An attitude control system for a satellite vehicle within the earth's atmosphere is shown in Figure P7.6. The transfer functions of the system are

and

(a) Draw the root locus of the system as K varies from 0 to ˆž.
(b) Determine the gain K that results in a system with a settling time (with a 2% criterion) less than 12 seconds and a damping ratio for the complex roots greater than 0.50.
Figure P7.6
Satellite attitude control.

K(s 0.20) G(s) (s 0.90) (s 0.60)(s 0.10) (s 2 j1.5)(s 2 j1.5) G,(s) = s 4.0 Satellite dynamics Controller (s) Desired attitude -