Question 8 (Total 15 marks) The approximate form of Dutch roll mode can be described in the state-space form as follow: Consider T-38 Talon aircraft, a fighter trainer, with the following

flight condition: Flight Conditions Altitude Airspeed (a) (b) (c) mass Ixx Izz Ixz Air density Wing area Wing span [Y₂ Y₂ - Uo] M-K³H+K 25,000 ft 123.7 m/s 4,540 kg 5,965 kgm² 46,097 kgm² (1) (ii) (iii) 0 kgm² 0.549 kg/m³ 15.79 m² 7.69 Derivatives Yv Ny Yp N₂ Y₁ Nr Y₂ N₂ -1.260 0.240 0 0.0430 0 -0.170 0.160 -0.103 Appraise the characteristic equation of the Dutch Roll Mode Based on MIL-8785C, T-38 is a Class IV, CAT A aircraft, evaluate the flying quality of the open loop characteristic. (1) Which Level does the open loop T-38 meets? (ii) What is the requirement for meeting the highest requirement? A state feedback control system using rudder feedback is proposed to improve the damping ratio of the Dutch roll mode. So that it meets the MIL-8785C requirement as minimum o meets the requirement. Appraise the characteristic equation of the desired Dutch roll mode. Evaluate the system controllability Matrix. Design the Gain schedule (vector K) to achieve the improved flying quality that meets the MIL-8785C requirement.