Q1) Phase (deg) Controller Design 1. Any signs of plagiarism from any source will be penalized. 2. Submit a comprehensive Handwritten report explaining all necessary steps including conclusions and final remarks. 3. Submit all MATLAB/Simulink file also attach your MATLAB output in your report. Problem Statement: Figure 1 shows the frequency response of an open-loop system. Bode Diagram Gm = 94.4 dB (at 59.1 rad/s), Pm = 0.567 deg (at 0.141 rad/s) Magnitude (dB) -50 -100 -150 -200 -250 -135 -180 -225 50 0 -270 10-1 10º 101 102 Frequency (rad/s) 103 104 Fig. 1: Bode diagram of an open-loop system. You need to identify and find the transfer function that represents the given system. 1) Determine the type and the order of the open-loop system. 2) Discuss the stability of the system without control. Assignment: System Identification and Controller Design Q2) 3) Investigate the step response of the uncontrolled closed-loop system with unity feedback. Design a controller (of your choice) as shown in Fig. 2 to have a gain margin > 10 dB and a phase margin of 63.5° at a cross-over frequency w = 100 rad/s. 1) Discuss and comment on the stability and the step-response of the closed-loop controlled system. 2) Tune the controller found in part Q2)1) to completely eliminate (if possible) the overshoot of the controlled system. 3) Design a PID controller for the given system to possibly achieve the same design requirements. 4) Tune the PID controller to possibly remove the overshoot of the controlled system and comment on your design. 5) Verify your answers via numerical simulation. R u y Gc(s) GP(S) + Fig.2: Closed-loop controlled system. 2