Poles and Zeros of a Transfer Function with Solved Problems(Hindi)

POLES AND ZEROS OF TRANSFER FUNCTION:
The transfer function for linear control system is expressed as

G(s)=(𝐴(𝑠))/(𝐵(𝑠))="a0sn + a1sn−1 + a2sn−2 +………+ an " /(" b0sm + b1sm−1 + b2sm−2 +………+ bm " )

When numerator and denominator are factorized

G(s)=(𝐴(𝑠))/(𝐵(𝑠))=𝐾 ( "(s−s1)(s−s2)" ………."(s−sn)" )/("(s−sa)(s−sb)" ……."(s−sm)" )

Zeros:
In transfer function if we put s equal to s1, s2, s3……., sn
then transfer function is zero.

Hence s1, s2, s3……., sn zeros of transfer function

Poles:
In transfer function if we put s equal to sa, sb, sc……., sm
then transfer function is infinite.

Hence sa, sb, sc……., sm poles of transfer function

Problems:
Q1.For the transfer function plot the poles and zeros in s-plane and determine the value of transfer function at s=2
Q2.The pole-zero plot for the transfer function is given, the value of transfer function at s=1
is 3.2, Determine the transfer function and gain factor K.