def example_ct_fdsid():
n = 2
m = 3
p = 4
N = 100
T = 1.2e-1
A = np.random.randn(n, n)
B = np.random.randn(n, m)
C = np.random.randn(p, n)
D = np.random.randn(p, m)
D = D * 0
print(D)
# Create frequency function
fset = np.arange(0, N, dtype='float') / N
w = 2 * np.pi * fset
# wexp = np.exp(1j*2 * np.pi * fset)
fd = fsid.fresp(1j * w, A, B, C, D)
uf = np.random.randn(N, m) + 1j * np.random.randn(N, m)
yf = fsid.fdsim((A, B, C, D), uf, 1j * w)
wd = fsid.cf2df(w, T)
# Estimate ss model from ffdata
Ae, Be, Ce, De, xt, s = fsid.fdsid((wd, yf, uf),
n,
n * 2,
estTrans=False,
estimd=True)
# Convert to CT
Aec, Bec, Cec, Dec = fsid.bilinear_d2c((Ae, Be, Ce, De), T)
# Frequency response of estimated model
fde = fsid.fresp(1j * w, Aec, Bec, Cec, Dec)
print('CT FD: || G-Ge ||/||G|| = ',
linalg.norm((fd - fde) / linalg.norm(fd)))
print(Dec)
Ae, Be, Ce, De, xt, s = fsid.fdsid((w, yf, uf),
n,
n * 2,
CT=True,
T=T,
estimd=False)
fde2 = fsid.fresp(1j * w, Ae, Be, Ce, De)
print('CT2 FD: || G-Ge ||/||G|| = ',
linalg.norm(fd - fde2) / linalg.norm(fd))
print(De)
def example_fdsid():
import matplotlib.pyplot as plt
n = 2
m = 3
p = 4
N = 100
A = np.random.randn(n, n)
lam = linalg.eig(A)[0]
rho = np.max(np.abs(lam))
## Here we create a random stable DT system
A = A / rho / 1.01
B = np.random.randn(n, m)
C = np.random.randn(p, n)
D = np.random.randn(p, m)
## random excitation signal
u = np.random.randn(N, m)
## Time domain simulation
y = fsid.lsim((A, B, C, D), u)
plt.plot(y)
plt.show()
## Crfeate the N point DFT of the signals
yf = np.fft.fft(y, axis=0)
uf = np.fft.fft(u, axis=0)
fset = np.arange(0, N, dtype='float') / N
w = 2 * np.pi * fset
wexp = np.exp(1j * 2 * np.pi * fset)
fddata = (w, yf, uf)
Ae, Be, Ce, De, xt, s = fsid.fdsid(fddata, n, 2 * n, estTrans=True)
print('singular vales=', s)
fde = fsid.fresp(wexp, Ae, Be, Ce, De)
fd = fsid.fresp(wexp, A, B, C, D)
print('With estTrans=true')
print('|| G-Ge ||/||G|| = ', linalg.norm(fd - fde) / linalg.norm(fd))
Ae1, Be1, Ce1, De1, xt1, s = fsid.fdsid(fddata, n, 2 * n, estTrans=False)
print('singular vales=', s, ' model order n=', n)
fde = fsid.fresp(wexp, Ae, Be, Ce, De)
fd = fsid.fresp(wexp, A, B, C, D)
print('|| G-Ge ||/||G|| = ', linalg.norm(fd - fde) / linalg.norm(fd))
def example_1():
n = 2
m = 3
p = 4
N = 100
A = np.random.randn(n, n)
lam = linalg.eig(A)[0]
rho = np.max(np.abs(lam))
## Here we create a random stable DT system
A = A / rho / 1.01
B = np.random.randn(n, m)
C = np.random.randn(p, n)
D = np.random.randn(p, m)
## random excitation signal
u = np.random.randn(N, m)
## Time domain simulation
y = fsid.lsim((A, B, C, D), u)
#plt.plot(y)
#plt.show()
## Create the N point DFT of the signals
yf = np.fft.fft(y, axis=0)
uf = np.fft.fft(u, axis=0)
