Basics of Compensators

Q. The transfer function of a position servo system is given as
$G\left(s\right)=\frac{1}{s(s+1)}.$

A first order compensator is designed in a unity feedback configuration so that poles of the compensated system are placed at $-1\pm j1$ and -4. The transfer function of the compensated system is

1. $\frac{s+3}{2(s+3)}$
2. $\frac{2s+3}{(s+5)}$
3. $\frac{5(s+1.6)}{s+5}$
4. $\frac{3(2s+3)}{s+4}$

Q. A double integrator plant, $G\left(s\right)=\frac{K}{s^2},H\left(s\right)=1$ is to be compensated to acheive the damping ratio $\zeta =0.5$ and an undamped natural frequency, ${\omega }_n=5rad/sec$. Which one of the following compensator $G_c\left(s\right)$ will be suitable?

1. $\frac{s+3}{s+9.9}$
2. $\frac{s+9.9}{s+3}$
3. $\frac{s-6}{s+8.33}$
4. $\frac{s+6}{s}$

Q. Which of the following statements is incorrect?

1. Lead compensator is used to reduce the settling time
2. Lag compensator is used to reduce the steady state error
3. Lead compensator may increase the order of a system
4. Lag compensator always stabilizes an unstable system