Sum of Transfer results a ValueError: Noncausal transfer functions are not allowed.

[jamestjsp]

Sum of multiple higher order transferfunction results in a 'ValueError: Noncausal transfer functions are not allowed.' I have written PolyFrac class and do arithmetic then convert to Transfer object works fine!

The below code can be used to reproduce the issue.

import numpy as np
import harold

class PolyFrac():
    def __init__(self, num, den) -> None:
        self.num = num
        self.den = den
        self._num = np.polynomial.Polynomial(self.num[::-1])
        self._den = np.polynomial.Polynomial(self.den[::-1])
    def __add__(self, other):
        self._rnum = self._num * other._den + self._den * other._num
        self._rden = self._den * other._den
        return PolyFrac(self._rnum.coef[::-1], self._rden.coef[::-1])

num = [0.00048873990334,0.00008022868673,0.000004688964039,0.000000119457633,0.000000001314395,0.00000000000487 ]
den = [713971.3912200001,157343.82838884002,14104.582786048937,663.9560606101594,17.793303846830465,0.27893627449232,0.002591707015312,
       0.00001456551703,0.000000046427704,0.000000000061138]
G1 = PolyFrac(num,den)
Gh1 = harold.Transfer(num, den)
num = [0.000248910547815,0.000040859701097,0.000002388044438,0.000000060838627,0.000000000669409,0.00000000000248]
den = [468539.19521279994,104086.4548127616,9436.270955826356,451.5149614339922,12.39566355720315,0.201316286426998,0.001963464678425,
       0.000011684559727,0.000000040217318,0.000000000061138]
G2 = PolyFrac(num,den)
Gh2 = harold.Transfer(num, den)
num = [0.000589835421362,0.000096823936248,0.000005658873075,0.000000144167363,0.000000001586277,0.000000000005877]
den = [2416.14684,524.28995448,45.95699773796595,2.091367387046341,0.053136840811452,0.000764126679123,0.000006184705029,0.000000028361462,
       0.000000000061138]
G3 = PolyFrac(num,den)
Gh3 = harold.Transfer(num, den)

G4 = G1+G2+G3
Gh4 = Gh1+Gh2+Gh3

G = harold.Transfer(G4.num, G4.den)
print(G.dcgain)
print(Gh4.dcgain)

[ilayn]

I am still looking at this and it needs some major surgery apparently. Since the poles and zeros are very close it cancels some but doesn't the rest leading to noncausal models. I'll keep on working on it as time permits.