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

The Nyquist plot of a loop transfer function G$$(j\omega )$$ H$$(j\omega )$$, of a system encloses the (-1, j0) point. The gain margin of the system is

The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$ Using Nyquist criterion, find the condition for the closed loop system to be stable.

The transfer function of a phase lead controller is $${\textstyle{{1 + 3Ts} \over {1 + Ts}}}.$$ The maximum value of phase provided by this controller is