Question

How to form a transfer function with given zeros and poles?

Answer 1

Breginning with basics

Let's say we have a transfer function defined as a ratio of two polynomials:
H(s) = N(s) / D(s)
Where N(s) and D(s) are simple polynomials.

•Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting N(s) = 0 and solving for s. The polynomial order of a function is the value of the highest exponent in the polynomial.

•Poles are the roots of D(s) (the denominator of the transfer function), obtained by setting D(s) = 0 and solving for s . Because of our restriction above, that a transfer function must not have more zeros than poles, we can state that the polynomial order of D(s) must be greater than or equal to the polynomial order of N(s) .

Just remember that,
By equating Numerator of Transfer function, zeros are obtained
By equating Denominator of Transfer function, poles are obtained

Now, for an example, look attachment
N(s)= 4s-4
4s-4=0
=>zero at s=1
D(s)=s(s+2)(s+3)
s(s+2)(s+3)=0
=> poles at 0,-2,-3


hope it helps...