Adaptive cruise control (ACC) for vehicles has been available for several years now. It was created on the top of cruise control that originates roughly in the 1950’s. The ACC is to enhance the automatic driving by keeping a safety distance set by a driver to another vehicle in front. The ACC is basically about balancing between the vehicle speed and the distance between two vehicles.

For control engineering education purposes, the ACC is a good and a clear example of control engineering. Basically, anyone can understand the scope of the ACC requiring little effort on motivating the need for the ACC. Second, the ACC engineering task can be divided into well-defined, separate tasks of dynamic modelling, control design and control tuning which all can be verified by applying dynamic, time-domain simulation.

The literature of the ACC recognizes several differential equation models to be worked upon. This paper introduces one of them, which despite its simplicity captures the essence of a vehicle behavior allowing the design of the ACC. Through simulations, also the control design and tuning are explained and treated with simulation results.