Control method for high-density transportation of multiple-particle motor train unit group based on virtual coupler

Abstract

This invention discloses a control method for high-density transportation of multi-mass EMU train groups based on virtual couplers. Specifically, it involves: establishing a multi-mass longitudinal dynamic model for a single EMU; establishing a multi-train communication topology based on adjacency communication; and designing a distributed optimal cooperative controller for multiple EMU train groups based on model predictive control algorithms, under the constraints of couplers within the EMU train group and virtual couplers between EMU train groups, according to the current operating status and braking characteristic parameters of the trains, as well as the latest operating status of adjacent trains obtained from the communication topology. Firstly, this method enables each power unit of a single EMU train group to quickly track the desired speed while ensuring that the coupler displacement remains within a safe range. Secondly, the controller can also achieve high-speed cruising operation with virtual coupling of the EMU train groups, satisfying the constraints of virtual couplers between EMU train groups. This improves track utilization while avoiding collisions, and the strategy also satisfies the optimal constraints for passenger comfort.

Description

Technical Field

[0001] This invention relates to the field of EMU cooperative control, and in particular to a control method for high-density transportation of multi-mass EMU groups based on virtual couplers. Background Technology

[0002] In recent years, the annual growth rate of high-speed rail passenger demand has exceeded 10%, placing higher demands on railway carrying capacity. The carrying capacity of the railway system is closely related to the operating speed of high-speed trains (EMUs) and the construction of new lines. Further enhancing the carrying capacity of high-speed railways has become an increasingly urgent need. Increasing EMU operating speed, constructing new lines, and increasing operating density can increase railway carrying capacity, but increasing EMU operating speed and constructing new lines cannot be sustained indefinitely with railway development. Therefore, increasing EMU operating density is a feasible solution. Virtual coupling technology can effectively reduce train tracking intervals, significantly improving transport capacity without altering existing facilities such as tracks and lines, providing more flexible and universal services during peak hours, and improving train operation. Multiple EMUs are virtually coupled into a virtual coupled EMU group. The study investigates how to meet the virtual coupler requirements while avoiding collisions within the EMU group, ensuring coordinated high-speed cruising. Simultaneously, considering actual operating conditions, comfort and minimizing energy consumption are also required. Achieving all of these control objectives is a challenging task. EMU group control based on virtual couplers can significantly improve railway transport density and increase railway capacity.

[0003] When high-speed trains operate on railway lines, collision avoidance control between trains generally employs two modes: fixed block and moving block. To improve the operating density of high-speed trains, moving block based on multi-train cooperative control has received increasing attention. Initial research focused on high-speed trains operating under the protection of a moving block system (MBS). The minimum distance between trains was directly determined by the separation principle of the block system within the train control system. This principle stipulates that the distance between adjacent trains should not be less than the margin value specified by the block system. Currently, the moving block system allows a minimum distance, which is calculated using absolute braking distance, enabling trains under MBS to separate within a sufficient distance. However, with the increase in operating speed, the absolute braking distance increases dramatically, and the minimum distance under MBS still cannot meet the requirements of high-speed scenarios.

[0004] With breakthroughs in line communication technology, Train-to-Train (T2T) communication has been proposed for EMU (Electric Multiple Unit) operation control. Based on T2T, the communication mode of EMUs can be modeled as a topological graph. Using graph theory, information coupling between EMUs can be established. To further reduce the tracking distance between trains while ensuring safe train operation, virtual coupling (VC) is proposed based on the relative braking distance principle of MBS (Motor-Mounted System) and T2T. This allows high-speed railway virtual coupled EMUs to maintain consistent speeds and safe distances between trains. EMU groups based on virtual coupling (VC) can significantly improve railway transport capacity. However, because there are no rigid couplers connecting them into a fixed form, controlling the safe and stable distance between trains remains a problem. Therefore, designing a distributed controller that can satisfy state constraints and control input constraints while also meeting optimization indicators such as passenger comfort is crucial for ensuring the safety and efficiency of virtual coupled train cooperative operation. Summary of the Invention

[0005] To address the aforementioned problems and meet operational and control input constraints, this invention provides an optimal control method for high-density multi-mass transportation of EMU trainsets based on virtual couplers, as detailed below.

[0006] Step 1: The modeling of a single-unit EMU is considered to be composed of multiple carriages connected by flexible couplers. The EMU is subject to rolling resistance and aerodynamic drag. The power unit is connected by couplers and can be represented as an "elastic-damped" component. Its dynamic equation can be expressed as:

[0007]

[0008] In the formula, k i and d i These are the stiffness coefficient and damping constant of the coupler system, respectively.

