The pole-zero diagram of the longitudinal motion of an airplane is given in Fig. 8 in terms of output angle of attack a and input elevator deflection : -1.0 2.65 *-0.092 -0.043 Figure 8 1) Write down the characteristic equation, D(s), of the short period motion mode based on the pole-zero diagram given in Fig. 8; 2) Determine the damping ratio (C) and natural frequency () of the short period mode; 3) Assume the open-loop transfer function of the output a with respect to the input & for short period motion mode is given by: a(s) 0.006s+1.7278 8. (s) D(s) Design static gain KSAS in Fig. 9 such that the closed-loop damping ratio equals to 0.707. 4) If the above designed static control gain KSAS cannot satisfy the performance requirement, how a PID controller to be implemented? Please draw a block diagram for a PID controller in transfer function format to replace the block KSAs in Fig. 9; State the role of the proportional (P), integral (1), and derivative (D) controller gain respectively in terms of a better control performance of the closed-loop system showed in Fig. 9; de KSAS a(s) 8, (s) Figure 9 5) Based on the KSAS determined in 3) and the corresponding closed-loop system in Fig. 9, calculate and show an approximate sketch of the system response a(t) when the airplane is subject to a unit step input (t)= 1 for 1> 0; 6) List the four fundamental characteristics (performance requirements) to represent the performance of an airplane, which we have described during the lectures. Write and mark the five performance specifications on the above sketched unit step response you have obtained in 5).