Lead Compensator

Q. The open-loop transfer function of a plant is given as $G\left(s\right)=\frac{1}{s^2-1}.$ If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

1. $\frac{10(s-1)}{s+2}$
2. $\frac{10(s+4)}{s+2}$
3. $\frac{10(s+2)}{s+10}$
4. $\frac{2(s+2)}{s+10}$

Q. The transfer function of a phase-lead compensator is given by
$G_e\left(s\right)=\frac{1+3Ts}{1+Ts}whereT>0.$
The maximum phase-shift provided by such a compensator is

1. $\pi /2$
2. $\pi /3$
3. $\pi /4$
4. $\pi /6$

Q. The pole zero configuration of a phase lead compensator is given by

1. 
   
2. 
3. 
4. 

Q. The transfer function of a phase lead compensator is given by
$D\left(s\right)=\frac{3(s+\frac{1}{3T})}{(s+\frac{1}{T})}$
The frequency (in rad/sec), at which $\angle D\left(j\omega \right)$ is maximum is

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

Q. The transfer function of a compensator is given as
$G_c\left(s\right)=\frac{s+a}{s+b}$

The phase of the above lead compensator is maximum at ____ when a = 1 and b = 2

1. $\sqrt{2}rad/s$
2. $\sqrt{3}rad/s$
3. $\sqrt{6}rad/s$
4. $1/\sqrt{3}rad/s$

Q. A lead compenstor used for a closed loop controller has the following transfer function
$\frac{K(1+\frac{s}{a})}{(1+\frac{s}{b})}$
For such a lead compensator

1. $a<b$
2. $b<a$
3. $a>Kb$
4. $a<Kb$

Q. A phase lead network has the transfer function $G\left(s\right)=\frac{1+0.2s}{1+0.05s}.$
The angular frequency at which the maximum phase shift for the network occurs is_____.

1. 20 rad/s
2. 200 rad/s
3. 100 rad/s
4. 10 rad/s

Q.

A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is$G_c\left(s\right)=\frac{s+2}{s+4},$ the value of $RC$ is

1. 0.5

Q. The transfer function of a compensator is given as $G_c\left(s\right)=\frac{s+1}{s+2}$
The phase of the above lead compensator is maximum at

1. $\sqrt{2}rad/s$
2. $\sqrt{3}rad/s$
3. $\sqrt{6}rad/s$
4. $1/\sqrt{3}rad/s$

Q. The transfer function of a compensator is given as
$G_c\left(s\right)=\frac{s+a}{s+b}$

$G_c\left(s\right)$ is lead compensator if

1. a = 1, b = 2
2. a = 3, b = 2
3. a = -3, b = -1
4. a = 3, b = 1

Q. The transfer function of a compensator isgiven as
$G_c\left(s\right)=\frac{s+a}{s+b}$
$G_c\left(s\right)$ is a lead compensator if

1. $a=1,b=2$
2. $a=3,b=2$
3. $a=-3,b=-1$
4. $a=3,b=1$

Q. A compensator transfer function for a feedback system is given by,
$C\left(s\right)=\frac{4s+1}{0.4s+1}$
The inferences which can be drawn by analysis of transfer function are given below:
1. The transfer function shows nature of a lead compensator.
2. The value of $\alpha$ for the compensator is 0.1.
3. The compensator increases the bandwidth in a closed loop system leading to faster time response.
Which of the given inferences are correct?

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

Q. The phase lead compensations used to

1. increase rise time and decrease overshoot
2. decrease both rise time and overshoot
3. increase bot rise time and overshoot
4. decrease rise time and increase overshoot.

Q. For the following feedback system $G\left(s\right)=\frac{1}{(s+1)(s+2)}.$ The 2%-setting time of the step response is required to be less than $2seconds$.

Which one of the following compensators
$C\left(s\right)$ acheives this?

1. $3\left(\frac{1}{s+5}\right)$
2. $5(\frac{0.03}{s}+1)$
3. $2(s+4)$
4. $4\left(\frac{s+8}{s+3}\right)$