What is the zero of this TF

Discussion in 'Math' started by fadelo, Nov 3, 2012.

Apr 12, 2011
22
0
Hello
I'm confused when working with transfere function in order to know poles and zeroz the for functions having (K) = gain in the numerator for examble

g(s)H(s)=k/s(s+4)(s+2)

here the poles are s=-4 and s=-2 ok what is the zero??

ks/(s+6)(s+2)

regards

2. panic mode Senior Member

Oct 10, 2011
1,330
305
your transfer function can be represented as
k*(A1*A2*A3*....) / (B1*B2*B3*...)
where A are zeroes and B are poles.

it should be obvious that whan any of A is zero, transfer function is zero.
when any of B is zero we get division by zero which is a pole.

each of A and B terms has general form
Ai=s+ci
or
Bj=s+cj

in case of

H(s)=ks/ (s+6)(s+2)

there is only one zero: A1=s
but there are two poles
B1=s+6 and B2=s+2)
since we are intersted in cases where A and B are zero, solutions are
A1: s=0
B1: s=-6
B2: s=-2

when you plot Bode diagram, you will use those values of s as corner frequencies.

in case of H(s)=k/s(s+4)(s+2)
there is no zeroes because numerator does not have any s-terms
we only have three poles:
B1=s
B2=s+6
B3=s+2

they are zero values when s=0, s=-2 ans s=-6

Apr 12, 2011
22
0
Thnx a milion sir now I could proceed my solutions in root locis and bode plot

regards

Nov 12, 2012
2
0