Train cooperative control method based on speed curve interval optimization setting strategy

Abstract

The invention relates to the technical field of train cooperative control, in particular to a train cooperative control method based on a speed curve interval optimization setting strategy, and the method comprises the steps: building a train simple substance point dynamic feature model; according to the train simple substance point dynamic characteristic model, a train dynamic model is obtained and discretized; according to the discretized train dynamics model, optimizing a train tracking operation curve interval to obtain a train reference speed optimal interval; according to the train reference speed optimal interval, a leading train interval objective function and a following train interval objective function are established and optimized, and the optimal control acceleration is obtained to control the train. According to the maglev train operation curve interval optimization method provided by the invention, a continuous and limited optimal speed reference is provided for multi-train cooperation, and a layered cooperative control strategy is provided by adopting a set optimal speed interval, so that efficient, energy-saving and comfortable cooperative tracking operation of multiple maglev trains is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of train group collaborative optimization control methods, and in particular to a train collaborative control method based on a speed curve interval optimization setting strategy. Background Art

[0002] The concept of virtual train marshaling was first proposed by European scholars. Train-to-train communication replaces traditional physical connections between multiple trains, allowing multiple trains to track and run at the same speed and with small spacing, effectively improving rail transportation capacity. The collaborative optimization control of maglev train groups based on virtual marshaling is a research hotspot in the field of rail transportation optimization control.

[0003] Under the condition of close tracking of maglev trains, the operating states of each train unit are strongly coupled. When complex nonlinear disturbances occur, the train needs to adjust its speed frequently, resulting in the risk of failure of the set optimal target speed curve. At the same time, the braking characteristics of maglev trains are easily affected by the external environment. Frequent adjustment of train speed may cause the virtual marshaling maglev train to fail to ensure stable operation of the queue. The existing method of optimizing a single speed curve cannot meet the control requirements of marshaling trains under close tracking conditions. Therefore, it is necessary to carry out research on the optimization of train reference speed intervals. The prior art proposes a train separation model based on relative operation, which predicts the boundary of the running curve of the previous train and reduces the safe distance of the train. However, complex line conditions are not considered, and the model may not be able to adapt. The prior art also considers the traction braking characteristics and line conditions of high-speed trains, and uses a dual speed curve optimization method to set the train reference speed curve to reduce energy consumption. This method requires two optimizations, with large calculation amount and poor real-time performance, and cannot meet the needs of real-time control of close tracking of trains.

[0004] The maglev train adopts electromagnetic induction non-contact speed measurement mode and a hybrid braking method of electric braking and hydraulic braking. Under the interference of complex electromagnetic environment and environmental factors, the measurement and positioning accuracy is easily affected and the braking characteristics are highly nonlinear, which brings huge challenges to the precise and efficient coordinated control of the maglev train. Summary of the invention

[0005] The purpose of the present invention is to provide a train cooperative control method based on a speed curve interval optimization setting strategy, propose a maglev train operation curve interval optimization method, provide a continuous and limited optimal speed reference for multi-vehicle cooperation, adopt the set optimal speed interval, and propose a hierarchical cooperative control strategy to achieve efficient, energy-saving and comfortable cooperative tracking operation of multiple vehicles of the maglev train.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A train cooperative control method based on a speed curve interval optimization setting strategy, comprising:

[0008] Establish a single-particle dynamics characteristic model for trains;

[0009] According to the train single-particle dynamics characteristic model, a train dynamics model is obtained and discretized;

[0010] According to the discretized train dynamics model, the train tracking curve interval is optimized to obtain the optimal train reference speed interval;

[0011] According to the optimal interval of train reference speed, the leading train interval objective function and the following train interval objective function are established and optimized to obtain the optimal control acceleration to control the train.

[0012] Optionally, the train tracking operation curve interval is optimized to obtain the optimal train reference speed interval including:

[0013] According to the target parking point, a speed limit value of each point before the target parking point is obtained, and a speed limit curve is obtained according to the speed limit value of each point;

[0014] According to the speed limit curve, the maximum speed of the train and the line speed limit, an upper limit of the train reference speed is obtained;

[0015] According to the tracking efficiency evaluation index, the comfort evaluation index and the operation energy consumption evaluation index, the lower limit of the train reference speed is obtained;

[0016] The optimal interval of the train reference speed is obtained according to the upper limit of the train reference speed and the lower limit of the train reference speed.

