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|---|---|---|
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@@ -40,6 +40,7 @@ | |
| \fi | ||
| \usepackage{showexpl} | ||
| \lstset{% | ||
| explpreset={numbers=none}, | ||
| language=[LaTeX]Tex, | ||
| basicstyle=\ttfamily\tiny, | ||
| commentstyle=\itshape\ttfamily\tiny, | ||
|
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@@ -53,6 +54,7 @@ | |
| \usepackage{geometry} | ||
| \geometry{lmargin=2in,rmargin=1in,tmargin=1in,bmargin=1in} | ||
| \usetikzlibrary{decorations.markings,arrows.meta,spy,backgrounds} | ||
| \usepackage[nottoc]{tocbibind} | ||
| \EnableCrossrefs | ||
| \CodelineIndex | ||
| \RecordChanges | ||
|
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@@ -64,21 +66,21 @@ | |
| %</driver> | ||
| % \fi | ||
| % | ||
| % \CheckSum{1362} | ||
| % \CheckSum{1375} | ||
| % | ||
| % \changes{v1.0}{2021/10/25}{Initial release} | ||
| % \changes{v1.0.4}{2021/11/05}{Fixed unintended optional argument macro expansion} | ||
| % \changes{v1.0.6}{2021/11/18}{Fixed issue \#3} | ||
| % \changes{v1.0.7}{2021/12/02}{Removed unnecessary semicolons} | ||
| % \changes{v1.0.7}{2022/01/18}{Updated documentation} | ||
| % \changes{v1.0.8}{2022/07/06}{Added a new class option `declutter'} | ||
| % | ||
| % \GetFileInfo{bodeplot.sty} | ||
| % | ||
| % \DoNotIndex{\newcommand,\xdef,\gdef,\def,\edef,\addplot,\approx,\arabic,\opt,\typ,\obj,\else,\if@pgfarg,\fi,\begin,\end,\feature,\footnotesize,\draw,\detokenize,\DeclareOption,\foreach,\ifdim,\ifodd,\Im,\Re,\let,\newif,\nextgroupplot,\noexpand,\expandafter,\unexpanded,\PackageError,\PackageWarning,\relax,\RequirePackage,\tikzset,\pgfmathsetmacro,\pgfmathtruncatemacro,\ProcessOptions} | ||
| % | ||
| % \title{The \textsf{bodeplot} package\thanks{This document | ||
| % corresponds to \textsf{bodeplot}~v1.0.7, | ||
| % dated January 18, 2021.}} | ||
| % corresponds to \textsf{bodeplot}~v1.0.8, | ||
| % dated July 06, 2022.}} | ||
| % \author{Rushikesh Kamalapurkar \\ \texttt{[email protected]}} | ||
| % | ||
| % \maketitle | ||
|
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@@ -87,9 +89,16 @@ | |
| % \section{Introduction} | ||
| % | ||
| % Generate Bode, Nyquist, and Nichols plots for transfer functions in the canonical (TF) form \begin{equation}G(s) = e^{-Ts}\frac{b_ms^m+\cdots+b_1s+b_0}{a_ns^n+\cdots+a_1s+a_0}\label{eq:TF}\end{equation} and the zero-pole-gain (ZPK) form \begin{equation}G(s) = Ke^{-Ts}\frac{(s-z_1)(s-z_2)\cdots(s-z_m)}{(s-p_1)(s-p_2)\cdots(s-p_n)}.\label{eq:ZPK}\end{equation} In the equations above, $b_m,\cdots,b_0$ and $a_n,\cdots,a_0$ are real coefficients, $T\geq 0$ is the loop delay, $z_1,\cdots,z_m$ and $p_1,\cdots,p_n$ are complex zeros and poles of the transfer function, respectively, and $K\in \Re$ is the loop gain. For transfer functions in the ZPK format in (\ref{eq:ZPK}) \emph{with zero delay}, this package also supports linear and asymptotic approximation of Bode plots. | ||
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| % \textbf{Limitation:} in TF form, the phase angles are always between 0 and 360$^\circ$, As such, the Bode phase plots and the Nyquist and Nichols plots will have phase wrapping discontinuities. I do not know how this can be rectified, pull requests are welcome! | ||
| % | ||
| % \subsection{External Dependencies} | ||
| % By default, the package uses |gnuplot| to do all the computations. If |gnuplot| is not available, the |pgf| package option can be used to do the calculations using the native |pgf| math engine. Compilation using the |pgf| math engine is typically slower, but the end result should be the identical. | ||
| %\subsection{Directory Structure} | ||
| % Since version 1.0.8, the |bodeplot| package places all |gnuplot| temporary files in the working directory. The package option |declutter| restores the original behavior where the temporary files are placed in a folder called |gnuplot|. | ||
| % \subsection{Limitations} | ||
| % \begin{itemize} | ||
| % \item In TF form, the phase angles are always between 0 and 360$^\circ$. As such, the Bode phase plots and the Nyquist and Nichols plots will have phase wrapping discontinuities. I do not know how this can be rectified, pull requests are welcome! | ||
