Abstract

Cooperative adaptive cruise control (CACC), as an extension of adaptive cruise control (ACC), is an intelligent transportation approach for connected and automated vehicles. By using vehicle-to-vehicle information, CACC improves longitudinal tracking performance, traffic throughput, and string-stable platoon behavior. However, controller tuning remains sensitive to vehicle-dynamics parameters, spacing-policy selection, fractional-order dynamics, and communication delay. This paper presents an analytical parameter-space-based fractional-order PD (FOPD) controller synthesis framework for string-stable CACC systems. For the constant-time headway spacing policy, the controller parameters are investigated in the (kp,kd,μ) parameter space, where the fractional differentiation order μ is considered as an additional design variable. To obtain the feasible stabilizing regions, the fractional-order characteristic equation is evaluated on the imaginary axis, and the delay-dependent stability boundaries are derived through a frequency-domain boundary-locus formulation. The stabilizing gain regions are constructed through the complex-root boundary (CRB), real-root boundary (RRB), and infinite-root boundary (IRB), which provide an interpretable graphical basis for controller-gain and fractional-order selection. In addition, the effect of the headway time on the admissible stability region is examined jointly with the fractional order. The proposed structure is implemented with a feedforward controller that uses the acceleration information of the preceding vehicle under a predecessor-vehicle-following communication topology. The selected fractional-order CACC (FO-CACC) controller is validated in an eight-vehicle platoon simulation environment and compared with integer-order ACC (IO-ACC), fractional-order ACC (FO-ACC), and integer-order CACC (IO-CACC) configurations. The results show that the proposed parameter-space approach enables systematic FOPD tuning and that the selected FO-CACC controller satisfies the frequency-domain string-stability requirement while maintaining smooth time-domain responses in position, velocity, acceleration, headway time, spacing error, and control input. Additional simulations under the New European Driving Cycle (NEDC) and the FTP-75 (Federal Test Procedure 1975) driving cycles further indicate that the proposed FO-CACC structure maintains accurate spacing regulation and bounded acceleration behavior under standard drive-cycle conditions. Overall, the results indicate that the fractional-order parameter provides an effective design freedom for improving string-stable cooperative platoon performance.

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