Problem 2: (30 points) The parameter values and operating conditions for a buck converter are given below. It is desired to regulate the inductor current constant at 5 A. Vn: 72V: Vo nominal : 40V; Rioad =82; faw =100 kH: L= 100uH, C=100 F, ESR=0.12 (a) Design a controller based on k-Factor approach to achieve a bandwidth of 5 kHz and a phase margin of 60. Show the design steps and equations. (Hint: the required plant transfer function is derived in class notes) Problem 3: (30 points) (a) Perform a time domain simulation of the buck converter of Problem 2 with the designed controller and study the performance of the system for step change in load resistance from 8 2 to 62 with the current reference kept at 5 A. (b) Perform a time domain simulation of the buck converter of Problem 2 with the designed controller and study the performance of the system for step change in inductor current reference from 4A to 6A with load resistance of 8 2.