Automotive cruise control system

Automotive Cruise Control System have been developed in order to improve safety and comfort for vehicle occupants. A system (also known as adaptive, active or autonomous cruise control) uses a number of sensors in order to provide the information to an Electronic Control Unit (ECU) regarding the distance to a vehicle in front. According to this information and an ECU algorithm, a vehicle a equipped with such system will maintain the desirable distance to a car in front with the required dynamic response to a sensor’s signal.
Write an introduction to the history of the development of Automotive Cruise Control Systems and principle of operation of these systems. Provide example of such systems used on vehicles.
An automotive intelligent cruise control system is shown in figure. For this system:
1) Determine the close-loop transfer function;
2) What values of the controller gain, k, will give the close-loop system the following characteristics:
a) The damping ration of 0.7;
b) The peak overshoot of a step of 15%;
c) Settling time of 4 seconds within 2% accuracy of the steady-state value for a system with the damping ratio 0.7
3) What will be the steady-state error of the system to a unit step?
4) Use the Routh-Hurwitz method to determine the value of K for which the system will be stable;
5) Calculate poles of the closed-loop system with the controller gain obtained in position 2.
6) Create the pole-zero plot on the complex(S-plane).
7) What you can say about the stability of the close-loop system according to the results obtain in Position 6?
8) Matlab.
9) Graphs, tables and diagrams to support the work.
10) Follow Harvard stlye for the list and the in text referencing it is attached file with this order .
11) Report structure.
G1(s)=1/(s+12); G1(s)- is the transfer function of an actuator;
G2(s)=10/(s+2); G2(s)-is the transfer function of a pant;
H(s)=1; H(s)-is the transfer function of a measurement system (a sensor).

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