Commit ef7b2b25 authored by Martin Vítek's avatar Martin Vítek

Add initial boost converter model

parent c8f7fbce
......@@ -8,6 +8,7 @@
*autosave*
#*cache*
*_saved_*
*.sch-bak
#Eagle
*.b#*
......@@ -39,3 +40,25 @@
**.idea/
**cmake-build-debug/
**cmake-build-release/
# Latex
*.aux
*.log
*.in
*.out
*.lua
*.pdf
*.synctex.gz
*.tex.bak
*.toc
*.dvi
*.tdo
*.bak
*.bbl
*.blg
*.bbl
*.bcf
*.blg
*.xml
*.lof
*.lot
\documentclass[a4paper, oneside, 12pt, final, hidelinks]{article}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage{siunitx}
\usepackage[czech]{babel}
\usepackage{csquotes}
\usepackage{fontspec}
\usepackage[final]{pdfpages}
\usepackage{outlines}
\usepackage{minted}
\usepackage{physics}
\usepackage{amsmath}
\usepackage{nicematrix}
%\usepackage{showframe}
\sisetup{range-phrase = \text{--}, group-separator = \text{\,}, group-four-digits = true, output-decimal-marker = {,}}
\MakeOuterQuote{"}
\setminted
{
frame=lines,
framesep=2mm,
baselinestretch=1.2,
fontsize=\footnotesize,
linenos=true,
}
\setmintedinline[c++]
{
frame=none,
baselinestretch=1.2,
fontsize=\footnotesize,
linenos=false,
}
\begin{document}
\title{Model zvyšujícího měniče digitronových hodin}
%\author{Martin Vítek}
\maketitle
%
%\tableofcontents
%\newpage
\section{Zvyšující měnič}
\begin{figure}[!h]
\centering
\includegraphics[width=\textwidth]{../BP/pictures/zvysujici_menic}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section{Q24 v uzavřeném stavu}
\begin{figure}[!ht]
\centering
\includegraphics[width=.9\textwidth]{boost_model/boost_model_closed.pdf}
\end{figure}
\begin{align}
U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \\
-C_{out}\derivative{u_c}{t} &= \frac{u_c}{R_{63}+R_{load}}
\end{align}
\vspace{1em}
\centerline{}
\begin{align}
\derivative{i_l}{t} &= \frac{1}{L_3}U_{in}-\frac{R_{62}+R_{Q25}+R_{L3}+R_{Q24}}{L_3}i_l \\
\derivative{u_c}{t} &= -\frac{1}{C_{out}(R_{63}+R_{load})}u_c
\end{align}
\vspace{1em}
\centerline{}
\begin{align}
%\renewcommand\arraystretch{1.3}
\derivative{}{t}
\begin{bNiceMatrix} i_l \\ i_c \end{bNiceMatrix}
&=
\begin{bNiceMatrix}
-\frac{R_{62}+R_{Q25}+R_{L3}+R_{Q24}}{L_3} & 0 \\
0 & -\frac{1}{C_{out}(R_{63}+R_{load})}
\end{bNiceMatrix}
\begin{bNiceMatrix}i_l \\ u_c \end{bNiceMatrix}
+
\begin{bNiceMatrix} \frac{1}{L_3} \\ 0 \end{bNiceMatrix}
U_{in}
\end{align}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section{Q24 v otevřeném stavu}
\begin{figure}[!ht]
\centering
\includegraphics[width=.9\textwidth]{boost_model/boost_model_opened.pdf}
\end{figure}
\begin{align}
U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{s_{D6}}i_l + u_c \\
C_{out}\derivative{u_c}{t} &= i_l - \frac{u_c}{R_{63}+R_{load}}
\end{align}
\vspace{1em}
\centerline{}
\begin{align}
\derivative{i_l}{t} &= \frac{1}{L_3}(U_{in}-u_c)-\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3}i_l \\
\derivative{u_c}{t} &= \frac{1}{C_{out}}i_l-\frac{1}{C_{out}(R_{63}+R_{load})}u_c
\end{align}
\vspace{1em}
\centerline{}
\begin{align}
\derivative{}{t}
\begin{bmatrix} i_l \\ i_c \end{bmatrix}
=
\begin{bmatrix}
-\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3} & -\frac{1}{L_3} \\
\frac{1}{C_{out}} & -\frac{1}{C_{out}(R_{63}+R_{load})}
\end{bmatrix}
\begin{bmatrix}i_l \\ u_c \end{bmatrix}
+
\begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
U_{in}
\end{align}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section{"Zprůměrování" stavového modelu}
\begin{align}
\overline{A} =A_1d + A_2(1-d) \\
\overline{B} = B_1d + B_2 (1-d)
\end{align}
$A_1$, $B_1$ - Q24 v uzavřeném stavu, $A_2$, $B_2$ - Q24 v otevřeném stavu.
\vspace{1em}
\centerline{}
\begin{align}
\derivative{}{t}
\begin{bmatrix} i_l \\ i_c \end{bmatrix}
=
\begin{bmatrix}
-\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3} & -\frac{1-d}{L_3} \\
\frac{1-d}{C_{out}} & -\frac{1}{C_{out}(R_{63}+R_{load})}
\end{bmatrix}
\begin{bmatrix}i_l \\ u_c \end{bmatrix}
+
\begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
U_{in}
\end{align}
\subsection{Odezva otevřené smyčky pro různé hodnoty střídy}
\begin{figure}[!ht]
\centering
\includegraphics[width=1\textwidth, trim=4.8cm 1cm 4.3cm 1.8cm,clip]{figures/open_loop_response}
\end{figure}
\end{document}
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%% Nixie clock boost converter
% Converter parameters
R62 = 0.2;
R63 = 4.7;
RQ25 = 23e-3;
RL3 = 1.1;
RsD6 = 2;
Rload = 12e3;
L3 = 680e-6;
Cout = 1.4e-6;
Uin = 12;
f = 23437.5;
d = 0.93;
% State space matrices - switch closed
A1 = [ -(R62+RQ25+RL3+RsD6)/L3, 0;
0 , -1/(Cout*(R63+Rload))];
B1 = [ 1/L3;
0 ];
% State space matrices - switch opened
A2 = [ -(R62+RQ25+RL3+RsD6)/L3, -1/L3;
1/Cout , -1/(Cout*(R63+Rload))];
B2 = [ 1/L3;
0 ];
% State space matrices - averaged
Aa = A1.*d + A2.*(1-d);
Ba = B1.*d + B2.*(1-d);