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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]: