The system with the open loop transfer function GsHs - 1ss2-s-1 has a gain margin of

G(s)H(s) = 1s(s^2+s+1) ω when ∠ G(s)H(s) = 180^∘ 180 = 90 tan^ 1ω1 ω ^2 90 = tan^ 1ω1 ω^2 1 ω ^2 =0 ω _pc= 1 rad/sec Value of gain at ω _pc = 1 |G(s) ...

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

Byju's Answer

Other

Control Systems

Basics on Gain Margin

The system wi...

Question

The system with the open loop transfer function $G (s) H (s) = \frac{1}{s (s^{2} + s + 1)}$ has a gain margin of

- 6 d B

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

0 d B

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

3.5 d B

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

6 d B

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

Open in App

Solution

The correct option is B $0 d B$
$G (s) H (s) = \frac{1}{s (s^{2} + s + 1)}$
$ω$ when $∠ G (s) H (s) = - 180^{\circ}$
$- 180 = - 90 - {tan}^{- 1} \frac{ω}{1 - ω^{2}}$
$- 90 = - {tan}^{- 1} \frac{ω}{1 - ω^{2}}$
$1 - ω^{2} = 0$
$ω_{p c} = 1 r a d / s e c$
Value of gain at $ω_{p c} = 1$
$| G (s) H (s) | = \frac{1}{\sqrt{(1 - ω^{2})^{2} + | j ω |^{2}}}$
$∴$ G.M = $- 20 l o g 1 = 0$

Suggest Corrections

Similar questions

Q. The gain margin of a unity feedback control system with the open loop transfer function is

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

Q. If the open loop transfer function of negative feedback control system is

G (s) H (s) = \frac{K}{(s + 1)^{3}}

, then the gain K for a closed loop pole to be at

(- \frac{1}{2} + j \frac{\sqrt{3}}{2}) i s

Q. The open-loop transfer function of a feedback control system is

\frac{1}{(s + 1)^{3}}

The gain margin of the system is

Q. In the fifgure, the Nyquist plot of the open -loop transfer function

G (s) H (s)

of a system is shown. If

G (s) H (s)

has one right-hand pole, the closed loop system is

Q. A unity feedback control system has an open-loop transfer function

G (s) = \frac{K}{s (s^{2} + 7 s + 12)} .

The gain

K

for which

s = - 1 + j 1

will lie on the root locus of the system is

Join BYJU'S Learning Program

The system with the open loop transfer function G(s)H(s)=1s(s2+s+1) has a gain margin of

The correct option is B 0 dBG(s)H(s)=1s(s2+s+1) ω when ∠G(s)H(s)=−180∘ −180=−90−tan−1ω1−ω2 −90=−tan−1ω1−ω2 1−ω2=0 ωpc=1 rad/sec Value of gain at ωpc=1 |G(s)H(s)|=1√(1−ω2)2+|jω|2 ∴ G.M = −20 log 1=0

The system with the open loop transfer function $G (s) H (s) = \frac{1}{s (s^{2} + s + 1)}$ has a gain margin of