As the most popular active safety driving technology, adaptive cruise control is favored by major car producers and their end-users. This report presents the history, and the functional and regulatory requirements of the ACC (adaptive cruise control) systems, and also introduces three popular controllers and their design approaches. Then a full or partial realization of the ACC function is accomplished by modelling of the ACC system in MATLAB/ Simulink (R2021b) and using the three controllers for simulation respectively. Finally, through a set of designed test scenarios and the simulations accordingly, the designs of the ACC systems are validated, followed by a discussion on the advantages and disadvantages of each control methodology.