[0017] Optionally, the upper limit of the train reference speed is:

[0018] ;

[0019] The lower bound of the train reference speed is:

[0020] ;

[0021] ;

[0022] Where V̅ is the upper limit of the train reference speed, is the maximum speed of the train, Limit the speed of the line. is the speed limit curve, is the lower limit of the train reference speed, , , They are tracking efficiency evaluation index, comfort evaluation index, and operation energy consumption evaluation index. is the minimum acceleration change of the i-th train at time t, is the acceleration change of the i-th train at time t, is the maximum acceleration change of the i-th train at time t, is the train speed, is the initial speed of the train, is the final speed of the train.

[0023] Optionally, establishing the leading train section objective function and the following train objective function includes:

[0024] Obtaining a discretized system model, and obtaining a control increment according to the discretized system model;

[0025] According to the control increment, a conventional rolling optimization objective function without interval constraints is obtained;

[0026] According to the optimal interval of train reference speed, the predicted value and interval distance are defined as , where k represents a discrete moment, ;

[0027] Determine interval relaxation factor : ,in, It represents the predicted speed value at time k+j in the future. To allow the prediction speed to exceed the interval boundary, j is the jth prediction step size;

[0028] According to the interval relaxation factor and the conventional rolling optimization objective function without interval constraints to obtain the interval optimization objective function;

[0029] According to the interval optimization objective function, the leading train interval objective function and the following train objective function are constructed respectively.

[0030] Optionally, constructing the leading train interval objective function according to the interval optimization objective function includes: selecting the midpoint of the optimal interval of the train reference speed as the leading train target tracking curve, and establishing the leading train interval objective function according to the interval optimization objective function.

[0031] Optionally, the leading train section objective function is optimized as follows:

[0032] ;

[0033] ;

[0034] in, is the leader train interval objective function, M is the total predicted step length based on interval constraints, is the speed of the leading train at time k, is the target value control item, is the control term for the deviation between the predicted value and the interval boundary, To control the incremental control term, , , is the weight coefficient, Indicates the maximum braking deceleration of the leading train; Indicates the maximum traction acceleration of the leading train; represents the control acceleration of the leading train at time k for the future time k+j, It is expressed as the target speed value at time k+j, It is expressed as the predicted speed value at time k+j in the future.

[0035] Optionally, constructing the following train section objective function includes: constructing the following train section objective function according to an expected distance and relative speed between the following train and the leading train.

[0036] Optionally, the objective function of the following train section is optimized as follows:

[0037] ;

[0038] ;

[0039] in, To optimize the objective function for following the train, , , are the tracking distance deviation between the train and the preceding vehicle, the weight of the tracking speed deviation and the control increment weight, represents the predicted value of the actual tracking distance between the i-th train and the i+1-th train at the future time k+j predicted at the current time k, represents the target value of the tracking distance between the i+1th train and the i+2th train at the future time k+j predicted at the current time k, represents the speed of the i-th train at the current time k and the predicted speed at the future time k+j, represents the speed of the i+1th train at the current time k and the predicted speed at the future time k+j, l i is the length of the i-th train.

[0040] The beneficial effects of the present invention are as follows: the present invention introduces the concept of reference speed interval, and by relaxing the speed point constraint, comprehensively tracks the efficiency, comfort and energy consumption multi-objectives to establish an optimization model, and generates a dynamic speed interval boundary. The upper layer plans the reference trajectory based on the interval constraint, and the lower layer designs the model prediction controller for precise tracking, forming a hierarchical collaborative framework, which not only ensures the overall coordination of the formation, but also takes into account the flexibility of single vehicle operation.