| % \item Use of the |declutter| option with other directory management tools such as a |tikzexternalize| prefix is not recommended. | ||
| % \end{itemize} | ||
| % \clearpage | ||
| % \section{TL;DR} | ||
| % All Bode plots in this section are for the transfer function (with and without a transport delay) | ||
| % \begin{equation} | ||
|
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@@ -112,13 +121,12 @@ | |
| {100} | ||
| \end{LTXexample} | ||
|
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||
| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Bode plot in TF format with arrow decoration, transport delay, and color customization | ||
| Bode plot in TF format with arrow decoration, transport delay, and color customization (note the phase wrapping) | ||
| \begin{LTXexample}[pos=r,width=0.5\textwidth] | ||
| \BodeTF[% | ||
| samples=1000, | ||
| plot/mag/{blue,thick}, | ||
| plot/ph/{green,thick}, | ||
| tikz/{>=latex}, | ||
|
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@@ -129,9 +137,11 @@ Bode plot in TF format with arrow decoration, transport delay, and color customi | |
| ] | ||
| {num/{10,2,2.6,0},den/{1,1,100.25},d/0.01} | ||
| {0.01} | ||
| {100} | ||
| {500} | ||
| \end{LTXexample} | ||
|
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Linear approximation with customization | ||
|
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@@ -151,8 +161,6 @@ Linear approximation with customization | |
| {100} | ||
| \end{LTXexample} | ||
|
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Plot with delay and customization | ||
|
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@@ -172,6 +180,8 @@ Plot with delay and customization | |
| {100} | ||
| \end{LTXexample} | ||
|
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Individual gain and phase plots with more customization | ||
|
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@@ -225,8 +235,6 @@ Individual gain and phase plots with more customization | |
| \end{LTXexample} | ||
| \end{minipage} | ||
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Nichols chart | ||
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@@ -251,6 +259,8 @@ Nichols chart in TF format | |
| {100} | ||
| \end{LTXexample} | ||
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Multiple Nichols charts with customization | ||
|
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@@ -274,8 +284,6 @@ Multiple Nichols charts with customization | |
| \end{NicholsChart} | ||
| \end{LTXexample} | ||
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Nyquist plot | ||
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@@ -311,6 +319,8 @@ Nyquist plot in TF format with arrows | |
| {30} | ||
| \end{LTXexample} | ||
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Multiple Nyquist plots with customization | ||
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@@ -329,8 +339,6 @@ Multiple Nyquist plots with customization | |
| \end{NyquistPlot} | ||
| \end{LTXexample} | ||
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| \hrulefill | ||
| \clearpage | ||
| \hrulefill | ||
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| Nyquist plots with additional commands, using two different macros | ||
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@@ -390,6 +398,7 @@ Nyquist plots with additional commands, using two different macros | |
| \end{minipage}} | ||
|
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| \hrulefill | ||
| \clearpage | ||
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| % \iffalse | ||
| %</ignore> | ||
|
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@@ -794,13 +803,18 @@ Nyquist plots with additional commands, using two different macros | |
| % \begin{macro}{gnuplot@id} | ||
| % \begin{macro}{gnuplot@prefix} | ||
| % \changes{v1.0.3}{2021/11/03}{Added jobname to gnuplot prefix} | ||
| % \changes{v1.0.8}{2022/07/06}{Fixed issue \#6} | ||
| % \begin{macro}{gnuplot@degrees} | ||
| % This code is needed to support both |pgfplots| and |gnuplot| simultaneously. New macros are defined for the |pow| and |mod| functions to address differences between the two math engines. We start by processing the |pgf| class option. | ||
| % This code is needed to support both |pgfplots| and |gnuplot| simultaneously. New macros are defined for the |pow| and |mod| functions to address differences between the two math engines. We start by processing the |pgf| and |declutter| class options. | ||
