Commit 39c6ecdd authored by Martin Vítek's avatar Martin Vítek

Fixed discretization

parent 7ec0bba1
......@@ -191,11 +191,67 @@ U_{in}
\end{align}
\section{Diskretizace}
\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{1}{L_3} \\
\frac{\overline{i_L}}{C_{out}} & 0
\end{bmatrix}
\begin{bmatrix}
D \\ U_{in}
\end{bmatrix}
\end{align}
\vspace{1em}
\centerline{}
\begin{align}
\begin{bmatrix}
i_{l,t+1} \\ u_{c,t+1}
\end{bmatrix}
=
\boldsymbol{A}
\begin{bmatrix}i_l \\ u_c \end{bmatrix}
+
\boldsymbol{B}
\begin{bmatrix}
D \\ U_{in}
\end{bmatrix}
\end{align}
\begin{align}
\begin{bmatrix}
i_{l,t+1} \\ u_{c,t+1}
\end{bmatrix}
=
\boldsymbol{A}
\begin{bmatrix}i_l \\ u_c \end{bmatrix}
+
\begin{bmatrix}
\boldsymbol{B}_{1,1} \\ \boldsymbol{B}_{1,2}
\end{bmatrix}
D +
\begin{bmatrix}
\boldsymbol{B}_{2,1} \\ \boldsymbol{B}_{2,2}
\end{bmatrix}
U_{in}
\end{align}
\section{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}^*
\Delta_{t+1} &= \Delta_t + (u_{c,t} - u_{c,t}^*)\mathrm{d}t
\end{align}
\begin{align}
......@@ -204,26 +260,28 @@ U_{in}
\end{bmatrix}
&=
\begin{bmatrix}
-\frac{R_{in}}{L_3} & 0 & 0\\
0 & -\frac{1}{C_{out}R_{out}} & 0 \\
0 & 1 & 1 \\
\boldsymbol{A}_{1,1} & \boldsymbol{A}_{1,2} & 0 \\
\boldsymbol{A}_{2,1} & \boldsymbol{A}_{2,2} & 0 \\
0 & \mathrm{d}t & 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}} \\
\boldsymbol{B}_{1,1} \\
\boldsymbol{B}_{1,2} \\
0
\end{bmatrix}
D +
\begin{bmatrix}
\frac{1}{L_3} \\ 0 \\ 0
\boldsymbol{B}_{2,1} \\
\boldsymbol{B}_{2,2} \\
0 \\
\end{bmatrix}
U_{in} +
\begin{bmatrix}
0 \\ 0 \\ -1
0 \\ 0 \\ -\mathrm{d}t
\end{bmatrix}
u_{c,t}^*
\end{align}
......
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