The Bell-Boeing V-22 Osprey Tiltrotor is both an airplane and helicopter. Its advantage is the ability to rotate its engine 90° from a vertical position for takeoffs and landings and

then to switch the engines to a horizontal position for cruising as an airplane. The altitude control system in the helicopter mode is shown in the block diagram. (a) Determine the root locus as K varies and determine the range of K for a stable system. (b) For K = 280, find the actual y(t) for a unit step input r(t)and all the transient response characteristics. G_{c}(s)=\frac{K\left(s^{2}+1.5 s+0.5\right)}{s} \quad G_{p}(s)=\frac{1}{(20 s+1)(10 s+1)(0.5 s+1)}