[0041] Compared with traditional optimization algorithms, this invention significantly reduces energy consumption while improving tracking efficiency, and controls the comfort index within a reasonable range. This invention effectively balances multi-objective conflicts through flexible speed intervals and hierarchical optimization mechanisms, and provides an intelligent control solution that takes into account safety, comfort and energy saving for high-density tracking operations of maglev trains. It has theoretical value and practical significance for promoting the intelligent development of low-speed and medium-speed maglev transportation in cities. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 This is a schematic diagram of the train hierarchical cooperative control principle of an embodiment of the present invention;

[0044] Figure 2 A comparison diagram of a target speed curve set by the target speed interval optimization method proposed in an embodiment of the present invention and a target speed curve obtained by the PSO method;

[0045] Figure 3 This is a comparison chart of tracking efficiency indicators of the interval optimization method and the PSO method according to an embodiment of the present invention;

[0046] Figure 4 This is a comparison chart of energy consumption between the interval optimization method and the PSO method in an embodiment of the present invention;

[0047] Figure 5 A train speed position diagram of the hierarchical cooperative control method, distributed model predictive control and fuzzy model predictive control proposed in an embodiment of the present invention;

[0048] Figure 6 A train speed error diagram of the hierarchical cooperative control method, distributed model predictive control and fuzzy model predictive control proposed in an embodiment of the present invention;

[0049] Figure 7 A train tracking spacing diagram of the hierarchical cooperative control method, distributed model predictive control and fuzzy model predictive control proposed in an embodiment of the present invention;

[0050] Figure 8 The present invention is a flow chart of a train cooperative control method based on a speed curve interval optimization setting strategy according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] like Figure 8 As shown, this embodiment provides a train cooperative control method based on a speed curve interval optimization setting strategy, including:

[0054] Establish a single-particle dynamics characteristic model for trains;

[0055] According to the train single-particle dynamics characteristic model, the train dynamics model is obtained and discretized;

[0056] According to the discretized train dynamics model, the train tracking curve interval is optimized to obtain the optimal train reference speed interval;

[0057] According to the optimal interval of train reference speed, the objective function of the leading train interval and the objective function of the following train interval are established and optimized to obtain the optimal control acceleration to control the train.

[0058] The research object of this embodiment is a virtual marshaled maglev train group. The marshaled train queue consists of Train composition, train coordination control framework such as Figure 1 As shown. Assuming that the internal interaction force of the train can be ignored, the single-particle dynamic characteristic model of the train is established here:

[0059] ;

[0060] Where i is the i-th train in the virtual formation, and represent the speed and acceleration of the i-th train at time t, respectively. is the speed of the i-th train at time t, is the control acceleration of the i-th train, is the acceleration of the i-th train caused by the basic resistance and additional resistance.

[0061] The train dynamics equations can be written in a more compact form as follows:

[0062] ;

[0063] in, for , The state vector composed of is the continuous state vector of the position and speed of the i-th train at time t; is the control acceleration of the i-th train, is the equivalent acceleration of the i-th train caused by external disturbance; A is the system matrix, B is the control input matrix, and C is the disturbance matrix. A, B, and C define the dynamic relationship between state, control input, and disturbance. The train state sampling is generally in discrete form, which is convenient for numerical optimization, so it is discretized as:

[0064] ;

[0065] in, represents the position of the i-th train at time k and speed The discrete state vector of The discrete state vector representing the position and velocity of the i-th train at time k+1; represents the control acceleration of the i-th train at time k; It represents the equivalent acceleration of the i-th train caused by the external disturbance at time k.

[0066] The goal of the leading train is to follow the reference trajectory, and the goal of each following train is to shorten the distance to the preceding train as much as possible while satisfying the safety constraints. The distance between trains in the formation must be greater than the safety distance required after braking, which can be defined as:

[0067] ;

[0068] in, is the position of train i at time k, is the position of train i+1 at time k, is the length of the i-th train. The safety distance that needs to be ensured when the train is stationary can be defined as:

[0069] ;

[0070] in, For safe parking margin, is the speed of train i at time k, is the speed of train i+1 at time k, is the deceleration rate of the i-th train during emergency braking, is the deceleration rate of the i+1th train during emergency braking. and The two parameters ensure that the distance between trains in a formation is greater than the safety distance required after braking. The safety distance, as a feedback signal generated by the speed reference interval, will correct the speed interval boundary in real time.

[0071] This embodiment adopts the reference speed interval method to relax the constraint of a single target speed point, thereby enhancing the flexibility of the control process. The optimal reference speed interval of the train is obtained by processing the multi-objective constraint problem. , displacement occurs at small velocity increments:

[0072] ;

[0073] in, , are the positions of the leading train at time k and k+1 respectively, , are the speeds of the leading train at time k and k+1 respectively, , are the accelerations of the leading train at time k and k+1 respectively.

