def Pade3(t):
"""Third order Pade approximation"""
num = poly([-t*t*t, 12*t*t, -60*t, 120])
den = poly([t*t*t, 12*t*t, 60*t, 120])
num = num.mult(1.0/den[0])
den = den.mult(1.0/den[0])
return tf(num, den)
def Pade2(t):
"""Second order Pade approximation"""
num = poly([t*t, -6*t, 12])
den = poly([t*t, 6*t, 12])
num = num.mult(1.0/den[0])
den = den.mult(1.0/den[0])
return tf(num, den)
def Pade4(t):
"""Fourth order Pade approximation"""
num = poly([t*t*t*t, -20*t*t*t, 180*t*t, -840*t, 1680])
den = poly([t*t*t*t, 20*t*t*t, 180*t*t, 840*t, 1680])
num = num.mult(1.0/den[0])
den = den.mult(1.0/den[0])
return tf(num, den)
def Pade4(t):
"""Fourth order Pade approximation"""
num = poly([t * t * t * t, -20 * t * t * t, 180 * t * t, -840 * t, 1680])
den = poly([t * t * t * t, 20 * t * t * t, 180 * t * t, 840 * t, 1680])
num = num.mult(1.0 / den[0])
den = den.mult(1.0 / den[0])
return tf(num, den)
def Pade3(t):
"""Third order Pade approximation"""
num = poly([-t * t * t, 12 * t * t, -60 * t, 120])
den = poly([t * t * t, 12 * t * t, 60 * t, 120])
num = num.mult(1.0 / den[0])
den = den.mult(1.0 / den[0])
return tf(num, den)
def Pade2(t):
"""Second order Pade approximation"""
num = poly([t * t, -6 * t, 12])
den = poly([t * t, 6 * t, 12])
num = num.mult(1.0 / den[0])
den = den.mult(1.0 / den[0])
return tf(num, den)
def Pade5(t):
"""Fifth order Pade approximation"""
num = poly([-t*t*t*t*t, 30*t*t*t*t, -420*t*t*t, 3360*t*t, -15120*t, 30240])
den = poly([t*t*t*t*t, 30*t*t*t*t, 420*t*t*t, 3360*t*t, 15120*t, 30240])
num = num.mult(1.0/den[0])
den = den.mult(1.0/den[0])
return tf(num, den)
def Pade1(t):
"""First order Pade approximation"""
num = poly([-t, 2])
den = poly([t, 2])
num = num.mult(1.0 / den[0])
den = den.mult(1.0 / den[0])
return tf(num, den)
def Pade1(t):
"""First order Pade approximation"""
num = poly([-t, 2])
den = poly([t, 2])
num = num.mult(1.0/den[0])
den = den.mult(1.0/den[0])
return tf(num, den)
def Pade5(t):
"""Fifth order Pade approximation"""
num = poly([
-t * t * t * t * t, 30 * t * t * t * t, -420 * t * t * t, 3360 * t * t,
-15120 * t, 30240
])
den = poly([
t * t * t * t * t, 30 * t * t * t * t, 420 * t * t * t, 3360 * t * t,
15120 * t, 30240
])
num = num.mult(1.0 / den[0])
den = den.mult(1.0 / den[0])
return tf(num, den)
def callback(self):
p1 = tf([100], poly([1, 10]) * poly([1, 10]))
p2 = tf([1], [1, 1])
p3 = tf([0.5], [1, 0.05])
return p1 * (p2 + p3)
def callback(self, n):
a = poly([1, 1])
for i in range(1, int(n)):
a = a * poly([1, 1])
return tf([1], list(a))
def callback(self, Alpha):
num = (poly([1, 1]) * poly([Alpha, 1])) * (poly([Alpha * Alpha, 1]) * \
poly([Alpha * Alpha * Alpha, 1]))
return tf([1], num)
def callback(self, k, T1, T2, T3, T4, Tt, pade_order):
num = poly([k * T4, k])
den = poly([T1, 1]) * poly([T2, 1]) * poly([T3, 1])
return tf(num, den) * pade_index[int(pade_order)](Tt)
def callback(self, k, T1, T2):
return tf([-T1 * k, k], poly([T1, 1]) * poly([T2, 1]))
def callback(self, Omega, Zeta):
return tf([Omega * Omega], poly([1, 1]) * poly([1, 2 * Zeta * Omega, Omega * Omega]))
def callback(self):
den = (poly([1, 0]) * poly([1, 1])) * (poly([1, 1]) * poly([1, 36]))
return tf(poly([1, 6]) * poly([1, 6]), den)
def callback(self, Alpha):
return tf([-Alpha, 1], (poly([1, 1]) * poly([1, 1])) * poly([1, 1]))
def callback(self, Tau, pade_order):
return tf([1], poly([Tau, 1]) * poly([Tau, 1])) * \
pade_index[int(pade_order)](1)
