The transfer function of the system shown in the given figure is:
The transfer function of the system shown in the given figure is:
A. G<sub>1</sub> + G<sub>2</sub>
B. (G<sub>1</sub> + G<sub>2</sub>) /2
C. G<sub>1</sub>/ (1 – 2G<sub>1</sub>G<sub>2</sub>)
D. G<sub>1</sub>/ (1+2G<sub>1</sub>G<sub>2</sub>)
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
A transfer function is defined as the ratio of Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output]/L[input]
\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}\)
Application:
Y(s) = G2 R(s) – C(s)
C(s) = G1 R(s) + Y(s)
= G1 R(s) + [G2 R(s) – C(s)]
⇒ C(s) = G1 R(s) + G2 R(s) – C(s)
⇒ 2C(s) = (G1 + G2) R(s)
The transfer function of the system,
\(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{{G_1} + {G_2}}}{2}\)
