The linearized equations of perturbed longitudinal motion for a given flight condition are given (in SI units) by: u=200.00 +0.035a-9.810-0.18u q=-0.65q-0.25-a-1.28 =q-0.25u-0.6a-0.0356 1) Determine the trim/equilibrium flight speed of the aircraft; Describe why trim is needed for aircraft modeling and analysis? How to determine a trim/equilibrium flight condition? Why dimensional equations of motion need to be converted to non-dimensional equations of motion? and how to achieve the non-dimensional conversion by using the longitudinal equations of motion as example? 2) Calculate the transfer function model relating changes in angle of attack (a) to changes in elevator (8.); 3) Analyze static stability of the aircraft in angle of attack (a). Please show your analysis steps. Problem 4 [30 marks] For the above simplified F-16 longitudinal subsystem shown in the highlighted grey area, if transfer function between elevator control surface deflection (de) and angle of attack (a) is given as follows: AERO 480 and MECH 6091 - Flight Control Systems 4/4- Midterm Examination. 17:45-20:15. Oct. 28, 2021 -0.083(s+0.086s+0.0594)(s+35.4) 8 (s+0.168s+0.0832)(s+1.75)(s-0.5825). Pilot Command Aircraft Transfer Functions Control Gain & Filter Surface Actuator 8/10 22 AOA Transducer K Washout Filter Rate Gyro Accelerometer http://en.wikipedia.org/wiki/F16 Gain & Filter Fig. 9.6 Simplified F-16 longitudinal FBW block diagram. -15 S+15 The control surface actuator dynamics is represented by first-order transfer function- angle of attack sensor dynamics is represented by 1 and the gain K, is designed as Ka = 0.45. The 1) Please state what are static stability and dynamic stability of an aircraft, and the difference between these two types of stability; State why stability derivatives and control derivatives need to be defined, and how the stability derivatives link to aerodynamic coefficients by using the lift aerodynamic coefficient CL as an example; 2) Calculate the closed-loop transfer function of the highlighted grey area; 3) Is this inner closed-loop system statically stable? Please judge your answer by using The Routh Table calculations as we showed in the lecture; 4) Mark the open-loop poles and zeros in s-plane; Plot the root-locus plot for the closed-loop transfer function of the highlighted grey area (Extended from course MECH 371 or ECE 372 and Optional; 4 bonus marks if you solve this sub-question 4)).