【Paper】2019_ Distributed Cooperative Control of a High-speed Train

2019_Distributed Cooperative Control of a High-speed Train

1. Introduction

2. Modeling of a high-speed train

For high-speed trains with multiple carriages , The adjacent carriages are connected by couplers , The coupler is installed under the floor of the connection point of the adjacent carriage . At run time , The coupler plays an important role in reducing the impact force , Avoid collision by transmitting the internal force of the train in the longitudinal direction . The behavior of the coupler can be approximately described by the spring model , The train internal force generated by the coupler is a function of the coupler displacement . here , The restoring force of the coupler is assumed to be a linear function of the relative displacement and relative velocity between two adjacent cars .

$$f(e_i(t))=k{e}_i(t)+d{\dot{e}}_i(t)\text{\hspace{1em}(2)}$$

Put the second in the train 1 The mass of the cars 、 The position and speed are expressed as m i、x i and v i. We assume that all cars have the same mass , namely m i = m, For all i = 1, 2, - -, n. For a train composed of a trolley without a traction motor , We can regard this kind of car and its head car with motor as a unit （ for example , see [10], [11]）. For the sake of simplicity , In this paper , We think of each car as a particle , It is assumed that the train motion model is based on the distributed driving type , Each car has its own motor , To better ensure safety and comfort . that , be based on [19] The basic modeling structure described in , The motion of the high-speed train is described as follows .

For a high-speed train , Let's assume that No 1 A car can get the information of its adjacent cars , And only the second 1 Two cars from RBC Receive real-time reference speed and displacement information . therefore , An orderly group of carriages in a high-speed train operates in a connected communication topology .

3. Distributed control for a high-speed train

here , We put the speed of the first car - The reference velocity and displacement in the distance curve are expressed as ：
$${\dot{x}}_r(t)=v_r(t)\text{\hspace{1em}(6)}$$

For the first $i$ car , We will be the first to $i$ The position difference and speed difference between the vehicle and the reference displacement and speed are respectively defined as

$$\begin{array}{rl}{\tilde{x}}_i& =x_i-x_r+2l(i-1),\\ {\tilde{v}}_i& =v_i-v_r\end{array}\text{\hspace{1em}(7)}$$

4. Simulation