Car and train platoon simulations

Abstract

Detailed simulations of car and train platoons are critical steps towards successful implementations of the platooning technologies. This paper developed a simulation method that can be used for both car and train platoon simulations. The method includes three main parts: (1) a scalable adaptive longitudinal space controller, (2) 2D multibody dynamics simulations that consider wheel-rail contact (Polach model), tyre-road contact (Magic Formula), suspensions and in-train forces, and (3) a scalable parallel computing method that processes the dynamics simulation of each individual vehicle (one car or one carriage) by using one independent computer core. Two case studies were conducted to simulate a 6-car platoon and a 3-train platoon on real-world road and track. The maximum space errors for the car platoon and the train platoon results were about 0.32 and 0.23 m, respectively. When the platoons were running at a steady speed, space errors were well controlled within ±0.05 m for both car and train platoons. Example dynamics results were presented including wheel-rail contact forces, tyre-road contact forces, and carbody vibrations. This information can be used to conduct a wide range of related studies such as passenger ride comfort and system damage assessments.

Railway Virtual Coupling: A Survey of Emerging Control Techniques

“…For any 𝑖, 𝑗 ∈ 𝒱, the adjacency element 𝑎 0 means that there is an information link from node 𝑗 to node 𝑖; and 𝑎 0, otherwise. Reaching this step, a typical motion model for each train 𝑖 ∈ 𝒱 can be given as [32,33]: where 𝑥 , and 𝑣 , denote the longitudinal position and velocity of train 𝑖 at the continuous time 𝑡 ∈ ℝ , respectively; 𝛾 represents the effect of rotational inertia of rotational components such as wheelsets and motor rotors; 𝑀 𝑀 𝑀 denotes the unknown mass of the train with 𝑀 being the nominal (measured) part and 𝑀 being the uncertain part of the mass, respectively; 𝐹 , is the tractive/brake (T/B) force; 𝐹 , is the rolling resistance; 𝐹 , is the curving resistance; 𝐹 , is the track gradient force; 𝜔 , stands for the other uncertain inputs that were not specifically modelled by the previous components; 𝑘 , , 𝑘 , , 𝑘 , are the basic empirical parameters for train rolling resistance; 𝑘 , is an extra resistance parameter for tunnel resistance; 𝑔 is the gravity constant; 𝑘 is curving resistance coefficient; 𝑅 𝑥 , is track curve radius; and 𝜃 𝑥 , is the track gradient. Note that, when the track profile can be identified beforehand and the real-time train speed information is available, one may further define a normalized control (acceleration) input 𝑢 , 𝐹 , 𝐹 , 𝐹 , 𝐹 , / 1 𝛾 𝑀 and a lumped unknown input 𝑤 , 1 𝛾 𝑀 𝑣 , 𝜔 , / 1 𝛾 𝑀 .…”

“…Y MPC [34] 3rd MPC [55] 2nd Y Y Y MPC [56] 2nd MPC [57] 2nd Y Y MPC [39] 2nd Y ML [37] 2nd Y Y ML [32,33] 2nd Y Y Y CBC [58][59][60] 2nd CBC [64] 2nd Y CBC [61] 3rd CBC [36] 3rd Y Y CBC [62,63] 2nd Y Y Y CFC…”

“…6. For example, for the train motion model expressed by (2.8), a representative T2T-based VC controller for each train 𝑖 ∈ 𝒱 can be constructed as [32,33]:…”

“…When it comes to the controller design, this means that each train can employ not only information from its direct predecessors (and/or successors) but also information from its underlying neighbors specified by a suitable T2T communication topology as shown in Fig.6. For example, for the train motion model expressed by (2.8), a representative T2T-based VC controller for each train 𝑖 ∈ 𝒱 can be constructed as[32,33]:…”

Research on Composite Braking Mode Switching Strategy Based on Fuzzy Algorithm

“…[ 3,4 ] However, electric vehicles will produce certain impact and vibration when braking. [ 5,6 ] Therefore, it is of great significance to study the control strategy of electromechanical composite braking system.…”