bodeplot

LaTeX package to plot Bode, Nichols, and Nyquist diagrams.

Inspired by the bodegraph package.

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.

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

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

Added functionality:

• 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 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.
• Support for linear and asymptotic approximation of magnitude and phase plots of any transfer function given poles, zeros, and gain.

Main Bode/Nyquist/Nichols commands: Given Zeros, Poles, Gain, and Delay (Bode plots support asymptotic and linear approximation for systems without delays):

• \BodeZPK[object1/type1/{options1},object2/type2/{options2},...]{z/{zeros},p/{poles},k/gain,d/delay}{min-frequency}{max-frequency}
• \NicholsZPK[plot/{options},axes/{options}]{z/{zeros},p/{poles},k/gain,d/delay}{min-frequency}{max-frequency}
• \NyquistZPK[plot/{options},axes/{options}]{z/{zeros},p/{poles},k/gain,d/delay}{min-frequency}{max-frequency}

Given Numerator and denominator coefficients and delay (does not support approximation yet):

• \BodeTF[object1/type1/{options1},object2/type2/{options2},...]{num/{coeff},den/{coeff},d/delay}{min-frequency}{max-frequency}
• \NicholsTF[plot/{options},axes/{options}]{num/{coeff},den/{coeff},d/delay}
• \NyquistTF[plot/{options},axes/{options}]{num/{coeff},den/{coeff},d/delay}

Other new environments and associated commands:

• BodePlot environment
  • \addBodeZPKPlots[{approximation1/{plot-options1}},{approximation2/{plot-options2}},...]{plot-type (phase or magnitude)}{z/{zeros},p/{poles},k/gain,d/delay}
    • \addBodeTFPlot[plot-options]{plot-type (phase or magnitude)}{num/{coeff},den/{coeff},d/delay}
    • \addBodeComponentPlot[plot-options]{basic_component_plot_command}
      • Basic component plot commands: (append Lin to get linear approximation and Asymp to get asymptotic approximation) (change Pole to Zero to get inverse plots) (change Mag to Ph to get phase plots)
      • \MagK{a} - Pure gain, G(s) = a.
      • \MagPole{a}{b} - Single pole at s = a+bi, G(s) = 1/(s - a-bi).
      • \MagCSPoles{z}{w} - Cannonical Second order system, G(s) = 1/(s^2 + 2zws + w^2).
      • \MagSOPoles{a}{b} - Second Order system, G(s) = 1/(s^2 + as + b).
      • \MagDel{T} - Pure delay, G(s) = exp(-Ts) (does not admit asymptotic approximation).
• NicholsChart environment
  • \addNicholsZPKChart[plot-options]{z/{zeros},p/{poles},k/gain,d/delay}
    • \addNicholsTFChart[plot-options]{num/{coeff},den/{coeff},d/delay}
• NyquistPlot environment
  • \addNyquistZPKPlot[plot-options]{z/{zeros},p/{poles},k/gain,d/delay}
    • \addNyquistTFPlot[plot-options]{num/{coeff},den/{coeff},d/delay}

Limitation: TF commands are wrapped between 0 and 360 degrees in pgf mode.