[0009] Step 2: Considering the interference of the basic running resistance encountered by the train during operation, the unit basic running resistance during the operation of the EMU is given by the Davis equation:

[0010]

[0011] In the formula, c0, c1, and c2 are the basic operating drag coefficients, which are generally measured through wind tunnel experiments.

[0012] Step 3: Considering passenger comfort requirements, the kinematic equations of the high-speed train are described as follows:

[0013]

[0014] In the formula,

[0015] Step 4: For consecutive trains that can communicate with each other, assume that the exchange of operational information occurs between the first carriage of the following train and the last carriage of the preceding train, and let s i,j (t) represents the displacement of the j-th power unit of the i-th trainset, and the neighborhood of the i-th trainset is defined as:

[0016]

[0017] In the formula: β is the vehicle-to-vehicle wireless communication radius.

[0018] Step 5: Based on the communication relationships between the train sets, the dynamic model of the train set group is as follows:

[0019]

[0020] in, For coordinated operation of multiple units (MMUs), if there is coupling between power unit q and power unit j... otherwise, Let v0 be the desired cruising speed of the EMU.

[0021] Step 6: Inspired by the actual coupler connecting the EMU power unit, the safety distance between two adjacent EMUs is abstracted into the concept of a "virtual coupler." The displacement of the virtual coupler can be described as:

[0022] s safe (t)=d L +d+hv i (t)

[0023] Where d L d is the length of the train set, h is the length of the virtual coupler. i These are parameters to be determined; the coupler includes a linear term, which will significantly reduce the safety distance.

[0024] s i-1 (t)-s i (t)-d L ≥s safe

[0025] Step 7: According to the Taylor expansion, the linear dynamic equation around v0 is obtained as follows:

[0026]

[0027] Step 8: Define the state of the j-th power unit of train i as: x i,j (t)=[Δs i ,Δv i,j ,Δa i,j ] T , where Δs iThe deviation relative to the length d of the previous train and the virtual coupler can be expressed as:

[0028]

[0029] In the formula, d L d is the length of the train set, h is the length of the virtual coupler, and h is a parameter to be determined.

[0030] Δv i,j The speed difference between the power units can be expressed as:

[0031]

[0032] Δa i,j The acceleration difference between the power units can be written as:

[0033]

[0034] Assuming each power unit has the same mass, i.e., m i.j =m, then we have Selecting the speed difference and acceleration difference of the power unit as output variables, the state equation of the EMU based on the virtual coupler can be written as:

[0035]

[0036] y i,j (t)=C i,j x i,j (t)

[0037] Where f is a linear function of the state variable and the input variable,

[0038] Step 9: Changes in speed limits caused by track and environmental conditions lead to changes in train cruising speed. For each train in the virtual coupled EMU, the speed limit constraint can be written as: 0 ≤ v i,j (t)≤v max , where v max =max{v c ,v1,v p}, middle v c The speed limit is defined by v1 in the design of the EMU (Electric Multiple Unit) rolling stock, and v1 is the maximum permissible speed determined by the track operating conditions. p The maximum permissible speed for safe operation of the EMU is calculated based on real-time information transmitted from the ground and the EMU's own performance.

[0039] Changes in acceleration affect passenger comfort, and the relevant constraint can be expressed as: -a1≤a i,j (t)≤a2

[0040] In addition, the control output constraints of the EMU (Electric Multiple Unit) were considered: U min U max For minimum control input and maximum control input,

[0041] Constraint sets can be represented as control constraint sets and safety constraint sets, as follows:

[0042]

[0043] Safety constraints:

[0044]

[0045] in:

[0046] φ1(x i,j ) = s i-1 (t)-s i (t)-D min -D L

[0047] φ2(x i,j ) = v i,j (t)

[0048] φ3(x i,j ) = v max -v i,j (t)

[0049] φ4(x i,j ) = a i,j (t)

[0050] φ5(x i,j )=a1-a i,j (t)

[0051] Step 10: The control objective is to minimize the speed difference between train sets while ensuring that the virtual couplers connecting the power units are within a safe range, and to achieve stable operation with consistent speed in a balanced state, that is:

[0052]

[0053] Step 11: In the design and operation of high-speed trains, fully considering the optimization of passenger comfort indicators is a crucial research direction. Passenger comfort index f r It can be defined as:

[0054]

[0055] f i,j =ω1|a i,j |+ω2|jerki,j |

[0056] f r =max{f i,j}i=1,…,nj=1,…n i

[0057] In the formula: jerk i,j The impact rate of the power unit is expressed as the rate of change of acceleration, where ω1 and ω2 are weighting coefficients, and f i,j f serves as the evaluation index for the ride comfort of each power unit. r If f is the index of passenger comfort for the entire railway section, then r The smaller the amplitude, the better the overall ride comfort.

