3092019q3 Please Answer All Parts Of The Question 1 (60.57 KiB) Viewed 34 times
3092019q3 Please Answer All Parts Of The Question 2 (54.78 KiB) Viewed 34 times
Question 3 (a) The transfer function for the unaugmented F-4C Phantom aircraft at 35000ft at Mach 1.2 is given by: a(s) n(s) = -20.6(8 + 0.013)(8 +0.62) rad/rad (52 +0.017s +0.002)(52 + 1.74s + 29.49) (i) Develop the characteristics equation and solve for the frequency and damping factor of the two stability modes. (4 marks) (ii) Name and list the characteristics of both Stability Modes. (4 marks) (iii) When an impulse elevator input is applied, what will be the steady state value of pitch angle? (5 marks) (b) To improve the damping ratio of the higher frequency mode to 0.7071, a control algorithm is proposed using elevator as feedback as shown in Figure Q3(b-1): Demand + Response E Σ Elevator angle n(s) ) Aircraft dynamics G(s) 0(3) Feedback gain Ke Figure O3(-1)
The root locus plot of the augmented characteristics is as follows: 4 4 Ko = 0.643 Re = 1.06 N = Ke = 1.49 Ko = 1.87 0 Imaginary Axis (seconds -4 -6 -6 6 -2 0 2 Real Axis (seconds) Figure 03(b-2): Root Locus Plot of KAG ( (i) Apply Figure Q3(b-2) to identify the Root where the damping ratio is approximately 0.7071. What is the complex number of the Root? (4 marks) Hence or otherwise, appraise the corresponding gain Ko. (2 marks) (iii) Based on this gain Ke, formulate the augmented characteristic equation in polynomial. (6 marks)
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