GATE Chemical 2024 | Question: 38

Question

​​​​​​For the block diagram shown in the figure, the correct expression for the transfer function $G_{d}=\frac{y_{1}(s)}{d(s)}$ is

• A. $\frac{-G_{p 1} G_{c 2}}{\left(1+G_{c 1} G_{c 2} G_{p 1}\right)\left(1+G_{c 2} G_{p 2}\right)}$
• B. $\frac{-G_{p 1} G_{c 2}}{1+G_{c 2} G_{p 2}+G_{c 1} G_{c 2} G_{p 1} G_{p 2}}$
• C. $\frac{-G_{p 1} G_{c 2}}{1+G_{c 2} G_{p 2}+G_{c 1} G_{c 2} G_{p 1}}$
• D. $\frac{1}{1+G_{c 2} G_{p 2}+G_{c 1} G_{c 2} G_{p 1} G_{p 2}}$