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CSGv1.2 modifications
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‎.gitignore

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/tmp
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RegT2E.pdf
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*.synctex
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*.preview.pdf
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tmp/*
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RegT2.pdf
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*.acn
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*.acr
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*.alg
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*.aux
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*.bbl
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*.blg
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*.dvi
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*.fdb_latexmk
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*.glg
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*.glo
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*.gls
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*.idx
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*.ilg
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*.ind
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*.ist
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*.lof
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*.log
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*.lot
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*.maf
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*.mtc
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*.mtc0
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*.nav
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*.nlo
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*.out
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*.pdfsync
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*.ps
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*.snm
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*.synctex.gz
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*.toc
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*.vrb
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*.xdy

‎.project

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<?xml version="1.0" encoding="UTF-8"?>
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<projectDescription>
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<name>RegT2E</name>
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<name>RegT2</name>
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<comment></comment>
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<projects>
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</projects>

‎.settings/org.eclipse.core.resources.prefs

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eclipse.preferences.version=1
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encoding/<project>=UTF-8

‎.settings/org.eclipse.core.runtime.prefs

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eclipse.preferences.version=1
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line.separator=\n

‎.texlipse

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bibrefDir=
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outputFormat=pdf
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tempDir=tmp
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mainTexFile=RegT2E.tex
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outputFile=RegT2E.pdf
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mainTexFile=RegT2.tex
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outputFile=RegT2.pdf
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langSpell=
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markDer=true
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srcDir=

‎README.markdown ‎README.md

+1-1

‎RegT2E.tex ‎RegT2.tex

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‎bilder/Empirisch_Regeln.jpg ‎images/Empirisch_Regeln.jpg

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‎bilder/PI_Regler.jpg ‎images/PI_Regler.jpg

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‎bilder/PT1_Bode.jpg ‎images/PT1_Bode.jpg

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‎bilder/PT1_Glied.jpg ‎images/PT1_Glied.jpg

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‎bilder/PT1_Nyq.jpg ‎images/PT1_Nyq.jpg

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‎bilder/PT2_Bode.jpg ‎images/PT2_Bode.jpg

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‎bilder/PT2_Nyq.jpg ‎images/PT2_Nyq.jpg

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‎bilder/PT2_glied.jpg ‎images/PT2_glied.jpg

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‎bilder/T_Glied.jpg ‎images/T_Glied.jpg

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‎bilder/bode-approx-ampl-4.png ‎images/bode-approx-ampl-4.png

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‎bilder/bode-approx-ampl-5.png ‎images/bode-approx-ampl-5.png

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‎bilder/bode-approx-ampl-6.png ‎images/bode-approx-ampl-6.png

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‎bilder/bode-approx-ampl-hp-ord1.png ‎images/bode-approx-ampl-hp-ord1.png

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‎bilder/bode-approx-ampl-tp-ord1.png ‎images/bode-approx-ampl-tp-ord1.png

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‎bilder/bode-approx-konst.png ‎images/bode-approx-konst.png

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‎bilder/bode-approx-phase-4.png ‎images/bode-approx-phase-4.png

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‎bilder/bode-approx-phase-5.png ‎images/bode-approx-phase-5.png

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‎bilder/bode-approx-phase-6.png ‎images/bode-approx-phase-6.png

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‎bilder/bode-stabilitaet.png ‎images/bode-stabilitaet.png

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‎bilder/feedback.png ‎images/feedback.png

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‎bilder/fg_iglied.jpg ‎images/fg_iglied.jpg

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‎bilder/fg_pglied.jpg ‎images/fg_pglied.jpg

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‎bilder/fg_pt1glied.jpg ‎images/fg_pt1glied.jpg

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‎bilder/fg_tglied.jpg ‎images/fg_tglied.jpg

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‎bilder/iglied.jpg ‎images/iglied.jpg

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‎bilder/pglied.jpg ‎images/pglied.jpg

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‎bilder/phasenreserve.png ‎images/phasenreserve.png

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‎bilder/pt1glied.jpg ‎images/pt1glied.jpg

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‎bilder/pt2glied.jpg ‎images/pt2glied.jpg

