Apply the Ziegler-Nichols method to a second-order + dead time process 8 (8) (T18 +1)(T28 +1) where kp = 1.5F/gpm, . = 5 minutes, 1 = 3 minutes, -2 = 15 minutes. a. Use a Bode plot to find critical (ultimate) proportional gain (kcu) for a P-only controller that will make the closed-loop system nominally stable (gain margin = 1, phase margin = 0). Also, find the ultimate period. b. Find the gain and phase margins for a Ziegler-Nichols P-only controller. How much gain uncertainty can be tolerated? How much dead-time uncertainty can be tolerated? C. Find the gain and phase margins for a Zielger-Nichols PI controller. How much gain uncertainty can be tolerated? How much dead-time uncertainty can be tolerated? d. Find the gain and phase margins for a Zielger-Nichols PID controller. How much gain uncertainty can be tolerated? How much dead-time uncertainty can be tolerated? e. Would you recommend the Ziegler-Nichols tuning if you desired the following gain and phase margins: gain margin, > 2.5; phase margin, > 60? f. Compare the closed-loop responses, for step setpoint changes, of the controllers obtained in b-d. Show both output and manipulated input responses. Recommend a set of tuning parameters