Commit f14aeed8 authored by Martin Vítek's avatar Martin Vítek

Add linearization and integration

parent 22ade6c0
......@@ -76,7 +76,6 @@ U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \
\centerline{}
\begin{align}
%\renewcommand\arraystretch{1.3}
\derivative{}{t}
\begin{bNiceMatrix} i_l \\ u_c \end{bNiceMatrix}
&=
......@@ -90,7 +89,6 @@ U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \
\begin{bmatrix} U_{in} \\ u_{D6} \end{bmatrix}
\end{align}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section{Q24 v otevřeném stavu}
......@@ -164,4 +162,69 @@ U_{in}
\end{figure}
\subsection{Linearizace}
\begin{align}
D &= 1-d \\
R_{in} &= R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}} \\
R_{out} &= R_{63}+R_{load}
\end{align}
\begin{align}
\derivative{}{t}
\begin{bmatrix} i_l \\ u_c \end{bmatrix}
=
\begin{bmatrix}
-\frac{R_{in}}{L_3} & 0 \\
0 & -\frac{1}{C_{out}R_{out}}
\end{bmatrix}
\begin{bmatrix}i_l \\ u_c \end{bmatrix}
+
\begin{bmatrix}
-\frac{\overline{u_c}}{L_3} \\
\frac{\overline{i_L}}{C_{out}}
\end{bmatrix}
D
+
\begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
U_{in}
\end{align}
\subsection{Integrace}
\begin{align}
\Delta_{u_c} &= u_c - u_c^* \\
\int \Delta_{u_c} &= \Delta \\
\Delta_{t+1} &= \Delta_t + u_{c,t} - u_{c,t}^*
\end{align}
\begin{align}
\begin{bmatrix}
i_{l,t+1} \\ u_{c,t+1} \\ \Delta_{t+1}
\end{bmatrix}
&=
\begin{bmatrix}
-\frac{R_{in}}{L_3} & 0 & 0\\
0 & -\frac{1}{C_{out}R_{out}} & 0 \\
0 & 1 & 1 \\
\end{bmatrix}
\begin{bmatrix}
i_{l,t} \\ u_{c,t} \\ \Delta_t
\end{bmatrix}
+
\begin{bmatrix}
-\frac{\overline{u_c}}{L_3} \\
\frac{\overline{i_L}}{C_{out}} \\
0
\end{bmatrix}
D +
\begin{bmatrix}
\frac{1}{L_3} \\ 0 \\ 0
\end{bmatrix}
U_{in} +
\begin{bmatrix}
0 \\ 0 \\ -1
\end{bmatrix}
u_{c,t}^*
\end{align}
\end{document}
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