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)

"""compute for additive parametric uncertainty"""

"""The condition for robust stability is derived & gives: RS <==> K*S < 1/W_A

with Lp = Gp*K = k*(G + W_A*delta_I)"""

def W_A(Gn, G): # We take W_A = l_A , Additive error (l_A = G'- G)

return np.abs(Gn - G)

def S(G, K):

return 1/(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()

#Plotting with multiplicative uncertainty

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='--')

#Plotting with additive uncertainty

plt.figure(2)

plt.loglog(w, K(s, 1.13)*np.abs(S(G(s), K(s, 1.13))))

plt.loglog(w, K(s, 0.31)*np.abs(S(G(s), K(s, 0.31))))

line = plt.loglog(w, 1/np.abs(W_A(Gnom(s), G(s))))

plt.title(r'Figure 7.13 with additive uncertainty')

plt.xlabel(r'Frequency [rad/s]', fontsize=14)

plt.ylabel(r'Magnitude', fontsize=15)

plt.legend(('S1 (not RS)','S2 is RS'), loc=1)

plt.setp(line, linestyle='--')

plt.show()