A train collaborative control method based on a speed curve interval optimization setting strategy

Abstract

The present invention relates to the technical field of train cooperative control, and particularly to a train cooperative control method based on an optimized setting strategy for speed curve intervals, including: establishing a single-mass-point dynamic characteristic model of a train; obtaining a train dynamic model according to the single-mass-point dynamic characteristic model of the train and discretizing it; optimizing the train tracking operation curve interval according to the discretized train dynamic model to obtain the optimal interval of the train reference speed; establishing an interval objective function for the leading train and an interval objective function for the following train according to the optimal interval of the train reference speed and optimizing them to obtain the optimal control acceleration to control the train. The present invention proposes an optimized method for the operation curve interval of a maglev train, provides a continuous and finite optimal speed reference for multi-train cooperation, adopts the set optimal speed interval, and proposes a hierarchical cooperative control strategy to achieve efficient, energy-saving, and comfortable cooperative tracking operation of multiple maglev trains.

Description

Technical Field

[0001] The present invention relates to the technical field of collaborative optimization control methods for train groups, and particularly to a train collaborative control method based on an optimal setting strategy for speed curve intervals. Background Art

[0002] The concept of virtual train formation was first proposed by European scholars. Multiple trains communicate vehicle-to-vehicle to replace traditional physical connections, enabling multiple trains to run in close pursuit at the same speed with small spacings, thereby effectively improving the rail transit transportation capacity. The collaborative optimization control of maglev train groups based on virtual formation is a research hotspot in the current field of rail transit optimization control.

[0003] Under the condition of close pursuit of maglev trains, the operating states of each train unit are strongly coupled. When complex non-linear disturbances occur, the trains need to frequently adjust their speeds, resulting in a risk of failure for the set optimal target speed curve. At the same time, the braking characteristics of maglev trains are easily affected by the external environment. Frequent speed adjustments of maglev trains may cause the virtual formation of maglev trains to be unable to ensure stable queue operation. Existing methods for optimizing a single speed curve cannot meet the control requirements of formation trains under close pursuit conditions. Therefore, it is necessary to conduct research on the optimization of the train reference speed interval. The existing technology has proposed a train separation model based on relative operations to predict the operating curve boundary of the previous train, reducing the train safety distance. However, complex line conditions are not considered, and the model may not be adaptable. The existing technology also considers the traction and braking characteristics of high-speed trains and line conditions, 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 a large amount of calculation and poor real-time performance, and cannot meet the requirements of real-time control for close pursuit of trains.

[0004] Maglev trains use an electromagnetic induction non-contact speed measurement mode and a hybrid braking method of electric braking and hydraulic braking. Under the interference of complex electromagnetic environments and the influence of environmental factors, the measurement and positioning accuracy are easily affected, and the braking characteristics are highly non-linear, posing a huge challenge to the precise and efficient collaborative control of maglev trains. Summary of the Invention

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

[0006] To achieve the above purpose, the present invention provides the following solution:

[0007] A train collaborative control method based on an optimal setting strategy for speed curve intervals, comprising:

[0008] Establish a single-mass-point dynamic characteristic model of the train;

[0009] According to the single-mass-point dynamic characteristic model of the train, obtain the train dynamic model and discretize it;

[0010] According to the discretized train dynamic model, optimize the train tracking operation curve interval to obtain the optimal interval of the train reference speed;

[0011] According to the optimal interval of the train reference speed, establish the leading train interval objective function and the following train interval objective function and optimize them to obtain the optimal control acceleration to control the train.

[0012] Optionally, optimizing the train tracking operation curve interval to obtain the optimal interval of the train reference speed includes:

[0013] According to the target stopping point, obtain the speed limit value of each point before the target stopping point, and according to the speed limit value of each point, obtain the speed limit curve;

[0014] According to the speed limit curve, the maximum train speed and the line speed limit, obtain the upper bound of the train reference speed;

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

[0016] According to the upper bound of the train reference speed and the lower bound of the train reference speed, obtain the optimal interval of the train reference speed.

