Basics on Phase Margin

Q. The open loop transfer function of a unity feedback control system is given as $G\left(s\right)=\frac{as+1}{s^2}.$ The value of 'a' to give a phase margin of ${45}^{\circ }$ is equal to.

1. 0.141
2. 0.441
3. 0.841
4. 1.141

Q. The open loop transfer function of a unity feedback system is given by $G\left(s\right)=\frac{3e^{-2s}}{s(s+2)}$
The gain and phase crossover frequencies in rad/sec are, respectively

1. $0.632and1.26$
2. $0.632and0.485$
3. $0.485and0.632$
4. $1.26and0.632$

Q. If the compensated system shown in the figure has a phase margin of ${60}^{\circ }$ at the crossover frequency of 1 rad /sec, then value of the gain k is

1. 0.366
2. 0.732
3. 1.366
4. 2.738

Q. The phase margin of the system for which loop gain $GH\left(j\omega \right)=\frac{1}{(j\omega +1{)}^3}$is

1. $-\pi$
2. $\pi$
3. 0
4. $\pi /2$

Q. A unity feedback system has the following open loop frequency response :

$\omega \left(rad/sec\right)$	2	3	4	5	6	8	10
|G$j\omega$|	7.5	4.8	3.15	2.25	1.70	1.00	0.64
$\angle$$(j\omega$)	$-{118}^o$	$-{130}^o$	$-{140}^o$	$-{150}^o$	$-{157}^o$	$-{170}^o$	$-{180}^o$

The gain and phase margin of the system are

1. $0dB,-{180}^o$
2. $3.88dB,-{170}^o$
3. $0dB,{10}^o$
4. $3.88dB,{10}^o$

Q. A unity feedback control loop with an open loop transfer funciton of the from $\frac{K}{s(s+\sigma )}$ has a gain cross-over frequency of 1 rad/sec and a phase margin is ${60}^o$. If an element having a transfer function $\frac{s-\sqrt{3}}{s+\sqrt{3}}$ is inserted into the loop, the phase margin will become

1. $0^o$
2. ${30}^o$
3. ${45}^o$
4. ${60}^o$