def testSiso(self):
"mixsyn with SISO system"
from control import tf, augw, hinfsyn, mixsyn
from control import ss
# Skogestad+Postlethwaite, Multivariable Feedback Control, 1st Ed., Example 2.11
s = tf([1, 0], 1)
# plant
g = 200/(10*s+1)/(0.05*s+1)**2
# sensitivity weighting
M = 1.5
wb = 10
A = 1e-4
w1 = (s/M+wb)/(s+wb*A)
# KS weighting
w2 = tf(1, 1)
p = augw(g, w1, w2)
kref, clref, gam, rcond = hinfsyn(p, 1, 1)
ktest, cltest, info = mixsyn(g, w1, w2)
# check similar to S+P's example
np.testing.assert_allclose(gam, 1.37, atol = 1e-2)
# mixsyn is a convenience wrapper around augw and hinfsyn, so
# results will be exactly the same. Given than, use the lazy
# but fragile testing option.
np.testing.assert_allclose(ktest.A, kref.A)
np.testing.assert_allclose(ktest.B, kref.B)
np.testing.assert_allclose(ktest.C, kref.C)
np.testing.assert_allclose(ktest.D, kref.D)
np.testing.assert_allclose(cltest.A, clref.A)
np.testing.assert_allclose(cltest.B, clref.B)
np.testing.assert_allclose(cltest.C, clref.C)
np.testing.assert_allclose(cltest.D, clref.D)
np.testing.assert_allclose(gam, info[0])
np.testing.assert_allclose(rcond, info[1])
P = augw(G,wp,wu) #generalized plant P
P = minreal(P)
wps = tf(wp)
Gs= tf(G)
Is= tf(I)
# correct generalized plant
p11 = wps
p12 = wps*Gs
p21 = -Is
p22 = -Gs
K2 = h2syn(P, 2, 2)
# H INF CONTROLLER
K, CL, gam, rcond = hinfsyn(P,2,2) #generalized plant incorrect so doing mixsyn
print(gam)
#open loop plot
openloop = triv_sigma(G*K, w)
openloop2 = triv_sigma(G*K2, w)
plt.figure(1)
plt.semilogx(w, 20*np.log10(openloop[:, 0]), label=r'G*K')
plt.semilogx(w, 20*np.log10(openloop2[:, 0]), label=r'G*K2')
plt.ylim([-50, 50])
plt.ylabel('magnitude [dB]')
plt.xlim([1e-3, 1e3])
plt.xlabel('freq [rad/s]')
plt.title('open loop')
plt.grid(1)
plt.legend()
# Augmented plant P = con.augw(G, w1, w2) #generalized plant P P = con.minreal(P) # H 2 CONTROLLER K2 = con.h2syn(P, 1, 1) L = G * K2 Ltf = con.ss2tf(L) So2 = 1.0 / (1.0 + Ltf) So2 = con.minreal(So2) To2 = G * K2 * So2 To2 = con.minreal(To2) # H INF CONTROLLER K, CL, gam, rcond = con.hinfsyn(P, 1, 1) print(gam) L = G * K Ltf = con.ss2tf(L) So = 1.0 / (1.0 + Ltf) So = con.minreal(So) To = G * K * So To = con.minreal(To) plt.figure(1) sw1 = triv_sigma(1.0 / w1, w) sigS = triv_sigma(So, w) sigS2 = triv_sigma(So2, w) plt.semilogx(w, 20 * np.log10(sw1[:, 0]), label=r'$\sigma_1(1/W1)$')
import control
import numpy as np
num = np.array([1.])
den = np.array([1, -1.])
my_tf = control.tf(num, den)
print(my_tf)
print(control.hinfsyn(my_tf, 1, 1))
def hinf(tf, tol):
"""
Computes the H-inf norm
:param tf:
:return:
"""
best = 0
gammal =
gammah =
while (gammah - gammal) / 2 > 2*tol*gammal:
# Form M
# check eigenvaleus
# update gammas
return best
import numpy import control m = 1. k = 0.4 zeta = 0.01 b = numpy.sqrt(k / m) * 2 * m * zeta #G = control.tf(1,[m, 0., 0.]) G = control.tf([1.], [m, b, k]) f_bandwidth = 100.0 w_bandwidth = 2 * numpy.pi * f_bandwidth A = 0.01 M = 2 w1 = control.tf([1 / M, w_bandwidth], [1.0, A * w_bandwidth]) w2 = control.tf([1.], [1.]) w3 = control.tf([1.0, w_bandwidth / M], [A, w_bandwidth]) control.bode((G, w1, w3)) P = control.augw(G, w1=w1, w2=None, w3=w3) ## K, CL, gam, rcond = control.hinfsyn(P, 1, 1) #K, CL, gam, rcond = control.h2syn(P,1,1) C = control.ss2tf(K) S = 1 / (1 + C * G) T = G * C / (1 + C * G) control.bode((S, 1 / w1))