If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\left(t\right),\;\left\{where\;F\left(s\right)\;is\;the\;L\left[f\left(t\right)\right]\right\}$$

Consider a unity feedback control system with open-loop transfer function $$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)}$$ . The steady state error of the system due to a unit step input 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 transfer function of a phase lead controller is $${\textstyle{{1 + 3Ts} \over {1 + Ts}}}.$$ The maximum value of phase provided by this controller is