Simplifying transfer functions?

I have come across a simple example that puzzles me a little.

import control

s = control.TransferFunction.s

G1 = 1 / (1 + 3 * s)**2
G2 = 3 * (1 + 1 / 2 / s)
print(-G2 * control.feedback(G1, G2))

       -3 s^2 - 1.5 s
-----------------------------
9 s^4 + 6 s^3 + 4 s^2 + 1.5 s

The absence of automatic factorization and simplification here does not surprise me, but I would expect a function in the toolbox that would perform such an operation. Perhaps a control.simplify, which applied to the transfer function above would return the following function.

       -3 s - 1.5
-----------------------------
9 s^3 + 6 s^2 + 4 s + 1.5

Maybe I don’t know where to look, but I have not found such a function.

For the record, sympy allows me to do:

import sympy as sp

s = sp.symbols('s')

G1 = 1 / (1 + 3 * s)**2
G2 = 3 * (1 + 1 / 2 / s)

def feedback(G1, G2, sign=-1):
    return G1 / (1 - sign * G1 * G2)

G = -G2 * feedback(G1, G2)

print(G)
print(sp.simplify(G))
print(sp.expand(sp.simplify(G)))
print(sp.simplify(sp.expand(sp.simplify(G))))

(-3 - 1.5/s)/((3*s + 1)**2*((3 + 1.5/s)/(3*s + 1)**2 + 1))
(-3*s - 1.5)/(s*(3*s + 1)**2 + 3*s + 1.5)
-3*s/(9*s**3 + 6*s**2 + 4*s + 1.5) - 1.5/(9*s**3 + 6*s**2 + 4*s + 1.5)
(-3*s - 1.5)/(9*s**3 + 6*s**2 + 4*s + 1.5)

[ilayn]

Integer coefficients as opposed to what?

Floats. Read more about it on Wilkinson’s polynomial

[amosnier]

@juanodecc, thanks a lot, I had missed the text

cancelling pole-zero pairs in transfer functions

in the documentation of that function. Gives me:

         -0.3333 s - 0.1667
------------------------------------
s^3 + 0.6667 s^2 + 0.4444 s + 0.1667

which is quite good.