The overall closed loop transfer function CsRs represented in the figure- will be

Blocks G_1 and nbsp;G_2 are in parallel ∴ nbsp; G_1+G_2 To the above result H_1 is in negative feedback ∴G_1+G_21+(G_1+G_2)H_1 To the above result of G_3 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Force on a Current Element

The overall c...

Question

The overall closed loop transfer function $\frac{C (s)}{R (s)}$ represented in the figure, will be

\frac{(G_{1} (s) + G_{2} (s)) G_{3} (s)}{1 + (G_{1} (s) + G_{2} (s)) (H_{1} (s) + G_{3} (s))}

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

\frac{(G_{1} (s) + G_{3} (s))}{1 + G_{1} (s) H_{1} (s) + G_{2} (s) G_{3} (s)}

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

\frac{(G_{1} (s) - G_{2} (s)) H_{1} (s)}{1 + (G_{1} (s) + G_{3} (s)) (H_{1} (s) + G_{1} (s))}

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

\frac{G_{1} (s) G_{2} (s) H_{1} (s)}{1 + G_{1} (s) H_{1} (s) + G_{1} (s) G_{3} (s)}

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

Open in App

Solution

The correct option is A $\frac{(G_{1} (s) + G_{2} (s)) G_{3} (s)}{1 + (G_{1} (s) + G_{2} (s)) (H_{1} (s) + G_{3} (s))}$
Blocks $G_{1}$ and $G_{2}$ are in parallel
$∴ G_{1} + G_{2}$

To the above result $H_{1}$ is in negative feedback

$∴ \frac{G_{1} + G_{2}}{1 + (G_{1} + G_{2}) H_{1}}$

To the above result of $G_{3}$ is in series

$∴ \frac{(G_{1} + G_{2}) G_{3}}{1 + (G_{1} + G_{2}) H_{1}}$

To the above result feedback is '1'

$∴ \frac{C (s)}{R (s)} = \frac{(G_{1} + G_{2}) G_{3}}{1 + (G_{1} + G_{2}) [H_{1} + G_{3}]}$

$= \frac{(G_{1} (s) + G_{2} (s)) G_{3} (s)}{1 + (G_{1} (s) + G_{2} (s)) (H_{1} (s) + G_{3} (s))}$

Suggest Corrections

Similar questions

Q. The closed loop system of figure is stable if the transfer function

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

_____.

Q. The Closed loop transfer function of a control system is given by

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

. For the input r(t) = sin t, the steady response c(t)______.

Q. For the system shown in figure the transfer function

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

is equal to :

Q. Consider a closed-loop system shown in Figure(A) below. the root locus for its is shown in Figure (B). the closed loop transfer function for the system is

Q. Consider the following Nyquist plot of loop transfer function over

ω = 0 t o ω = \infty

. which of these plots represents a stable closed loop system

Join BYJU'S Learning Program

The overall closed loop transfer function C(s)R(s) represented in the figure, will be

The overall closed loop transfer function $\frac{C (s)}{R (s)}$ represented in the figure, will be