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‎bilder/tglied.jpg ‎images/tglied.jpg

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‎sections/BodeApproximation.tex

+18-18
Original file line numberDiff line numberDiff line change
@@ -10,93 +10,93 @@ \subsection{Approximation des Bode-Diagramms}
1010
\\ \hline
1111
Keine, konstanter Faktor &
1212
$\alpha e^{j \beta}$ &
13-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-konst.png}} &
13+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-konst.png}} &
1414
\, Konstant: $20 \log \alpha$ &
15-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-konst.png}} &
15+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-konst.png}} &
1616
Konstant: $\beta$
1717
\\ \hline
1818
Pol im Ursprung &
1919
$\frac{\alpha}{s}$ &
20-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-tp-ord1.png}} &
20+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-tp-ord1.png}} &
2121
\begin{tabular}{l}
2222
Lineare Steigung: $-20 dB/Dek.$ \\
2323
$0dB$ bei $\omega = \alpha$
2424
\end{tabular} &
25-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-konst.png}} &
25+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-konst.png}} &
2626
Konstant: $-\frac{\pi}{2}$
2727
\\ \hline
2828
Nullstelle im Ursprung &
2929
$\alpha s$ &
30-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-hp-ord1.png}} &
30+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-hp-ord1.png}} &
3131
\begin{tabular}{l}
3232
Lineare Steigung: $+20 dB/Dek.$ \\
3333
$0dB$ bei $\omega = \frac{1}{\alpha}$
3434
\end{tabular} &
35-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-konst.png}} &
35+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-konst.png}} &
3636
Konstant: $+\frac{\pi}{2}$
3737
\\ \hline
3838
Reeller Pol &
3939
$\frac{1}{s + \alpha}$ &
40-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-4.png}} &
40+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-4.png}} &
4141
\begin{tabular}{ll}
4242
$\omega < \alpha$: & Konstant $-20 \log \alpha$ \\
4343
$\omega > \alpha$: & $-20dB/Dek.$
4444
\end{tabular} &
45-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-phase-4.png}} &
45+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-phase-4.png}} &
4646
\begin{tabular}{ll}
4747
$\omega < \frac{\alpha}{10} $: & Konstant $0$ \\
4848
$\omega > 10 \alpha$: & Konstant $-\frac{\pi}{2}$
4949
\end{tabular}
5050
\\ \hline
5151
Reeller Pol &
5252
$\frac{\alpha}{s + \alpha}$ &
53-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-4.png}} &
53+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-4.png}} &
5454
\begin{tabular}{ll}
5555
$\omega < \alpha$: & Konstant $0dB$ \\
5656
$\omega > \alpha$: & $-20dB/Dek.$
5757
\end{tabular} &
58-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-phase-4.png}} &
58+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-phase-4.png}} &
5959
\begin{tabular}{ll}
6060
$\omega < \frac{\alpha}{10}$: & Konstant $0$ \\
6161
$\omega > 10 \alpha$: & Konstant $-\frac{\pi}{2}$
6262
\end{tabular}
6363
\\ \hline
6464
Reelle Nullstelle &
6565
$s + \alpha$ &
66-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-5.png}} &
66+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-5.png}} &
6767
\begin{tabular}{ll}
6868
$\omega < \alpha$: & Konstant $20 \log \alpha$ \\
6969
$\omega > \alpha$: & $+20dB/Dek.$
7070
\end{tabular} &
71-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-phase-5.png}} &
71+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-phase-5.png}} &
7272
\begin{tabular}{ll}
7373
$\omega < \frac{\alpha}{10}$: & Konstant $0$ \\
7474
$\omega > 10 \alpha$: & Konstant $+\frac{\pi}{2}$
7575
\end{tabular}
7676
\\ \hline
7777
Reelle Nullstelle &
7878
$\frac{s + \alpha}{\alpha}$ &
79-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-5.png}} &
79+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-5.png}} &
8080
\begin{tabular}{ll}
8181
$\omega < \alpha$: & Konstant $0dB$ \\
8282
$\omega > \alpha$: & $+20dB/Dek.$
8383
\end{tabular} &
84-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-phase-5.png}} &
84+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-phase-5.png}} &
8585
\begin{tabular}{ll}
8686
$\omega < \frac{\alpha}{10}$: & Konstant $0$ \\
8787
$\omega > 10 \alpha$: & Konstant $+\frac{\pi}{2}$
8888
\end{tabular}
8989
\\ \hline
9090
Konjugiert-komplexe Pole &
9191
$\frac{1}{s^2+s\frac{\omega_p}{q_p}+\omega_p^2}$ &
92-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-6.png}} &
92+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-6.png}} &
9393
\begin{tabular}{ll}
9494
$\omega < \omega_p$: & Konstant $-40 \log \omega_p$ \\
9595
$\omega > \omega_p$: & $-40dB/Dek.$ \\
9696
Überhöhung: & $\frac{\omega_p}{2}$ bis $2\omega_p$ \\
9797
Maximum: & $20 \log q_p$ bei $\omega = \omega_p$
9898
\end{tabular} &
99-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-phase-6.png}} &
99+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-phase-6.png}} &
100100
\begin{tabular}{ll}
101101
$\omega < \frac{\omega_p}{10^{\frac{1}{2q_p}}}$: & Konstant $0$ \\
102102
$\omega > \omega_p 10^{\frac{1}{2q_p}}$: & Konstant $-\pi$ \\
@@ -105,14 +105,14 @@ \subsection{Approximation des Bode-Diagramms}
105105
\\ \hline
106106
Konjugiert-komplexe Pole &
107107
$\frac{\omega_p^2}{s^2+s\frac{\omega_p}{q_p}+\omega_p^2}$ &
108-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-ampl-6.png}} &
108+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-ampl-6.png}} &
109109
\begin{tabular}{ll}
110110
$\omega < \omega_p$: & Konstant $0dB$ \\
111111
$\omega > \omega_p$: & $-40dB/Dek.$ \\
112112
Überhöhung: & $\frac{\omega_p}{2}$ bis $2 \omega_p$ \\
113113
Maximum: & $20 \log q_p$ bei $\omega = \omega_p$
114114
\end{tabular} &
115-
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./bilder/bode-approx-phase-6.png}} &
115+
\parbox[c][1cm]{1cm}{\includegraphics[width=1cm]{./images/bode-approx-phase-6.png}} &
116116
\begin{tabular}{ll}
117117
$\omega < \frac{\omega_p}{10^{\frac{1}{2q_p}}}$: & Konstant $0$ \\
118118
$\omega > \omega_p 10^{\frac{1}{2q_p}}$: & Konstant $-\pi$ \\

