Answer Happy

(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 0,(s) Σ Elevator angle n(s) Aircraft dynamics G(s) Response As) Feedback gain K, Figure 03(b-1) The root locus plot of the augmented characteristics is as follows: 6 4. Ke = 0.643 Ke = 1.06 ko = 1.49 Ko = 1.87 Imaginary Axis (seconds =) -6 -6 -2 0 2 4 6 Real Axis (seconds "1) Figure Q3(b-2): Root Locus Plot of KG (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) (ii) Hence or otherwise, appraise the corresponding gain Ko. (2 marks) (iii) Based on this gain Ko, formulate the augmented characteristic equation in polynomial. (6 marks)