[0074] Furthermore, the train tracking operation curve interval is optimized to obtain the optimal train reference speed interval including:

[0075] According to the target parking point, the speed limit value of each point before the target parking point is obtained, and the speed limit curve is obtained according to the speed limit value of each point;

[0076] Obtain the upper limit of the train reference speed according to the speed limit curve, the maximum train speed and the line speed limit;

[0077] According to the tracking efficiency evaluation index, the comfort evaluation index and the operation energy consumption evaluation index, the lower limit of the train reference speed is obtained;

[0078] According to the upper limit of the train reference speed and the lower limit of the train reference speed, the optimal interval of the train reference speed is obtained.

[0079] Specifically, after determining the target parking point, the speed limit value of each point ahead is inferred to obtain the speed limit curve The upper limit of the train reference speed should also take into account the maximum speed that the train can reach. , and line speed limit , in order to ensure safety, the upper limit of the train reference speed V̅ should take the minimum value of multiple speed limits, that is:

[0080] ;

[0081] The optimization effect of marshaling train tracking operation is generally evaluated from the aspects of tracking efficiency, comfort, and tracking operation energy consumption. In this embodiment, the lower bound of the train reference speed curve is obtained by optimizing various performance indicators.

[0082] ①Tracking efficiency evaluation indicators:

[0083] ;

[0084] ;

[0085] in, is the tracking distance between the i-th train and the following train, is the position of the i-th train, is the number of train sets, To track efficiency performance indicators, The smaller the value, the higher the tracking efficiency.

[0086] ②Comfort evaluation index:

[0087] ;

[0088] ;

[0089] in, , are the acceleration and acceleration change rate of the i-th train, , is the weighting coefficient, is the train i comfort performance index, is the comfort performance index, The smaller the value, the higher the comfort.

[0090] ③Operation energy consumption evaluation indicators:

[0091] ;

[0092] in, It is the total energy consumption evaluation index of the interval tracking train. The smaller the value, the lower the energy consumption. , are the running distance of train i in each iteration cycle and the total number of iteration cycles, is the energy consumption per unit distance of the i-th train. The lower bound of the train reference speed curve can be described as:

[0093] ;

[0094] ;

[0095] in, is the minimum acceleration change of the i-th train at time t, is the acceleration change of the i-th train at time t, is the maximum acceleration change of the i-th train at time t, is the train speed, is the initial speed of the train, is the final speed of the train.

[0096] Furthermore, establishing the leading train section objective function and the following train objective function includes:

[0097] Obtain a discretized system model, and obtain a control increment according to the discretized system model;

[0098] According to the control increment, a conventional rolling optimization objective function without interval constraints is obtained;

[0099] According to the optimal interval of train reference speed, the predicted value and interval distance are defined as , where k represents a discrete moment, k=0,1,2…;

[0100] Determine interval relaxation factor : ,in, It represents the predicted speed value at time k+j in the future. To allow the prediction speed to exceed the interval boundary, j is the jth prediction step size;

[0101] According to the interval relaxation factor and the conventional rolling optimization objective function without interval constraints to obtain the interval optimization objective function;

[0102] According to the interval optimization objective function, the leading train interval objective function and the following train objective function are constructed respectively.

[0103] Specifically, this embodiment proposes a hierarchical collaborative control method, and the design of the hierarchical control framework is as follows: Figure 1 As shown, the specific implementation steps include:

[0104] The predictive controller is designed at the lower level to track the trajectory of the upper level planning. The discretized system equation can be expressed as:

[0105] ;

[0106] Define the state increment:

[0107] ;

[0108] Define the control increment:

[0109] ;

[0110] in, is the predicted state vector for the next moment k+1, which is determined by the current state and control acceleration Generated by equation of state; is the state vector (position, velocity) at the current time k; is the control acceleration of k at the current moment; is the system output at the current time k.

[0111] The discretized system equation does not include disturbance terms. It more completely includes the state equation and the output equation. It is a discretized equation obtained based on the strict discretization method, and by defining an incremental model to focus on the changes in state and control, it can provide a smoother response.