fset = np.arange(0, N, dtype='float') / N
w = 2 * np.pi * fset
wexp = np.exp(1j * 2 * np.pi * fset)
fddata = (w, yf, uf)
# Test estimation of B D and Xt
Be, De, xt, resid2 = fsid.fdestim_bd(wexp,
yf,
uf,
A,
C,
estTrans=True,
dtype='float')
print('fdestim_bd and xt residual = ', resid2)
## Check that the frequency functions coincide
fde = fsid.fresp(wexp, A, Be, C, De)
fd = fsid.fresp(wexp, A, B, C, D)
print('|| H-He ||/||H|| = ', linalg.norm(fd - fde) / linalg.norm(fd))
xt = B[:, 0]
yy = fsid.fdsim((A, B, C, D), uf, wexp, xt)
Be, De, xte, resid1 = fsid.fdestim_bd(wexp, yy, uf, A, C, estTrans=True)
# print('fdestim_bd residual = ', resid1)
print('fdestim_bd residual xt= ', linalg.norm(xt - xte) / linalg.norm(xt))
Ce, De, resid1 = fsid.fdestim_cd(wexp, yy, uf, A, B, xt, estTrans=True)
# Be, De, resid1 = fdestim_bd(wexp, yy, uf, A, C, estTrans=False)
# print('fdestim_cd residual = ', resid1)
fddata = (w, yf, uf)
Ae, Be, Ce, De, xt, s = fsid.fdsid(fddata, n, 2 * n, estTrans=True)
# Ae, Be, Ce, De, xt, s = fsid.fdsid(fddata, n, 2*n, estTrans=False)
print('singular vales=', s)
fde = fsid.fresp(wexp, Ae, Be, Ce, De)
fd = fsid.fresp(wexp, A, B, C, D)
print('|| H-He ||/||H|| = ', linalg.norm(fd - fde) / linalg.norm(fd))
return
def example_2():
n = 2
m = 3
p = 4
N = 100
u = np.random.randn(N, m)
A = np.random.randn(n, n)
lam = linalg.eig(A)[0]
rho = np.max(np.abs(lam))
A = A / rho / 1.01
B = np.random.randn(n, m)
C = np.random.randn(p, n)
D = np.random.randn(p, m)
y = fsid.lsim((A, B, C, D), u)
# plt.plot(y)
# plt.show()
yf = np.fft.fft(y, axis=0)
uf = np.fft.fft(u, axis=0)
fset = np.arange(0, N, dtype='float') / N
w = 2 * np.pi * fset
wexp = np.exp(1j * 2 * np.pi * fset)
fddata = (w, yf, uf)
Be, De, xt, resid2 = fsid.fdestim_bd(wexp,
yf,
uf,
A,
C,
estTrans=True,
dtype='float')
print('fdestim_bd residual = ', resid2)
fde = fsid.fresp(wexp, A, Be, C, De)
fd = fsid.fresp(wexp, A, B, C, D)
print('|| H-He ||/||H|| = ', linalg.norm(fd - fde) / linalg.norm(fd))
xt = B[:, 0]
yy = fsid.fdsim((A, B, C, D), uf, wexp, xt)
Be, De, xt, resid1 = fsid.fdestim_bd(wexp, yy, uf, A, C, estTrans=True)
# Be, De, resid1 = fdestim_bd(wexp, yy, uf, A, C, estTrans=False)
print('fdestim_bd residual = ', resid1)
Ce, De, resid1 = fsid.fdestim_cd(wexp, yy, uf, A, B, xt, estTrans=True)
# Be, De, resid1 = fdestim_bd(wexp, yy, uf, A, C, estTrans=False)
print('fdestim_cd residual = ', resid1)
fddata = (w, yf, uf)
Ae, Be, Ce, De, xt, s = fsid.fdsid(fddata, n, 2 * n, estTrans=True)
# Ae, Be, Ce, De, s = fdsid(fddata, n, 2*n, estTrans=False)
print('singular vales=', s)
fde = fsid.fresp(wexp, Ae, Be, Ce, De)
fd = fsid.fresp(wexp, A, B, C, D)
print('|| H-He ||/||H|| = ', linalg.norm(fd - fde) / linalg.norm(fd))
return