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Pablo gallegos edited untitled.tex
almost 9 years ago
Commit id: 553e8af1f721329521c498ff12f8650f0ca738f4
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\textit{Oh, an empty article!}
Las ecuaciones que modelan el sistema son las
siguiente siguientes
\begin{align}
\frac{dh_1}{dt}=u1-\frac{a_1}{A_1\sqrt{2gh_1} \frac{dh_1}{dt}=\frac{u_1}{A_1}-\frac{a_1}{A_1}\sqrt{2gh_1}
\end{align}
Linearización
\begin{eqnarray}
\frac{d\Delta %Linearización
%\begin{eqnarray}
%\frac{d\Delta h_1}{dt}&=-\sqrt{2g}\frac{a_1}{A_1}\frac{\Delta h_1}{2\sqrt{h_{1,0}}}+ \frac{\Delta u_1}{A_1} \\
\frac{d\Delta %\frac{d\Delta h_2}{dt}&=\sqrt{2g}\frac{a_1}{A_2}\frac{\Delta h_1}{2\sqrt{h_{1,0}}} -\sqrt{2g}\frac{a_2}{A_2}\frac{\Delta h_2}{2\sqrt{h_{2,0}}} \\
\frac{d\Delta %\frac{d\Delta h_3}{dt}&=\sqrt{2g}\frac{a_2}{A_3}\frac{\Delta h_2}{2\sqrt{h_{2,0}}} -\sqrt{2g}\frac{a_3}{A_3}\frac{\Delta h_3}{2\sqrt{h_{3,0}}}+\frac{\Delta u_2}{A_3}\\
\frac{d\Delta %\frac{d\Delta h_4}{dt}&=\sqrt{2g}\frac{a_3}{A_4}\frac{\Delta h_3}{2\sqrt{h_{3,0}}} -\sqrt{2g}\frac{a_4}{A_4}\frac{\Delta h_4}{2\sqrt{h_{4,0}}}
\end{eqnarray}
Funciones %\end{eqnarray}
%Funciones de transferencia
\begin{eqnarray}
H_1&=\frac{U_1}{(S+\sqrt{2g}\frac{a_1}{A_1}\frac{1}{2\sqrt{h_{1,0}}})A1}\\
H_2&=\frac{\sqrt{2g}\frac{a_1}{A_2}\frac{H_1}{2\sqrt{h_{1,0}}}}{(S+\sqrt{2g}\frac{a_2}{A_2}\frac{1}{2\sqrt{h_{2,0}}})}\\
H_3&=\frac{\sqrt{2g}\frac{a_2}{A_3}\frac{H_2}{2\sqrt{h_{2,0}}}+\frac{U_2}{A_3}}{(S+\sqrt{2g}\frac{a_3}{A_3}\frac{1}{2\sqrt{h_{3,0}}})}\\
H_4&=\frac{\sqrt{2g}\frac{a_3}{A_4}\frac{H_3}{2\sqrt{h_{3,0}}}}{(S+\sqrt{2g}\frac{a_4}{A_4}\frac{1}{2\sqrt{h_{4,0}}})}\\
\end{eqnarray} %\begin{eqnarray}
%H_1&=\frac{U_1}{(S+\sqrt{2g}\frac{a_1}{A_1}\frac{1}{2\sqrt{h_{1,0}}})A1}\\
%H_2&=\frac{\sqrt{2g}\frac{a_1}{A_2}\frac{H_1}{2\sqrt{h_{1,0}}}}{(S+\sqrt{2g}\frac{a_2}{A_2}\frac{1}{2\sqrt{h_{2,0}}})}\\
%H_3&=\frac{\sqrt{2g}\frac{a_2}{A_3}\frac{H_2}{2\sqrt{h_{2,0}}}+\frac{U_2}{A_3}}{(S+\sqrt{2g}\frac{a_3}{A_3}\frac{1}{2\sqrt{h_{3,0}}})}\\
%H_4&=\frac{\sqrt{2g}\frac{a_3}{A_4}\frac{H_3}{2\sqrt{h_{3,0}}}}{(S+\sqrt{2g}\frac{a_4}{A_4}\frac{1}{2\sqrt{h_{4,0}}})}\\
%\end{eqnarray}
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