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

[0018] ;

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

[0020] ;

[0021] ;

[0022] Among them, \(\overline{V}\) is the upper bound of the train reference speed, is the maximum train speed, is the line speed limit, is the speed limit curve, is the lower bound of the train reference speed, , , are the tracking efficiency evaluation index, the comfort evaluation index, and the operation energy consumption evaluation index respectively, 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 interval objective function and the following train objective function includes:

[0024] Obtain the discretized system model, and according to the discretized system model, obtain the control increment;

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

[0026] According to the optimal interval of the train reference speed, define the predicted value and the interval distance as , where k represents the discrete time, ;

[0027] Determine the interval relaxation factor : , where represents the predicted speed value at time k for the future time k + j, is the relaxation amount allowing the predicted speed to exceed the interval boundary, and j is the j-th prediction step;

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

[0029] According to the interval optimization objective function, construct the leading train interval objective function and the following train objective function 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, optimizing the leading train interval objective function to:

[0032] ;

[0033] ;

[0034] where is the leading train interval objective function, M is the total prediction step based on interval constraints, is the speed of the leading train at time k, is the target value control item, is the deviation control item of the predicted value and the interval boundary, is the control increment control item, , , are the weight coefficients, represents the maximum braking deceleration of the leading train; represents 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, represents the target speed value at time k + j, represents the predicted speed value at time k for the future time k + j.

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

[0036] Optionally, optimizing the following train interval objective function is:

[0037] ;

[0038] ;

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

[0040] The beneficial effects of the present invention are as follows: The present invention introduces the concept of a reference speed interval, relaxes the speed point constraint, establishes an optimization model by integrating multiple objectives of tracking efficiency, comfort, and energy consumption, and generates a dynamic speed interval boundary. The upper layer plans the reference trajectory based on the interval constraint, and the lower layer designs a model predictive controller to accurately track, 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, the present invention significantly reduces energy consumption while improving the tracking efficiency, and controls the comfort index within a reasonable range. Through the flexible speed interval and hierarchical optimization mechanism, the present invention effectively balances multi-objective conflicts, provides an intelligent control solution that takes into account safety, comfort and energy conservation for the high-density tracking operation of maglev trains, and has theoretical value and practical significance for promoting the intelligent development of urban medium and low-speed maglev transportation. Description of the Drawings

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0043] Figure 1 It is the schematic diagram of train hierarchical collaborative control for the embodiment of the present invention;

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

[0045] Figure 3 It is the comparison diagram of the tracking efficiency indexes of the interval optimization method and the PSO method in the embodiment of the present invention;

[0046] Figure 4 It is the comparison diagram of energy consumption between the interval optimization method and the PSO method in the embodiment of the present invention;

[0047] Figure 5 It is the train speed-position diagram of the hierarchical collaborative control method proposed in the embodiment of the present invention, the distributed model predictive control and the fuzzy model predictive control;

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

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

[0050] Figure 8 It is the flow chart of a train collaborative control method based on the speed curve interval optimization setting strategy in the embodiment of the present invention. Detailed Embodiments

[0051] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0052] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

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

[0054] Establish a single-mass-point dynamic characteristic model of the train;

[0055] According to the single-mass-point dynamic characteristic model of the train, obtain the train dynamic model and discretize it;

[0056] According to the discretized train dynamic model, optimize the train tracking operation curve interval to obtain the optimal interval of the train reference speed;

[0057] According to the optimal interval of the train reference speed, establish the interval objective function of the leading train and the interval objective function of the following train and optimize them to obtain the optimal control acceleration to control the train.

[0058] The research object of this embodiment is the maglev group train in virtual formation. The formation train queue consists of trains. The cooperative control framework of the formation train is as Figure 1 shown. Assuming that the internal interaction force of the train can be ignored, a single-mass-point 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 generated by the i-th train due to the basic resistance and additional resistance.

[0061] The train dynamic equation can be written in the following more compact form:

[0062] ;

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

[0064] ;

[0065] wherein, represents the discrete state vector of the position and speed of the i-th train at time k, representing the discrete state vector of the position and speed of the i-th train at time k + 1; represents the control acceleration of the i-th train at time k; represents the equivalent acceleration generated by the external disturbance on the i-th train at time k.

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

[0067] ;

[0068] wherein, is the position of train i at time k, is the position of train i + 1 at time k, being the length of the i-th train. is the safety distance to be guaranteed when the train is stationary, which can be defined as:

[0069] ;

[0070] wherein, is the safety stop margin, is the speed of train i at time k, is the speed of train i + 1 at time k, is the emergency braking deceleration rate of the i-th train, is the emergency braking deceleration rate of the i + 1-th train. and Two parameters constitute the distance between trains in the formation, ensuring that it is greater than the required safety distance after braking. As a feedback signal for generating the speed reference interval, the safety distance will correct the speed interval boundary in real time.

[0071] In this embodiment, the method of using the reference speed interval is adopted to relax the constraint of a single target speed point and enhance the flexibility of the control process. The optimal interval of the train reference speed is obtained by dealing with the multi-objective constraint problem. Assume the running state of the leading train , and the displacement occurs under a small speed increment:

[0072] ;

[0073] Among them, , are the positions of the leading train at times k and k + 1 respectively, , are the speeds of the leading train at times k and k + 1 respectively, , are the accelerations of the leading train at times k and k + 1 respectively.

