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), where

(a) Sketch the root locus when the controller is a gain, so that Gc(s) = K, and determine K when ζ for the roots with ωn > 2 is larger than 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 controller with Gc(s) = K1 + K2s = K(s + 2). Sketch the root locus for this system as K varies and determine a K so that the f of all the closed-loop roots is >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.

-18(x + 0.015)(s + 0.45) (s12s12)( 0.01s0.0025) G(s) Rudder Ailerons Elevator ControllerAircraft Pitch rale cemmand Pitch rate