جامعـة خليفـة Khalifa University Problem Statement: 1. This is a group assignment. 2. The maximum number of students in a group is two (ONLY one group will be of three)

3. Each group is required to submit a comprehensive report. 4. You must show an independent work. 5. Any signs of plagiarism from any source will be penalized. 6. Each group is required to submit a comprehensive typed report explaining all necessary steps including conclusions and final remarks. G (s) Figure 1 shows an operational amplifier analog circuit that describes a 5th-order Chebyshev Type I low-pass filter with a cut-off frequency of c = 1000 rad/s and 1dB ripple in the passband. = Vin 4642 = 4642 770 ECCE 323 Final Assignment 770 Controller Design ww 0.47 0.47 1500 ww 7349 0.477 4542 11893 4500 0.47 HE 0.47 46 The transfer function of the given filter is given by: Vout (S) V (s) 329300 289.5 s² + 468.4s + 429300 s² + 178.9s +988300 s + 289.5 X X - Vout Nov. 24, 2023 © R.K. Figure 1: A 5th-order Chebyshev Type-I Low-Pass Filter 122828246505000 (s² + 468.4s + 429300) (s² + 178.9s +988300) (s + 289.5) 988300 Assignment: System Identification and Controller Design The given filter is placed as a feedforward gain preceded by a controller,Gc(s), in a unity feedback closed-loop controlled system as shown in Figure 2. It is required to design a controller (of your choice) to have a gain margin > 5 dB and a phase margin of 60°. 1) Discuss and comment on the stability and the step response of the uncontrolled system. 2) Discuss and comment on the stability and the step-response of the closed-loop controlled system. 3) What can you do to improve the system step response and to minimize the overshoot of the controlled system? Verify your answer by numerical simulation. R + Gc(s) u GP(s) y Figure 2: Closed-loop controlled system.