Example_7_9.py

import numpy as np
import matplotlib.pyplot as plt

def G(s):
    return 3 * (-2 * s + 1) / ((5 * s + 1) * (10 * s + 1))

def K(s, kc):
    return kc * (12.7 * s + 1) / (12.7 * s)

def Wi(s):
    return (10 * s + 0.33) / ((10 / 5.25) * s + 1)

def Gnom(s):
    return 4 * (-3 * s + 1) / ((4 * s + 1) ** 2)

def l(Gn, G):
    return np.abs((Gn - G) / G)

def T(G, K):
    return (G * K) / (1 + G * K)

w = np.logspace(-3, 1, 300)
s = 1j*w

plt.figure(0)
plt.loglog(w, l(Gnom(s), G(s)), 'r', label='Relative Error')
plt.loglog(w, np.abs(Wi(s)), 'k', label='$W_I$')
plt.title(r'Figure 7.12')
plt.xlabel(r'Frequency [rad/s]', fontsize=14)
plt.ylabel(r'Magnitude', fontsize=15)
plt.legend()

plt.figure(1)
plt.loglog(w, np.abs(T(G(s), K(s, 1.13))), label='$T_1$ (not RS)')
plt.loglog(w, np.abs(T(G(s), K(s, 0.31))), label='$T_2$')
line = plt.loglog(w, 1/np.abs(Wi(s)), label='$1/W_I$')
plt.title(r'Figure 7.13')
plt.xlabel(r'Frequency [rad/s]', fontsize=14)
plt.ylabel(r'Magnitude', fontsize=15)
plt.legend()
plt.setp(line, linestyle='--')

plt.show()