudes et des phases pour la vitesse:
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\[
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\boxed{(v) = p\Omega \deriv[(\Phi_0)]{t}}
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\]
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\section{Schéma équivalent Behn-Eschenburg}
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\paragraph{Hypothèse}:
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\begin{itemize}
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\item RPS sinus
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\item MS non saturé , pole lisse , éuilibré
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\end{itemize}
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\begin{center}
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\begin{tabular}[c]{rl}
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\begin{minipage}[c]{0.3\linewidth}
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\begin{circuitikz}
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\draw (0,0) to[V] ++(0,2) to[L] ++(2,0) to[R] ++(2,0) to[open,v<=$V$] ++(0,-2) -- (0,0);
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\end{circuitikz}
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\end{minipage}
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&
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\begin{minipage}[h]{0.5\linewidth}
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\[
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\underline{E} = (j\mathcal{L}\omega+R) \underline{I} + \underline{V}
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\]
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\end{minipage}
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\end{tabular}
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\end{center}
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\subsection{Diagramme de Fresnel}
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On considère l'origine de phase sur $V$ et on se place en alternateur ie $\delta = Arg(E)-Arg(V) > 0$
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\subsubsection{Surexcitation}
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[schema fresnel]
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\begin{prop}
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$
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\|E\| > \|V\|
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$ on a alors :
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\[
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\begin{cases}
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P > 0 \\
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Q >0 \\
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\end{cases}
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\]
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\end{prop}
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\subsubsection{Sousexcitation}
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[schema fresnel]
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\begin{prop}
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$
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\|E\| < \|V\|
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$ on a alors :
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\[
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\begin{cases}
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P > 0 \\
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Q >0 \\
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\end{cases}
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\]
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\end{prop}
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\end{document}
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