[0112] Then the predicted output of the incremental control form can be expressed as:

[0113] ;

[0114] Without interval constraints, the conventional rolling optimization objective function is for:

[0115] ;

[0116] In the formula, is the total prediction step length without interval constraints, j is the jth prediction step length, Output for the next moment in the rolling optimization objective function The predicted value of is the target value, To control the acceleration increment, is the weight coefficient. Based on the speed interval boundary , the distance between the predicted value and the interval is defined as:

[0117] ;

[0118] To obtain the smallest , define the interval relaxation factor :

[0119] ;

[0120] Find the smallest When , we can find the minimum The interval optimization objective function can be transformed into:

[0121] ;

[0122] Where M is the total prediction step size based on the interval constraint.

[0123] Furthermore, according to the interval optimization objective function, constructing the leading train interval objective function includes: selecting the midpoint of the optimal interval of the train reference speed as the leading train target tracking curve, and establishing the leading train interval objective function according to the interval optimization objective function.

[0124] Specifically, the midpoint of the interval is taken as the target tracking curve of the leading train:

[0125] ;

[0126] Establishing the objective function of the leading train section :

[0127] ;

[0128] In the formula, is the target value control item, It is expressed as the predicted speed value at the future time k+j at the available time; It is expressed as the target speed value at time k+j; It is expressed as the amount of slack that allows the predicted speed to exceed the interval boundary; is the control item for the deviation between the predicted value and the interval boundary; Expressed as the control acceleration increment, is the control term for controlling the acceleration increment, , , is the weight coefficient.

[0129] The leading train interval constraint rolling optimization problem can be described as:

[0130] ;

[0131] in, is the speed of the leading train at time k; Indicates the maximum braking deceleration of the leading train; Indicates the maximum traction acceleration of the leading train, and Used to limit The change range of the acceleration is limited to avoid the sharp fluctuation of the control acceleration and ensure the smoothness of the dynamic response of the train; It represents the control acceleration of the leading train at time k for the future time k+j.

[0132] Furthermore, constructing the train following section objective function includes: constructing the train following section objective function according to the expected distance and relative speed between the following train and the leading train.

[0133] Specifically, the goal of following a train is to maintain the desired distance from the preceding train and to minimize the relative speed with the preceding train to ensure train synchronization. The following train optimization objective function J is established: F :

[0134] ;

[0135] In summary, the train following objective function can be described as:

[0136] ;

[0137] in, , , They are the tracking distance deviation, tracking speed deviation weight and control increment weight of the following train and the leading train. The tracking distance deviation weight can adjust the priority of speed tracking, the tracking speed deviation weight can control the tolerance to speed, and the control increment weight can suppress the fluctuation of acceleration and optimize passenger comfort to a certain extent. represents the predicted value of the actual tracking distance between the i-th train and the i+1-th train at the future time k+j predicted at the current time k, represents the target value of the tracking distance between the i+1th train and the i+2th train at the future time k+j predicted at the current time k, represents the speed of the i-th train at the current time k and the predicted speed at the future time k+j, It represents the speed of the i+1th train at the current time k and predicted at the future time k+j.

[0138] Specifically, the upper control obtains the optimal speed range of the train based on safety constraints and the establishment of a multi-objective optimization problem. The lower-level control first establishes the state space equation based on the discretized train dynamics model to complete the construction of the prediction model. In each control cycle, based on the current state To predict the state trajectory under the future step length and generate the control sequence; then, when designing the objective function, the weights of the tracking distance deviation, the tracking speed deviation and the control increment weight are included, and the weights are dynamically adjusted according to the real-time operation status, so that the priority of the multi-objective optimization problem is adaptive to the scene, and the interval relaxation factor is introduced Transform the speed range constraint into Soft constraints avoid the problem of being unable to search for the optimal solution due to disturbances and improve robustness; ultimately solving the optimal control acceleration The upper layer transmits the optimal speed range and the running track of the preceding vehicle to the lower layer. The lower layer tracks the actual speed and the actual tracking distance in real time and feeds them back to the upper layer. The upper layer re-optimizes the speed range based on the feedback and continuously iterates the optimization until convergence. The upper and lower layer collaborative mechanism forms a closed loop of "planning-tracking-feedback", providing an efficient and safe solution for high-density tracking of marshaled maglev trains.

[0139] The method of this embodiment is verified and analyzed below:

[0140] Based on the on-site operation data and train characteristic parameters of a medium- and low-speed maglev sightseeing express line, a maglev train multi-car marshaling tracking operation scenario was constructed on the MATLAB / Simulink simulation platform. Test experiments were carried out in this simulation environment to verify the effectiveness of the proposed target speed range optimization method and hierarchical collaborative control strategy. The experimental design and results analysis are as follows.

