How to input transfer function without simplifying it?

Question

Supermankid 2017-9-12

回答： Teja Muppirala 2017-9-13

Hi everyone,

Normally, we can give numerator = [ 1 0]; denominator =[1 1 4]; and system1=tf(num,den); but if the transfer function is like:

G(s) = {s + 2}/{s(s − 1)(s + 6)^2}

can I add this transfer function without simpligying (I mean without multiplying the denominators)

=> only from s(s-1)(s+6)^2

May be someone can provide some tips.

Walter Roberson 2017-9-12

G = tf([1 2],[1 0]) * tf(1,[1 -1]) * tf(1, [1 6])^2

Answer 1

Teja Muppirala 2017-9-13

s = tf('s')
G = (s+2)/(s*(s-1)*(s+6)^2)

This gives a transfer function (tf) with the polynomials expanded

G =
             s + 2
  ----------------------------
  s^4 + 11 s^3 + 24 s^2 - 36 s

Or you can express it as a ZPK (zero-pole-gain)

G = zpk((s+2)/(s*(s-1)*(s+6)^2))

Then you get

G =
       (s+2)
  ---------------
  s (s+6)^2 (s-1)