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).
The Bell-Boeing V-22 Osprey Tiltrotor is both an airplane and a helicopter. Its advantage is the ability to rotate its engines to 90° from a vertical position for takeoffs and landings as shown in Figure P7.33 (a), and then to switch the engines to a horizontal position for cruising as an airplane [20].The altitude control system in the helicopter mode is shown in Figure P7.33 (b). (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 the percentage overshoot and settling time (with a 2% criterion), (c) When K = 280 and r(t) = 0, find y(t) for a unit step disturbance, Td(s) = 1/s. (d) Add a pre filter between R(s) and the summing node so that
and repeat part (b).
