!pip install control

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


num1 = np.array([1])
den1 = np.array([1, 1])
G1 = tf(num1, den1)

num2 = np.array([100])
den2 = np.array([1, 100])
G2 = tf(num2, den2)

num3 = np.array([10000])
den3 = np.array([1, 2*0.1*100, 10000])
G3 = tf(num3, den3)

t = np.linspace(0, 5, 10000)
y, t = step(G1*G3, t)
y_r, t_r = step(G1, t)

plt.figure(dpi=100)
plt.plot(t, y, label='Full', alpha=0.8)
plt.plot(t_r, y_r, label='Reduced', alpha=0.8)
plt.xlabel(r'$t$ (sec)')
plt.ylabel(r'$y$')
plt.title('Step response')
plt.legend()
plt.grid()
plt.show()


num1 = np.array([1])
den1 = np.array([1, 1])
G1 = tf(num1, den1)

num2 = np.array([1])
den2 = np.array([1, 0.01])
G2 = tf(num2, den2)

num3 = np.array([1])
den3 = np.array([1, 0])
G3 = tf(num3, den3)

t = np.linspace(0, 5, 10000)
y, t = step(G1*G2, t)
y_r, t_r = step(G1*G3, t)

plt.figure(dpi=100)
plt.plot(t, y, label='Full', alpha=0.8)
plt.plot(t_r, y_r, label='Reduced', alpha=0.8)
plt.xlabel(r'$t$ (sec)')
plt.ylabel(r'$y$')
plt.title('Step response')
plt.legend()
plt.grid()
plt.show()


ts = np.arange(0, 15, 0.01)
G = tf([1], [1, 1])
K = tf([2, 2.5], [1, 0])
CL = feedback(K*G, 1, -1)
y, t = step(CL, ts)
print (CL)

plt.figure(dpi=100)
plt.plot(t,y)
plt.grid()


G1 = tf([2.5], [1, 3, 2.5])
G2 = tf([2, 0], [1, 3, 2.5])
y1, t1 = step(G1, ts)
y2, t2 = step(G2, ts)

plt.figure(dpi=100)
plt.plot(t1, y1)
plt.plot(t2, y2)
plt.plot(t, y)
plt.grid()
plt.show()