Parameter Space-Based Fractional-Order PD Controller Design and Analysis for Cooperative Adaptive Cruise Control Systems

Cooperative adaptive cruise control (CACC), an extension of adaptive cruise control (ACC), is an important intelligent transportation solution for future mobility. It leverages vehicle-to-vehicle information to improve longitudinal tracking, traffic throughput, energy consumption, and string stability. However, controller tuning remains sensitive to model uncertainties and communication delay. This paper presents an analytical parameter-space-based fractional-order PD (FOPD) controller tuning framework for the CACC problem. For the constant-time headway spacing policy, the fractional-order controller parameters are explored over the (kp, kd, µ) parameter space, accounting for plant uncertainties. To enable a tractable stability assessment for the commensurate fractional-order characteristic equation, a variable transformation is used to obtain an equivalent polynomial form, and stability is then verified using the Hurwitz criterion. The resulting parameter-space maps provide a transparent graphical approach to controller gain and fractional-order selection. Moreover, the CACC design is implemented by a feedforward controller that uses preceding vehicle acceleration information within the predecessor-vehicle-following communication topology. The proposed method is tested in a vehicle platoon simulation environment with respect to string stability and the time-domain responses of position, velocity, acceleration, and headway time. The fractional-order CACC is compared with integer-order controllers. Simulation studies under representative CACC maneuvers demonstrate that the proposed parameter-space approach enables systematic FOPD tuning and achieves improved performance requirements compared to integer-order PD control.