PD Control with Feedforward Compensation for String Stable Cooperative Adaptive Cruise Control in Vehicle Platoons

In this paper, we propose systematic controller design guidelines to ensure both individual vehicle stability and string stability in cooperative adaptive cruise control (CACC)-based platoon systems, assuming a homogeneous platoon where all vehicles share identical dynamic models. We rigorously demonstrate that the limitation of conventional adaptive cruise control (ACC) in maintaining the target inter-vehicle distance can be effectively overcome by incorporating the desired acceleration of the preceding vehicle as a static feedforward input. Furthermore, by formulating transfer functions in the frequency domain, we analytically derive the conditions required to ensure both individual vehicle stability and string stability of the CACC system. Building on this insight, we propose a practical and theoretically well-founded design guideline for determining the proportional, derivative, and feedforward gains of control input under a constant time gap spacing policy. The proposed guidelines are validated through simulations conducted in a realistic platooning scenario involving multiple vehicles.