# 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)
# magnitude and phase of K
plt.figure('Figure 2.21')
bode(K, -2, 1)
plt.show()
G = 5/((10*s + 1)*(s - 1))
Gd = Kd/((s + 1)*(0.2*s + 1))
K = 0.04/s * ((10*s + 1)**2)/((0.1*s + 1)**2)
L = G * K
# Transfer function between disturbance and output y
S = feedback(1, L)*Gd
# Transfer function between disturbance and controller input u
Gu = -S*K
plt.figure('Figure 5.16 (a)')
plt.subplot(1, 2, 1)
w = np.logspace(-2, 1, 1000)
wi = w*1j
plt.loglog(w, np.abs(G(wi)))
plt.loglog(w, np.abs(Gd(wi)))
plt.axhline(1, color='black', linestyle=':')
plt.title('(a) $|G|$ & $|G_d|$ with $k_d$=0.5')
plt.xlabel('Frequency [rad/s]')
plt.ylabel('Magnitude')
plt.legend(('$|G|$','$|G_d|$'), loc=1)
plt.subplot(1, 2, 2)
step_response_plot(S, Gu, t_end=10, constraint=1) #TODO y(t)const is not yet correct
plt.title('(b) Response to step in disturbance ($k_d=0.5$)')
plt.show()
Gd = Kd / ((s + 1) * (0.2 * s + 1))
K = 0.04 / s * ((10 * s + 1)**2) / ((0.1 * s + 1)**2)
L = G * K
# Transfer function between disturbance and output y
S = feedback(1, L) * Gd
# Transfer function between disturbance and controller input u
Gu = -S * K
plt.figure('Figure 5.16 (a)')
plt.subplot(1, 2, 1)
w = np.logspace(-2, 1, 1000)
wi = w * 1j
plt.loglog(w, np.abs(G(wi)))
plt.loglog(w, np.abs(Gd(wi)))
plt.axhline(1, color='black', linestyle=':')
plt.title('(a) $|G|$ & $|G_d|$ with $k_d$=0.5')
plt.xlabel('Frequency [rad/s]')
plt.ylabel('Magnitude')
plt.legend(('$|G|$', '$|G_d|$'), loc=1)
plt.subplot(1, 2, 2)
step_response_plot(S, Gu, t_end=10,
constraint=1) # TODO y(t)const is not yet correct
plt.title('(b) Response to step in disturbance ($k_d=0.5$)')
plt.show()
[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"
import numpy as np
import matplotlib.pyplot as plt
from utils import feedback, tf, marginsclosedloop
from utilsplot import step_response_plot, bodeclosedloop
s = tf([1, 0], 1)
G = 4 /((s - 1) * (0.02 * s + 1)**2)
Kc = 1.25
Tauc = 1.5
K = Kc * (1 + 1 / (Tauc * s))
L = K * G
T = feedback(L, 1)
S = feedback(1, L)
u = S * K
plt.figure('Figure 2.9')
step_response_plot(T, u, 4, 0)
plt.show()
plt.figure('Figure 2.15')
bodeclosedloop(G, K, -1, 2, margin=True)
plt.show()
#TODO there is a descrepancy with the phase plots
GM, PM, wc, wb, wbt, valid = marginsclosedloop(L)
print 'GM:' , np.round(GM, 2)
print 'PM:', np.round(PM / 180 * np.pi, 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)
Gd = Kd / ((s + 1) * (0.2 * s + 1))
K = 0.04 / s * ((10 * s + 1)**2) / ((0.1 * s + 1)**2)
L = G * K
# Transfer function between disturbance and output y
S = feedback(1, L) * Gd
# Transfer function between disturbance and controller input u
Gu = -S * K
plt.figure('Figure 5.16 (a)')
plt.subplot(1, 2, 1)
w = np.logspace(-2, 1, 1000)
wi = w * 1j
plt.loglog(w, np.abs(G(wi)))
plt.loglog(w, np.abs(Gd(wi)))
plt.axhline(1, color='black', linestyle=':')
plt.title('(a) $|G|$ & $|G_d|$ with $k_d$=0.5')
plt.xlabel('Frequency [rad/s]')
plt.ylabel('Magnitude')
plt.legend(('$|G|$', '$|G_d|$'), loc=1)
plt.subplot(1, 2, 2)
# TODO y(t)const is not yet correct
step_response_plot(S, Gu, t_end=10, constraint=1)
plt.title('(b) Response to step in disturbance ($k_d=0.5$)')
plt.show()
import matplotlib.pyplot as plt
from utils import feedback, tf, marginsclosedloop
from utilsplot import step_response_plot, bodeclosedloop
s = tf([1, 0], 1)
G = 4 / ((s - 1) * (0.02 * s + 1)**2)
Kc = 1.25
Tauc = 1.5
K = Kc * (1 + 1 / (Tauc * s))
L = K * G
T = feedback(L, 1)
S = feedback(1, L)
u = S * K
plt.figure('Figure 2.9')
step_response_plot(T, u, 4, 0)
plt.show()
plt.figure('Figure 2.15')
bodeclosedloop(G, K, -1, 2, margin=True)
plt.show()
# TODO there is a discrepancy with the phase plots
GM, PM, wc, wb, wbt, valid = marginsclosedloop(L)
print('GM:', np.round(GM, 2))
print('PM:', np.round(PM / 180 * np.pi, 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))
