1. Consider the automobile cruise-control system. Assume that the sensor gain

H(s) = 1 rather than the value of 0.4 as shown in the figure.

The design specifications are given as:i. Phase margin > 50⁰

ii. Gain margin_≥ 40 db.

a) What is the gain margin and phase margin of this uncompensated system?

b) Find the transfer function of a series compensator that will make the overall system satisfy the above given specifications.

c) Check the gain margin and phase margin whether the compensated system meets the above specifications.

d) From your designed compensator transfer function Gc(s), determine the values of resistors and capacitor of the compensating network.