Kc = 0.05
# plant model
G = 3 * (-2 * s + 1) / ((10 * s + 1) * (5 * s + 1))
# Controller model
K = Kc * (10 * s + 1) * (5 * s + 1) / (s * (2 * s + 1) * (0.33 * s + 1))
# closed-loop transfer function
L = G * K
# magnitude and phase of L
plt.figure('Figure 2.19')
bode(L, -2, 1)
# From the figure we can calculate w180
# w180 = 0.44
GM, PM, wc, wb, wbt, valid = marginsclosedloop(L)
print('GM:', np.round(GM, 2))
print('PM:', np.round(PM * np.pi / 180, 2), "rad or", np.round(PM, 2), "deg")
print('wb:', np.round(wb, 2))
print('wc:', np.round(wc, 2))
print('wbt:', np.round(wbt, 4))
# Response to step in reference for loop shaping design
# y = Tr, r(t) = 1 for t > 0
# u = KSr, r(t) = 1 for t > 0
plt.figure('Figure 2.20')
T = feedback(L, 1)
S = feedback(1, L)
u = K * S
step_response_plot(T, u, 50, 0)
[Kc, Taui, Ku, Pu] = ControllerTuning(G, method='ZN')
print 'Kc:', np.round(Ku/2.2, 3)
print 'Taui:', np.round(Pu/1.2, 3)
print 'Ku:', np.round(Ku, 3)
print 'Pu:', np.round(Pu, 3)
K1 = Kc * (1 + 1 / (Taui * s))
K = K1[0] # use this code to remove array
L = G * K
T = feedback(L, 1)
S = feedback(1, L)
u = S * K
plt.figure('Figure 2.8')
step_response_plot(T, u, 80, 0)
plt.show()
plt.figure('Figure 2.14')
bodeclosedloop(G, K, -2, 1, margin=True)
plt.show()
GM, PM, wc, wb, wbt, valid = marginsclosedloop(L)
print 'GM:' , np.round(GM, 2)
print "PM: ", np.round(PM, 1) , "deg or", np.round(PM / 180 * np.pi, 2), "rad"
print 'wb:' , np.round(wb, 2)
print 'wc:' , np.round(wc, 2)
print 'wbt:' , np.round(wbt, 2)
if valid: print "Frequency range wb < wc < wbt is valid"
else: print "Frequency range wb < wc < wbt is not valid"