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Construction of the LFC for the frequency transfer function (frd)

The frequency transfer function (frequency response) is defined using sets of frequencies and complex numbers expressing the system's response to these frequencies.
This is a convenient way to store system frequency response data for visualization or use in calculations.

Pkg.add("ControlSystemsBase")
In [ ]: 
using EngeeControlSystems # To use the frd function
using ControlSystemsBase # For the construction of the LFCH
using CSV # To download experimental data from the table
Loading data from a table
In [ ]: 
df = CSV.read("frd_data.csv", DataFrame)
freq = df.freq
resp = [parse(ComplexF64, r) for r in df.resp]; # Converting from String to ComplexF64

Creating a Frequency Response Model

In [ ]: 
sys = frd(resp, freq)
Out[0]:
frd(ComplexF64[0.23841984895937737 - 0.0019508505988724586im;;; 0.25400219150798586 - 0.0035114829943812854im;;; 0.24295100787892412 + 0.0018065135835565785im;;; … ;;; -7.792719980301814e-5 + 0.0008045520700888559im;;; -0.0001896945323066172 + 0.0006147494316645394im;;; 1.116473000890296e-5 + 0.0006156621012700552im], [0.1, 0.10274594854461801, 0.10556729942333293, 0.10846612314544048, 0.11144454707535631, 0.11450475699382817, 0.11764899870201859, 0.12087957966963436, 0.12419887072831304, 0.12760930781150914  …  78.36418966217519, 80.51602998770538, 82.72695874133697, 84.99859846090146, 87.33261623828437, 89.73072494285637, 92.19468447849992, 94.72630307515246, 97.32743861581504, 100.0], nothing, "seconds", "rad/timeunit")
Construction of the LFCH
In [ ]: 
magnitude, phase, _ = bode(sys, freq)
Out[0]:
([0.2384278301622347;;; 0.25402646280196745;;; 0.24295772414293115;;; … ;;; 0.0008083171914251253;;; 0.0006433512876484359;;; 0.0006157633263977576], [-0.46880749163629404;;; -0.7920417471113614;;; 0.42602703045454404;;; … ;;; -264.4677100629009;;; -252.85123290043435;;; -271.038916961609], [0.1, 0.10274594854461801, 0.10556729942333293, 0.10846612314544048, 0.11144454707535631, 0.11450475699382817, 0.11764899870201859, 0.12087957966963436, 0.12419887072831304, 0.12760930781150914  …  78.36418966217519, 80.51602998770538, 82.72695874133697, 84.99859846090146, 87.33261623828437, 89.73072494285637, 92.19468447849992, 94.72630307515246, 97.32743861581504, 100.0])
In [ ]: 
magnitude = reshape(magnitude, size(magnitude, 3),)
phase = reshape(phase, size(phase, 3),)
Out[0]:
256-element Vector{Float64}:
   -0.46880749163629404
   -0.7920417471113614
    0.42602703045454404
   -1.0400851545567138
   -1.757285611061378
   -0.4572532835944419
    2.0688061063360683
   -0.5731712493801628
    0.22512626521159854
   -0.9097604824609797
   -3.0282154711474245
   -0.0793722602111739
    2.327323942243346
    ⋮
 -254.55952891164728
 -259.66789284233107
 -253.52620714314904
 -265.78529244104374
 -256.87843361975564
 -271.8782200891723
 -262.35584773156495
 -256.0261319236719
 -270.1132862026374
 -264.4677100629009
 -252.85123290043435
 -271.038916961609
In [ ]: 
p1 = plot(freq, 20*log10.(magnitude), ylabel = "L, dB", legend = :none)
p2 = plot(freq, phase, xlabel = "Oh, I'm glad/s", ylabel = ", hail", legend = :none)
plot(p1, p2, layout = (2,1), grid = false, framestyle = :box, xscale=:log10, xlims = (0.1,100))
Out[0]: