The transfer function Y(s)/R(s) of the system shown is

A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}},$$ has an output y(t)=$$\cos \left( {2t - {\pi \over 3}} \right),$$ for input signal x(t)=$$p\cos \left( {2t - {\pi \over 2}} \right).$$ Then the system parameter 'p' is

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

A unity negative feedback closed loop system has a plant with the transfer function $$G(s) = {1 \over {{s^2} + 2s + 2}}$$ and a controller $${G_c}(s)$$ in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady sate error is