List of top Control Systems Questions on Routh and Nyquist criteria asked in GATE IN

The Nyquist plot of a stable open-loop system \( G(j\omega) \) is plotted in the frequency range \( 0 \leq \omega>\infty \) as shown. It is found to intersect a unit circle with center at the origin at the point \( P = -0.77 - 0.64j \). The points \( Q \) and \( R \) lie on \( G(j\omega) \) and assume values \( Q = 14.40 + 0.00j \) and \( R = -0.21 + 0.00j \). The phase margin (PM) and the gain margin (GM) of the system are _________
A unity-gain negative-feedback control system has a loop-gain \( L(s) \) given by \[ L(s) = \frac{6}{s(s-5)} \] The closed-loop system is _________