Automatic control of helicopters is necessary because, unlike fixed wing aircraft, the helicopter is quite unstable. A helicopter control system that uses an automatic control loop is shown in Figure 1.When the pilot is not using the command stick, the switch may be considered to be open. The dynamics of the helicopter transfer function are: G(s) = 25(s+ 0.03) (s+0.4) (s² -0.365 + 0.16) a) With the pilot control loop open (hands off), plot the root locus for the automatic stabilization loop. Determine the gain K, that results in a damping ratio for the complex closed-loop poles of = 0.707. b) For the gain K, determined in part a, determine the steady-state error due to a wind gust W(s) = c) With the pilot loop added (the switch closed), sketch the root locus as K₁ varies from 0 to - for the value of K, from part s. d) Recalculate the steady-state error when K₁ has a suitable value based on the root locus from part c.