[0058] Step 12: The cost function of the control system can be designed as follows:

[0059]

[0060] in Operating costs represent the deviation from equilibrium and the differences in control variables. Describes the Euclidean norm. Terminal constraints can be used to limit the prediction range H. p The terminal state at the end ensures stability. To satisfy closed-loop stability, the terminal constraints must satisfy... Q, R, and P are positive definite weight matrices.

[0061] Step 13: Remember These represent the predicted values ​​of x and u at time t+k, respectively; This is the optimal state sequence. For the optimal input sequence, H p H c These represent the prediction time domain and control time domain of model predictive control, respectively. For ease of calculation, H is generally used... c ≤H p In summary, considering the safety constraints and the limited input range, minimizing the spacing deviation and speed difference as the objectives to improve control efficiency, the optimal control problem for the EMU based on the virtual coupler is as follows:

[0062]

[0063]

[0064] x i,j (t|t)=x i,j (t)

[0065]

[0066]

[0067] Step 14: Simulate and verify the designed multi-high-speed train distributed cooperative control algorithm on a computer. By setting the simulation environment and adjusting the controller design parameters, the cooperative operation control effect of the high-speed train group is improved. The optimized distributed cooperative control algorithm is then loaded into the Automatic Train Operation (ATO) onboard equipment, thereby realizing the cooperative operation control of the high-speed train group. The beneficial effects of adopting the above technical solution are as follows:

[0068] 1. This invention fully considers the unique characteristics of distributed power in EMU trains, treating each power unit as an intelligent agent and using couplers to connect two adjacent power units within the same EMU. Simultaneously, virtual couplers are used to connect different EMU trains, thus constructing a virtual coupler EMU structure. Through in-depth research on acceleration changes during EMU operation, we propose a more practical controller based on a third-order virtual coupler EMU. This innovative control strategy effectively solves problems such as excessive acceleration and acceleration oscillations, significantly improving passenger comfort.

[0069] 2. Compared with existing virtual coupler EMU control methods, this invention introduces more comprehensive safety considerations and avoids simplifying or ignoring safety constraints. We incorporate braking distance into the safety constraints of the virtual coupler and design an applicable distributed model predictive control (DMPC) algorithm to ensure its feasibility. This algorithm allows for maintaining a small distance between trains when the EMU is running at low speed, thereby ensuring the line's traffic capacity. When the train is running at high speed and an emergency occurs, the braking distance increases, effectively avoiding rear-end collisions and ensuring the safe operation of the train.

[0070] 3. Finally, through experiments, we successfully ensured that the virtual coupler displacement remained within a safe range and that each EMU could quickly and accurately track the desired speed curve. This innovative control method not only improved passenger comfort but also provided a reliable guarantee for the safe operation and efficient transportation of EMUs. Attached Figure Description

[0071] Figure 1 This is a flowchart of the virtual coupler EMU group collaborative operation control method of the present invention;

[0072] Figure 2 This is a structural diagram of a high-speed train.

[0073] Figure 3 For a train group system based on virtual couplers;

[0074] Figure 4 This is a graph showing the train group under initial disturbance according to an embodiment of the present invention;

[0075] Figure 5 This is a graph illustrating the simultaneous presence of initial disturbance and external interference in the high-speed train group of the present invention. Detailed Implementation

[0076] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. The following examples are used for...

[0077] This invention is described but not intended to limit its scope.

[0078] The flow chart of the virtual coupled high-speed train group cooperative operation control method of the present invention is as follows: Figure 1 As shown, the structure of the EMU is as follows: Figure 2 As shown, the principle of high-speed train group cooperative operation based on virtual couplers is as follows: Figure 3 As shown, the specific control method is as follows:

[0079] Step 1: The modeling of a single-train EMU is considered as consisting of multiple carriages connected by flexible couplers, which can be represented as an "elastic-damped" component. Its dynamic equation can be expressed as:

[0080]

[0081] In the formula, k i and d i These are the stiffness coefficient and damping constant of the coupler system, respectively.