[0141] (1) Verification of operation curve interval optimization method:

[0142] The initial position of the marshaling train (unit: m) is set to: s1=60, s2=30, s3=0, and the target speed curve is set by the target speed interval optimization method proposed in this embodiment, and compared with the target speed curve obtained by the PSO method, as shown in FIG. Figure 2 As shown in Figure 2. A comparative analysis is conducted based on three key performance indicators: tracking efficiency, comfort, and energy consumption. Figure 3 As shown in the figure, the average tracking spacing of the curve generated by interval optimization is 50.03m, and the average tracking spacing of the curve generated by the PSO method is 50.33m. The tracking efficiency of interval optimization is improved by 0.61% compared with that of PSO.

[0143] From the comfort comparison in Table 1, it can be seen that the maximum comfort index of the PSO curve is 1.20, which is beyond the comfort range (>1.0). The method proposed in this embodiment controls the maximum value to 0.95, ensuring that the riding effect is within the comfortable range. It can be seen that the method in this embodiment is effective in improving riding comfort.

[0144] Table 1

[0145]

[0146] like Figure 4 As shown in the figure, the energy consumption of the curve generated by interval optimization is 17.499KW.h, and the energy consumption of the curve generated by the PSO method is 17.993KW.h. The energy consumption of interval optimization is reduced by 2.74% compared with the PSO method.

[0147] (2) Verification of hierarchical collaborative control method:

[0148] The three maglev trains are taken as the research object, with the initial positions (m): s1=60, s2=30, s3=0, and the initial speeds (m / s) are all set to 0. The hierarchical cooperative control method proposed in this embodiment is used to perform multi-train tracking operation control, and the simulation control results of the distributed model predictive control (DMPC) and fuzzy model predictive control (Fuzzy-MPC) are compared. The quantitative simulation comparison results are shown in Figure 2. Figure 5-Figure 7 shown.

[0149] ①Dynamic characteristics analysis:

[0150] Figure 5 This is the time displacement diagram of the train formation. There is no intersection during the tracking process of the three trains, indicating that there is no collision. Figure 6 As shown, the standard deviation of the speed error of the hierarchical cooperative control of this embodiment is 0.12 m / s, which is 52% lower than that of DMPC (0.25 m / s), highlighting the dynamic tracking accuracy of the method of this embodiment. Figure 7 It shows that the layered cooperative control method has the smallest tracking interval fluctuation. The layered method reduces the fluctuation amplitude of the tracking interval by 37%, shortens the steady-state convergence time of the marshaling coordination to 45s, and can enable the marshaling train to reach the coordinated operation state more quickly.

[0151] ② Comprehensive performance evaluation:

[0152] As shown in Table 2, the comparison of hierarchical collaborative control and DMPC control indicators, the average comfort and maximum comfort of hierarchical collaborative control are better than DMPC and FuzzyMPC. The average comfort index of hierarchical collaborative control is 0.62, which is better than DMPC (0.85) and Fuzzy-MPC (0.78). The total energy consumption of the method in this embodiment is reduced to 16.8 kW.h, which saves 5.2%~8.7% compared with the comparison method. The tracking efficiency of the three control methods is slightly different. The standard deviation of the average spacing of the method in this embodiment is only 0.45 m, which is significantly optimized compared with DMPC (0.82m).

[0153] Table 2

[0154]

[0155] This embodiment proposes a hierarchical collaborative control method based on speed interval optimization, breaking through the limitations of existing research, innovatively introducing the concept of reference speed interval, and by relaxing the speed point constraints, comprehensively tracking efficiency, comfort and energy consumption to establish an optimization model and generate dynamic speed interval boundaries. The upper layer plans the reference trajectory based on the interval constraints, and the lower layer designs the model predictive controller for precise tracking, forming a hierarchical collaborative framework that not only ensures the overall coordination of the formation, but also takes into account the flexibility of single vehicle operation.

[0156] Compared with traditional optimization algorithms, the method of this embodiment significantly reduces energy consumption while improving tracking efficiency, and controls the comfort index within a reasonable range. The method of this embodiment effectively balances multi-objective conflicts through flexible speed intervals and hierarchical optimization mechanisms, and provides an intelligent control solution that takes into account safety, comfort and energy saving for high-density tracking operations of maglev trains. It has theoretical value and practical significance for promoting the intelligent development of low-speed and medium-speed maglev transportation in cities.