‎sections/Diverses.tex

+1-1
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@@ -19,6 +19,6 @@ \section{Diverses}
1919

2020

2121
\subsection{Graphisch Phasen-/Verstärkungsreserve}
22-
\includegraphics[width=7cm]{./bilder/bode-stabilitaet.png} \\
22+
\includegraphics[width=7cm]{./images/bode-stabilitaet.png} \\
2323
Phasen-/Verstärkungsreserve = Phasen-/Amplitudenrand
2424

‎sections/GegenkopplungStabilitaet.tex

+27-27
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@@ -10,7 +10,7 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
1010

1111

1212
%P-Glied
13-
P & \parbox[c][2cm]{3cm}{\input{./tikzBilder/PGlied}}
13+
P & \parbox[c][2cm]{3cm}{\input{./tikz/PGlied}}
1414
&
1515
\begin{tabular}{lll}
1616
$y = Ku$ & & \\
@@ -20,14 +20,14 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
2020
\\ \cline{2-3}
2121
&
2222
&
23-
\parbox[c]{3cm}{\input{./tikzBilder/PGliedNyquist}} \quad
24-
\parbox[c]{6cm}{\input{./tikzBilder/PGliedBode}}
23+
\parbox[c]{3cm}{\input{./tikz/PGliedNyquist}} \quad
24+
\parbox[c]{6cm}{\input{./tikz/PGliedBode}}
2525
\\
2626
\specialrule{2pt}{0pt}{0pt}
2727

