Question

simplify the block diagram:—

Explanation:

Step1: Consider forward - path transfer function

The forward - path transfer function $G_{p}(s)=G(s)$.

Step2: Consider feedback - path transfer function

The feedback - path transfer function $H(s)=H_1(s)+H_2(s)G(s)$.

Step3: Apply closed - loop transfer function formula

The closed - loop transfer function $T(s)=\frac{G(s)}{1 + G(s)(H_1(s)+H_2(s)G(s))}=\frac{G(s)}{1 + G(s)H_1(s)+G(s)^2H_2(s)}$.

Answer:

$T(s)=\frac{G(s)}{1 + G(s)H_1(s)+G(s)^2H_2(s)}$