def testDamp(self):
"""Test damp()"""
A = np.array([[-0.2, 0.06, 0, -1], [0, 0, 1, 0], [-17, 0, -3.8, 1],
[9.4, 0, -0.4, -0.6]])
B = np.array([[-0.01, 0.06], [0, 0], [-32, 5.4], [2.6, -7]])
C = np.eye(4)
D = np.zeros((4, 2))
sys = ss(A, B, C, D)
wn, Z, p = damp(sys, False)
# print (wn)
np.testing.assert_array_almost_equal(
wn, np.array([4.07381994, 3.28874827, 3.28874827, 1.08937685e-03]))
np.testing.assert_array_almost_equal(
Z, np.array([1.0, 0.07983139, 0.07983139, 1.0]))
print('GHp1/(1+GHp1) = ', cloop1)
print('GHp2/(1+GHp2) = ', cloop2)
print('GHp3/(1+GHp3) = ', cloop3)
#
# Polos e zeros de malha fechada
# comando pole() obtem os polos do sistema
# e zero() obtem os zeros do sistema
#
print('\nPOLOS E ZEROS DE MALHA FECHADA')
print('-------------')
print('Polos e zeros cloop1')
print('Polos = ', co.pole(cloop1))
print('Zeros = ', co.zero(cloop1))
print('COEF. DE AMORTECIMENTO E FREQ. NATURAL')
print('_____Polos____________zeta_______omegan')
co.damp(cloop1)
print('-------------')
print('Polos e zeros cloop2')
print('Polos = ', co.pole(cloop2))
print('Zeros = ', co.zero(cloop2))
print('COEF. DE AMORTECIMENTO E FREQ. NATURAL')
print('_____Polos____________zeta_______omegan')
co.damp(cloop2)
print('-------------')
print('Polos e zeros cloop3')
print('Polos = ', co.pole(cloop3))
print('Zeros = ', co.zero(cloop3))
print('COEF. DE AMORTECIMENTO E FREQ. NATURAL')
print('_____Polos____________zeta_______omegan')
co.damp(cloop3)
#
# exercicio de atraso / PI #G = co.tf(1,[1,3,2]) * co.tf(1,[1,10]) #Gc = 64 ##Gc2 = co.tf(64*np.asarray([1,0.1]),[1,0]) #Gc2 = co.tf(64*10*np.asarray([10,1]),[100,1]) # exercicio de avanço / PD G = co.tf(1,[1,10,24,0]) Gc = 63 Gc2 = co.tf(100*np.asarray([1/3,1]),[1/12,1]) #avanco #Gc2 = co.tf(191*np.asarray([1/6,1]),[1]) #PD T = np.linspace(0,20,3000) co.damp(co.feedback(G*Gc,1)) y,t = co.step(co.feedback(G*Gc,1),T) u,t = co.step(co.feedback(Gc,G),T) co.damp(co.feedback(G*Gc2,1)) y2,t = co.step(co.feedback(G*Gc2,1),T) u2,t = co.step(co.feedback(Gc2,G),T) plt.subplot(2,1,1) plt.plot(t,y,t,y2) plt.grid() plt.legend(['y1','y2']) plt.subplot(2,1,2) plt.plot(t,u,t,u2) plt.grid() plt.legend(['u1','u2'])
plt.figure(figsize=(10, 8))
for K in KPKD:
KP, KD = K
KI = 4
# To construct the closed-loop transfer function Gcl from theta^d to theta ,
# we have a number of options:
# (1) we can use the command "feedback" as introduced earlier.
######
Gcl = cm.feedback((KP + KD * s) * G, 1) # PD controller
# Gcl = cm.feedback((KP + KD * s + KI/s) * G, 1) # PID controller
print(Gcl)
print(cm.pole(Gcl))
cm.damp(Gcl, True)
######
# (2) If you are interested to know how Eq. (6.18) is derived,
# you may want to use the following general rule:
# +++++++++++++++++++
# Gcl = <Transfer function of the open loop between the input and output>/(1
# + <Transfer function of the closed loop>)
# +++++++++++++++++++
# Accordingly:
######
# Gcl = (KP*G + KD*s*G)/(1 + KP*G + KD*s*G)
######
# Gd = (G) / (1 + (KP + KD * s) * (G))
Gd = (G) / (1 + (KP + KD * s + KI/s) * (G))
"""**Importação Matplotlib**
"""
import matplotlib.pyplot as plt
"""**Analise:**"""
y,t=ctr.step(GEx2)
wn=5
z=0.6
F=ctr.tf([wn**2],[1,2*z*wn,wn**2])
y,t=ctr.step(F)
plt.plot(t,y)
plt.xlabel('Tempo, Segundos')
plt.ylabel('Saída $y(t)$')
plt.title('Resposta ao degrau unitário:')
plt.grid()
print(F)
ctr.damp(F)
ctr.stepinfo(F)