sta_demo.py

"""
The content of this module is based on the original work:

    "Subspace Identification for Linear Systems, Theory, Implementation, Applications"
                           Van Overschee P., De Moor B.
                        Kluwer Academic Publishers, (1996)
"""

import numpy as np
import scipy.signal

from subid import subid
from bode import bode_plot

a = np.array([[0.603, 0.603, 0, 0],
              [-0.603, 0.603, 0, 0],
              [0, 0, -0.603, -0.603],
              [0, 0, 0.603, -0.603]])

b = np.array([[1.1650, -0.6965],
              [0.6268, 1.6961],
              [0.0751, 0.0591],
              [0.3516, 1.7971]])

c = np.array([[0.2641, -1.4462, 1.2460, 0.5774],
              [0.8717, -0.7012, -0.6390, -0.3600]])

d = np.array([[-0.1356, -1.2704],
              [-1.3493, 0.9846]])

m = 2  # Number of inputs
l = 2  # Number of outputs

N = 1000
t = np.arange(1, N + 1)
u = np.array([np.sin(t).T, np.sin(t + 3.14/2).T]).T.reshape(-1, 2)
# u = np.sin(t).reshape(-1,1)
dt = 1

syst = (a, b, c, d, dt)
t, y, x = scipy.signal.dlsim(syst, u)

bode_plot(*syst)

max_order = 8

i = 2 * max_order // l

n = 4

A, B, C, D, K, Ro, ss = subid(y, i, n, u=u)

syst2 = (A, B, C, D, dt)

bode_plot(*syst2)