!pip install control

import numpy as np
import matplotlib.pyplot as plt
from control.matlab import *

num = np.array([1])
den = np.array([1, 1, 0])
G = tf(num, den)

ar = 2
rlocus(G)
fig = plt.gcf().set_size_inches(8, 8)
plt.xlim([-ar, ar]), plt.ylim([-ar, ar])
plt.grid()
plt.show()

num = np.array([1,2])
den = np.array([1,4,0,0])
G = tf(num, den)

ar = 10
rlocus(G)
fig = plt.gcf().set_size_inches(8, 8)
plt.xlim([-ar, ar]), plt.ylim([-ar, ar])
plt.grid()
plt.show()

zeros = [9j, -9j, -5]
poles = [0, 0, 10j, -10j]
G = zpk(zeros, poles, 1)

ar = 20
rlocus(G)
fig = plt.gcf().set_size_inches(8, 8)
plt.xlim([-ar, ar]), plt.ylim([-ar, ar])
plt.grid()
plt.show()

zeros = [1]
poles = [2, 3, -10]
G = zpk(zeros, poles, 1)

ar = 20
rlocus(G)
fig = plt.gcf().set_size_inches(8, 8)
plt.xlim([-ar, ar]), plt.ylim([-ar, ar])
plt.grid()
plt.show()

zeros = [1]
poles = [2, 3, -10, -20]
G = zpk(zeros, poles, 1)

kvec_ = [0,10,200,1050]
rlist, klist = rlocus(G, kvec_,plot=False);
print(rlist)

ar = 20
rlocus(G)
fig = plt.gcf().set_size_inches(8, 8)
plt.xlim([-ar, ar]), plt.ylim([-ar, ar])
plt.plot(rlist[2].real, rlist[2].imag, "rx", label=f"K={kvec_[2]}") 
plt.plot(rlist[3].real, rlist[3].imag, "gx", label=f"K={kvec_[3]}") 
plt.legend()
plt.grid()
plt.show()


zr = [-3, 11j, -11j]
pl = [0, 0, 10j, -10j,-11,-11]
G = zpk(zr, pl, 1)

ar = 20
rlocus(G)
fig = plt.gcf().set_size_inches(8, 8)
plt.xlim([-ar, ar]), plt.ylim([-ar, ar])
plt.grid()
plt.show()