DP7.1 A high-performance aircraft, shown in Figure DP7.1(a), uses the ailerons, rudder, and elevator to steer through a three-dimensional flight path [20]. The pitch rate control system for a fighter aircraft at 10,000 m and Mach 0.9 can be represented by the system in Figure DP7.1(b).

(a) Sketch the root locus when the controller is a gain, so that G s c ( ) = K, and determine K when ζ for the roots with ωn > 2 is ζ ≥ 0.15 (seek a maximum ζ ).

(b) Plot the response q t( ) for a step input r(t) with K 

as in (a).

(c) A designer suggests an anticipatory con

troller with G s c ( ) = + K K 1 2 s K = + ( ) s 2 . Sketch the root locus for this system as K varies and deter

mine a K so that the damping ratio of all the closed

loop roots is ζ  > 0.8.

(d) Plot the response q(t) for a step input r(t) with K as in (c). 

FIGURE DP7.1 (a) High- performance aircraft. (b) Pitch rate control system. R(s) Pitch rate command Ailerons Rudder Controller Ge(s) + (a) Elevator Aircraft -18(s+0.015)(s +0.45) (s2+1.2s+12)(s2+0.01s+0.0025) (b) Q(s) Pitch rate