| % \begin{macrocode} | ||
| \newif\if@pgfarg\@pgfargfalse | ||
| \DeclareOption{pgf}{% | ||
| \@pgfargtrue | ||
| } | ||
| \newif\if@declutterarg\@declutterargfalse | ||
| \DeclareOption{declutter}{% | ||
| \@declutterargtrue | ||
| } | ||
| \ProcessOptions\relax | ||
| % \end{macrocode} | ||
| % Then, we define two new macros to unify |pgfplots| and |gnuplot|. | ||
|
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@@ -812,16 +826,25 @@ Nyquist plots with additional commands, using two different macros | |
| \newcommand{\n@pow}[2]{(#1)**(#2)}% | ||
| \newcommand{\n@mod}[2]{(#1)-(floor((#1)/(#2))*(#2))}% | ||
| % \end{macrocode} | ||
| % Then, we create a counter so that a new data table is generated and for each new plot. If the plot macros have not changed, the tables, once generated, can be reused by |gnuplot|, which reduces compilation time. | ||
| % Then, we create a counter so that a new data table is generated and for each new plot. If the plot macros have not changed, the tables, once generated, can be reused by |gnuplot|, which reduces compilation time. The |declutter| option is used to enable the |gnuplot| directory to declutter the working directory. | ||
| % \begin{macrocode} | ||
| \newcounter{gnuplot@id}% | ||
| \setcounter{gnuplot@id}{0}% | ||
| \tikzset{% | ||
| gnuplot@prefix/.style={% | ||
| id=\arabic{gnuplot@id}, | ||
| prefix=gnuplot/\jobname | ||
| }% | ||
| } | ||
| \if@declutterarg | ||
| \tikzset{% | ||
| gnuplot@prefix/.style={% | ||
| id=\arabic{gnuplot@id}, | ||
| prefix=gnuplot/\jobname | ||
| }% | ||
| } | ||
| \else | ||
| \tikzset{% | ||
| gnuplot@prefix/.style={% | ||
| id=\arabic{gnuplot@id}, | ||
| prefix=\jobname | ||
| }% | ||
| } | ||
| \fi | ||
| % \end{macrocode} | ||
| % Then, we add |set angles degrees| to all |gnuplot| macros to avoid having to convert from degrees to radians everywhere. | ||
| % \begin{macrocode} | ||
|
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@@ -833,10 +856,12 @@ Nyquist plots with additional commands, using two different macros | |
| }% | ||
| } | ||
| % \end{macrocode} | ||
| % If the operating system is not Windows, we create the |gnuplot| folder if it does not already exist. \changes{v1.0.2}{2021/11/01}{Fixed issue \#1} | ||
| % If the operating system is not Windows, and if the |declutter| option is not passed, we create the |gnuplot| folder if it does not already exist. \changes{v1.0.2}{2021/11/01}{Fixed issue \#1} | ||
| % \begin{macrocode} | ||
| \ifwindows\else | ||
| \immediate\write18{mkdir -p gnuplot}% | ||
| \if@declutterarg | ||
| \immediate\write18{mkdir -p gnuplot}% | ||
| \fi | ||
| \fi | ||
| \fi | ||
| % \end{macrocode} | ||
|
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@@ -1399,7 +1424,7 @@ Nyquist plots with additional commands, using two different macros | |
| % \end{macrocode} | ||
| %\end{macro} | ||
| % \begin{macro}{\build@TF@plot} | ||
| % This is an internal macro to build parametric Bode magnitude and phase functions by computing the magnitude and the phase given numerator and denominator coefficients and delay (input |#3|). The functions are assigned to user-supplied global magnitude and phase macros (inputs |#1| and |#2|). | ||
| % This is an internal macro to build parametric Bode magnitude and phase functions by computing the magnitude and the phase given numerator and denominator coefficients and delay (input |#3|). The functions are assigned to user-supplied global magnitude and phase macros (inputs |#1| and |#2|). \changes{v1.0.8}{2022/07/05}{Included phase due to delay in wrapping.} | ||
| % \begin{macrocode} | ||
| \newcommand{\build@TF@plot}[3]{% | ||
| \gdef\num@real{0}% | ||
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@@ -1451,7 +1476,7 @@ Nyquist plots with additional commands, using two different macros | |
| \fi | ||
| }% | ||
| \xdef#2{(\n@mod{atan2((\num@im),(\num@real))-atan2((\den@im),% | ||
| (\den@real))+360}{360}-\loop@delay*180*t/pi)}% | ||
| (\den@real))-\loop@delay*180*t/pi+360}{360})}% | ||
| \xdef#1{(20*log10(sqrt((\n@pow{\num@real}{2})+(\n@pow{\num@im}{2})))-% | ||
| 20*log10(sqrt((\n@pow{\den@real}{2})+(\n@pow{\den@im}{2}))))}% | ||
| } | ||
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