# era_msd.py

# Johannes Kaisinger, 4 July 2024

#

# Demonstrate estimation of State Space model from impulse response.

# SISO, SIMO, MISO, MIMO case

import numpy as np

import matplotlib.pyplot as plt

import os

import control as ct

# set up a mass spring damper system (2dof, MIMO case)

# Mechanical Vibrations: Theory and Application, SI Edition, 1st ed.

# Figure 6.5 / Example 6.7

# m q_dd + c q_d + k q = f

m1, k1, c1 = 1., 4., 1.

m2, k2, c2 = 2., 2., 1.

k3, c3 = 6., 2.

A = np.array([

[0., 0., 1., 0.],

[0., 0., 0., 1.],

[-(k1+k2)/m1, (k2)/m1, -(c1+c2)/m1, c2/m1],

[(k2)/m2, -(k2+k3)/m2, c2/m2, -(c2+c3)/m2]

])

B = np.array([[0.,0.],[0.,0.],[1/m1,0.],[0.,1/m2]])

C = np.array([[1.0, 0.0, 0.0, 0.0],[0.0, 1.0, 0.0, 0.0]])

D = np.zeros((2,2))

xixo_list = ["SISO","SIMO","MISO","MIMO"]

xixo = xixo_list[3] # choose a system for estimation

match xixo:

case "SISO":

sys = ct.StateSpace(A, B[:,0], C[0,:], D[0,0])

case "SIMO":

sys = ct.StateSpace(A, B[:,:1], C, D[:,:1])

case "MISO":

sys = ct.StateSpace(A, B, C[:1,:], D[:1,:])

case "MIMO":

sys = ct.StateSpace(A, B, C, D)

dt = 0.1

sysd = sys.sample(dt, method='zoh')

response = ct.impulse_response(sysd)

response.plot()

plt.show()

sysd_est, _ = ct.eigensys_realization(response,r=4,dt=dt)

step_true = ct.step_response(sysd)

step_true.sysname="H_true"

step_est = ct.step_response(sysd_est)

step_est.sysname="H_est"

step_true.plot(title=xixo)

step_est.plot(color='orange',linestyle='dashed')

plt.show()

if 'PYCONTROL_TEST_EXAMPLES' not in os.environ:

plt.show()