Urged by a close future perspective of a traffic flow made of a mix of human-driven vehicles and automated vehicles (AVs), research has recently focused on studying the traffic flow characteristics of Adaptive Cruise Controls (ACCs), the most typical AV. However, in most works, the ACC system is studied under a simplifying and unrealistic assumption, or the ACC system modeled is inaccurate. This paper proposes a general hierarchical control system to model ACC systems with several assumptions based on the deficiencies above. Moreover, a field experiment was conducted, and the corresponding experimental data was used to verify the proposed hierarchical control system and assumptions. In addition, string stability is explored along with sensitivity analyses of control parameters based on an example under the constant time gap policy. The results show that different upper-level controller parameters have different delays, where the delay of the speed is negligible; the introduction of actuator delay and lag in the lower-level controller can significantly improve the model goodness of fit. Furthermore, optimizing the delay and lag in the lower-level controller can significantly enhance the string stability of ACCs than optimizing the control parameters.