Polar Nyquist plots

[togo65]

In order to generate a Nyquist plot for my book on control systems (heavily using Julia and examples from ControlSystems.jl and DynamicalSystems.jl), and in order to explain how simple it is to do controller design using polar coordinates, I am forced to use TikZ or Asymptote because I don't think it's possible to do this with the aforementioned packages.

Of course, it is vital to plot and print polar plots with strictly controlled aspect ratios otherwise the circles become ellipses and reading gain and phase (from printed plots) becomes irksome to say the least. I am of the old school that insists that students should try to use "manual" techniques before switching to CACSD (e.g. MATLAB, Scilab, and your packages, to name but a few, and presumably AI) in order that they can internalise what is going on before they use CACSD methods, which obviously I like to demonstrate.

Here's an extract from my book: Unfortunately, MATLAB\text{\textsuperscript\textregistered}, and Julia (\texttt{ControlSystems.jl}) both default to plotting Nyquist diagrams using rectilinear axes. This can be confusing when you are just beginning to get used to polar diagrams.

Please could the nyquistplot() function have an option for correctly scaled polar graph paper as a background?

[baggepinnen]

Is this what you have in mind? JuliaControl/ControlSystems.jl#1065 adds a polar=true option to the Makie version of nyquistplot:

using ControlSystemsBase, GLMakie  # or CairoMakie

P = tf(4, [1, 2, 1, 0])  # 4 / (s(s+1)²)
CSMakie.nyquistplot(P; polar=true, rlimits=(0, 3), unit_circle=true)

This draws the Nyquist curve in a Makie.PolarAxis, so the polar graph paper (circles of constant magnitude and rays of constant phase) is drawn natively by the plotting library: the grid re-ticks automatically when the axis limits change, the aspect ratio is correct by construction, and it survives interactive zooming in GLMakie. The Ms_circles/Mt_circles/unit_circle/critical_point options work in polar mode as well, and rlimits limits the radial axis, which is useful for systems with poles on or near the imaginary axis.

Note that the Makie support in ControlSystemsBase is currently marked experimental. The Plots.jl recipe could in principle gain a similar option via projection := :polar, but Plots' polar axes are less polished than Makie's PolarAxis, so the Makie backend seemed like the better home for this feature.

[baggepinnen]

[togo65]

Yes, absolutely! Many thanks! Except when I cut n paste your code into mine I get:

[togo65]

[togo65]

[baggepinnen]

Are you using the development version of ControlSystems on the PR branch I linked? The PR is not merged yet so it will not work if you use the released version of ControlSystems?

Run the following to install the developement version (in a new julia REPL) and then try again

using Pkg
Pkg.add(url="https://github.com/JuliaControl/ControlSystems.jl", subdir="lib/ControlSystemsBase", rev="polar-nyquist")

[togo65]

Oops! More haste = less speed. NOW it works, thank you so much! 🥇

[togo65]

Here's one I produced using TikZ, based on a TikZ example:
nyquistPlot.pdf
It would be great if I could get this sort of control over the number of radial lines etc. but I appreciate that's a lot of work. I have had a play around with polar plots in GLMakie a while back. I'll look under the hood a bit and maybe submit a PR if I can work it out.

[baggepinnen]

Run Pkg.update() and then restart, then try

  using ControlSystemsBase, GLMakie  # or CairoMakie

  P = tf(4, [1, 2, 1, 0])
  CSMakie.nyquistplot(P; polar=true, rlimits=(0, 3), unit_circle=true,
      rticks = 0:0.5:3,                            # major magnitude circles
      rminorticks = Makie.IntervalsBetween(5),     # minor circles every 0.1
      thetaminorticks = Makie.IntervalsBetween(3), # phase rays every 15°
      rminorgridvisible = true,
      thetaminorgridvisible = true)