CH08_SEC08_1_TransferFunction.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
from control.matlab import *
import slycot
from scipy import signal
# Python control toolbox available at https://python-control.readthedocs.io/

plt.rcParams['figure.figsize'] = [8, 8]
plt.rcParams.update({'font.size': 18})

s = tf(np.array([1,0]),np.array([0,1]))
G = 1/(s**2 + s + 2)
w, mag, phase = bode(G)

A = np.array([[0,1],[-2,-1]])
B = np.array([0,1]).reshape((2,1))
C = np.array([1,0])
D = 0
G = ss2tf(A,B,C,D)

ia,it = impulse(G)

plt.plot(it[[0,-1]],np.array([0,0]),'k:')
plt.plot(it,ia)
plt.title('Impulse Response')
plt.ylabel('Amplitude')
plt.xlabel('Time')
plt.show()