Frontmatter

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using Plots, ControlSystemsBase, Plots.Measures, PlutoUI
5.0 s

Inverse Bode plots

Based on the figures below estimate the transfer function(s) that could have generated them.

Problem 1
md"""## Inverse Bode plots

Based on the figures below estimate the transfer function(s) that could have generated them.

#### Problem 1
"""
125 μs

Draw asymptotes:

md"""Draw asymptotes: $(@bind p1_asymptotes CheckBox(default=false))"""
86.2 ms
begin
num1 = [1/2, 1]
den1 = [1]
p1func(x) = x/2
local sys = tf(num1, den1)
local bb = bodeplot(sys,label=false, layout=(1,2), xminorticks=true, yminorticks=true, minorgrid=true, xlabel="Frequency [rad/s]", size=(800, 350), bottom_margin=3mm, left_margin=2mm)
local zz = plot!(bb[1], ylim = (0.1, 100))
local zz = plot!(bb[2], ylim=(-5,95))
if p1_asymptotes
hline!(bb[1], [1], label=false, line=:dash)
scatter!(bb[1], [2], [1], label=false, marker=:o)
hline!(bb[2], [0, 45, 90], label=false, line=:dash)
vline!(bb[2], [2], label=false, line=:dash)
plot!(bb[1], [0.1, 100], p1func.([0.1, 100]), label=false)
end
zz
end
3.6 s

Problem 2

Draw asymptotes:

md"""#### Problem 2

Draw asymptotes: $(@bind p2_asymptotes CheckBox(default=false))
"""
2.8 ms
begin
num2 = [900]
den2 = [1, 12, 900]
local sys = tf(num2, den2)
local bb = bodeplot(sys,label=false, layout=(1,2), xminorticks=true, yminorticks=true, minorgrid=true, xlabel="Frequency [rad/s]", size=(800, 350), bottom_margin=3mm, left_margin=2mm)
bb = plot!(bb[1], ylim=(0.001, 8))
p2func(x) = (x/30)^(-2)
if p2_asymptotes
hline!(bb[2], [0, -90, -180], label=false, line=:dash)
vline!(bb[1], [30], label=false, line=:dash)
vline!(bb[2], [30], label=false, line=:dash)
plot!(bb[1], [5, 300], p2func.([5, 300]), label=false, line=:dash)
scatter!(bb[1], [30], [p2func(30)], marker=:o, label=false)
hline!(bb[1], [1], label=false, line=:dash)
end
bb
end
500 ms

Bode plots

Problem 3

Draw the Bode plot for the below transfer function

$$G(s) = \dfrac{s+500}{500s+1}$$
md"""## Bode plots

#### Problem 3
Draw the Bode plot for the below transfer function

```math
G(s) = \dfrac{s+500}{500s+1}
```
"""
128 μs

Draw asymptotes:

md"""Draw asymptotes: $(@bind p3_asymptotes CheckBox(default=false))"""
603 μs
begin
num3 = [1, 500]
den3 = [500, 1]
local sys = tf(num3, den3)
bb = bodeplot(sys,label=false, layout=(1,2), xminorticks=true, yminorticks=true, minorgrid=true, xlabel="Frequency [rad/s]", size=(800, 350), bottom_margin=3mm, left_margin=2mm)
local pp1 = plot(xaxis=:log, yaxis=:log, xlim=xlims(bb[1]), ylim=ylims(bb[1]), xminorticks=true, yminorticks=true, minorgrid=true, xlabel="Frequency [rad/s]", ylabel="Magnitude")
local pp2 = plot(xaxis=:log, xlim=xlims(bb[2]), ylim=(-95,5), xminorticks=true, yminorticks=true, minorgrid=true, xlabel="Frequency [rad/s]", ylabel="Phase (deg)")
if p3_asymptotes
pp1 = vline!(pp1, [1/500, 500], label=false)
pp2 = vline!(pp2, [1/500, 500], label=false)
pp2 = hline!(pp2, [0,-90], label=false)
pp1 = hline!(pp1, [1/500, 500], label=false)
vline!(bb[1], [1/500, 500], label=false)
vline!(bb[2], [1/500, 500], label=false, ylim=(-95,5))
hline!(bb[2], [0,-90], label=false)
hline!(bb[1], [1/500, 500], label=false)
269 ms

Check solution:

md"""Check solution: $(@bind p3sol CheckBox(default=false))"""
520 μs