A control system is represented by the block diagram shown in figure.

ratio is $\frac{C (s)}{R (s)}$

\frac{G_{1} G_{3} + G_{1} G_{2}}{1 + G_{3} G_{2} + G_{3} H_{1} + G_{1} G_{3} H_{2} + G_{1} G_{2} H_{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{G_{1} G_{3} + G_{1} G_{2}}{1 + G_{3} + H_{1} + G_{1} G_{3} H_{2} + G_{1} G_{3} H_{2}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{G_{1} G_{3} + G_{1} G_{2}}{1 + G_{3} H_{1} + G_{2} + G_{1} G_{3} H_{2} + G_{1} G_{2} H_{2}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{G_{1} G_{3} + G_{1} G_{3}}{1 + G_{3} H_{1} + G_{3} + G_{1} G_{3} H_{2} + G_{1} G_{2} H_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{G_{1} G_{3} + G_{1} G_{2}}{1 + G_{3} G_{2} + G_{3} H_{1} + G_{1} G_{3} H_{2} + G_{1} G_{2} H_{2}}$
$\frac{G_{1} G_{3} + G_{1} G_{2}}{1 + G_{3} + G_{2} + G_{3} H_{1} + G_{1} G_{3} G_{2} + G_{1} G_{2} H_{2}}$
Signal flow graph of the system is

Forwartd paths:
$P_{1} = G_{1} G_{3}$
$P_{2} = G_{1} G_{2}$
Feedback loops:
$L_{1} = - G_{3}$
$L_{2} = - G_{2}$
$L_{3} = - G_{3} H_{1}$
$L_{4} = - G_{1} G_{3} H_{2}$
$L_{3} = - G_{1} G_{2} H_{2}$
Mason's gain formula,

$\frac{C}{R} = \frac{P_{K} Δ_{K}}{Δ}$

$\frac{C}{R} = \frac{G_{1} G_{3} + G_{1} G_{2}}{1 + G_{3} + G_{2} + G_{3} H_{1} + G_{1} G_{3} H_{2} + G_{1} G_{2} H_{2}}$

Suggest Corrections

Similar questions

\frac{C (s)}{R (s)} = \frac{s}{s^{2} + s + 1}

G (s)

ξ = \sqrt{3}

\frac{C (s)}{R (s)}

\frac{C (s)}{R (s)}

Join BYJU'S Learning Program