This project requires to design a closed loop control system as shown in the block diagram in Figure 3 which can meet the following time domain specifications given in Table -1 e(s) V(s) PID controller G(s) Figure 3 Closed-loop diagram Table -1 Time domain specifications. Step response characteristics Settling time Overshoot Steady-state error Design values less than 2 seconds less than 5% less than 1% 0(s) Closed Loop System With reference to Figure 3. Q8. Derive the transfer function of the system closed loop system. Q9. Obtain the step response of the system with time domain parameters overshoot, settling time, peak time, and the steady-state error shown Figure 3 for the following scenarios I. P-controller Proportional constant (Kp) = 50 II. P-controller Proportional constant (Kp) = 100, III. IV. V. VI. P-controller Proportional constant (Kp) = 150 Pl controller Kp = 75 and Ki = 1 Pl controller Kp = 75 and Ki = 100 Discuss your results Q10. By incorporating a derivative constant in the PID controller with following cases I. Kp = 75, K = 200, K = 1 II. Kp = 75, K = 200, Ka = 5 Kp = 75, Ki = 200, Ka = 10 III. Calculate the overshoot, settling time, and steady-state error in this case. Are the results acceptable? If not, explain which specification needs to be improved. Simulink Model Q11. Develop a Simulink model outlining all the elements of the block diagram in Figure (2) for the unstable second order control system). Use the Simulink block PID from Matlab/Simulink library as a controller. Obtain the time reponse of the system with time domain specifciations in the Table -1 General Q12. Discuss the effect of each of the PID parameters on the dynamics of a closed-loop system and demonstrate how to use a PID controller to improve a system's performance