[0074] Furthermore, optimizing the train tracking operation curve interval to obtain the optimal interval of the train reference speed includes:

[0075] According to the target stopping point, obtain the speed limit value of each point before the target stopping point, and according to the speed limit value of each point, obtain the speed limit curve;

[0076] According to the speed limit curve, the maximum train speed and the line speed limit, obtain the upper bound of the train reference speed;

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

[0078] According to the upper bound of the train reference speed and the lower bound of the train reference speed, obtain the optimal interval of the train reference speed.

[0079] Specifically, after determining the target stopping point, the speed limit value of each point ahead is deduced backward to obtain the speed limit curve . The upper bound of the train reference speed also needs to consider the maximum train speed , as well as the line speed limit . To ensure safety, the upper bound V̅ of the train reference speed should take the minimum value of multiple speed limits, that is:

[0080] ;

[0081] The problem of following running of formation trains is generally evaluated for the optimization effect from several aspects such as following efficiency, comfort, and following running energy consumption. In this embodiment, the lower bound of the reference speed curve of the train is obtained by optimizing each performance index.

[0082] ① Following efficiency evaluation index:

[0083] ;

[0084] ;

[0085] Among them, is the following spacing between the i-th train and the following train, is the position of the i-th train, is the number of train formations, is the following efficiency performance index, The smaller the value, the higher the following efficiency.

[0086] ② Comfort evaluation index:

[0087] ;

[0088] ;

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

[0090] ③ Running energy consumption evaluation index:

[0091] ;

[0092] Among them, is the total energy consumption evaluation index of the following trains in the section. The smaller the value, the smaller the energy consumption. , are respectively the running distance of train i in each iteration period and the total number of iteration periods, is the unit distance energy consumption of the i-th train. The solution of the lower bound of the reference speed curve of the train can be described as:

[0093] ;

[0094] ;

[0095] Among them, 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 train speed, is the final train speed.

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

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

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

[0099] According to the optimal interval of the train reference speed, define the predicted value and the interval distance as , where k represents the discrete time, k = 0, 1, 2...;

[0100] Determine the interval relaxation factor : , where represents the predicted speed value at time k for the future time k + j, is the relaxation amount allowing the predicted speed to exceed the interval boundary, and j is the j-th prediction step;

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

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

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

[0104] Design a predictive controller in the lower layer to track the trajectory planned by the upper layer. The discretized system equation can be expressed as:

[0105] ;

[0106] Define the state increment:

[0107] ;

[0108] Define the control increment:

[0109] ;

[0110] Among them, is the predicted state vector at the next moment k+1, which is generated from the current state and the control acceleration through the state equation; is the state vector (position, velocity) at the current moment k; is the control acceleration at the current moment k; is the system output at the current moment k.

[0111] The discretized system equation does not contain the disturbance term. It more completely includes the state equation and the output equation. It is a discretized equation obtained based on a strict discretization method. And by defining the incremental model to focus on the change amounts of the state and the control, it can provide a smoother response.

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

[0113] ;

[0114] In the case without interval constraints, the conventional rolling optimization objective function is:

[0115] ;

[0116] In the formula, is the total predicted step length without interval constraints, j is the jth predicted step length, is the predicted value of the output at the next moment in the rolling optimization objective function, is the target value, is the control acceleration increment, is the weight coefficient. Based on the velocity interval boundary , the predicted value and the interval distance are defined as:

[0117] ;

[0118] To obtain the minimum , the interval relaxation factor is defined as:

[0119] ;

[0120] When obtaining the minimum , the minimum can be obtained. The interval optimization objective function can be changed to:

[0121] ;

[0122] Among them, M is the total predicted step length under interval constraints.

[0123] Furthermore, according to the interval optimization objective function, the construction of 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, taking the midpoint of the interval as the leading train target tracking curve:

[0125] ;

[0126] Establishing the leading train interval objective function :

[0127] ;

[0128] In the formula, is the target value control term, represents the predicted speed value at time k + j for future time; represents the target speed value at time k + j; represents the relaxation amount allowing the predicted speed to exceed the interval boundary; is the control term for the deviation between the predicted value and the interval boundary; represents the control acceleration increment, is the control term for the control acceleration increment, , , are the weight coefficients.

