import matplotlib.pyplot as plt
from utils import tf
from utilsplot import bode
# Trasfer function of L(s)
s = tf([1, 0], 1)
L = 3*(-2*s + 1)/((10*s + 1)*(5*s + 1))
plt.figure('Figure 2.7')
plt.title('Bode plots of L(s) with Kc = 1')
bode(L, -2, 1)
plt.show()
import matplotlib.pyplot as plt
from utils import tf
from utilsplot import bode
G = tf([5], [10, 1], deadtime=2)
plt.figure('Figure 2.2')
plt.title('Bode plots of G(s)')
bode(G, -3, 1)
plt.show()
# 1 to 4 are the important frequency domain measures used to assess
# performance and characterise speed of response
s = tf([1, 0], 1)
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')
import matplotlib.pyplot as plt
from utilsplot import bode
from utils import tf
s = tf([1, 0])
for power in range(1, 4):
G = 1/(s + 1)**power
bode(G)
plt.show()
import matplotlib.pyplot as plt
from utils import tf
from utilsplot import bode
s = tf([1,0], 1)
G = 30*(s + 1)/((s + 10)*(s + 0.01)**2)
plt.figure('Figure 2.3')
bode(G, -3, 3)
plt.title('Figure 2.3: Bode plot of transfer function ' + r'$L_1 = \frac{30(s + 1)}{(s + 10)(s + 0.01)^2}$'
+ '\n', fontsize = 13, y = -1)
plt.show()
import matplotlib.pyplot as plt
from utils import tf
from utilsplot import bode
s = tf([1,0], 1)
G = 30*(s + 1)/((s + 10)*(s + 0.01)**2)
plt.figure('Figure 2.3')
bode(G, -3, 3)
plt.show()
import matplotlib.pyplot as plt
from utilsplot import bode
from utils import tf
s = tf([1, 0])
for power in range(1, 4):
G = 1 / (s + 1)**power
bode(G)
plt.show()
