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??
what about this examble also:

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

regards

 

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

 

Thnx a milion sir now I could proceed my solutions in root locis and bode plot

regards

 

Hello! Here is an exemple of fast solving of your problem.
http://www.numberempire.com/equationsolver.php?function=ks/(s+6)*(s+2)&var=s&answers=
When you will be working with transfere function next time, You could use
Equation Solver and Inverse function.
My students always use it when the homework came out Checking if their answers are right.
Good luck!