A satellite antenna has a motor-driven positioning system where the input is the voltage to the motor and the output is the yaw angle of the antenna. The system has the transfer function: Y(s) == 5 U(s) s(s+5)(s+1) The root locus plot of the system is shown in Figure Q3. Q 3(a) [3 Marks] The closed-loop system is required to have a percentage overshoot of 5% and a 2% settling time of 1s. Determine the required location of the closed-loop dominant poles. Q 3(b) [15 Marks] Design a controller for the system to meet the performance specified in part (a). (Include a sketch of the s-plane with the open loop poles and zeros as well as the closed-loop design point as part of your solution). Q3(c) [2 Marks] Explain why derivative control action can often be difficult to successfully implement in practice. 3 2 1 0 -1 -2 -3 -6 5 Figure Q3 O