[0082] Step 2: Considering the interference of the basic running resistance encountered by the train during operation, the unit basic running resistance during the operation of the EMU is given by the Davis equation:

[0083]

[0084] In the formula, c0, c1, and c2 are the basic operating drag coefficients, which are generally measured through wind tunnel experiments, v i Let be the velocity of power unit i.

[0085] Step 3: Considering passenger comfort requirements, the kinematic equations of the EMU (Electric Multiple Unit) subjected to basic running resistance disturbances are described as follows:

[0086]

[0087] In the formula,

[0088] Step 4: Real-time information exchange between trains is conducted through an inter-train wireless communication system. Due to limited wireless communication capabilities, high-speed trains can only communicate with other trains within the wireless communication range. For consecutive trains that can communicate with each other, assume that the exchange of operational information occurs between the first carriage of the following train and the last carriage of the preceding train. Let s i,j (t) represents the displacement of the j-th power unit of the i-th trainset. The neighborhood of the i-th trainset is defined as:

[0089]

[0090] In the formula: β is the vehicle-to-vehicle wireless communication radius.

[0091] Step 5: Inspired by the actual coupler connecting the EMU power units, the safety distance between two adjacent EMUs is abstracted into the concept of a "virtual coupler." The displacement of the virtual coupler can be described as:

[0092] s safe (t)=d L +d+hv i (t)

[0093] Where d L d is the length of the train set, h is the length of the virtual coupler. i These are parameters to be determined; the coupler includes a linear term, which will significantly reduce the safety distance.

[0094] s i-1 (t)-s i (t)-d L ≥s safe

[0095] Step 6: Based on the communication relationships between the train sets, the dynamic model of the train set group is as follows:

[0096]

[0097] in, For coordinated operation of multiple units (MMUs), if there is coupling between power unit q and power unit j... otherwise, Let v0 be the desired cruising speed of the EMU.

[0098] Step 7: According to the Taylor expansion, the linear dynamic equation around v0 is obtained as follows:

[0099]

[0100] Step 8: Define the state of the j-th power unit of train i as x i,j (t)=[Δs i,Δv i,j ,Δa i,j ] T Selecting the speed difference and acceleration difference of the power unit as output variables, the state equation of the EMU based on the virtual coupler can be written as:

[0101]

[0102] y i,j (t)=C i,j x i,j (t)

[0103] Where f is a linear function of the state variable and the input variable,

[0104] Step 9: Determine the constraint sets. The control constraint set and the safety constraint set are represented as follows:

[0105] Control constraint set:

[0106]

[0107] Safety constraints:

[0108]

[0109] in:

[0110] φ1(x i,j ) = s i-1 (t)-s i (t)-D min -D L

[0111] φ2(x i,j ) = v i,j (t)

[0112] φ3(x i,j ) = v max -v i,j (t)

[0113] φ4(x i,j ) = a i,j (t)

[0114] φ5(x i,j )=a1-a i,j (t)

[0115] Step 10: In this study, the goal is to achieve distributed optimal regulation of a single EMU based on couplers, and also distributed optimal regulation of a group of EMUs based on virtual couplers, within an algorithmic framework, while satisfying the various constraints mentioned above. One of these constraints is to minimize the speed difference between EMUs while ensuring that the virtual couplers connecting the power units are within a safe range, and to achieve stable operation with consistent speed in a balanced state.

[0116]

[0117] Step 11: Passenger comfort index f r It can be defined as:

[0118]

[0119] f i,j =ω1|a i,j |+ω2|jerk i,j |

[0120] f r =max{f i,j}i=1,…,nj=1,…n i

[0121] In the formula: jerk i,j The impact rate of the power unit is expressed as the rate of change of acceleration, where ω1 and ω2 are weighting coefficients, and f i,j f serves as the evaluation index for the ride comfort of each power unit. r If f is the index of passenger comfort for the entire railway section, then r The smaller the amplitude, the better the overall ride comfort.

[0122] Step 12: The cost function of the control system can be designed as follows:

[0123]

[0124] Step 13: Considering the safety constraints and the limited input range, minimizing the spacing deviation and speed difference is taken as the objective to improve control efficiency. The optimal control problem of the EMU based on the virtual coupler is as follows:

[0125]

[0126]

[0127] x i,j (t|t)=x i,j (t)

[0128]

[0129]

[0130] Step 14: Experiment with the designed distributed cooperative control algorithm for multiple high-speed trains. By setting the simulation environment and adjusting the controller parameters, the cooperative operation control of the high-speed train group is achieved. In the simulation, two EMU trains form an EMU group system. EMU 1 has 3 power units, and EMU 2 has 2 power units, simulating two common scenarios in cooperative train operation:

[0131] (1) Evaluation of the control performance of the method given an initial disturbance such as an initial velocity difference or a spacing error;

[0132] (2) Consider the control performance evaluation under mixed disturbances, including external disturbances that cause changes in the maneuverability of the leading train due to changes in speed limits and initial disturbances with initial speed differences.