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

[0130] ;

[0131] Among them, is the speed of the leading train at time k; represents the maximum braking deceleration of the leading train; represents the maximum traction acceleration of the leading train, and are used to limit the change range to avoid violent fluctuations in the control acceleration and ensure the smoothness of the train's dynamic response; represents the control acceleration of the leading train at time k for future time k + j.

[0132] Furthermore, the construction of the following train interval objective function includes: constructing the following train interval objective function according to the expected distance and relative speed between the following train and the preceding train.

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

[0134] ;

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

[0136] ;

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

[0138] Specifically, the upper-layer control obtains the optimal speed range of the train based on safety constraints and establishing a multi-objective optimization problem ; The lower-layer control first establishes a 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 at the future time step to generate a control sequence; Then when designing the objective function, the weights of the tracking distance deviation, the tracking speed deviation, and the control increment are incorporated, and the weights are dynamically adjusted according to the real-time operating state, making the priority of the multi-objective optimization problem adapt to the scenario, and introducing an interval relaxation factor to transform the speed range constraint into a soft constraint, avoiding the problem of being unable to search for the optimal solution caused by disturbances, and improving the robustness; Finally, the optimal control acceleration The upper layer transmits the optimal speed interval and the running trajectory of the leading vehicle to the lower layer. The lower layer tracks in real time and feeds back the actual speed and the actual tracking distance to the upper layer. The upper layer re-optimizes the speed interval based on the feedback and continuously iterates and optimizes until convergence. The upper and lower layer coordination mechanism forms a closed loop of "planning - tracking - feedback", providing an efficient and safe solution for the high-density tracking of formation maglev trains.

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

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

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

[0142] Set the initial positions (unit: m) of the formation trains as: s1 = 60, s2 = 30, s3 = 0. Use the target speed interval optimization method proposed in this embodiment to set the target speed curve and compare it with the target speed curve obtained by the PSO method, as Figure 2 shown. Comparative analysis is carried out from three key performance indicators: tracking efficiency, comfort, and energy consumption. As Figure 3 shown, the average tracking distance of the curve generated by interval optimization is 50.03 m, and the average tracking distance of the curve generated by the PSO method is 50.33 m. The tracking efficiency of interval optimization is 0.61% higher than that of PSO.

[0143] As can be seen from the comfort comparison in Table 1, the maximum comfort index of the PSO curve, 1.20, has exceeded the comfortable range (>1.0). The method proposed in this embodiment controls the maximum value within 0.95, ensuring that the riding effect is within the comfortable range. It can be seen that the method of this embodiment has a good effect in improving riding comfort.

[0144] Table 1

[0145]

[0146] As Figure 4 shown, the energy consumption of the curve generated by interval optimization is 17.499 KW·h, and the energy consumption of the curve generated by the PSO method is 17.993 KW·h. The energy consumption of interval optimization is 2.74% lower than that of the PSO method.

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

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

[0149] ① Dynamic characteristic analysis:

[0150] Figure 5 This is the time - displacement diagram of the formation train. There is no intersection during the tracking process of the three trains, indicating that no collision occurs. As Figure 6 shown, the standard deviation of the speed error of the hierarchical collaborative control in 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 in this embodiment. Figure 7 It shows that the hierarchical collaborative control method has the smallest fluctuation in the tracking distance. The hierarchical method reduces the fluctuation amplitude of the tracking distance by 37%, and the steady - state convergence time of the formation collaboration is shortened to 45 s, enabling the formation train to reach the collaborative operation state faster.

[0151] ② Comprehensive performance evaluation:

[0152] As shown in Table 2, the comparison of control indicators between hierarchical collaborative control and DMPC, the average comfort and maximum comfort of hierarchical collaborative control are better than those of DMPC and FuzzyMPC. The average comfort index of hierarchical collaborative control is 0.62, which is better than that of 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, saving 5.2% - 8.7% compared with the comparative methods. The tracking efficiencies of the three control methods are relatively close. The standard deviation of the average distance of the method in this embodiment is only 0.45 m, which is significantly optimized compared with DMPC (0.82 m).

[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. The concept of a reference speed interval is innovatively introduced. By relaxing the speed - point constraints, an optimization model is established by integrating multiple objectives of tracking efficiency, comfort, and energy consumption to generate the boundary of the dynamic speed interval. The upper layer plans the reference trajectory based on interval constraints, and the lower layer designs a model predictive controller to accurately track, forming a hierarchical collaborative framework that not only ensures the overall collaboration 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 the tracking efficiency, and controls the comfort index within a reasonable range. Through the flexible speed range and hierarchical optimization mechanism, the method of this embodiment effectively balances multi-objective conflicts, providing an intelligent control solution that takes into account safety, comfort and energy conservation for the high-density tracking operation of maglev trains, and has theoretical value and practical significance for promoting the intelligent development of urban medium and low-speed maglev transportation.

