bodeplot

LaTeX package to plot Bode, Nichols, and Nyquist diagrams. Inspired by the bodegraph package.

Author: Rushikesh Kamalapurkar (rlkamalapurkar@gmail.com)

License: LPPL-1.3c

New features:

1. (v3.0) - All plotting commands use a simplified PGF-style key/value syntax
2. (v3.1) - If Python with scipy and numpy is available with --shell-escape then pole zero maps can be plotted for systems in TF format using \PoleZeroMapTF and the \BodeTF and \addBodeTFPlots commands support linear and asymptotic approximations.
3. (v3.1) - If Python with scipy and numpy is available with --shell-escape then the phase plots in pgf mode are no longer wrapped.

Limitations

1. TF commands are wrapped between -180 and 180 degrees in pgf mode unless Python with scipy and numpy is available with --shell-escape.
2. Version 1.0.8 and newer store gnuplot temporary files in the working directory. Use class option declutter to restore pre-v1.0.8 behavior. Option declutter can cause errors if used with a tikzexternalize prefix.
3. Before version 1.2, in pgf mode, the package set trig format plots to rad globally. Version 1.2 onwards, this option is passed to each addplot command individually so it does not affect non-bodeplot plots. To roll back to pre-v1.2 behavior, load the package with \usepackage[pgf]{bodeplot}[=2024-02-06].

Compilation instructions

1) latex bodeplot.ins to generate bodeplot.sty 2) To compile documentation (needs gnuplot on system PATH):

lualatex --shell-escape bodeplot.dtx
makeindex -s gind.ist bodeplot.idx
makeindex -s gglo.ist -o bodeplot.gls bodeplot.glo
lualatex --shell-escape bodeplot.dtx
lualatex --shell-escape bodeplot.dtx

Added functionality over bodegraph

• New \BodeZPK and \BodeTF commands to generate Bode plots of any transfer function given either poles, zeros, gain, and delay, or numerator and denominator coefficients and delay.
• Support for linear and asymptotic approximation of magnitude and phase plots of any transfer function.
• Support for pole-zero maps.
• All plots are fully customizable using pgf options (see package documentation for a full list of commands, environments, and options).
• Support for unstable poles and zeros.
• Support for complex poles and zeros.
• Support for general stable and unstable second order transfer functions.
• Support for both gnuplot (default) and pgfplots (package option pgf).
• Support for rad/s (default) and Hz (package option Hz or pgf key frequency unit=Hz for per-plot change) frequency units.
• Support for deg (default) and rad (package option rad or pgf key phase unit=rad for per-plot change) phase units.

Basic Bode/Nyquist/Nichols commands

See package documentation for the complete key reference, command list, and environment options.

Starting v3.0, all plotting commands use a simplified PGF-style key/value syntax.

• Zeros–poles–gain (ZPK) form with optional delay:

latexBodeZPK% domain=0.001:100, samples=1000, mag plot={blue, thick}, ph plot={green, thick}, phase unit=rad%{% zeros={0,-0.1-0.5i,-0.1+0.5i}, poles={-0.5-10i,-0.5+10i}, gain=10, delay=0.01% }

  Use the same interface with `\NicholsZPK[...]` or `\NyquistZPK[...]` to generate Nichols and Nyquist plots. Approximation options ( `linear`, `asymptotic`) are available for systems without delays through the `approx=...` key.

- Transfer-function (TF) form:

latex BodeTF% domain=0.001:100, samples=1000, frequency unit=Hz%{% numerator={10,2,2.6,0}, denominator={1,1,100.25}, delay=0.01% }

  The TF syntax is shared by `\NicholsTF[...]` and `\NyquistTF[...]`. Approximation options ( `linear`, `asymptotic`) are available for systems without delays through the `approx=...` key if `Python` with `scipy` and `numpy` is available via `--shell-escape`.

## Basic pole-zero map commands
*See package documentation for the full list of keys.*

- Given zeros and poles (gain and delay are ignored by the plot):

latex PoleZeroMapZPK% axes={width=6cm, height=6cm}, plot={blue, thick}%{% zeros={0,-0.1-0.5i,-0.1+0.5i}, poles={-0.5-10i,-0.5+10i}, gain=10, delay=0.01% }

- Given numerator and denominator (requires `Python` with `scipy` and `numpy` is available via `--shell-escape`) (delay is ignored by the plot)

latex PoleZeroMapTF% axes={width=6cm, height=6cm}, plot={blue, thick}%{% numerator={10,2,2.6,0}, denominator={1,1,100.25}, delay=0.01% }