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@@ -51,16 +51,12 @@ By plotting the gang of four under unit feedback for the process
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```math
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P(s) = \dfrac{1}{(s + 1)^4}
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```
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```jldoctest PIDDESIGN; output = false
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```@example PIDDESIGN
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using ControlSystems, Plots
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P = tf(1,[1,1])^4
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gangoffourplot(P,tf(1))
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save_docs_plot("pidgofplot.svg"); # hide
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# output
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```
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we notice that the sensitivity function is a bit too high around frequencies ω = 0.8 rad/s. Since we want to control the process using a simple PI-controller, we utilize the
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function [`loopshapingPI`](@ref) and tell it that we want 60 degrees phase margin at this frequency. The resulting gang of four is plotted for both the constructed controller and for unit feedback.
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We could also consider a situation where we want to create a closed-loop system with the bandwidth ω = 2 rad/s, in which case we would write something like
Here we specify that we want the Nyquist curve `L(iω) = P(iω)C(iω)` to pass the point `|L(iω)| = rl = 1, arg(L(iω)) = -180 + phasemargin = -180 + 60`
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The gang of four tells us that we can indeed get a very robust and fast controller with this design method, but it will cost us significant control action to double the bandwidth of all four poles.
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