2828

2929
%I-Glied
30-
I & \parbox[c][2cm]{3cm}{\input{./tikzBilder/IGlied}}
30+
I & \parbox[c][2cm]{3cm}{\input{./tikz/IGlied}}
3131
&
3232
\begin{tabular}{lll}
3333
$\dot{y} = Ku$ & & \\
@@ -37,14 +37,14 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
3737
\\ \cline{2-3}
3838
&
3939
&
40-
\parbox[c]{3cm}{\input{./tikzBilder/IGliedNyquist}}
41-
\parbox[c]{6cm}{\input{./tikzBilder/IGliedBode}}
40+
\parbox[c]{3cm}{\input{./tikz/IGliedNyquist}}
41+
\parbox[c]{6cm}{\input{./tikz/IGliedBode}}
4242
\\
4343
\specialrule{2pt}{0pt}{0pt}
4444

4545

4646
%D-Glied
47-
D & \parbox[c][2cm]{3cm}{\input{./tikzBilder/DGlied}}
47+
D & \parbox[c][2cm]{3cm}{\input{./tikz/DGlied}}
4848
&
4949
\begin{tabular}{lll}
5050
$y = K\dot{u}$ & & \\
@@ -54,14 +54,14 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
5454
\\ \cline{2-3}
5555
&
5656
&
57-
\parbox[c]{3cm}{\input{./tikzBilder/DGliedNyquist}}
58-
\parbox[c]{6cm}{\input{./tikzBilder/DGliedBode}}
57+
\parbox[c]{3cm}{\input{./tikz/DGliedNyquist}}
58+
\parbox[c]{6cm}{\input{./tikz/DGliedBode}}
5959
\\
6060
\specialrule{2pt}{0pt}{0pt}
6161

6262

6363
%PT1_Glied
64-
$PT_1$ & \parbox[c][2cm]{3cm}{\input{./tikzBilder/PT1Glied}}
64+
$PT_1$ & \parbox[c][2cm]{3cm}{\input{./tikz/PT1Glied}}
6565
&
6666
\begin{tabular}{lll}
6767
$T\dot{y}+y=Ku$ & $y(0)=0$ & \\
@@ -72,16 +72,16 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
7272
\\ \cline{2-3}
7373
&
7474
&
75-
\parbox[c]{3.7cm}{\input{./tikzBilder/PT1GliedNyquist}}
76-
\parbox[c]{6cm}{\input{./tikzBilder/PT1GliedBode}}
75+
\parbox[c]{3.7cm}{\input{./tikz/PT1GliedNyquist}}
76+
\parbox[c]{6cm}{\input{./tikz/PT1GliedBode}}
7777
\\
7878
\specialrule{2pt}{0pt}{0pt}
7979

8080

8181
%PT2_Glied
8282
$PT_2$ &
8383
\begin{minipage}{3cm}
84-
\includegraphics[width=3cm]{./bilder/PT2_glied.jpg}
84+
\includegraphics[width=3cm]{./images/PT2_glied.jpg}
8585
\end{minipage}
8686
&
8787
\begin{tabular}{lll}
@@ -99,18 +99,18 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
9999
\end{tabular}
100100
\\ \cline{2-3}
101101
& \begin{minipage}{3cm}
102-
\includegraphics[angle = {-0.3}, width=3cm]{./bilder/PT2_Nyq.jpg}
102+
\includegraphics[angle = {-0.3}, width=3cm]{./images/PT2_Nyq.jpg}
103103
\end{minipage}
104104
& \begin{minipage}{12cm}
105-
\includegraphics[angle = {0.2}, width=8cm]{./bilder/PT2_Bode.jpg}
105+
\includegraphics[angle = {0.2}, width=8cm]{./images/PT2_Bode.jpg}
106106
\end{minipage} \rule[-5mm]{0mm}{35mm}
107107
\\
108108
\specialrule{2pt}{0pt}{0pt}
109109