[0157] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A train cooperative control method based on speed curve interval optimization setting strategy, characterized in that: include: Establish a single-particle dynamics characteristic model for trains; According to the train single-particle dynamics characteristic model, a train dynamics model is obtained and discretized; According to the discretized train dynamics model, the train tracking curve interval is optimized to obtain the optimal train reference speed interval; According to the optimal interval of train reference speed, the leading train interval objective function and the following train interval objective function are established and optimized to obtain the optimal control acceleration to control the train.

2. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 1 is characterized in that: Optimize the train tracking curve interval to obtain the optimal train reference speed interval including: According to the target parking point, a speed limit value of each point before the target parking point is obtained, and a speed limit curve is obtained according to the speed limit value of each point; According to the speed limit curve, the maximum speed of the train and the line speed limit, an upper limit of the train reference speed is obtained; According to the tracking efficiency evaluation index, the comfort evaluation index and the operation energy consumption evaluation index, the lower limit of the train reference speed is obtained; The optimal interval of the train reference speed is obtained according to the upper limit of the train reference speed and the lower limit of the train reference speed.

3. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 2 is characterized in that: The upper limit of the train reference speed is: ； The lower bound of the train reference speed is: ； ； Where V̅ is the upper limit of the train reference speed, is the maximum speed of the train, Limit the speed of the line. is the speed limit curve, is the lower limit of the train reference speed, , , They are tracking efficiency evaluation index, comfort evaluation index, and operation energy consumption evaluation index. is the minimum acceleration change of the i-th train at time t, is the acceleration change of the i-th train at time t, is the maximum acceleration change of the i-th train at time t, is the train speed, is the initial speed of the train, is the final speed of the train.

4. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 3 is characterized in that: Establishing the leading train section objective function and the following train objective function includes: Obtaining a discretized system model, and obtaining a control increment according to the discretized system model; According to the control increment, a conventional rolling optimization objective function without interval constraints is obtained; According to the optimal interval of train reference speed, the predicted value and interval distance are defined as , where k represents a discrete moment, ; Determine interval relaxation factor : ,in, It represents the predicted speed value at time k+j in the future. To allow the prediction speed to exceed the interval boundary, j is the jth prediction step size; According to the interval relaxation factor and the conventional rolling optimization objective function without interval constraints to obtain the interval optimization objective function; According to the interval optimization objective function, the leading train interval objective function and the following train objective function are constructed respectively.

5. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 4 is characterized in that: According to the interval optimization objective function, constructing the leading train interval objective function includes: selecting the midpoint of the optimal interval of the train reference speed as the leading train target tracking curve, and establishing the leading train interval objective function according to the interval optimization objective function.

6. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 4 is characterized in that: The objective function of the leading train section is optimized as follows: ； ； in, is the leader train interval objective function, M is the total predicted step length based on interval constraints, is the speed of the leading train at time k, is the target value control item, is the control term for the deviation between the predicted value and the interval boundary, To control the incremental control term, , , is the weight coefficient, Indicates the maximum braking deceleration of the leading train, Indicates the maximum traction acceleration of the leading train, represents the control acceleration of the leading train at time k for the future time k+j, It is expressed as the target speed value at time k+j, It is expressed as the predicted speed value at time k+j in the future.

7. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 1 is characterized in that: Constructing the following train section objective function includes: constructing the following train section objective function according to the expected distance and relative speed between the following train and the preceding train.

8. The train cooperative control method based on speed curve interval optimization setting strategy according to claim 6 is characterized in that: The objective function of the following train section is optimized as follows: ； ； in, To optimize the objective function for following the train, , , are the tracking distance deviation between the train and the preceding vehicle, the weight of the tracking speed deviation and the control increment weight, represents the predicted value of the actual tracking distance between the i-th train and the i+1-th train at the future time k+j predicted at the current time k, represents the target value of the tracking distance between the i+1th train and the i+2th train at the future time k+j predicted at the current time k, represents the speed of the i-th train at the current time k and the predicted speed at the future time k+j, represents the speed of the i+1th train at the current time k and the predicted speed at the future time k+j, l i is the length of the i-th train.

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