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Question 3 (25 marks) The Northrop T-38 Talon is a two-seat, twinjet supersonic jet trainer. It was the world's first supersonic trainer and is also the most produced. The T-38 remains in service as of 2020 in several air forces. The lateral-directional characteristic equation at flight condition of M0.8, sea level is: (s -0.0014)(8 + 4.145)(s2 + 1.649s + 38.44) = 0 (a) Appraise all lateral-directional modes of the aircraft by computing the oscillation frequency, damping ratio, and time constant (4 marks) (b) Based on MIL8785C, apply the flying quality rating to evaluate the flying quality of the aircraft's dutch roll mode. (6 marks) To enhance the direction stability, the following closed loop control is proposed. PC 1 ki Formulate the characteristic equation of the closed loop transfer function if the open loop transfer function is as following: r = -11.01(s + 0.302)(s + 0.366) (s + 4.11) (s - 0.0014)(s + 4.145)(2 + 1.649s + 38.44) 3 (6 marks) (d) The corresponding root locus plot is shown in Figure 3(d)(1). Figure 3(d)(ii) shows the root loci at various gain setting. Using these plots, appraise the performance of the control design, and answer the following: (ii) (111) How does the stability of spiral-roll mode change with increasing gain? How does the stability of the roll mode change with increasing gain? How does the damping ratio and undamped frequency of dutch-roll mode change with increasing gain? (9 marks)
Root Locus 7 8 Imaginary Axis (seconds) K (s + 0.302)( + 0.366) (s + 4.11) (s - 0.0014)(s + 4.145)(2 +1.649s + 38.44) 1 0 -7 -1 0 Real Axis (seconds) Figure 3(d)(i): Root Locus Plot Root Locus System overallt Gain:0 Pole:-0.824 +6.141 Damping: 0.133 Overshoot (%): 65.8 Frequency (rad's): 62 7 Dutch Roll Mode 6 System: overall Gain: 7.19 Pole: -4.38 + 4.811 Damping 0.673 Overshoot (%): 5.75 Frequency (rad/s): 6:51 System overall Gain: 3.8 Pole:-2.71 +5.78 Damping: 0.425 Overshoot (%): 22.9 Frequency (rad/s): 6:38 System overall Gain: 10.4 Pole-594 +2.91 Damping: 0.899 Overshoot (%): 0.158 Frequency (rad's): 6.61 Imaginary Axis (seconds) 1 System Overall Gain: Pole: -4.14 Damping 1 Overshoot (%): 0 Frequency (radis): 4.14 Systeme overall Systemoverall Gain: 19.9 Gain 424 Pole:-277 Pole: -1.51 Damping: 1 Damping: 1 Overshoot (%): 0 Overshoot (%) 0 Frequency (rad/s): 2.77 Frequency (rad/s): 1.51 System Overall Gain: 718 Pole:-022 Damping: 1 Overshoot (%): 0 Frequency (rad/s). 0.22 System: overallt Gain:0 Pole: 0.0014 Damping - 1 Overshoot (%): 0 Frequency (rad's): 0.0054 -7 Spiral-Roll Mode Roll Mode Real Axis (seconds) Figure 3d (ii) : Root Loci at various Gain