Stable Platoon Control For Virtually Coupled Train Set Under Interference Conditions

In view of the growing demand for rail transport,it is urgent to improve the use of existing resources,such as lines and trains.The concept of Virtual Coupling(VC)is regarded as a breakthrough to the traditional train operation and control,which brings benefits as unit trains under VC are allowed to operate much closer to one another,forming a virtually coupled train set(VCTS).Shorter unit-train separation within the VCTS can improve the capacity of existing lines.Meanwhile,the number of unit trains in a VCTS can be determined by transportation tasks and demands,increasing the load rate and avoiding empty load conditions.To benefit from VC,the stable formation and movement of a VCTS should be guaranteed.However,the safe and stable separation between unit trains in the VCTS is a problem under interference conditions,such as hard constraints,braking performance limits,communication delays,and uncertain disturbances.Given that there are no rigid couplers to connect unit trains into a fixed formation,the interference between successive unit trains in a VCTS becomes non-negligible.Various maneuvers of the previous unit train have a significant impact on the operating behavior of subsequent unit trains,resulting in fluctuating spacing and,consequently,an unstable VCTS.Accordingly,in recent years,it has become an active research topic on how to minimize the disturbances and maintain a consistently stable separation between unit trains in the VCTS.To address this issue,this thesis focuses on methods of stable platoon control for the VCTS with complicated constraints,limits,delays,and disturbances.Based on the analysis of VCTS characteristics,system models,controllers,and optimization algorithms are deliberately designed.To ensure the feasibility,local stability,string stability,and robustness of controllers,sufficient conditions are mathematically derived and proved.Specifically,the main contributions of this thesis are summarized as follows.(1)The fundamental models of the VCTS are first established.Combining the structure of the Automatic Train Operation(ATO)system and the basic characteristics of the VCTS,a distributed optimal control framework is constructed based on the on-board ATO system and train-to-train communication.Three models are proposed corresponding to different situations,including the deterministic model,the parameter-varying model,and the uncertain model.After modeling,the optimal control problem is further formulated according to the rolling horizon optimization strategy,i.e.,model predictive control(MPC).The applicability of the MPC approach is discussed and analyzed,which provides ideas and insights for later studies.(2)Aiming at handling the coupled constraint of safe separation between unit trains,this study presents a distributed model predictive control(DMPC)approach to solve the constrained VCTS control problem.Particularly,the proposed control method considers the coupled constraint of safety braking distances and the individual constraint of restricted traction/braking performance.A sequential solution algorithm is developed to decouple the coupled constraint of neighboring unit trains within the prediction horizon,reducing the complexity of the problem.To guarantee feasibility and stability,a terminal controller and an invariant terminal set of the DMPC are designed.For rigor,sufficient conditions of the feasibility and asymptotic stability are mathematically proved and derived.Based on the data of the Beijing-Shanghai high-speed railway line,numerical experiments are conducted to verify the correctness of derived sufficient conditions and the effectiveness of the proposed control method under interference and disturbances.(3)For the stable platoon control problem of heterogeneous VCTS with different braking performance under varying speed limits,an analytical optimal method is proposed based on the parameter-varying model and Pontryagin’s maximum principle(PMP).The proposed control strategy focuses on both local and string stability under varying maneuvers.Specifically,a parameter-varying model is firstly formulated to describe the VCTS dynamics under speed limits,based on which an optimal control formulation is then constructed considering constraints of safe separation,speed limits,and train dynamic performance.To solve the proposed constrained optimal control problem,an analytical algorithm is given based on PMP with a discount factor.Further,local and string stability are analyzed,and sufficient conditions of stability are mathematically derived to guarantee stable platoon control for both homogeneous and heterogeneous VCTS.Numerical simulations are conducted to verify the correctness of derived sufficient stability conditions and the effectiveness of the proposed control strategy under varying maneuvers and disturbances.(4)During operations,communication delays and uncertain disturbances(caused by strong wind and unmodeled air drag)are inevitable,which usually results in speed fluctuations and an unstable VCTS.In this study,a tube-based control approach for the VCTS is developed,focusing on optimizing the control performances and meanwhile guaranteeing local and string stability with considering communication delays and uncertain disturbances.Specifically,a tube MPC framework is constructed to handle safety constraints and regulate uncertain disturbances.To ensure the system state fluctuation range,the local stability is mathematically proved by designing the constraint sets for states and control inputs based on the robust invariant set theory.Further,to guarantee the disturbance attenuation through the VCTS string with delays,the string stability can be achieved through proper coefficient tuning within the stable region derived from the frequency-domain analysis.Finally,simulation-based experiments verify the effectiveness of the proposed approach to regulate unit train states within a tube that is smaller than the boundary of uncertain disturbances.Results demonstrate that the VCTS can be asymptotically stable and string stable facing disturbances and delays.Moreover,the proposed control strategy shows better robustness and higher efficiency than a traditional MPC method.