1. A tiltrotor aircraft shown in Figure 1-a is both an airplane and a helicopter. It can position its engine in a vertical position for takeoff and landing as a helicopter, and then rotate its engine 90 degrees to a horizontal configuration for cursing as an airplane. The altitude control system of the helicopter mode is shown in Figure 1-b. • Determine the root locus of this system as K varies between zero (0) and infinity (infinity). • Determine the range of K for a stable system • For K = 280, find the response y(t) to a unit step input r(t), and the corresponding Percentage overshoot (PO) and the settling time (T_s, with 2% criterion) • For K = 280, and r(t) = 0, find the response y(t) to a unit step disturbance 2. An arm of a space robot is shown in Figure 2-1 with its corresponding block diagram shown in Figure2-b. Perform the following tasks: • For a proportional controller Gc=Kp, determine the value of Kp such that the percentage overshoot P.O.-3%. • Plot the system response to a unit step input for the value of Kp determined in the previous task • Design a proportional -derivative controller (PD) using ITAE method with wn = 8 • Determine the required prefilter Gp(S). • Determine the system response to a step input after you add the PD and prefilter to the system. • Design a proportional-integral controller (PI) and a prefdilter using ITAE method. • Determine the system response to a step input after you add the Pi and prefilter to the system. • Design a proportional-integral-derivative controller (PID) and a prefilter using ITAE method such that the settling time T, <4 sec based on a 2% criterion. • What is your recommendation for the most appropriate controller among P, PD, PI, and PID for this system? TAs Controller Arm R- Gas) GO sEs+9 Fig 2-6 F’3 2-a Document Preview:

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