[0133] Experiment 1: The main parameters of the EMU are shown in Table 1, the initial parameters are shown in Table 2, the controller parameters are shown in Table 3, and the comfort evaluation criteria are shown in Table 4.

[0134] Table 1 Main parameters of the EMU (Electric Multiple Unit)

[0135]

[0136] Table 2 Initial Parameters of EMU

[0137]

[0138] Table 3 Controller Parameters

[0139]

[0140] Table 4 Comfort Evaluation Indicators

[0141]

[0142] Set the simulation step size to 10ms and the simulation time to 100s.

[0143] Simulation results are as follows Figure 4-5 As shown

[0144] Through analysis Figure 4 The following conclusions can be drawn:

[0145] 1. As the speed of the EMU increases, the coupler will undergo a slight change before returning to an equilibrium state. The proposed method keeps the coupler displacement within a safe range, ensuring the safe operation of the EMU. The above results prove that the strategy designed in this invention has good control performance for trains with initial disturbances.

[0146] 2. The comfort jerk value calculated by the formula is 0.4377. As can be clearly seen from the data in Table 2, passengers will feel very comfortable under this condition.

[0147] 3. When the train speed finally reaches the expected value, we observe that the virtual coupler length converges to 150 meters, and the train runs safely with a smaller spacing, achieving high-density transportation.

[0148] Experiment 2 aims to study the control performance of the leading train under different maneuvers caused by external disturbances. The train performance is the same as in Experiment 1. To better illustrate the effectiveness of this algorithm, this experiment includes an initial disturbance, i.e., a speed difference between the trains; it is assumed that the speed limit of the trains will change abruptly, as shown below:

[0149]

[0150] The results are shown in the figure below. Through analysis... Figure 5 The following conclusions can be drawn:

[0151] 1. The proposed cooperative control method can maintain good speed tracking performance. Each train set runs at maximum acceleration. When the speed changes abruptly, the acceleration is within the allowable range and the speed tracks the reference speed relatively quickly.

[0152] 2. The comfort jerk is 0.504. As shown in Table 2, the comfort evaluation criteria indicate that the control method meets the comfort constraints.

[0153] 3. The proposed method keeps the coupler displacement within a safe range, ensuring the safe operation of the EMU. As the speed of the EMU increases, the coupler changes slightly from its original equilibrium state, and the coupler displacement returns to equilibrium. This indicates that the same train achieves consistent speed within a short period of time. During operation, the displacement of all couplers always varies between the pre-set safety values ​​and does not exceed the safety range, indicating that the control algorithm can handle mixed disturbances.

[0154] 4. Improved line capacity: As the speed of the EMU increases, when a sudden change in speed occurs, the virtual coupler error can quickly converge to 0. The initial length of the virtual coupler is 50m. As the speed of the EMU increases, in order to prevent collisions, the displacement of the virtual coupler gradually increases. When the speed of the EMU reaches 288km / h, the length of the virtual coupler reaches 250m. When the speed of the EMU is lower, the length of the virtual coupler will be compressed to ensure the line capacity.

[0155] 5. Under the control algorithm designed in this invention, the train coupler and the virtual coupler simultaneously meet the constraints. This strategy of dynamically adjusting the length of the virtual coupler can enhance the safety of high-speed train operation, ensure rapid response to speed changes, and avoid potential collisions. In addition, the flexible adjustment of the virtual coupler length optimizes the utilization capacity of the line and provides an efficient solution for traffic management of trains at different speeds.

