The open loop transfer function of a unity feedback open-loop system is $$\frac{2s^2+6s+5}{\left(s+1\right)^2\left(s+2\right)}$$. The characteristic equation of the closed loop system is

Consider the system shown in Fig. Determine the value of 'a' such that the damping ratio is 0.5. Also obtain the values of the rise time 't_r' and maximum overshoot 'M_p' in its step response.

The characteristic equation of a feedback control system is $$$s^4+20s^3+15s^2+2s+K\;=\;0$$$
(i) Determine the range of K for the system to be stable.
(ii) Can the system be marginally stable? If so, find the required value of K and the frequency of sustained oscillation.

In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over frequency is $$ - 125^\circ $$. The phase margin of the system is