A Fractional-Order Proportional-Derivative Controller Synthesis for String-Stable Cooperative Adaptive Cruise Control Systems
Fractal and Fractional, cilt.10, sa.7, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 10 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/fractalfract10070465
- Dergi Adı: Fractal and Fractional
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: cooperative adaptive cruise control, fractional-order control, parameter-space approach, proportional-derivative controller, string stability, vehicle platooning
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
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 (Formula presented.) parameter space, where the fractional differentiation order (Formula presented.) 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.