This study investigates the constraint-force driven control problem of virtual coupling. To solve the constraint force, the explicit equation of vehicle motion with equality constraints is established using the Udwadia–Kalaba approach. First of all, this study introduces a brief overview of virtual coupling concepts in the European Railway Traffic Management System and some scenes of virtual coupling. The control method is proposed to enable the mechanical system to follow the designed constraint. Moreover, the dynamic model for virtual coupling problem is established. Second, combined with the dynamic model, the equation constraint is designed to make the rail vehicle movenment reach the control objective. By solving the equation based on the Udwadia–Kalaba approach, the control inputs that can render the vehicle to move along the desired trajectory. Third, numerical simulation results demonstrate the effectiveness of the proposed method in virtual coupling problem.
AradiSBécsiTGáspárP (2015) Estimation of running resistance of electric trains based on on-board telematics system. International Journal of Heavy Vehicle Systems22(3): 277–291.
2.
AstolfiAMeniniL (2002) Input/output decoupling problems for high speed trains. In: Proceedings of the 2002 American control conference (IEEE Cat. No.CH37301), Anchorage, AK, 8–10 May 2002. Washington, DC: IEEE Computer Society.
3.
ChenY-HZhangX (2010) Adaptive robust approximate constraint-following control for mechanical systems. Journal of the Franklin Institute347(1): 69–86.
4.
Di MeoCDi VaioMFlamminiF, et al. (2019) ERTMS/ETCS virtual coupling: proof of concept and numerical analysis. IEEE Transactions on Intelligent Transportation Systems21(6): 2545–2556.
5.
DongHNingBCaiB, et al. (2010) Automatic train control system development and simulation for high-speed railways. IEEE Circuits and Systems Magazine10(2): 6–18.
6.
FelezJKimYBorrelliF (2019) A model predictive control approach for virtual coupling in railways. IEEE Transactions on Intelligent Transportation Systems20(7): 2728–2739.
7.
FlamminiFMarroneSNardoneR, et al. (2018) Towards railway virtual coupling. In: ESARS-ITE Europe 2018 - 5th international conference on electrical systems for aircraft, ESARS and ITEC, Nottingham, UK, 7–9 November 2018. Washington, DC: IEEE Computer Society.
8.
Fraga-LamasPFernandez-CaramesTMCastedoL (2017) Towards the Internet of smart trains: a review on industrial IoT-connnected reailways. Sensors17(6): 1457.
9.
FurnessNvan HoutenHArenasL, et al. (2009) ERTMS Level 3: the game-changer. IRSE News232: 2–9.
10.
GoikoetxeaJ (2016) Roadmap towards the wireless virtual coupling of train. In: Proceeding international workshop on communication technologies vehicles, San Seastian, Spain, 6–7 June 2016, pp. 3–9. Cham: Springer.
11.
HuTLinZChenBM (2002) An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica38(2): 351–359.
12.
HuangJYe-HwaCZhongZ (2013) Udwadia-Kalaba approach for parallel manipulator dynamics. Journal of Dynamic Systems Measurement and Control135(6): 061003.
13.
JiaDLuKWangJ, et al. (2016) A survey on platoon-based vehicular cyber-physical systems. IEEE Communications Surveys & Tutorials18(1): 263–284.
14.
LiSYangLGaoZ (2016) Adaptive coordinated control of multiple high-speed trains with input saturation. Nonlinear Dynamics83(4): 2157–2169.
15.
LiSYangLLiK, et al. (2014) Robust sampled-data cruise control scheduling of high speed train. Transportation Research Part C: Emerging Technologies46: 274–283.
16.
MitchellIGoddardEMontesF, et al. (2009) ERTMS level 4, train conveys or virtual coupling. International Technology Commitee219: 2223–2231.
17.
MorenoJRieraJMHaroLD, et al. (2015) A survey on future railway radio communications services: challenges and opportunities. IEEE Communications Magazine53(10): 62–68.
18.
NausGJLVugtsRPAPloegJ, et al. (2010) String-stable CACC design and experimental validation: a frequency-domain approach. IEEE Transactions on Vehicular Technology59(9): 4268–4279.
19.
SantiniSSalviAValenteAS, et al. (2017) A consensus-based approach for platooning with intervehicular communications and its validation in realistic scenarios. IEEE Transactions on Vehicular Technology66(3): 1985–1999.
20.
SongQSongYDTangT, et al. (2011) Computationally inexpensive tracking control of high-speed trains with traction/braking saturation. IEEE Transactions on Intelligent Transportation Systems12(4): 1116–1125.
21.
UnterhuberPLehnerAde Ponte MullerF (2016) Measurement and analysis of ITS-G5 in railway environments. In: Proceeding international workshop commmunication technology vehicles, San Seastian, Spain, 6–7 June 2016, pp. 62–73. Cham: Springer.
22.
WangJRakhaHA (2018) Longitudinal train dynamics model for a rail transit simulation system. Transportation Research Part C: Emerging Technologies86: 111–123.
23.
WuQSpiryaginMColeC (2016) Longitudinal train dynamics: an overview. Vehicle System Dynamics54(12): 1688–1714.
24.
XuJDuYChenYH, et al. (2018) Adaptive robust constrained state control for non‐linear maglev vehicle with guaranteed bounded airgap. IET Control Theory & Applications12(11): 1573–1583.
25.
YangZHuangJZhanyiH, et al. (2020) Utilising bidirectional inequality constraints in optimal robust control for heterogeneous vehicular platoons. IET Intelligent Transport Systems14(7): 802–811.
26.
YinHChenY-HDejieY (2018) Vehicle motion control under equality and inequality constraints: a diffeomorphism approach. Nonlinear Dynamics95: 175–194.
27.
ZhaoHZhenSChenY-H (2013) Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory. Chinese Journal of Mechanical Engineering26(5): 839–850.
28.
ZhaoRChenYHJiaoS, et al. (2017) Adaptive robust constraint-following control for mechanical systems with leakage and dead-zone. In: 2017 IEEE 56th annual conference on decision and control (CDC), Melbourne, AU, 12–15 December 2017, pp. 3308–3315. Washington, DC: IEEE Computer Society.
29.
ZhaoXMChenYHZhaoH, et al. (2018) Udwadia–Kalaba equation for constrained mechanical systems: formulation and applications. Chinese journal of mechanical engineering31(1): 1–14.
30.
ZhouYZhangZ (2014) High-speed train control based on multiple-model adaptive control with second-level adaptation. Vehicle System Dynamic52(2): 637–652.
31.
ZhuanXXiaX (2006) Cruise control scheduling of heavy haul trains. IEEE Transactions on Control Systems Technology14(4): 757–766.