[0157] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A train collaborative control method based on a speed curve interval optimization setting strategy, characterized in that Including: Establish a single-mass-point dynamic characteristic model of the train; According to the single-mass-point dynamic characteristic model of the train, obtain the train dynamic model and discretize it; According to the discretized train dynamic model, optimize the train tracking operation curve interval to obtain the optimal interval of the train reference speed; Optimizing the train tracking operation curve interval to obtain the optimal interval of the train reference speed includes: According to the target stopping point, obtain the speed limit value of each point before the target stopping point, and according to the speed limit value of each point, obtain the speed limit curve; According to the speed limit curve, the maximum train speed and the line speed limit, obtain the upper bound of the train reference speed; According to the tracking efficiency evaluation index, the comfort evaluation index and the operation energy consumption evaluation index, obtain the lower bound of the train reference speed; According to the upper bound of the train reference speed and the lower bound of the train reference speed, obtain the optimal interval of the train reference speed; The upper bound of the train reference speed is: ； The lower bound of the train reference speed is: ； ； Among them, is the upper bound of the train reference speed, is the maximum speed of the train, is the line speed limit, is the speed limit curve, is the lower bound of the train reference speed, and and are respectively the evaluation index of tracking efficiency, the evaluation index of comfort, and the evaluation index of operation energy consumption, 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; Tracking efficiency evaluation index: ； ； wherein, is the tracking interval between the i-th train and the following train, is the position of the i-th train, is the number of train formations; Comfort evaluation index: ； ； Among them, and are the acceleration and the acceleration change rate of the i-th train respectively, and are the weighting coefficients, is the comfort performance index of train i; Operation energy consumption evaluation index: ； Among them, , are respectively 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; According to the optimal interval of the train reference speed, establish the interval objective function of the leading train and the interval objective function of the following train and optimize them to obtain the optimal control acceleration to control the train.

2. The train collaborative control method based on the optimized setting strategy of the speed curve interval according to claim 1, characterized in that, Establishing the interval objective function of the leading train and the objective function of the following train includes: Obtain the discretized system model, and according to the discretized system model, obtain the control increment; According to the control increment, obtain the conventional rolling optimization objective function without interval constraints; Based on the optimal range of the train reference speed, the predicted value and the interval distance are defined as , where k represents the discrete time ; Determine the interval relaxation factor : , where represents the predicted speed value at time k for the future time k + j, is the relaxation amount allowing the predicted speed to exceed the interval boundary, and j is the j-th prediction step; According to the interval relaxation factor and the conventional rolling optimization objective function without interval constraints, an interval optimization objective function is obtained; According to the interval optimization objective function, respectively construct the interval objective function of the leading train and the interval objective function of the following train.

3. The train cooperative control method based on the optimized setting strategy for the speed curve interval according to claim 2, characterized in that According to the interval optimization objective function, constructing the interval objective function of the leading train includes: selecting the midpoint of the optimal interval of the train reference speed as the target tracking curve of the leading train, and according to the interval optimization objective function, establish the interval objective function of the leading train.

4. The train cooperative control method based on the optimized setting strategy for the speed curve interval according to claim 2, characterized in that Optimizing the interval objective function of the leading train is: ； ； Among them, is the objective function of the leading train in the section, M is the total predicted step length under section constraints, is the speed of the leading train at time k, is the target value control term, is the deviation control term between the predicted value and the section boundary, is the control increment control term, and and are weight coefficients, represents the maximum braking deceleration of the leading train, represents 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, represents the target speed value at time k + j, represents the predicted speed value at time k for the future time k + j.

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

6. The train cooperative control method based on the optimized setting strategy for the speed curve interval according to claim 4, characterized in that Optimizing the interval objective function of the following train is: ； ； Among them, is the optimization objective function for following the train, , , are the weights of the tracking distance deviation, tracking speed deviation and control increment deviation between the train and the preceding train respectively, represents the predicted value of the actual tracking spacing between the \(i\)-th train at the current time \(k\) and the \((i + 1)\)-th train at the future time \(k + j\), represents the target value of the tracking spacing between the \((i + 1)\)-th train at the current time \(k\) and the \((i + 2)\)-th train at the future time \(k + j\), represents the speed of the \(i\)-th train at the current time \(k\) and the predicted future time \(k + j\), represents the speed of the \((i + 1)\)-th train at the current time \(k\) and the predicted future time \(k + j\), \(l\) i is the car length of the \(i\)-th train.

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