A large helicopter uses two tandem rotors rotating in opposite directions, as shown in Figure P7.33(a). The controller adjusts the tilt angle of the main rotor and thus the forward motion as shown in Figure DP7.2.The helicopter dynamics are represented by

and the controller is selected as

(a) Sketch the root locus of the system and determine K when ζ of the complex roots is equal to 0.6.
(b) Plot the response of the system to a step input r(t) and find the settling time (with a 2% criterion) and overshoot for the system of part (a). What is the steady-state error for a step input?
(c) Repeat parts (a) and (b) when the ζ of the complex roots is 0.41. Compare the results with those obtained in parts (a) and (b).
Figure DP7.2
Two-rotor helicopter velocity control.

G) 41985 I0 s4.5s 9" Helicopter dynamics Controller Tilt angle