Answer Happy

(a) The equation below describes the behaviour of a second-order system where u and y are the input and output variables. d'y +8.2 +1.6y=5u dt dt² (i) Derive the Laplace-domain transfer function for the system and calcu- late its DC gain, damping ratio and undamped natural frequency. (ii) Sketch the step response of the system to an input step of height 2. Clearly label the axes and justify the shape of the step response. (b) Draw a block diagram of a feedback control system, comprising the system in part 1a), a proportional controller, and an output sensing element. Calculate the proportional controller and feedback gains required to give zero steady- state error and a damping ratio of 0.5. Clearly show all working. (c) Explain how your feedback control system in part 1 (b) could be modified to give the same damping ratio but a higher frequency-response bandwidth. Use a block-diagram to illustrate your answer.