Basics on Gain Margin

Q. The gain margin of a unity feedback control system with the open loop transfer function is
$G\left(s\right)=\frac{(s+1)}{s^2}$

1. 0
2. $\frac{1}{\sqrt{2}}$
3. $\sqrt{2}$
4. $\infty$

Q. The phase cross-over frequency of the transfer function $G\left(s\right)=\frac{100}{(s+1{)}^3}$ in rad/s is

1. $\sqrt{3}$
2. $\frac{1}{\sqrt{3}}$
3. 3
4. $3\sqrt{3}$

Q. An open loop transfer function of a unity negative feedback control system is given by,
$G\left(s\right)=\frac{K}{s(s+a)(s+b)}$
If the gain margin of the system is 32 dB for K = 2, then the value of K required to get the gain margin of 25 dB will be

1. 4.48
2. 38.1
3. 1.12
4. 6.38

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

1. $-6dB$
2. $0dB$
3. $3.5dB$
4. $6dB$

Q. The open loop transfer function of a unity fedback system is given by $G\left(s\right)=\left(e^{-0.1s}\right)/s$. The gain margin of this system is

1. 11.95 dB
2. 17.67 dB
3. 21.33 dB
4. 23.9 dB

Q. The gain margin and the phase margin of a feedback system with $G\left(s\right)H\left(s\right)=\frac{s}{(s+100{)}^3}$ are

1. $0dB,0^{\circ }$
2. $\infty ,\infty$
3. $\infty ,0^{\circ }$
4. $88.5dB,\infty$

Q. The open-loop transfer function of a feedback control system is $\frac{1}{(s+1{)}^3}$

The gain margin of the system is

1. 16
2. 8
3. 4
4. 2