110110

111111
%Tt_Glied
112112
$T_t$ &
113-
\parbox[c][2cm]{3cm}{\input{./tikzBilder/TtGlied}}
113+
\parbox[c][2cm]{3cm}{\input{./tikz/TtGlied}}
114114
&
115115
\begin{tabular}{lll}
116116
$y=\begin{cases}
@@ -123,8 +123,8 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
123123
\\ \cline{2-3}
124124
&
125125
&
126-
\parbox[c]{3cm}{\input{./tikzBilder/TtGliedNyquist}}
127-
\parbox[c]{6cm}{\input{./tikzBilder/TtGliedBode}}
126+
\parbox[c]{3cm}{\input{./tikz/TtGliedNyquist}}
127+
\parbox[c]{6cm}{\input{./tikz/TtGliedBode}}
128128
\\
129129
\specialrule{2pt}{0pt}{0pt}
130130
\end{longtable}
@@ -139,16 +139,16 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
139139
% \hline
140140
% $P$-Glied & $I$-Glied & $PT_1$-Glied & $T_t$-Glied \\
141141
% \begin{minipage}{3cm}
142-
% \includegraphics[width=3cm]{./bilder/pglied}
142+
% \includegraphics[width=3cm]{./images/pglied}
143143
% \end{minipage} &
144144
% \begin{minipage}{3cm}
145-
% \includegraphics[width=3cm]{./bilder/iglied}
145+
% \includegraphics[width=3cm]{./images/iglied}
146146
% \end{minipage} &
147147
% \begin{minipage}{4cm}
148-
% \includegraphics[width=3cm]{./bilder/pt1glied}
148+
% \includegraphics[width=3cm]{./images/pt1glied}
149149
% \end{minipage} &
150150
% \begin{minipage}{3cm}
151-
% \includegraphics[width=3cm]{./bilder/tglied}
151+
% \includegraphics[width=3cm]{./images/tglied}
152152
% \end{minipage} \\
153153
% \hline
154154
% $y=Ku$ & $\dot{y} = Ku$ & $T\dot{y}+y = Ku$ & $y=u(t-T_t)$ \\
@@ -168,16 +168,16 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
168168
% \hline
169169
% & & & \\
170170
% \begin{minipage}{3cm}
171-
% \includegraphics[width=2.7cm]{./bilder/fg_pglied}
171+
% \includegraphics[width=2.7cm]{./images/fg_pglied}
172172
% \end{minipage} &
173173
% \begin{minipage}{3cm}
174-
% \includegraphics[width=3cm]{./bilder/fg_iglied}
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@@ -214,7 +214,7 @@ \section{Gegenkopplung und Stabilität \formelbuch{107}}
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& $\Phi_{res}$ & Phasenreserve
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\end{tabular}
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\includegraphics[width=6.2cm]{./bilder/phasenreserve.png}
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\includegraphics[width=6.2cm]{./images/phasenreserve.png}
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\subsection{Sprungantwort und Stabilität \formelbuch{135}}
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\subsubsection{Stabilitätssatz für ein System 2. Ordnung \formelbuch{137}}

‎sections/PidRegler.tex

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@@ -35,7 +35,7 @@ \section{PID-Regler \formelbuch{147}}
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Weitere Formeln in der LTI-Grundglieder Tabelle
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\subsection{PI-Regler \formelbuch{174}}
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\includegraphics[width=10cm]{./bilder/PI_Regler.jpg} \\
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\includegraphics[width=10cm]{./images/PI_Regler.jpg} \\
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\fbox{$G(j\omega)=K_R \frac{1+j\omega T_N}{j\omega T_N}$}\qquad
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\fbox{$arg(G(j\omega))=\arctan(\omega T_N)-\frac{\pi}{2}$}\qquad
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\fbox{$|G(j\omega)| = \frac{K_R \sqrt{1+(\omega T_n)^2}}{T_n \omega}$}
@@ -55,7 +55,7 @@ \section{PID-Regler \formelbuch{147}}
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Das PD-Glied entspricht dem inversen PT$_1$-Glied.
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\subsection{Empirische Einstellregeln \formelbuch{188}}
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\begin{minipage}[b]{5cm}
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UTF des angenäherten Modells:\\ \\
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$G_0(j\omega)=\frac{K_s}{1+j\omega T_g}e^{-j\omega T_u}$

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