Robotics Control System

A system has poles at $-2$ and $-4$. What can be said about its time response?
(i) Oscillatory
(ii) Slow response
(iii) Overdamped
(iv) Underdamped

The block diagram of a simple servo system is shown below

(i) If $k = 10$, determine the values of 'a' and 'b' to give an overshoot of $16\%$ and a time constant of $0.1$ sec to a unit step input.
(ii) Determine $t_r$, $t_p$, $\omega_d$ and $t_{ss}$ if $k = 40$.

The open-loop transfer function of a unity feedback system is given by
$$G(s) = \frac{k}{s(1 + sT)}$$
where $k$ and $T$ are positive constants. By what factor should the amplifier gain be reduced so that the peak overshoot of the unit-step response of the system is reduced from $75\%$ to $25\%$.