Automatic control of helicopters is necessary because, unlike fixed-wing aircraft which possess a fair degree of inherent stability, the helicopter is quite unstable. A helicopter control system that utilizes an automatic control loop plus a pilot stick control is shown in Figure P7.5. When the pilot is not using the control stick, the switch may be considered to be open. The dynamics of the helicopter are represented by the transfer function

(a) With the pilot control loop open (hands-off control), sketch the root locus for the automatic stabilization loop. Determine the gain K2 that results in a damping for the complex roots equal to ζ = 0.707.
(b) For the gain K2 obtained in part (a), determine the steady-state error due to a wind gust Td(s) = 1/5.
(c) With the pilot loop added, draw the root locus as K1 varies from zero to ˆž when K2 is set at the value calculated in part (a).
(d) Recalculate the steady-state error of part (b) when K1 is equal to a suitable value based on the root locus.
Figure P7.5
Helicopter control.

Transcribed Image Text:

25(s 0.03) (s 0.4) (s2 0.36s0.16) G(s)- Controlane Disturhance Pilot Helicopter dynamics Stick G(s) Pitch attitude RAS) 12s Switch Automatic stabilization K2(s +I)