Commit 8c0e65ee authored by Kristian Soltesz's avatar Kristian Soltesz
Browse files

almost done documenting

parent 3b673be9
......@@ -49,7 +49,10 @@ The software consists of three scripts for {PID}. The underlying methods for the
\bibentry{pidIE}
\end{itemize}
\noindent The code present in the \PIDopt package is due to the authors of the above works. Please acknowledge these works through citation if you use the methods in your research.
\noindent Please acknowledge these works through citation if you use the methods in your research.
The \PIDopt package has been put together by Kristian Soltesz. Parts of the code are slight modifications of code written by Martin Hast and Chriss Grimholt, who have given their permission to use and distribute the code.
\section{Getting started}
\subsection{Installation}
......@@ -101,7 +104,7 @@ whereas \pidIAE (see \cite{pidIAE} for details) and \pidfIAE (see \cite{pidfIAE}
\begin{equation}
\text{IAE} = \int_0^\infty |e(t)| dt.
\end{equation}
These objectives are standard within process control, and sound within a much broader application scope. A thorough introduction is provided in \cite{astrom06}.
These objectives are standard within process control, and sound within a much broader application scope. A thorough introduction is provided in \cite{astrom06,garpinger15}.
Robustness of the control loop is enforced by constraining the sensitivity function
\begin{equation}
......@@ -152,24 +155,11 @@ Minimizing IE \eqref{eq:ie}, as is done by \pidIE, has the advantage of being eq
\begin{axis}[
xlabel=$t$,
ylabel=$e(t)$]
\addplot[color=red,mark=x] coordinates {
(2,-2.8559703)
(3,-3.5301677)
(4,-4.3050655)
(5,-5.1413136)
(6,-6.0322865)
(7,-6.9675052)
(8,-7.9377747)
};
% FIXME: plot with axis middle, narrow and no tick marks
\addplot [color=black,solid,line width = 2pt]table[x=t,y=y1,col sep=space] {steps.dat};
\addplot [color=black,dashed,line width = 2pt]table[x=t,y=y2,col sep=space] {steps.dat};
\end{axis}
\end{tikzpicture}
%\resizebox{.8\columnwidth}{!}{
%\begin{tikzpicture}[scale=.5]
%\begin{axis}[xlabel=$t$,ylabel=$e(t)$]
%\end{axis}
%\end{tikzpicture}
%}
\caption{The figure shows the load step response of two closed-loop control systems. Most users would prefer the one drawn in solid, which has a significantly smaller IAE than the dashed. However, due to the repetitive zero crossings, the IE of the dashed response is smaller than that of the solid line.}
\label{fig:ievsiae}
\end{figure}
......@@ -268,6 +258,110 @@ number={{TFRT-1105}}
}
\end{filecontents}
\begin{filecontents*}{steps.dat}
t y1 y2
0 0 0
0.1515 0 0
0.3030 0 0
0.4545 0 0
0.6061 0 0
0.7576 0 0
0.9091 0 0
1.0606 0.0588 0.0588
1.2121 0.1911 0.1911
1.3636 0.3049 0.3049
1.5152 0.4026 0.4026
1.6667 0.4866 0.4866
1.8182 0.5588 0.5588
1.9697 0.6208 0.6208
2.1212 0.6686 0.6670
2.2727 0.6936 0.6853
2.4242 0.6996 0.6787
2.5758 0.6900 0.6503
2.7273 0.6674 0.6027
2.8788 0.6343 0.5383
3.0303 0.5926 0.4592
3.1818 0.5444 0.3682
3.3333 0.4926 0.2698
3.4848 0.4399 0.1684
3.6364 0.3881 0.0678
3.7879 0.3387 -0.0283
3.9394 0.2930 -0.1168
4.0909 0.2516 -0.1949
4.2424 0.2154 -0.2601
4.3939 0.1844 -0.3107
4.5455 0.1586 -0.3459
4.6970 0.1379 -0.3652
4.8485 0.1218 -0.3690
5.0000 0.1097 -0.3580
5.1515 0.1011 -0.3337
5.3030 0.0953 -0.2978
5.4545 0.0917 -0.2524
5.6061 0.0897 -0.1999
5.7576 0.0888 -0.1429
5.9091 0.0885 -0.0837
6.0606 0.0883 -0.0248
6.2121 0.0881 0.0314
6.3636 0.0875 0.0830
6.5152 0.0865 0.1282
6.6667 0.0848 0.1656
6.8182 0.0826 0.1943
6.9697 0.0798 0.2137
7.1212 0.0764 0.2237
7.2727 0.0726 0.2243
7.4242 0.0685 0.2163
7.5758 0.0641 0.2003
7.7273 0.0596 0.1775
7.8788 0.0551 0.1492
8.0303 0.0507 0.1169
8.1818 0.0464 0.0820
8.3333 0.0423 0.0461
8.4848 0.0386 0.0106
8.6364 0.0351 -0.0232
8.7879 0.0320 -0.0539
8.9394 0.0292 -0.0807
9.0909 0.0267 -0.1027
9.2424 0.0245 -0.1193
9.3939 0.0226 -0.1303
9.5455 0.0210 -0.1355
9.6970 0.0196 -0.1352
9.8485 0.0184 -0.1296
10.0000 0.0174 -0.1194
10.1515 0.0164 -0.1051
10.3030 0.0156 -0.0876
10.4545 0.0149 -0.0678
10.6061 0.0142 -0.0466
10.7576 0.0136 -0.0249
10.9091 0.0129 -0.0035
11.0606 0.0123 0.0167
11.2121 0.0117 0.0350
11.3636 0.0112 0.0508
11.5152 0.0106 0.0637
11.6667 0.0100 0.0733
11.8182 0.0094 0.0794
11.9697 0.0088 0.0821
12.1212 0.0083 0.0815
12.2727 0.0077 0.0777
12.4242 0.0072 0.0711
12.5758 0.0067 0.0622
12.7273 0.0063 0.0514
12.8788 0.0058 0.0393
13.0303 0.0054 0.0264
13.1818 0.0050 0.0132
13.3333 0.0047 0.0004
13.4848 0.0043 -0.0117
13.6364 0.0040 -0.0226
13.7879 0.0038 -0.0319
13.9394 0.0035 -0.0394
14.0909 0.0033 -0.0449
14.2424 0.0031 -0.0484
14.3939 0.0029 -0.0497
14.5455 0.0027 -0.0490
14.6970 0.0025 -0.0465
14.8485 0.0024 -0.0423
15.0000 0.0023 -0.0368
\end{filecontents*}
\begin{filecontents}{steps.csv}
% FIXME: cvs data here
\end{filecontents}
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