[0156] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, technical solutions formed by replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A control method for high-density transportation of multi-mass EMU train groups based on virtual couplers, characterized in that, Includes the following steps: Step 1: The modeling of a single-unit EMU is considered to be composed of multiple carriages connected by flexible couplers. The EMU is subject to rolling resistance and aerodynamic drag. The power unit is connected by couplers and can be represented as an "elastic-damped" component. Its dynamic equation can be expressed as: In the formula, and These are the stiffness coefficient and damping constant of the coupler system, respectively. Step 2: Considering the interference of the basic running resistance encountered by the train during operation, the unit basic running resistance during the operation of the EMU is given by the Davis equation: In the formula, and The basic operating drag coefficient was measured through wind tunnel experiments; Step 3: Considering passenger comfort requirements, i.e., taking into account the rate of change of acceleration, the kinematic equations of the EMU are described as follows: In the formula, , ; Step 4: For consecutive trains that can communicate with each other, assume that the exchange of operational information occurs between the first carriage of the following train and the last carriage of the preceding train. Indicates the first The first EMU The displacement of the power unit, the first The neighborhood of a train is defined as: In the formula: The vehicle-to-vehicle wireless communication radius; Step 5: Based on the communication relationships between the train sets, the dynamic model of the train set group is as follows: in, , For the coordinated operation of high-speed trains, if the power unit and power unit There is coupling between them. ,otherwise, ;set up This is the desired cruising speed of the high-speed train; Step 6: Inspired by the actual coupler connecting the EMU power unit, the safety distance between two adjacent EMUs is abstracted into the concept of a "virtual coupler." The displacement of the virtual coupler can be described as: in The length of the EMU (Electric Multiple Unit). It is the length of the virtual coupler. These are parameters to be determined; the coupler includes a linear term, which will significantly reduce the safety distance. Step 7: According to the Taylor expansion, obtain the surrounding... The linear dynamic equation is: ； Step 8: Define the EMU (Electric Multiple Unit) The state of the j-th power unit is: in The deviation relative to the length d of the previous train and the virtual coupler can be expressed as: In the formula, The length of the EMU (Electric Multiple Unit). It is the length of the virtual coupler. Parameters to be determined; The speed difference between the power units can be expressed as: The acceleration difference between the power units can be written as: Assuming each power unit has the same mass, that is = Then there is , Choosing the speed difference and acceleration difference of the power unit as output variables, the state equation of the EMU based on the virtual coupler can be written as: Where f is a linear function of the state variable and the input variable, ; Step 9: Changes in speed limits caused by track and environmental conditions lead to changes in train cruising speed. For each train in the virtual coupled EMU, the speed limit constraint can be written as: ,in ,middle Speed ​​limits designed for high-speed trains. The maximum permissible speed is determined by the operating conditions of the line. The maximum permissible speed for safe operation of the EMU is calculated based on real-time information transmitted from the ground and the EMU's own performance. Changes in acceleration can affect passenger comfort, and the relevant constraints can be expressed as: In addition, the control output constraints of the EMU (Electric Multiple Unit) were considered: ,in For minimum control input and maximum control input, For ease of description, the following constraint set is used: Control constraint set: Safety constraints: in: ， ， ； Step 10: While ensuring the virtual coupler connecting the power unit is within a safe range, minimize the speed difference between the train sets and achieve stable operation with consistent speed in a balanced state, that is: This indicates that the train sets did not deviate from the expected spacing and there was no speed difference between adjacent trains. Step 11: In the design and operation of high-speed trains, fully considering the optimization of passenger comfort indicators is a crucial research direction. Passenger comfort indicators It can be defined as: In the formula: The impact rate of the power unit is expressed as the rate of change of acceleration. These are the weighting coefficients. The evaluation indexes for the ride comfort of each power unit, As an indicator of passenger comfort for the entire railway section, The smaller the amplitude, the better the overall ride comfort; Step 12: The cost function of the control system can be designed as follows: in Operating costs represent the deviation from equilibrium and the differences in control variables. Describes the Euclidean norm. Terminal constraints can be used to limit the prediction range. The terminal state at the end ensures stability. To satisfy closed-loop stability, the terminal constraints must satisfy... Q, R, and P are positive definite weight matrices. Step 13: Remember Represent Time for the first time and The predicted value; This is the optimal state sequence. For the optimal input sequence, These represent the prediction time domain and control time domain of model predictive control, respectively, for ease of calculation. In summary, considering the safety constraints and the limited input range, minimizing the spacing deviation and speed difference as the objectives to improve control efficiency, the optimal control problem for the EMU based on the virtual coupler is as follows: ； Solving the above equation yields the optimal control for high-density transportation of multi-mass EMU train groups with virtual couplers. Step 14: Simulate and verify the designed multi-high-speed train distributed cooperative control algorithm on a computer. By setting the simulation environment and adjusting the design parameters of the controller, the cooperative operation control effect of the high-speed train group reaches a good state. Load the train distributed cooperative control algorithm with adjusted parameters into the ATO on-board equipment of the Automatic Train Operation system to realize the cooperative operation control of the high-speed train group.

Images