How to find roots for particular value of gain "K" using Root Locus method in Julia?

Question

I am looking for a method to calculate the numerical values of the roots of a function using the root locus method in Julia. I have found some documents to plot the root locus but couldn't find a method to get the numerical values of those roots for particular 'K'.

using ControlSystems
    K = 100
    a = 5
    b = 10
    G = 1 + K^b / (x^(b-1) * (x - a))

I want to find the roots of "G" using the root locus method in Julia.

Could you please help?

Thank you

Answer 1

The function rlocusplot is available if you import the full ControlSystems package as opposed to just ControlSystemsBase (downside is a very long initialization time).

This worked for me:

using Plots, ControlSystems
plotly()

s = tf("s")
K, b, a = 100, 10, 5
G = 1 + K^b / (s^(b-1) * (s - a))
rlocusplot(G)