import numpy as np
a, b, T, s, w, x, z, I = symbols('a b T s w x z I')
bilinear_transform = {s: 2 / T * (z - 1) / (z + 1)}
# Continuous time transfer function from I(s) to w(s) of the following plant
# model:
# dw/dt = a*w + b*I
G_s = b / (s - a)
G_z_num, G_z_den = G_s.subs(bilinear_transform).as_numer_denom()
G_z_den = Poly(G_z_den, z)
G_z_num = Poly(G_z_num / G_z_den.LC(),
z) # divide by leading coefficient of den
G_z_den = G_z_den.monic() # make denominator monic
assert (G_z_den.coeffs()[0] == 1)
kp = Poly(G_z_num.coeffs()[0], z)
G_z_N_p = G_z_num - kp * G_z_den
print(kp)
print(G_z_N_p)
print(G_z_den)
from sympy import symbols, Poly
import numpy as np
a, b, T, s, w, x, z, I = symbols('a b T s w x z I')
bilinear_transform = {s: 2 / T * (z - 1) / (z + 1)}
from sympy import symbols, Poly
import numpy as np
a, b, T, s, w, x, z, I = symbols('a b T s w x z I')
bilinear_transform = {s : 2/T*(z-1)/(z+1)}
# Continuous time transfer function from I(s) to w(s) of the following plant
# model:
# dw/dt = a*w + b*I
G_s = b/(s-a)
G_z_num, G_z_den = G_s.subs(bilinear_transform).as_numer_denom()
G_z_den = Poly(G_z_den, z)
G_z_num = Poly(G_z_num / G_z_den.LC(), z) # divide by leading coefficient of den
G_z_den = G_z_den.monic() # make denominator monic
assert(G_z_den.coeffs()[0] == 1)
kp = Poly(G_z_num.coeffs()[0], z)
G_z_N_p = G_z_num - kp * G_z_den
print(kp)
print(G_z_N_p)
print(G_z_den)
from sympy import symbols, Poly
import numpy as np
a, b, T, s, w, x, z, I = symbols('a b T s w x z I')
bilinear_transform = {s : 2/T*(z-1)/(z+1)}
