For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of the step response is required to be less than 2 seconds. Which one of the following compensators C(s) achieves this?

The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, when connected in feedback as shown below, the approximate value of K_a that will reduce the time constant of the closed-loop system by one hundred times as compared to that of the open-loop system is

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer function has these properties?

Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions

Group I $$$P=\frac{25}{s^2+25}\;\;\;\;\;Q=\frac{36}{s^2+20s+36}$$$ $$$R=\frac{36}{s^2+12s+36}\;\;\;\;\;S=\frac{49}{s^2+7s+49}$$$

Group II