65. Root locus diagrams

Root locus diagrams show where the roots of the characteristic equation lie for different values of controller gain. The control library has a built-in function for plotting these diagrams.

import control

from matplotlib import pyplot as plt

%matplotlib inline

s = control.tf([1, 0], 1)

def rlocus(order, tau_p, K):
    Gp = 1/(tau_p*s + 1)**order
    Gc = 1

    L = Gp*Gc
    CL = K*L/(1 + K*L)
    control.root_locus(L);
    control.pzmap(CL)
    plt.title('')

from ipywidgets import interact

interact(rlocus, order=(1, 5), tau_p=(0.1, 2.), tau_i=(1., 20), K=(0.01, 200))

<function __main__.rlocus(order, tau_p, K)>